Conservation Voltage Reduction Measurement and

Evaluation in MV/LV Distribution Networks Equipped with

ECOTAP VPD

Master Thesis

For attainment of the academic degree of

Master of Science in Renewable Energy Systems

Faculty Maschinenbau

at the University of Applied Sciences Ingolstadt

Submitted by:

Anthony Chigozie Igiligi

Matriculation Nr: 00095173

July 2021

Title: Name:

First examiner: Prof. Dr.-Ing. Daniel Navarro Gevers

Second examiner: Prof. Dr.-Ing. Sabine Bschorer

Company: Maschinenfabrik Reinhausen GmbH

Supervisor: Armin Vielhauer

i

Abstract

The application of voltage reduction in medium and low voltage grids has been implemented since

the 1980s using several approaches. Conservation Voltage Reduction (CVR) as one approach in

the Volt/Var Optimization (VVO) scheme uses on-load tap changers (OLTC) on Voltage

Regulated Distribution Transformers (VRDT) to reduce or increase the voltage setpoint, thereby

reducing the amount of active and reactive power supply in a network. There are established

limits and protocols for CVR deployment stipulated by the various network regulatory agencies.

A top-down estimation approach was applied in this research, using measurement data from

substation transformers.

Research in this field has proven that a CVR factor of 0,7 – 1,5 for peak demand reduction can

be achieved. Likewise, a CVR factor of 0,6 – 0,9 for continuous energy savings can also be

achieved by reducing the voltage setpoint by 2,5%. In this research, random tap changes were

deduced from a set of annual measurements of voltage and power, and using a direct method, a

CVR factor ranging from 0,95 to 1,31 was obtained. Using a continuous voltage reduction protocol

over a one-month period, a CVR factor for energy and energy savings of 0,71 and 3,69% was

obtained, respectively. In the end, proof for the validity of the results from the power demand

reduction by testing various scenarios, hypotheses and isolating the impact of PV integration on

the network was presented.

ii

Acknowledgment

This research work was successful because of the tremendous support I got from the Business

Development Exploration and the entire Exploration division of Maschinenfabrik Reinhausen

GmbH. They provided me with all necessary technical support, data, and working resources and

ensured that this research project was completed successfully. Special thanks to my thesis

supervisor Armin Vielhauer for his tremendous contribution, support, and guidance throughout

the various stages of this research. I also extend my gratitude to Uwe Firnhaber and Markus Riepl

for their technical support and for aiding my continuous collaboration with other stakeholders

within MR and other external organizations. I also want to thank Dr. Manuel Sojer for supporting

this research.

I want to use this opportunity also to thank my academic supervisor Prof. Dr.-Ing. Daniel Navarro

Gevers for providing immerse support and guidance and ensuring that this report is well written

and meets the academic and university standard. I also thank you for giving me some direction

when I was faced with significant technical challenges. I thank the university for allowing me to

learn and grow professionally through the resources and academic and extra-curricular

engagements it provides.

iii

List of Figures

Figure 2-1: VRDT benefits in LV grid. (FNN, 2016) .................................................................................. - 5 - Figure 2-2: ECOTAP VPD, with the control unit. (MR, 2016) ................................................................... - 6 - Figure 2-3 Grid topology with VRDT selection in LV network. .................................................................. - 7 - Figure 2-4 Regulation bandwidth for conventional transformer and VRDT (FNN, 2016) ......................... - 7 - Figure 2-5: Voltage control thresholds for VRDTs .................................................................................... - 8 - Figure 2-6: Load estimate of SVR and MLR compared to actual load (Wang & Wang, 2014) ..............- 12 - Figure 2-7: CVR factors of 5 feeders (Wang & Wang, 2014) .................................................................- 13 - Figure 2-8: Annual temperature profile in Regensburg. source (Weather and Climate, 2021) ..............- 15 - Figure 3-1: Representation of the test VRDT connection point. .............................................................- 18 - Figure 3-2: Voltage signal properties in a single tapping operation ........................................................- 18 - Figure 3-3: Step voltage versus response signal. ...................................................................................- 19 - Figure 3-4: Noise and uncertainty influence on 𝐶𝑉𝑅𝑓 estimation ...........................................................- 19 - Figure 3-5: Stationary voltage measurements with and without noise. ..................................................- 20 - Figure 3-6: Probability distribution function of a normal distribution [source: (Fallon & Hyman, 2020) ..- 21 - Figure 3-7: Stationary time series voltage data. .....................................................................................- 22 - Figure 3-8: ACF of daily voltage readings ...............................................................................................- 23 - Figure 3-9: PACF of daily voltage readings. ...........................................................................................- 23 - Figure 3-12: Preprocessing process for the time-series data .................................................................- 25 - Figure 3-13: Histogram and CDF of Tuesday voltage readings .............................................................- 26 - Figure 3-14: ARIMA evaluation process .................................................................................................- 28 - Figure 3-15: PDF of Saturday 1 voltage residuals ..................................................................................- 28 - Figure 3-16: Box plot of Monday data samples. .....................................................................................- 29 - Figure 4-1: Voltage profile of a single tap operation ...............................................................................- 32 - Figure 4-2: Estimating CVR by the direct method...................................................................................- 33 - Figure 4-3: Topology of the LV network. .................................................................................................- 34 - Figure 4-4: PV yield in Freiburg. (Fraunhofer ISE, 2021) .......................................................................- 35 - Figure 4-5: Annual power demand profile ...............................................................................................- 35 - Figure 4-6: Reshaped monthly time series .............................................................................................- 35 - Figure 4-7: NaN removal by interpolation ...............................................................................................- 36 - Figure 4-8: Line plot of voltage rise. ........................................................................................................- 36 - Figure 4-9: Changes in voltage according to the algorithm. ...................................................................- 37 - Figure 4-10: Voltage profiles 𝑈1, 𝑈2, 𝑈3, 20th Jan. 2020 .........................................................................- 37 - Figure 4-11: Voltage profile at tap change timestamps ..........................................................................- 38 - Figure 4-12: One-week power demand profile........................................................................................- 38 - Figure 4-13: Process flow for CVR factor evaluation ..............................................................................- 39 - Figure 4-14: Box plot of the CVR factors ................................................................................................- 40 - Figure 4-15: Distribution of the CVR factors. ..........................................................................................- 40 - Figure 4-16: Distribution of randon samples of voltage and power changes. .........................................- 40 - Figure 4-17: Annual CVR factors for active power, 2020 .......................................................................- 41 - Figure 4-18: Changes in randomly sampled active power measurements .............................................- 42 - Figure 4-19: Stationarity of random voltage and power changes. ..........................................................- 43 - Figure 4-20: Voltage, active, and reactive power profile during a tap change. .......................................- 44 - Figure 5-1: Load profiles on test days .....................................................................................................- 46 - Figure 5-2: Multilinear Regression evaluation process for energy savings. ...........................................- 48 - Figure 5-3:Scatter plot of estimated energy to real energy. ....................................................................- 49 - Figure 5-4: Estimated and real energy profile for April 2021 ..................................................................- 49 - Figure 5-5: CVR factor for energy ...........................................................................................................- 50 - Figure 5-6: CVR factor for energy without PV output. ............................................................................- 50 - Figure 5-7 Energy savings applied to the PV system LCOE. .................................................................- 52 -

iv

List of Tables

Table 2-1: Filtering rules for CVR factor estimation (Shim et al. 2017) ..................................................- 13 - Table 4-1: 20th January timestamps ........................................................................................................- 36 - Table 4-2: Averaging intervals, CVR factors and percentage of outliers ................................................- 44 -

v

List of Abbreviations

AR Autoregression

ARIMA Autoregressive Integrated Moving Average

ACF Auto-Correlation Function

ADF Augmented Dickey Fuller test

CAPEX Capital Expenses

CDF Cumulative Density Function

CDH Cooling Degree Hours

CL Confidence Limit

CVR Conservation Voltage Reduction

𝑪𝑽𝑹𝒇 Conservation Voltage Reduction Factor

DER Distributed Energy Resources

DG Distributed Generation

DOW Day of Week

DR Demand Response

ENWL Eastern Network Ltd.

EOL End of Line

EV Electric Vehicle

GARCH Generalized Autoregressive Conditional Heteroscedasticity

GSP Gross State Product

HDH Heating Degree Hours

HV High Voltage

IID Independently and Identically Distributed

KDE Kernel Density Function

KEPCO Korea Hydro & Nuclear Power Co., Ltd

KPSS Kwiatkowski-Phillips-Schmidt-Shin test

LCC Lifecycle Cost

LCOE Levelized Cost of Energy

LTC Load Tap Changer

LV Low Voltage

vi

MAD Mean Absolute Deviation

MAPE Mean Absolute Percentage Error

MLR Multi-Linear Regression

MR Maschinenfabrik Reinhausen GmbH

MV Medium Voltage

OLS Ordinary Least Squares

O&M Operation and Maintenance

OLTC On-Load Tap Changer

PACF Partial Autocorrelation Function

PDF Probability Density Function

PV Photovoltaic

RES Renewable Energy Resources

RMSE Root Mean Square Error

SARIMA Seasonal Autoregressive Integrated Moving Average

SCADA Supervisory Control and Data Acquisition

SVR Support Vector Regression

TG Time Group

TOD Time of Day

VAT Value Added Tax

VRDT Voltage-regulated Distributed Transformers

VRSA Voltage Ranking Search Algorithm

VSM Voltage Sensitivity Method

VVO Volt/Var Optimization

WACC Weighted Average Cost of Capital

ZIP Impedance Current Power

vii

Table of Contents

Abstract ………………………………………………………………………………………………… i

Acknowledgement ……………………………………………………………………………………. ii

List of Figures ……………………………………………………………………………………….... iii

List of Tables ……………………………………………………………………………………….… iv

Abbreviation …………………………………………………………………………………………. . . v

Introduction ............................................................................................................ - 1 -

1.1 Background .................................................................................................................. - 1 -

1.2 Research Motivation ..................................................................................................... - 2 -

1.3 Objectives and Scope ................................................................................................... - 3 -

Literature Review................................................................................................... - 5 -

2.1 Operating Principles of VRDTs with ECOTAP VPD ...................................................... - 5 -

2.1.1 VRDT Components ................................................................................................ - 5 -

2.1.2 OLTC: ECOTAP VPD............................................................................................. - 6 -

2.1.3 Voltage Regulation ................................................................................................. - 6 -

2.2 CVR Factor Evaluation Techniques. ............................................................................. - 9 -

2.3 External Factors ......................................................................................................... - 14 -

2.4 Energy Savings Measurement Techniques ................................................................. - 16 -

Statistical Evaluation of Voltage Measurements .................................................. - 18 -

3.1 Voltage Noise ............................................................................................................. - 18 -

3.2 Terminologies ............................................................................................................. - 20 -

3.3 Preliminary Estimation ................................................................................................ - 24 -

3.3.1 Data Collection and Pre-processing ..................................................................... - 25 -

3.3.2 Data Analytics and Statistical Testing ................................................................... - 25 -

3.4 Statistical Modeling ..................................................................................................... - 27 -

3.5 Modelling Results ....................................................................................................... - 29 -

Power Demand Reduction. .................................................................................. - 30 -

4.1 CVR Factors ............................................................................................................... - 30 -

4.1.1 Baseline testing setup .......................................................................................... - 31 -

4.1.2 Power demand testing setup ................................................................................ - 31 -

4.2 CVR Factor Evaluation Methodology .......................................................................... - 31 -

4.2.1 Parameter Definition ............................................................................................ - 31 -

4.2.2 Test Site Description ............................................................................................ - 33 -

viii

4.2.3 Implementation .................................................................................................... - 35 -

4.3 Results ....................................................................................................................... - 39 -

4.4 Hypothesis Testing ..................................................................................................... - 42 -

4.4.1 Evaluation of Outliers. .......................................................................................... - 42 -

4.4.2 Randomized Control Group .................................................................................. - 42 -

4.4.3 Sensitivity to Averaging Intervals. ......................................................................... - 43 -

Energy Savings Evaluation .................................................................................. - 45 -

5.1 Estimation Approach .................................................................................................. - 45 -

5.1.1 Continuous Energy Testing Framework ............................................................... - 45 -

5.1.2 Parameter Definition and Selection ...................................................................... - 46 -

5.1.3 Preprocessing and Modeling with MLR ................................................................ - 47 -

5.2 Energy Savings Results .............................................................................................. - 49 -

5.3 Cost-benefit analysis .................................................................................................. - 51 -

Discussion and Conclusion .................................................................................. - 53 -

6.1 Discussion .................................................................................................................. - 53 -

6.2 Challenges and Future Work Direction ....................................................................... - 54 -

6.2.1 Future work .......................................................................................................... - 55 -

Reference List ...................................................................................................................... - 57 -

Appendix A .......................................................................................................................... - 61 -

Appendix B .......................................................................................................................... - 69 -

Appendix C .......................................................................................................................... - 76 -

Introduction

1.1 Background

Global electricity demand has increased substantially in recent years due to global warming, EV

production, and residential development. The increase in global warming implies that there will

be a corresponding increase in cooling demand for residential and industrial buildings. If the

average summer temperature increases by 5℃, there would be an associated increase in cooling

demand days which will, in turn, consume more power. As more EVs are rolled out of the factory,

the demand for establishing new charging stations outside the reach of the current grid setup

comes at a cost. There has been about a 6% increase in electricity demand in Germany since

1990, resulting in increased supply from distributed resources. This rise in demand is also

associated with increased commercial and residential developments in the service sector that

account for 71% of Germany’s GDP (IEA, 2020).

Demand is met with an increasing generation from Renewable Energy Sources (RES) such as

wind, solar, and hydropower on the supply side. Integrating these resources into the grid requires

a substantial apparatus for voltage stabilization and ensuring the quality of the voltage supplied.

On the other hand, optimizing power supply by deploying demand response (DR) and Volt/Var

Optimization (VVO) can save huge infrastructure costs in additional generation and expansion

while achieving set emission reduction targets 2050 (Le, Canizares, & Bhattacharya, 2015; Wang,

2015). The cost benefits of such actions are very substantial and feasible enough to investigate.

Utilities in Germany have begun to pay attention to this by researching further and carrying out

pilot tests. Demand response on the customer side means that they could participate in a

particular setup that requires constant interaction and control or participate in an automated DR

that saves time and extensive scheduling (Wang, 2015). These schemes depend on the RES

integration they deployed and how much they contribute to the overall energy demand.

Conversely, a VVO scheme and Conservation Voltage Reduction (CVR) are managed and

controlled by the utilities. They are the ones that determine the deployment benefits,

environmental and topological constraints, the periods – based on a clear understanding of

consumers’ historical demand and behavioral patterns. Power factor correction is the critical

technique of deploying VVO, while voltage level adjustment is associated with CVR (NRECA,

2014).

CVR technique involves using a reduced voltage setpoint to achieve load demand reduction from

residential and industrial consumers in a distribution grid. It determines the amount of load

demand reduction during peak and total energy savings achieved for a specific duration. By

carrying out this operation regularly or based on a scheme, the utility can channel the excess

energy towards critical demand areas or new expansion. A CVR factor (𝐶𝑉𝑅𝑓) is the ratio between

a percentage change in power or energy corresponding to a percentage change in the voltage

(equation 1-1). A transformer equipped with an on-load tap changer (OLTC) can regulate voltage

by using a switching mechanism that alters voltage levels step-by-step. There are nine steps/tap

positions in an OLTC (±4 with a neutral). A tapping operation can consist of 1 or 2 tap changes

with a pause duration of 3 seconds. A comprehensive and automated deployment scheme with

- 2 -

DR can be implemented by using a combination of advanced machine learning tools (to assess

and forecast scenarios with high efficiency) and SCADA systems with a control unit that actuates

tapping operation in the transformer. However, it might be difficult to scale because of the climate

and environmental conditions around the various deployment areas and the reliability of

measurements from sensors and smart meters.

𝐶𝑉𝑅𝑓 =%∆𝑃

%∆𝑈,

%∆𝐸

%∆𝑈 (1-1)

Where 𝑈, 𝑃, and 𝐸 represents voltage, power, and energy, respectively. In the recent past, the

application of CVR has resulted in noticeable savings in energy based on the results of the

research conducted so far. In such an application, the voltage can be lowered to a specific limit

that will not affect the end-user appliances. These limits are usually around ±10%; it is always

sustained till the end of the line. Many North American and European utilities have conducted

CVR in several test sites, and they have generally come up with a CVR factor for power that

ranges from 0,71 to 1,34. This means that a 1% reduction in voltage will result in a 0,7% reduction

in power consumption. The Smart Street project by ENWL in the United Kingdom was carried out

to determine the amount of energy savings that can be achieved in rural, urban, and dense urban

LV networks using CVR and other optimization processes. A 5 – 8% energy savings were

achieved, with a monetary value of up to 81,45€/a (ENWL, 2018). Such savings can offset an

equivalent amount of carbon on the generation side, thereby boosting investments in distributed

generation (DG). In 1991, research carried out by the Snohomish County achieved a CVR factor

for energy savings of 0,59 – 0,89 on three feeders (Kennedy & Fletcher, 1991). Current research

in this field with influence from RES, with the implementation of DR, shows that more savings can

be achieved by monitoring and automating voltage reduction during peak demand.

1.2 Research Motivation

Achieving voltage reduction goals comes with significant financial benefits for both the network

operator and the consumers. More network operators are willing to test this concept on a pilot

project on their selected test fields. The key testing equipment, a voltage-regulated distribution

transformer (VRDT) equipped with an OLTC on a single phase, is prevalent in the LV distribution

network. Since this asset is a viable regulating device before the end-of-line, it can directly

influence the magnitude of change in voltage more than the MV stations. At the EOL, there is a

higher potential of experiencing voltage limit violations due to voltage reduction and stability

issues. Due to this issue and the need for the network to expand beyond the EOL, there is a

growing demand for new transformers to ensure quality voltage supply. The key idea is that we

can achieve this expansion by using VRDTs equipped with an OLTC and using this setup to

further achieve CVR without incurring additional costs. Therefore, the business case of CVR on

VRDTs is a strong one that can be proven by showing the amount of energy savings and demand

reduction achieved by deploying it on any distribution network. This is the core focus of this thesis

project. ECOTAP® VPD® is one such OLTC that can deliver a reliable tapping operation.

To provide the best result possible for proving this business case, a test field should have average

gird and environmental characteristics and the best load mix on the consumer side. Based on an

- 3 -

established protocol, CVR testing can be deployed. An extensive set of measurements of voltage

adjustments is adequate for a sound statistical evaluation of CVR factors. Therefore, it is essential

to have as many taping operations as possible for a long duration. Other research I this area has

suggested deploying CVR on some selected feeders while the rest will serve as a control group.

A well-planned measurement and evaluation campaign can provide all the answers needed to

establish the business case of CVR.

1.3 Objectives and Scope

Implementing voltage reduction using a top-down approach involves using measurement data

from existing test fields/networks in MV/LV grids. Relevant measurement data for this evaluation

are voltage, active power, and reactive power on a single or three phases. The other approach is

bottom-up – using individual load models to define the behavior/reaction of various residential

load mixes under-voltage reduction. This method is more challenging as a specific load model

might not represent the entire network area as desired. In the top-down approach, however,

external factors such as weather and topology might affect the reliability of the evaluation results

together with voltage noise issues. Also, the top-down approach considers the LV network as a

black box. This implies that the load type and load mix in households connected to this grid are

unknown and used for load model simulation. All evaluations are based on the voltage response

at the bus bar of the secondary substations and other strategically placed sensors and smart

meters. Therefore, a vital part of this work shall focus on eliminating natural variations and noises

from voltage measurements and estimate a noise magnitude using a robust statistical approach.

However, this thesis does not cover instrument noise resulting from defects in the measurement

devices. Numerical and model errors are therefore considered to a large extent.

The key research questions that will be answered through this thesis are:

┃ How much power and energy can be saved by implementing CVR through VRDTs?

┃ Does PV integration in the network area impact the daily variation of the CVR factors for

power and energy?

┃ Is there a correlation between the estimated energy for normal operation and measured

energy during testing?

┃ What changes in CVR factors for power came with altering the averaging interval?

┃ And finally, does it make economic sense to deploy CVR on a continuous scheme?

Each of these questions is covered in the various sections of this thesis. In Chapter 2, I highlighted

the different literature and different approaches for CVR set up, measurement, and evaluation

and their results. Also, I discussed the operating principles of VRDTs and the various regulations

they abide by. Further emphasis was laid on the impact of environmental factors on determining

the best estimation of energy demand during CVR – on testing. An excellent statistical analysis

of voltage measurement for noise magnitude estimation was detailed in Chapter 3. Using an

iterative ARIMA model on dynamic sample sizes of voltage time-series and testing its statistical

characteristics produced a good result that can be useful in setting minimum tap change

magnitudes for CVR evaluation. Using the test field data in Southern Germany in Chapter 4, I

- 4 -

achieved accurate CVR factors for power in 2020. Also, in this chapter, you can find the seasonal

changes in CVR factors and how they are affected by PV integration (4.3). To end this chapter, I

discussed the various verification procedures on the basic assumptions and hypotheses deployed

in the evaluation (4.4). They also help to verify the answer to the scientific questions raised in this

project. In Chapter 5, I carried out the energy savings evaluation based on a new testing protocol

on our test field in April 2021. A substantial reduction in the voltage set point was established in

other to determine demand reduction in a continuous scheme. Using robust regression analysis,

I achieved potential savings results.

Several statistical and programming tools have been deployed during this evaluation, and I have

discussed them as much as possible in the contents of this report and in the Appendix. Each

question has been addressed using these tools and simple proven techniques that can be

replicated on similar datasets. Since we are dealing with massive datasets with up to 3,5 million

data points, process automation was necessary. These automation processes for data analytics

were achieved using the Python programming language. With this program, I was able to

preprocess and visualize the datasets and make sure that the hidden patterns were unraveled.

- 5 -

Literature Review

2.1 Operating Principles of VRDTs with ECOTAP VPD

Distribution networks are composed of primary and secondary sub-stations with supply power to

feeder lines connected to more than 100 consumers. A primary substation is operated with an

HV/MV power transformer which supplies power to secondary substations connected to it. The

critical power assets that aid this supply are the distribution transformers. Distribution

transformers operated at the secondary substation regulate the voltage at 11kV/0,4kV levels, an

MV/LV transition. At this level, voltage regulation can be deployed manually or automatically in

response to power demand. This distribution transformer is the last power asset where such

control can be deployed before the end-users (Tran et al., 2020).

The requirement for voltage regulation in a distribution transformer is achieved using a tap

changer. The role of the tap changer is to alter the ratio of the transformer winding to achieve

higher or lower voltage levels from a setpoint. An ordinary distribution transformer is equipped

with an off-circuit tap changer capable of delivering tapping operations when the transformer is

de-energized. This can only be achieved manually and on-premise (Oliveira Quevedo et al.,

2017). VRDTs, on the other hand, can also implement automated voltage control with an OLTC

remotely in addition to other configurations.

Figure 2-1: VRDT benefits in LV grid. (FNN, 2016)

Figure 2-1 above shows the additional capacity of VRDTs compared to ordinary distribution

transformers. Its ability to extend the voltage limits beyond the grid allows for more connections

without increasing generation capacity (Sojer, 2017). With this device, the network operators can

resolve limit violations with the OLTC following stipulated guidelines (Poppen, Matrose,

Schnettler, Smolka, & Hahulla, 2014). Thus, it is essential to develop an algorithm for voltage

regulation.

2.1.1 VRDT Components

The VRDT is composed of a transformer, a control device, and a control unit. The controlling

device performs the switching operation and is usually an OLTC in the case of active switching

on-load. The control device is typically an addition to the transformer and thus can have a different

- 6 -

OEM from the transformer. However, its tap positions should match the windings and other similar

features of the transformer considerably. For example, ECOTAP VPD is compatible with the SBG

Transformer GmbH, Germany VRDT products (Mokkapaty, Weiss, Schalow, & Declercq, 2017).

The control unit is an electronic system that actuates the OLTC on the high voltage side, using

an algorithm for voltage regulation. A voltage operation initiated by the control unit establishes

new voltage setpoints on the LV busbar (FNN, 2016). A typical control unit activates switching

protocol as follows:

┃ Determine/retrieve voltage measurement setpoint from a terminal point.

┃ Evaluate and determine the need for tapping based on the control algorithm.

┃ Initiate tapping on the control device.

┃ Display the status of the operation and general control parameters.

┃ Self-activate manual, automated or remote mode initiating and operating the tapping

(FNN, 2016).

2.1.2 OLTC: ECOTAP VPD

The ECOTAP VPD shown in Figure 2-2 is a vacuum OLTC that carries out tap operation when

the transformer is loaded and active. It is developed and manufactured by MR. The drive unit can

perform a maximum of 20 tapping operations per minute. The additional control unit is built to

withstand harsh weather and environmental conditions (-25℃ to +70℃) with an advanced voltage

regulation algorithm (MR, 2016).

Figure 2-2: ECOTAP VPD, with the control unit. (MR, 2016)

The device is compatible with VRDTs manufactured by most OEMs; also flexible, easily

adjustable, and safe to use following DIN EN 60076-1 provision and IP66 protection class. It is

configured with 17 tap positions with a change-over selector and can achieve ±825V per step

(MR, 2016). The drive unit and selector unit together make up the control and tap change

operation. The selector unit is directly connected to the taps of the VRDT windings and its moving

contacts. At position n, a switch operation moves the selector unit to n+1, makes contact, and

then disconnects from it. (Mokkapaty et al., 2017)

2.1.3 Voltage Regulation

The primary to secondary transitions of a transformer produces voltage changes associated with

impedance induced by load (𝑍𝑙) in relation to the primary side. Reflected impedance on the

primary side (𝑍𝑖𝑛) is related to 𝑍𝑙 as

𝑍𝑖𝑛 = 𝑎2𝑍𝑙 (2-1)

- 7 -

Where 𝑎2 is the ratio of the primary and secondary windings, which has a general relation as

follows.

𝐼𝑃

𝐼𝑆=

𝑈𝑆

𝑈𝑃=

𝑁𝑆

𝑁𝑝=

1

𝑎 (2-2)

The magnitude of 𝑈𝑃 − 𝑈𝑆 can be adjusted during the operation of the VRDT, with respect to some

outlined guidelines in DIN EN 50160 (Deutsche Kommission Elektrotechnik Elektronik

Informationstechnik in DIN und VDE, 2016). The per-unit magnitude of voltage regulation for

transformer with known primary 𝑈1 and secondary 𝑈2 voltages are expressed according to

(Todorovski, 2014) as

∆𝜇 = (𝑈1 𝑚⁄

𝑈2− 1) × 100 (2-3)

In a distribution network, voltage regulation is set by detecting voltage drops/rise below/above a

set percentage at the bus bar of the transformer. Static voltage drops are evaluated and used to

establish a desired voltage setpoint for operation. A percentage control threshold is used to

regulate the voltage level. Several topology and external factors can influence the extent of

voltage changes observed. They can be a feeder or grid specific. PV integration in the LV grid

gives rise to voltage stability and quality issues and affects efficiency.

Figure 2-3 Grid topology with VRDT selection in LV network.

(a) Conventional transformer (b) VRDT with an OLTC

Figure 2-4 Regulation bandwidth for conventional transformer and VRDT (FNN, 2016)

- 8 -

Voltage drops in the LV networks are affected by higher X/R ratios originating from higher

resistance which directly influences voltage rise in the case of PV power injection (Fraunhofer

ISE, 2021).

The need for VRDTs is determined based on terminal voltage limit deviation. According to EN

50160, VRDTs can be installed selectively, as shown in Figure 2-3, at points along with the

distribution where voltage limit violations occur. Therefore, the decoupling between the MV and

LV is necessary to create the voltage transition from the VRDT (FNN, 2016). Voltage limits

violations are set at ±10% of nominal voltage, such as the IEV 601-01-25 specification. A 230V

nominal voltage will have violations at 253V and 207V according to the regulation.

Figure 2-4(a) shows the voltage profile (rise/drop) in a distribution network where the distribution

transformer is not a VRDT. In this case, utilities regulate voltage levels from the substation and

seldom risk violating voltage limits due to the factors previously mentioned – mainly DG injection,

reactive power, and line characteristics. Therefore, in this case, the regulating bandwidth is not

decoupled from MV to LV grid. Thus, a lesser amount of voltage change (±1,2%) can be achieved

by a single tap change. On the other hand, a decoupled MV-LV setup (Figure 2-4(b)) shows that

a new bandwidth can be established for the enhanced voltage drop limits. This limit can be

adjusted: allowing more voltage drop and rise, or a balance of both. The OLTC can operate more

tap positions with higher magnitudes of voltage change (±2,5%).

A voltage regulation protocol can be implemented for a fixed voltage setpoint and a dynamic

voltage setpoint computed from feeder line characteristics and power flow. The latter protocol is

mainly adopted in a smart grid setup with cloud data storage, SCADA, and transmission

capability. Each of these protocols actuates the OLTC to tap according to the desired voltage

level. But before the tapping operation, limit violation or infringement should be detected.

Infringements are detected when the voltage on the secondary side exceeds the upper or lower

threshold for a delay duration of 10 seconds (FNN, 2016).

Figure 2-5: Voltage control thresholds for VRDTs

- 9 -

Proper voltage regulation can be implemented by monitoring the following control parameters,

which form part of the algorithmic evaluation:

┃ Define voltage setpoint 𝑈𝑡(𝑉): This is the desired voltage level at the secondary side of

the VRDT. However, a permitted bandwidth is allowed so that normal adjustments

occurring in the transformer can be contained. This is thus defined as a percentage

change from 𝑈𝑡 with the same magnitude for the upper and lower bands. In Figure 2-5, it

is placed at ±2,5% (𝑈𝑡±𝑑).

┃ Delay time 𝑇𝑑(𝑠): This is the allowable duration for voltage levels operating continuously

above 𝑈𝑡±𝑑 before a tap change is initiated. It is usually set at 10 seconds, although it can

vary from site to site.

┃ High-speed bandwidth: This is the percentage variation (±20%) (Poppen et al., 2014) from

𝑈𝑡 (𝑈𝑡±ℎ) at which a quick tap change is initiated as a result of a huge voltage drop/rise.

Here, the delay time 𝑇ℎ is about 1-2 seconds. This helps to avoid damage to the

transformer and LV grid.

Several searches have been conducted, and different schemes or voltage regulations have been

tried. (Delfanti, Merlo, & Monfredini, 2014) developed a quantitative procedure to determine the

viability of voltage strategies deployed locally in a digital network with or without a VRDT. It was

discovered that reactive power flows have a higher impact on the voltage limit infringements

defined by the R/X ratios. In (Xie et al., 2019), a voltage ranking search algorithm (VRSA) was

implemented both for OLTC tapping operation and demand response in a grid with substantial

influence from PV. It discussed the time-consuming genetic algorithm approach, particle swarm

optimization, and the voltage sensitivity method (VSM), which is widely adopted. These three

methods were compared analytically with the VRSA, and the result was that the proposed method

has a better performance with a reduced number of tap operations and voltage violations.

2.2 CVR Factor Evaluation Techniques.

CVR factor evaluation techniques define a systematic methodology for determining the ratio

between voltage reduction and peak power reduction. Its result helps the grid operator plan and

understand the seasons and times when deploying CVR will be most beneficial and assess the

overall quality of the operation (An, Liu, Zhu, Dong, & Hur, 2016). From a bottom-up approach,

load models are analyzed for each feeder connection on the secondary substation using several

methods categorized as static, dynamic (Choi et al., 2006), and composite load models (Arif et

al., 2018) (Renmu, Jin, & Hill, 2006). The most used model is the ZIP model for static load

modeling (Nam et al., 2013b) (Le et al., 2015). It represents impedance, constant current, and

constant power loads in the consumer side from which active and reactive power response can

be computed (Renmu et al., 2006). CVR's voltage variations induce system responses for

connected loads and are therefore directly related to the active and reactive power after CVR.

The effect of CVR on these networks can thus be modeled using the ZIP model. (An et al., 2016)

presented a simplified method for obtaining CVR factors from the reactive and active power

responses in a ZIP model. A composite load model was developed in (Castro, Moon, Elner,

- 10 -

Roberts, & Marshall, 2017) by combining individual load profiles of representative loads from

[domestic] appliances for each loaded class of the ZIP model. In (Nam, Kang, Lee, Ahn, & Choi,

2013a), a ZIP model was developed for nationwide CVR evaluation using an average of all

transformers in the testing setup, indicating transformer weighted influence represented by a

factor.

CVR factor for power is the ratio of the percentage change in power (active and reactive) to a

corresponding percentage change in voltage.

𝐶𝑉𝑅𝑓 =%(

(𝑃𝑝𝑟𝑒−𝑃𝑝𝑜𝑠𝑡)𝑃𝑝𝑟𝑒

⁄ )

%((𝑈𝑝𝑟𝑒−𝑈𝑝𝑜𝑠𝑡)

𝑈𝑝𝑟𝑒⁄ )

(2-4)

Therefore, a voltage setpoint (𝑈𝑝𝑜𝑠𝑡) can induce changes in power (𝑃𝑝𝑜𝑠𝑡) through CVR, and the

CVR factor determines its effectiveness. Many methodologies have been developed for

measuring/estimating power (𝑃𝑝𝑟𝑒) during testing (CVR-on) so that ∆𝑃 = 𝑃𝑝𝑟𝑒 − 𝑃𝑝𝑜𝑠𝑡. When a

1% reduction in voltage is associated with a 1% reduction in power, the CVR factor becomes 1

(Castro et al., 2017). The accuracy of the computed CVR factor depends on the accuracy of the

load estimates for an off condition (Wang, Begovic, & Wang, 2014). However, studying the voltage

changes and determining the voltage change magnitude that can produce substantial change

load is also important. The methodologies identified in (Wang & Wang, 2014) for computing CVR

factors (power and energy) include comparison-based, regression-based, synthesis-based, and

simulation-based methods. The two-feeder approach implemented in (Liu, Macwan, Alexander,

& Zhu, 2014) and (Kennedy & Fletcher, 1991) is a typical comparison method where two similar

feeders are used for testing. One feeder produces load demand for CVR-off condition while the

other produces loads for CVR-on resulting from the new voltage setting. However, using one

feeder, the CVR-on/off test can be carried out at different times but under similar weather and

loading conditions. (Wang et al., 2014) and (Short & Mee, 2012 - 2012) used a regression-based

model for estimating load for CVR-off during the testing condition. Using a linear regression model

in (Short & Mee, 2012 - 2012) CVR factors ranging from 0,5 to 0,9 were obtained. (Chen, Wu,

Lee, & Tzeng, 1995) applied the synthetic approach on individual load types based on their

voltage sensitivity function and used it to estimate energy consumption for industrial, commercial,

and residential consumers. This estimation method does not consider the environmental influence

on energy as it is done in a laboratory.

A comprehensive report on extensive field testing of CVR across substations in the USA shows

that for a 5% reduction in voltage, a corresponding 1% - 3% was observed in the power demand

(PJM, 2021). The observed changes in power are mostly affected by load mix and

characterization, network topology, and the time of day or season. The scope of CVR factor

evaluation depended on the period when the computation was implemented.

The CVR factor evaluation methodology developed by (Liu et al., 2014) was built on a testing

setup that deploys CVR-on operation on a feeder and CVR-off on another feeder with the same

network characteristics as the former. Evaluation parameters used to estimate real power from

voltage changes were modeled using linear regression as such

- 11 -

𝑝 ≈ 𝑋𝛽 + 𝛽𝑜1 (2-5)

Where 𝑋 = [𝑐, 𝑣, 𝑝𝑟𝑒𝑓 , 𝑠1, … , 𝑠4, ℎ1, … , ℎ24, 𝑑1, … , 𝑑7, 𝑓] ∈ R𝜏𝑥39. Parameter c to 𝑝 are time-

dependent and means temperature, bus voltage, and power, while the rest means season (4),

hour (24), and day (7), respectively. The last parameter represents the holiday. Using a parameter

weighting factor 𝛽2 that compares instantaneous power variation to voltage reduction; the CVR

factor can be estimated. However, this methodology was not applied towards peak shaving and

reactive loads and therefore not suitable. Parameter selection, ranking, grouping, preprocessing,

and standardization is applied to the data matrix 𝑋 before 𝛽2 estimation using regression analysis.

This CVR factor computation was applied to a 1% voltage reduction test setup for one year with

hourly resolution. Using this kind of methodology, a CVR factor of 0,71 was obtained for the

simulated CVR-on condition with a baseline condition (Liu et al., 2014). However, this study did

not indicate or determine the influence of system noise or uncertainties in the key parameters

𝑐, 𝑣, 𝑝𝑟𝑒𝑓.

The common approach of estimating load during normal operations for the testing period has

been applied in (Hossan & Chowdhury, 2017), (Wang & Wang, 2014), and (El-Shahat, Haddad,

Alba-Flores, Rios, & Helton, 2020) using various forms of statistical modeling. These methods

emphasize understanding the load composition and the relationship between voltage changes

and changes in load composition. In terms of error handling and uncertainty mitigation, their

approaches vary from one another. A load uncertainty prediction from the normal distribution of

the time series of response loads was applied by (Hossan & Chowdhury, 2017). The magnitude

of the uncertainty was directly determined from the 95% confidence limits of the standard

deviation of the load PDF.

(Shi & Renmu, 2003) developed a load model using ZIP for static and third-order induction motors

for dynamic loads. Thus, an improved composite load model structure, when compared with the

ZIP and induction model, shows better performance in predicting load during normal operations.

A linearized static-load (ZIP) model, according to (Nam et al., 2013a), provides a good measure

of average CVR factors across an entire network. (El-Shahat et al., 2020) also developed a ZIP

load model that determines active and reactive power based on voltage changes according to

these equations.

𝑃𝑖 =𝑈𝑎

2

𝑈𝑛2 𝑆𝑛𝑍% cos(𝑍𝜃) +

𝑈𝑎

𝑈𝑛𝑆𝑛𝐼% cos(𝐼𝜃) + 𝑆𝑛𝑃% cos 𝑃𝜃

𝑄𝑖 =𝑈𝑎

2

𝑈𝑛2 𝑆𝑛𝑍% sin(𝑍𝜃) +

𝑈𝑎

𝑈𝑛𝑆𝑛𝐼% sin(𝐼𝜃) + 𝑆𝑛𝑃% sin 𝑃𝜃

𝑍% + 𝐼% + 𝑃% = 1 (2-6)

When CVR was carried out in field tests of (Wang & Wang, 2014), measurement of active power,

reactive power, voltage, and the current was carried out at one-minute intervals. For a CVR-off

condition load modeling, a Multistage Support Vector Regression (MSVR) model was developed

using close independent predictor variables such as temperature, humidity, active power during

normal operations and post CVR. Then a Euclidian distance function is applied to the dataset to

- 12 -

select profiles (𝑃𝑖𝑘 at daily sample sizes) that is similar to the test period (𝑃𝑖) defined by a function

𝜀𝑝𝑘.

Where 𝜀𝑝𝑘 = ∑√(𝑃𝑖−𝑃𝑖𝑘)2

𝑚𝑎𝑥(𝑃𝑖𝑘).𝑁

𝑁𝑖=1,

𝑖∈𝑇1,𝑇3

When the index becomes smaller, then the load profile during normal operation becomes similar

to the test profile and thus can be used for modeling the MSVR (Wang & Wang, 2014). However,

a Multi-linear Regression (MLR) model can be used to carry out the same estimation for power,

but it is less accurate than the SVR. Therefore, the SVR handles estimation and numerical errors

better than the MLR. The training and test validation of the SVR and MLR model was done using

155 CVR-off day datasets and used to predict load for CVR-off day profile during the testing

period, as in Figure 2-6.

Figure 2-6: Load estimate of SVR and MLR compared to actual load (Wang & Wang, 2014)

Approaching CVR factor estimation by modeling load changes analytically, emphasis should be

placed on the accuracy of the estimated load. This is the center of methodology verification

adopted in this study: the difference in estimated CVR factor and that of an expected CVR factor.

This approach was tested on nine months of data from 5 feeders (during peak demand), and CVR

factors were obtained as shown below.

- 13 -

Figure 2-7: CVR factors of 5 feeders (Wang & Wang, 2014)

This methodology could be more suitable for estimating energy savings in a continuous

framework because it provides the best estimate of CVR-off power during the testing period.

Another methodology to consider is the one developed by (Shim et al., 2017) for the KEPCO pilot

testing. Active, reactive power, and voltage measurements from the CVR deployment and CVR

factor were computed using the Mean Absolute Deviation (MAD) direct method. This method also

involves applying various filtering measures on the voltage and power changes based on their

magnitude, causality, and direction of the initiating tap change. Percentage changes are

determined at the point of switching on the VRDT from measurement points on the feeders.

Changes in power are calculated directly from the corresponding datasets without estimating

CVR-off power by regression models, thus the direct method.

𝐶𝑉𝑅𝑓−𝑃 =(

𝑃𝑎𝑓𝑡−𝑃𝑝𝑟𝑒

𝑃𝑚𝑒𝑎𝑛𝑥100)

(𝑈𝑎𝑓𝑡−𝑈𝑝𝑟𝑒

𝑈𝑚𝑒𝑎𝑛𝑥100)

(2-7)

𝐶𝑉𝑅𝑓−𝑄 =(

𝑄𝑎𝑓𝑡−𝑄𝑝𝑟𝑒

𝑄𝑚𝑒𝑎𝑛𝑥100)

(𝑈𝑎𝑓𝑡−𝑈𝑝𝑟𝑒

𝑈𝑚𝑒𝑎𝑛𝑥100)

(2-8)

The rules for filtering according to the MAD method are outlined in the table below.

Table 2-1: Filtering rules for CVR factor estimation (Shim et al., 2017)

Filtering term Range Description

Voltage and load variation ∆𝑈 > 0, ∆𝑃 > 0 Voltage drop

∆𝑈 < 0, ∆𝑃 < 0 Voltage rise

Percentage voltage variation 0,5 < %∆𝑈 < 1,5 Voltage

MAD percent load variation 0,2 < %∆𝑃𝑀𝐴𝐷 < 2,0 Active load

0,2 < %∆𝑄𝑀𝐴𝐷 < 30,0 Reactive load

MAD CVR range 0,2 < 𝐶𝑉𝑅𝑀𝐴𝐷 < 2,0 Active

0,2 < 𝐶𝑉𝑅𝑀𝐴𝐷 < 30,0 Reactive

- 14 -

To account for uncertainties and variations in load, the MAD considers the maximum and

minimum loads in the dataset. The principal equations that define the CVR factor estimation

through MAD are as follows (Shim et al., 2017):

𝑃𝑀𝐴𝐷 = 1

𝑛∑ |𝑃𝑖 − 𝑃𝑚|𝑛

𝑖=1 (2-9)

%𝑃𝑀𝐴𝐷 = 𝑃𝑀𝐴𝐷

𝑃𝑚 𝑥 100[%]

%∆𝑃𝑚𝑖𝑛 = %∆𝑃 − %𝑃𝑀𝐴𝐷

%∆𝑃𝑚𝑎𝑥 = %∆𝑃 + %𝑃𝑀𝐴𝐷

𝐶𝑉𝑅𝑚𝑖𝑛 = %∆𝑃𝑚𝑖𝑛

%∆𝑈, 𝐶𝑉𝑅𝑚𝑎𝑥 =

%∆𝑃𝑚𝑎𝑥

%∆𝑈

𝐶𝑉𝑅𝑀𝐴𝐷 = 𝐶𝑉𝑅𝑚𝑖𝑛+𝐶𝑉𝑅𝑚𝑎𝑥

2 (2-10)

Applying these to the KEPCO pilot project, CVR factors for active power obtained were in the

range 0,721 to 0,784, while for the reactive power, the range was 7,364 to 18,725 (Shim et al.,

2017). The difference in the estimated CVR factors for active and reactive power results from

voltage impacts on the reactive load being more than that of the active load. One key observation

is that voltage changes of 0,5% to 1,5% stipulated in this methodology are insufficient to stimulate

a substantial change in the active power (Shim et al., 2017).

2.3 External Factors

The influence of external factors on load modeling is very important for computing the accurate

estimate of energy consumption during a CVR testing period. Various load types react to

environmental changes and routines of the consumer differently. The changes are seasonal and

dependent on events throughout the year. Therefore, the key factors are divided into two parts

with respect to the kind of observations they produce. They are either numerical or categorical

factors.

Numerical observations produce numerical results with decimals, and they have different values

at different times; they are non-finite. Examples are temperature, voltage, humidity, pressure,

irradiance, etc. A categorical observation produces finite characteristic values that show the

condition/status of the variable at a particular time. Examples are the hour of the day (24), day of

the week (7), holiday (1), the month of the year (12), season (4), etc. Both types of variables are

used as independent variables in modeling energy. The predicted parameter responds to them

independently and differently. This relationship between the variables is captured through their

correlation. Various research has been carried out to define load sensitivity to changes in

environmental factors and time.

(Chen et al., 1995) shows that temperature has the most influence on load change because

devices dependent on heating/cooling demand consume more power than others. Also, in terms

of significance to feeder power demand, the impact of temperature can be extrapolated to the

- 15 -

feeder level, considering the share of the temperature-dependent load to the overall consumption

profile. Extending the test period to yearly intervals, fluctuation in demand roughly follows the

changes in the annual temperature profile, and that is why the impact of CVR is more significant

during the winter than in summer.

There is a substantial difference in the influence of temperature on load between the temperate

and tropical climates. Temperate climates generally have a wide variation in temperature (-10℃

to 25℃) and thus require heating and cooling appliances. In contrast, tropical climates have a

narrow band of temperature variation (18℃ to 37℃) and thus require only cooling appliances.

Figure 2-8: Annual temperature profile in Regensburg. source (Weather and Climate, 2021)

It is expected that CVR factors remain even through the year in tropical regions. The load model

for this region could be built using additional parameters that follow consumer behavior and cycle.

Humidity as an influencing factor has a lower correlation to the demand load because it does not

directly influence the sensitivity of any appliance. It trends weakly with temperature. (Lefebvre et

al., 2008 - 2008) conducted research in Hydro Quebec and found that -10℃ resulted in a CVR

factor of 0,15 while 20℃ resulted in a 0,55 CVR factor.

The PV-output and solar irradiation data observed during the testing period or during baseline

testing influences demand reduction due to DER injection into the grid. As more PV plants are

integrated into the network, primary demand will also reduce, and so will the effect of CVR. Solar

irradiations vary daily and annually based on sunrise and sunset cycles and seasons of the year.

With higher irradiation, PV solar outputs increases and vise versa. Also, with more installation of

PV modules, there will be a gradual increase in total capacity, although this growth is geometric.

The categorical variables that represent seasons, times, and days play important roles in energy

demand estimation. They describe the status of various load mixes and the trend of the load

profile at any time. Different days have different total power demands. However, the hourly

variations in each day are similar to the weekdays and different on the weekends and holidays.

Studying several load profiles shows uniform behavior patterns and consumer demographics. For

example, the load profile of an office worker is different from that of a home office for a flexible

routine worker.

- 16 -

The load models developed in various research were based on the above-mentioned external

factors. (Erickson & Gilligan, 1982) built a multiple-regression model based on temperature,

DOW, seasons, holidays, network defects, and interruptions. (Short & Mee, 2012 - 2012) utilized

normalized temperature variables (heating/cooling degree hours) to determine load dependence.

The model shows a good estimation of the load. (Liu et al., 2014) built a linear model for reactive

power and energy savings using a range of variables described in 2.2. (Wang & Wang, 2014)

made use of temperature and humidity as external factors. (El-Shahat et al., 2020) developed a

neural network model for load estimations based on TOD, DOW, and temperature. In (Bechara,

2017) the model and CVR factor validation were set up using temperature, relative humidity, and

voltage. The model was a perfect fit for the CVR factor computation.

2.4 Energy Savings Measurement Techniques

Energy estimation techniques aim to determine the energy savings achieved from voltage

reduction by finding the difference in energy between the CVR-on load profile and the CVR-off

load profile during a testing period. The challenge with this computation is obtaining an accurate

estimate of energy for normal operation (CVR-off) during the testing period. Several regression

methods have been utilized, and each gave an approximate estimate similar to a normal

operation. Energy consumption is influenced by many external factors and conditions, which are

also location-specific, as discussed in 2.3.

Generally, an estimation model is built using a baseline dataset from normal operations in the

past. Before building an estimation model, it is relevant to place the testing at periods where the

baseline profiles are very similar to the testing profiles. It is also important to understand the

relationships between each variable with the load and use profiles where such similarity can be

detected (Bechara, 2017).

It was suggested that in using linear regression models to predict a load of normal operation

during the testing period on a feeder with the significant additional load from the testing period,

that a proper load adjustment should be implemented in the historical values before model

estimation. Additional loads originate from new connections, grid expansion, DER, EV loads, etc.,

(Draft Standard, IEEE P1885). In the long-term load forecasting research by (Hong, Wilson, &

Xie, 2014), load normalization was applied on historical loads for the prediction. A new parameter

called gross state product (GSP), a measure of economic growth, is used to normalize load. It

was assumed that load grows at the same rate as GSP; therefore, the load was divided by GSP

(Hong et al., 2014). Choosing the appropriate normalization parameter is important, but it is

dependent on the duration of testing. If energy savings measurement is determined annually, then

load growth rates should be normalized. The parameter can be derived from a comparison

variable when there is no base case. However, when the base case is present, a percentage

increment factor can be defined to reduce future loads (Draft Standard, IEEE P1885). The

magnitude of the growth parameter is location/feeder specific.

According to the mean absolute percentage error (MAPE), the accuracy of any proposed model

is dependent on the length/size of the historical dataset. (Hong et al., 2014) discovered an optimal

- 17 -

ratio between baseline and estimated sample sizes as 4:1. This ratio applies to all independent

variables useful for the modeling. The forecasting model was built with MLR for annual, monthly,

and hourly intervals.

In 2.2, it was discovered that SVR models are more effective at estimating load than MLR models.

A support vector regression uses margin functions or Euclidian distances to construct n-

dimensional hyperplanes that represent linear regressors and inherently expandable for non-

linear regressors (Wang et al., 2014). The accuracy of the CVR factors is dependent on the

accuracy of the estimated load, which itself is dependent on the similarity of the load profiles used

in training the model. Pre-selected profiles for training produced a MAPE of 0,29 while that of the

entire dataset produced 0,78 (Wang et al., 2014).

- 18 -

Statistical Evaluation of Voltage Measurements

3.1 Voltage Noise

The idea of statistical evaluation of voltage measurements is built on the need to explore the

properties of a dataset so that we can determine the impact of distortions and how they will affect

the results of the CVR factor (𝐶𝑉𝑅𝑓) evaluation. A good statistical evaluation should detect the

magnitude of the distortions in the voltage measurements; that will then help us ensure that the

tapping operations substantially affect the voltage signal in terms of the magnitude of change and

not just randomness.

Consider a site with a VRDT connected to the low voltage network, as shown below.

Figure 3-1: Representation of the test VRDT connection point.

Before producing the parameters for measurement, an original baseline (CVR-off) voltage reading

during normal operations will be obtained from the representative network under the same

conditions for CVR implementation. They shall then be evaluated for naturally occurring voltage

noise and the best duration of a tap change.

A VRDT with an OLTC supplying to the LV grid regulates voltage with a tap change at a certain

time of day (TOD) in response to demand and distributed energy resource integration changes.

The OLTC can also achieve CVR on the LV grid at 2,5% of nominal voltage (Hossan

& Chowdhury, 2017).

Figure 3-2: Voltage signal properties in a single tapping operation

- 19 -

In other to explain the importance of evaluating these voltage distortions, we shall consider a

case. A typical tap operation (influenced by distortion) using the ECOTAP VPD is shown in Figure

3-2 above. Switching operations on the VRDT respond to sustained voltage dip; slight dips are

not desirable and thus should not influence the CVR-on voltage measurements. ECOTAP VPD

responds to ±2% of 1pu dip at 10 secs delay time (Poppen et al., 2014). From Figure 3-2, a tap

change from 𝑈𝑡1 to 𝑈𝑡2 occurred at 𝑛 + 1 and produced a pure signal response 𝑈𝑟1 to 𝑈𝑟2. These

changes should produce similar magnitude such that 𝛥𝑈𝑡 ≈ 𝛥𝑈𝑟. Because of disturbance in the

system, an additional distortion is introduced into the CVR-on voltage 𝑈𝑒. Thus, the response

voltage now has an error component such that 𝛥𝑈𝑡 ≈ 𝛥𝑈𝑟 + 𝛥𝑈𝑒. This distortion can be observed

with or without CVR operation, and it remains constant in CVR-off voltage and CVR-on voltage

readings at the same time.

If measurements were taken at intervals of 𝑛(𝑚𝑖𝑛, 𝑠𝑒𝑐𝑠) the ideal signal after the step 𝑈𝑟2 should

correspond to the voltage step 𝑈𝑡2 and remain constant for 𝑛 + 2, 𝑛 + 3, … till the next tap at 𝑛 + 𝑖,

where 𝑖 = 1,2,3, … But at the intervals where tap operations did not occur, slight dips are not

enough to trigger the OLTC. This figure represents a typical voltage measurement that has a

maximum magnitude that is less than 50% of 𝛥𝑈𝑡. Let 𝑛 = 1,2,3, … , ∆𝑡. Without any prior

information on standard tapping operation, the 𝐶𝑉𝑅𝑓 Determined from this time series will have a

wide range, as shown in Figure 3-3.

Figure 3-3: Step voltage versus response signal.

Figure 3-4: Noise and uncertainty influence on 𝐶𝑉𝑅𝑓 estimation

Instead of taking measurements at 𝑛 ∈ ∆𝑡, we can apply statistical evaluation on this voltage.

What we want to achieve with this is to determine the magnitude of 𝛥𝑈𝑒 and define the minimum

tap change duration such that 𝛥𝑈𝑒 is always substantially lower than 𝛥𝑈𝑡. Thus, instead of

- 20 -

considering each point in the ∆𝑡 as a CVR point, instead, we analyze the data and consider 𝑛6, 𝑛7

as CVR points. A ∆𝑡 of 30 min with 𝑡𝑛+1 − 𝑡𝑛 of 2 min (lag) will have 15 data points.

Considering a stationary voltage measurement in time series for ∆𝑡, a signal with substantial

disturbances at every data point will look as shown in Figure 3-5(a), while a signal with few

disturbances will look like Figure 3-5(b).

(a) Voltage profile with noise (b) Voltage profile without noise

Figure 3-5: Stationary voltage measurements with and without noise.

Applying statistical modeling on this time series produces an error part 𝑈𝑒 that has the same

characteristics as white noise. It is normally distributed and stochastic. Its magnitude will be lower

than a voltage change during an actual tap operation.

MV feeder connection points in the primary substations are equipped with data recorders or smart

meters capable of measuring voltage, line current, active and reactive power, energy, 𝑐𝑜𝑠∅,

power factor, etc., in a time-dependent series. Measurements of this nature are inherently

probabilistic; the measured parameters contain elements of uncertainties that need to be

mitigated as part of the computation process (Zhang, Huang, & Bompard, 2018). Understanding

the baseline influence of voltage in the system will guide us to developing the best conditions

setups for testing CVR. This can be achieved by performing a statistical model on the voltage

data. If we can measure close to pure voltage impulse (devoid of noise) from the specified tap

settings, we can expect the CVR factors to be accurate.

3.2 Terminologies

These terminologies define the properties of the time series and evaluation process.

1. Time series data in the time domain

Univariate or multivariate time series measurements drawn from a stochastic process with mean

𝜇𝑡 and variance 𝜎𝑡2 are random observations within a uniformly increasing (district) time interval

(t) such that 𝑡 ∈ (0, ℵ). Where ℵ is the time duration of the entire observation. Since 𝑡 is discrete

and ℵ is finite, we can represent the time steps 𝑡𝑖+𝑛 with 𝑛 = 0,1,2,3, … , 𝑁. It is generally described

by a probability distribution of the Gaussian form. The discrete nature of the time series is such

that the difference between a unit time step in the forward or backward direction is always constant

- 21 -

at any time. Before carrying out statistical modeling, it is expected that all observations on t contain

real and non-zero values. Data analytics and cleaning techniques will be applied to handle such

occurrences (Palma, 2016).

2. Univariate normal distribution

There are various forms of probability distributions that describe sample data drawn from natural

observations. The normal distribution describes measurements that are autocorrelative or pure

random walks. A random walk process has no autocorrelation, is stationary, and it has a zero

mean. It is independently and identically distributed (iid) along with the time intervals. It is also a

stochastic process. An iid variable always shares the same probability distribution as others but

also mutually independent. A normal distribution is represented as a bell-shaped profile that

represents a Gaussian process.

Figure 3-6: Probability distribution function of a normal distribution [source: (Fallon & Hyman, 2020)

This distribution is centered around the mean and distributed such that the 95% probability of a

variable x is the area under 𝜇 − 2𝜎, 𝜇 + 2𝜎. The total area under the pdf curve evaluated by

advanced integration methods for all x values is 1 (Fallon & Hyman, 2020).

3. Seasonality

This is the property of time series data that shows a repetitive occurrence of observations within

a specific duration. Power measurements tend to display daily and annual seasonality. This can

be observed by plotting the profile of the measurement, as shown in Figure 4-12. It can also be

observed analytically through the plot of the autocorrelation function (ACF).

4. Null Hypothesis

This is a hypothesis 𝐻0 that indicates that the baseline assumption of indifference between a

measured observation and its counterpart derived from the same general population holds for

that variable's present and future values. This assumption remains true for each statistical

property until it is rejected by carrying out a test that proves otherwise (𝐻𝑎). According to the unit

root, the conditions for accepting and rejecting a null hypothesis are defined for each statistical

- 22 -

property. The unit root of a stochastic process is the root of its characteristic equation, which is

usually 1 (Orloff & Bloom, 2014).

5. Stationarity

Simply put, a stationary time series is one with a zero mean (𝜇 = 0) and a variance 𝜎2 > 0. A

non-stationary time series develops a trend, and the mean varies with substantial autocorrelation

as time increases.

Figure 3-7: Stationary time series voltage data.

The figure above describes a stationary time series that was obtained by detrending and

autocorrelative daily voltage reading using a differencing method. This also introduces linearity to

the time series, and it is the base assumption for any autoregressive integrated moving average

(ARIMA) modeling. The objective of differencing is to demean the time series to achieve

stationarity. Stationarity test of time series data can be carried out using the Augmented Dickey-

Fuller test (ADF) (Shumway & Stoffer, 2017) (Paolella, 2018) and the Kwiatkowski-Phillips-

Schmidt-Shin test (KPSS), assuming a 𝐻0 of stationarity (Paolella, 2018). It will be shown in the

subsequent sections that the daily voltage readings are non-stationary since we rejected the null

hypothesis.

6. Autocorrelation and Autoregression

Autocorrelation defines a time series property that describes the correlation or non-correlation of

an observation 𝑥𝑡 at time step 𝑡𝑖 from other observations at different time steps in the past (𝑡𝑖−𝑛).

This is a relevant property that is used to measure the characteristics of a series at various stages

of statistical modeling. Autoregression (AR) describes a property of a time series model that

derives predictions from previous observations in the time series based on a regression equation.

Not all-time series data are AR because of the non-linearity of its previous observations.

The ACF describes the autocorrelative relationship of lagged values of observations from an initial

observation 𝑥𝑡. A plot of the ACF shows the intrinsic trend, seasonality, heteroscedasticity, and

other dynamic properties hidden in the series. Generally, autocorrelation decreases as you step

further away from the origin. This is called damping. A lag of a time series is the interval of

- 23 -

incremental time used to estimate its statistical properties. For example, a time series 𝑋𝑛 with

1440 data points (in minutes) having 72 lags has each lag in 20 minutes.

Figure 3-8: ACF of daily voltage readings

The series is said to be autocorrelative when the ACF (ranging from 0 to 1) of the lags are above

the confidence limits (CL) of 95%. Where 𝐶𝐿 = 0 ± 2√𝑛

⁄

7. Partial Autocorrelation Function (PACF)

This is an ACF developed from a model where the trend, seasonality, and other dynamic

properties of the original time series are eliminated. This correlation of the residuals alone is

analyzed after applying the modeling method along with lagged values from the initial observation

𝑥𝑡. If we find a correlation in the residuals as described by the PACF, then it implies that there is

still an existing feature in the series that still produces correlation and, therefore, relevant in the

modeling. Such a feature can exist at the nth lag, and it thus makes the residual correlative. Instead

of considering the residual as pure white noise, we can reshape the sample size and remodel the

time series until we get a white noise in the residual with a 95% confidence limit.

Figure 3-9: PACF of daily voltage readings.

The important characteristics used to define the time series model (apart from autocorrelation,

stationarity, and trend) are the number of lags, sample size, p, q and d values.

- 24 -

The p, d, q are the key parameters for modeling an ARIMA, and they are derived from the ACF,

heteroskedasticity, and PACF plots of a time series data. The order of an AR process is the lag

of the PACF that precedes the first lag to fall below the confidence limit. An AR process has a

gradually decreasing ACF, while rapid changes occur in the PACF along with the lags (Paolella,

2018). In such a case, the AR(p) model is applied with 𝑝 = 1,2,3, … , 𝑛 orders. Error! Reference s

ource not found. shows an AR(2) process, where p = 2. (Palma, 2016).

A moving average (MA) process models a time series based on the past forecast errors following

a regression model. The MA(q) has a q value obtained from the first lag falling below the

confidence limit of a rapidly varying ACF. (Palma, 2016)

8. White Noise

A pure white noise has an ACF bellow the confidence limit of 5% at each of the lags. It is known

that all white noise are iid and stationary with a PACF that shows non-autocorrelation in more

than 95% of the lags. If we can characterize this noise, we can then use its statistical properties

for configuring the tap settings required for measuring accurate CVRs.

9. Autoregressive Integrated Moving Average (ARIMA)

An ARIMA(p,d,q) model combines an integrated (d), AR(p), and MA(q) process such that:

𝐴𝑅(𝑝) = 𝐴𝑅𝐼𝑀𝐴(𝑝, 0,0) or partial 𝐴𝑅𝐼𝑀𝐴(𝑝, 𝑑, 0)

𝑀𝐴(𝑞) = 𝐴𝑅𝐼𝑀𝐴(0,0, 𝑞) or partial 𝐴𝑅𝐼𝑀𝐴(0,0, 𝑞)

Partial ARIMA processes are introduced when non-stationarity exists at various portions of the

time series while higher-order differencing makes it stationary (Montgomery, Jennings, & Kulahci,

2008). In our voltage measurement, the first-order difference makes the time series stationary;

thus, our ARIMA model always contains a 𝑑 component for most sample sizes. When the sample

size reduces to 45 min, the time series becomes ARIMA(p,0,0) process purely. We should be

able to observe pure white noise at this point in the ACF plot of the residuals.

3.3 Preliminary Estimation

Time series evaluation techniques are determined from their general properties.

┃ A time series with seasonality is modeled using a Seasonal Autoregressive Integrated

Moving Average (SARIMA) model if it is univariate (Palma, 2016).

┃ If it exhibits heteroscedasticity and also univariate, it is modeled with the Generalized

Autoregressive Conditional Heteroscedasticity (GARCH) model (Paolella, 2018).

Heteroscedasticity occurs in non-stationary data with varying variance across different

samples, which is present in our voltage time series.

┃ All other forms of univariate stationary time series are modeled using the ARIMA model.

┃ There are other methods for evaluating both univariate and multivariate time series data,

and they are described in (Paolella, 2018) (van Nederpelt, 2009).

- 25 -

The voltage measurements of the substation were applied in this statistical analysis using the

ARIMA model. I first cleaned the data using preprocessing tools in python to ensure that the

observations are complete and valid. The time series were resampled using a finite shape of 1440

data points per day starting from 00:00:00 till 23:59:00 (05/09/2020 – 13/092020). Visualization

tools were employed at this state to observe the trend and seasonality of the data for the daily

samples. A general description (mean, std, min, quartiles, max, and delta) of the data shows how

they vary from each other. The day with the highest delta was selected for subsequent analysis.

(see Appendix A – Table 1)

In the next stage of the evaluation, I began to determine the statistical properties of the time series

– stationarity, probability distribution, linearity, and subsequently differenced to introduce

stationarity. Before this, I have already evaluated the ACF and PACF of the original sample to

observe the hidden patterns. At this stage, the ARIMA model was applied iteratively on various

sample sizes of the daily voltage measurement until white noise is obtained from the residuals.

The associated parameters – sample duration ∆𝑡 and residual noise magnitude were the outputs

of this evaluation.

3.3.1 Data Collection and Pre-processing

Figure 3-10: Preprocessing process for the time-series data

From 3.1, we discovered that data recorders sometimes produce measurements with missing

entries, noisy data points, outliers, or incorrect values. Other external factors such as weather,

temperature, special social events, and other unforeseen events can affect the measurement

(Zhang et al., 2018). Therefore, it is required that these factors are standardized across the entire

measurement.

The measurement is presented in *.csv and used as baseline input data for subsequent cleaning.

The data is first resampled in Figure 3-10, cleaned by removing null, NaN, and outliers. We must

also ensure that the time-step in the date-time is uniform and constant throughout the series by

comparing the number of observations with the expected number. Data preprocessing will be

applied at the various stages of this project, especially at points where we have new

measurements.

3.3.2 Data Analytics and Statistical Testing

The general equation for an AR time series model is

𝑦𝑡 + 𝑎1̂𝑦𝑡−1 + 𝑎2̂𝑦𝑡−2 + ⋯ + 𝑎�̂�𝑦𝑡−𝑝 = 𝑛�̂� (3-1)

- 26 -

Where 𝑦𝑡 is the original time series, 𝑎�̂� is the autoregressive parameter and 𝑛�̂� is the residual. A

correct model produces estimations (𝑦�̂�) of the time series with a portion of the original time series

represented as residuals.

𝑟𝑒𝑠𝑖𝑑𝑢𝑒 ≡ 𝑦𝑡 − 𝑦�̂� = 𝑛�̂� (3-2)

The accuracy of this type of model depends on the characteristics of the error or residual term

observed. The purpose of carrying out this analysis and testing is to ensure that the properties

and assumptions of the time series align with the requirements for employing a model that will

produce the best estimate of the residuals as white noise.

Table 1 in Appendix A shows that Sun_2 has the highest mean voltage, which indicates that more

loads are connected on that day, and when compared to the previous Sunday, it shows the same

or similar behavior. The data recorded on Monday shows measurements with the highest voltage

change while Sun_1 has the highest standard deviation. Tue, Wed, Fri, and Sat_2 have almost

the same delta value. The minimum voltage of 117.5V (-2.08% of nominal) was recorded on

Sat_1, while the maximum voltage of 123.4V (+2,83% of nominal) was recorded on Sun_2.

For further analysis, I selected the Tuesday profile because its descriptions are centralized among

the entire dataset. See Appendix A – Figure:1 for the daily voltage profiles.

Our 𝐻0 on Tuesday voltage profile is non-linearity and non-stationarity. Therefore, it is strongly

influenced by time of day (TOD). Linearity and stationarity test was carried out by OLS and ADF

using the python libraries of statsmodels (Skipper & Perktold, 2010). See Appendix A – Figure 2.

With an R2 value of 0,748, it shows that the data is non-linear in the interval of one 1day.

The ADF test for stationarity produced a p-value = 0,5938. With a p-value less than 0,05, we fail

to reject the 𝐻0.Thus, the time series has a unit root with a time-dependent structure. This applies

to the entire dataset since they were all drawn from similar samples and baseline conditions. See

Appendix A – 1.2.

(a) Probability density function (b) Cumulative density function

Figure 3-11: Histogram and CDF of Tuesday voltage readings

Alternatively, the KPSS test was applied as a complementary stationarity test, and the result

shows non-stationarity at 15 min intervals of time, producing a p-value of 0,0707.

- 27 -

In other to observe the sample distribution of the time series, a histogram and kernel density

function (KDE) shown below was produced.

The histogram in Figure 3-11 does not show pure normality in its distribution, and by applying

Lilliefors statistic (Andersson & Burberg, 2015), I confirmed this assumption when the p-value was

0,001. See Appendix A. The probability of having an observation greater than 122V or less than

119V is 0,13 and 0,05, respectively. The CDF plot shows that 95% of the data has less than or

equal to 122V readings.

3.4 Statistical Modeling

The ACF and PACF plot of the Sat_1 voltage readings (Appendix A – Figure 3) can observe

partial seasonality and high autocorrelation in the lags. At this stage, the data is non-stationary

and trending with gradual damping. The PACF still shows residual autocorrelation and does not

represent a pure white noise. It, therefore, describes an AR process in this sample size. Further

reshaping the dataset from 1440x1 to 360x4 and plotting the ACF and PACF still shows

autocorrelation (Appendix A – Figure 3 & 4).

Implementing the ARIMA process will require that we satisfy the condition of stationarity and non-

autocorrelation. Thus, we must difference the Monday time series as shown in Figure 3-8. The

ACF and PACF post-differencing shows that the autocorrelation and other trending characteristics

have been removed, and the dataset is ready for modeling. (Appendix A – Figure 5). The plot

shows non-autocorrelation and thus is adequate for modeling. I then evaluated the individual parts

of the time series to see which sample size produces the purest white noise following an

ARIMA(p,d,0) model.

The order p of the ARIMA(p,d,0) process was determined using the 𝑎𝑟_𝑠𝑒𝑙𝑒𝑐𝑡_𝑜𝑟𝑑𝑒𝑟( ) function

of statsmodels which was specified as ARIMA(19,1,0). There was still some correlation in the

residuals since 32% of the lag values were above the 95% confidence limit.

Reshaping the data to 4-six hours blocks (4x360) Sat_1[0], Sat_1[1], Sat_1[2], Sat_1[3] and

calculating their variances gave 0,0287, 0,0312, 0,1315 and 0,0503 respectively. The third

partition has the highest variance and thus more likely to show autocorrelation. ARIMA(6,1,0) was

applied further on Sat_1[2]. The residual ACF has 17% of its lags above the confidence limit and

thus not white noise.

Reshaping Sat_1[2] further to 4x90 array produced individual variances of 0,0772, 0,0941, 0,1618

and 0,1924 respectively. Applying ARIMA(1,1,0) as an AR process on the last sample of this new

array produced residuals where 7,5% of the lags were above the confidence limit. A further

reshape to 2x45 with variances of 0,2640 and 0,1206 produced an ACF of pure white noise with

21 lags using ARIMA(1,0,0). (see Appendix A – 1.4)

- 28 -

Figure 3-12: ARIMA evaluation process

The distribution of the residuals follows a normal distribution, as shown in Figure 3-13.

Figure 3-13: PDF of Saturday 1 voltage residuals

It is shown from this figure that changes of -0,5 to 0,5 in the voltage measurements (with 70%

probability) are noise in the system. Thus a 0,5V change in the system has a good chance of

being noise.

The challenges that could impact the consistency of this methodology would result from improper

pre-processing of the data. If there are noisy data points with high deviation from the mean, they

could project a strong correlation even in the residuals if these points are close to each other.

This would affect the distribution of the error and result in improper parameter estimates.

- 29 -

3.5 Modelling Results

The box plot shows that tap operations above ±0,4V shall yield noticeable changes in the voltage

signals for 𝐶𝑉𝑅𝑓 evaluation. A tapping operation at 𝛥𝑈𝑡 > 0,0042𝑝𝑢 should produce observable

signals in the measurement that is not noise. From the variance of the individual partitions, the

peak voltages during normal operations were recorded between 12:00 and 18:00. and

subsequently from 18:00 – 00:00. The number of tap operations 𝑁𝑡 versus the 𝛥𝑈𝑡 is inversely

proportional, but directly proportional to 𝛥𝑡. It will be adequate to deploy CVR on the active

partitions (14:00 – 21:00). On the right-hand side of the figure below, the box plot shows that by

partitioning the data set to 90 minutes, the magnitude of the noise/uncertainties can be more

accurately estimated.

(a) Full day data (b) 90 minutes data

Figure 3-14: Box plot of Monday data samples.

The evaluation result can be applied for 𝐶𝑉𝑅𝑓 determination in any other sample interval that has

the same baseline condition. The need for CVR is defined in any season by the external conditions

affecting increase demand during peak. The 𝐶𝑉𝑅𝑓 evaluation shall be measured at ∆𝑡 minutes

intervals throughout the day. The most accurate 𝐶𝑉𝑅𝑓 from ∆𝑡 shall represent the 𝐶𝑉𝑅𝑓 for that

interval. Therefore, if ∆𝑡 = 45𝑚𝑖𝑛, there shall be 32 𝐶𝑉𝑅𝑓 measurement in a day. Within a

particular TOD, we can carry out CVR at times where the variance of the CVR-off voltage is

highest. (Hossan & Chowdhury, 2017) defined unified weight factors for deciding when CVR is

going to be more beneficial for LV networks in DERs. The determined period based on 𝐶𝑉𝑅𝑓 and

loss factor for CVR implementation and energy savings corresponds to the intervals defined by

the variance of the sample sizes.

- 30 -

Power Demand Reduction.

4.1 CVR Factors

By carrying out 𝐶𝑉𝑅𝑓 evaluation, we hope to achieve the best estimation of the factor by which

we can reduce demand by supplying the minimum voltage required for safe operation. 𝐶𝑉𝑅𝑓−𝑝𝑜𝑤𝑒𝑟

considers potential savings at peak power and continuous demand to optimize savings during

those times. As a result, we will determine peak shaving and percentage reduction in demand for

active and reactive power. The ability to capture accurate 𝐶𝑉𝑅𝑓 from system responses of power

depends on the testing protocol and setup implemented. Key parameters such as current, voltage,

𝑐𝑜𝑠∅, active power, reactive power, tap positions, and measurement intervals play important roles

in this evaluation.

In the previous chapter, we discussed the influence of baseline voltage in the 𝐶𝑉𝑅𝑓 evaluation

and proposed an adequate tapping interval and magnitude that will reduce the impact of system

noise and uncertainties. Other error sources such as instrument and gain error were not evaluated

in that section. It shall benefit the network operator to know beforehand the kind of CVR testing

protocol to implement, combined with the historical knowledge of consumer power demand.

𝐶𝑉𝑅𝑓 for power, estimation is subsequently affected by measurement uncertainties and

distortions in current and voltage, statistical and device errors. Before the computation, it will be

important to describe the inherent delay in system response as a result of tapping operation. The

delay originates from the OLTC switching time of 3,42 seconds for ECOTAP VPD and the

system's delay response time (MR, 2016). The parameters vary according to the controllers,

network, feeder characteristics, and load mix. Therefore, the measurement resolutions should be

large enough to allow for these changes to occur. We aim to define a standard interval and

resolution applicable to our testing scenario.

The best 𝐶𝑉𝑅𝑓 computation methodology accounts for present natural variations in voltage and

power by applying several filters for maximum and minimum limits of power and voltage changes

resulting from sudden events like outages and natural distortions, respectively.

In other to ensure that voltage response magnitudes are significantly higher than the noise

magnitudes of the natural variations in the given voltage measurement (from section 3), we shall

carry out tapping operations ∆𝑈𝑡 from ±2,1% to ±5,5%. This range falls approximately within the

common execution intervals of CVRs which is 2% to 5%, according to (Le et al., 2015).

Consider a voltage noise magnitude of ±0,5V (0,42% of 120V nominal) and let this constitute 1/5

of the minimum voltage step. The actual minimum voltage step becomes 5 x 0,42% = 2,1%.

Conversely, if we allowed the tapping operation to be carried out at 1,25% per step, with a ∆𝑈𝑒 at

0,42%, it will be difficult to determine the impact of the voltage reduction in the network because

of this noise level ratio to the tap changes. According to the ZIP model, system response to

voltage variation varies a lot from system to system. Treating the load makeup of the system as

a black box helps us to standardize this factor. Pilot projects are eligible for deploying this testing

setup if their feeders supply areas with 8:2 residential and commercial loads (RTF, 2015).

- 31 -

4.1.1 Baseline testing setup

The baseline measurement is applied towards developing the best statistical model that can

estimate energy demand during CVR-off for the test periods. The accuracy of this type of model

depends on the correlation between energy and environmental factors during testing. Parameters

to consider for evaluation include energy, voltage, temperature, humidity, solar irradiation, PV

output, and wind speed. The duration of measurement should be seasonal, monthly, or annual

with 15 minutes resolution. To meet up with the “Benchmark Performance Thresholds”

requirements of (RTF, 2015), the period of baseline testing should be aligned with that of the

continuous testing setup. Therefore, if measurements are planned for two weeks in the winter

season, the baseline testing should fall within the same season and duration.

4.1.2 Power demand testing setup

The maximum duration for a complete tap operation (tap down, tap up) ∆𝑡 defined in the previous

chapter was 45 minutes. Let each pair of CVR operations last for 30 minutes. For a peak duration

of 4 hours, 8 CVR operations can be carried out using 30 minutes voltage reduction interval. The

overall testing period shall be determined by the allowable range of variations in temperature for

the season. For example, considering -10℃ to 5℃ range in the winter gives four weeks of testing

(25/12/2020 – 25/01/2021). However, annual measurements can be used to evaluate CVR

factors in a continuous scheme.

For a continuous scheme, voltage reduction is not induced during the testing period but rather a

desired voltage setpoint is created with an operating bandwidth of ±2%. The tap change occurs

when this bandwidth violation is sustained for 10 seconds. Our evaluation's total number of useful

tapping operations depends on how many violations and corrections occur in the testing period.

It occurs randomly but mostly during the peak period. We shall later discover that having large

data points of CVR factors over a large period with a known variance will help to produce a more

accurate estimation of the factor with higher confidence interval (Renmu et al., 2006).

4.2 CVR Factor Evaluation Methodology

4.2.1 Parameter Definition

The averaging interval (𝑡𝑚) of pre-CVR and post-CVR events for estimating the average voltage

and power can be determined by a simple statistical process. Before this, I would define the

minimum granularity of time-step (𝑡𝑖) for voltage measurement as an interval defined by the

duration of tapping operation and delay time. In our dataset, 𝑡𝑖 = 10𝑠.

The interval of 𝑡𝑖 should contain the following:

┃ Delay time before tap operation for a ±2% voltage bandwidth of 10 seconds (FNN, 2016).

┃ OLTC switching operation time. Approximately 3 seconds for ECOTAP VPD (MR, 2016)

(MR, 2016).

Therefore, the total time delay depends on the number of tap operations. A 5,5% voltage drop

requires between 2 – 3 tap operations depending on the type of OLTC. If each operation takes 3

seconds on average, plus 10 seconds delay time, a total time of 16 – 19 seconds is obtainable.

Therefore, 𝑡𝑖 should be greater than 20 s.

- 32 -

Figure 4-1: Voltage profile of a single tap operation

Voltage variations before a tap change (𝑈𝑖) and voltage variations after a tap change (𝑈𝑗) can

be averaged within a time interval 𝑡𝑚. A resolution 𝑡𝑖 found in the interval for evaluation constitutes

the number of samples 𝑛 in 𝑡𝑚. Thus, 𝑡𝑚 = 𝑛 × 𝑡𝑖.

Let 𝑈�̅� =1

𝑛∑ 𝑈𝑖

𝑛𝑖=𝑡𝑖

And 𝑈�̅� =1

𝑛∑ 𝑈𝑗

𝑛𝑗=𝑡𝑗

%∆𝑈 =𝑈𝑖̅̅ ̅−𝑈𝑗̅̅̅̅

𝑈𝑖̅̅ ̅× 100 (4-1)

An accurate interval for 𝑡𝑚 is affected by the standard deviation of 𝑛𝑈𝑖 or 𝑛𝑈𝑗 which is determined

by the duration of a tap operation 𝑡𝑑. Where 𝑡𝑚 ≤𝑡𝑑

2. Therefore 𝑡𝑖 < 𝑡𝑚 ≤

𝑡𝑑

2

The standard deviation of 𝑛(𝑈𝑖, 𝑈𝑗) ∈ 𝑡𝑚 is such that std(𝑈𝑖, 𝑈𝑗) ≤ 𝜎𝑚. Where 𝜎𝑚 is the

maximum standard deviation of a non-trending interval of 𝑡𝑚 – the interval that exhibits

stationarity.

To determine 𝑡𝑚, 𝜎𝑚, 𝜇𝑚:

┃ break down the time series into 𝑡𝑚 intervals

┃ compute max(std(𝑡𝑚𝑖)) or max(var(𝑡𝑚𝑖))

┃ let the interval of max(std(𝑡𝑚𝑖))/2 = 𝑡𝑚2

┃ percentage difference in mean of the two partitions should be less than 5%

%∆𝜇𝑚2 < 0,05 then there is no trend in 𝑡𝑚, thus the mean of 𝑈𝑖 will be 95% accurate. The

estimated averaging interval for the current measurement dataset using this approach is 1 min

for 10s granularity, which gives 𝑛 = 6.

CVR factor estimation by the direct method is defined as the ratio of the percentage change in

power to the percentage change in voltage. The number of samples that will be adequate for

estimating an accurate 𝐶𝑉𝑅𝑓 is dependent on the number of tap changes detected during the

testing period and active and reactive power variability. For each CVR factor estimate, the

- 33 -

variation in load affects its accuracy, and its nominal value influences the magnitude of this

variation. A sample data with a 20% change in 𝑃 has lesser variation than another with 50%

variation.

Figure 4-2: Estimating CVR by the direct method.

Let the number of samples for the 𝑡𝑚 interval be 𝑛𝑚. The mean values (𝑃𝑚𝑖, 𝑃𝑚𝑗) of active power

before (𝑘, 𝑙) and after (𝑙, 𝑞) the tap change, and their corresponding CVR factors can be defined

as follows.

𝑃𝑚𝑖 =1

𝑛𝑚∑ 𝑃𝑖

𝑛𝑚𝑖=𝑡𝑖

, 𝑃𝑚𝑗 =1

𝑛𝑚∑ 𝑃𝑗

𝑛𝑚𝑗=𝑡𝑖

%∆𝑃 =𝑃𝑚𝑖−𝑃𝑚𝑗

𝑃𝑚𝑖× 100 (4-2)

Similarly, %∆𝑄 =𝑄𝑚𝑖−𝑄𝑚𝑗

𝑄𝑚𝑖× 100 (4-3)

𝐶𝑉𝑅𝑓_𝑃 = %∆𝑃

%∆𝑈, 𝐶𝑉𝑅𝑓−𝑄 =

%∆𝑄

%∆𝑈 (4-4)

If the magnitude of the deviation (𝐷𝑖, 𝐷𝑗) approaches zero, the degree of uncertainty reduces.

This tendency is often encountered when the reactive power is stationary around zero. With these

parameters known, one can go ahead and compute the individual CVR factors for active and

reactive power across the seasons and time of day.

4.2.2 Test Site Description

The dataset of the following network area shows a continuous protocol of random tap operations

composed of voltage, active and reactive power measurements on three phases. A low voltage

grid with PV integration supplying 85 residential consumers in Southern Germany has a

secondary substation with tapping operation capability (ECOTAP VPD) on the transformers.

- 34 -

Figure 4-3: Topology of the LV network.

The transformer tapping operations were carried out year-round with an OLTC. The network area

has a 98kWp PV installed capacity connected to the substation, while the test field is equipped

with an additional 40kWp PV. There are also 15 smart meters connected at specified

measurement points on the grid. With the influence of PV, the annual demand changes are

expected to have an inverse pattern to the annual power output profile of the PV systems within

the network. According to the annual profile, the PV output is low or zero (on some days) during

the winter months and at night times. Thus, to isolate the impact of PV integration on the active

and reactive power demands, we shall focus on the periods where PV output is negligible.

The dataset measurement resolution across the three lines is 10 seconds for all measurement

parameters (P, Q, U). Monthly datasets were compiled in *.csv format and were made available

for evaluation. Therefore, a complete monthly observation contains 267.840 data points for each

phase and parameter. The measurements were extracted from the sensors in the substation

where the ECOTAP is operating. Further information on the type of LTC or its configuration is

currently unavailable.

- 35 -

(a) Monthly yield of a PV installation (b) Daily yield of PV installation

Figure 4-4: PV yield in Freiburg. (Fraunhofer ISE, 2021)

Based on the expected output of the PV system, four time groups (TG) were specified. 16:00 –

22:00, 22:00 – 04:00, 04:00 – 10:00 and 10:00 – 16:00 are 𝑇𝐺1, 𝑇𝐺2, 𝑇𝐺3 and 𝑇𝐺4 respectively. In

the winter months, the PV yield is always less than 30%, as shown above. In 𝑇𝐺2, zero yields are

expected from the PV system. Our initially targeted time groups for evaluating the CVR factor

results without PV influence will be 𝑇𝐺1 and 𝑇𝐺2.

Figure 4-5: Annual power demand profile

4.2.3 Implementation

The January, February, and December (2020) datasets were assembled for further processing.

The monthly datasets were reshaped into daily series for each parameter

(𝑃1, 𝑃2, 𝑃3, 𝑄1, 𝑄2, 𝑄3, 𝑈1, 𝑈2, 𝑈3)

Figure 4-6: Reshaped monthly time series

- 36 -

An algorithm for null or zero points detection is passed across the data at this stage, and an

estimated value is filled in by interpolation.

Figure 4-7: NaN removal by interpolation

Once all the parameters have been cleaned, the tap-change detection algorithm was launched.

The entire duration of a tap change operation was captured in two data points across the whole

measurement data. A sketch of Figure 4-20 for tap change detection is shown below.

Figure 4-8: Line plot of voltage rise.

The weighting functions a and b defines the change in voltage from 𝑈𝑡 to 𝑈𝑡+2 and from 𝑈𝑡+1 to

𝑈𝑡+3. At some point, the value of b is known to be greater than a. This occurs mostly in a tap-

down situation. If this binary condition is not specified, the actual change in voltage for a tap down

will not be captured because the only t will be defined as the point of origin for a tap change.

When a is greater than b, the point of origin of the tap change is t. When b is greater than a, the

point of origin of the tap change is t+1. The corresponding timestamp is recorded.

Table 4-1: 20th January timestamps

𝑈1 1564 2951 2952 4080 5877 5878 6097 6098 6189 6190 6557

𝑈2 1563 1564 2951 2952 4080 5877 5878 6097 6098 6189 6190 6557

𝑈3 1564 2951 2952 4080 5877 5878 6097 6098 6189 6190 6557

𝑈𝑡 1564 2951 4080 5877 6097 6189 6557

𝑈𝑟𝑎𝑛𝑑 1373 789 8479 7963 7228 7026 6959 6470 6567 6963 7424

A list of potential tap change timestamps is recorded for the individual voltage phases (𝑈1, 𝑈2, 𝑈3)

in the measurement according to the daily sample sizes.

a = 𝑎𝑏𝑠(𝑈𝑡 − 𝑈𝑡+2) ≥ 4,0𝑉

b = 𝑎𝑏𝑠(𝑈𝑡+1 − 𝑈𝑡+3) ≥ 4,0𝑉

𝑖𝑓 {𝑎 > 𝑏: 𝑡𝑏 > 𝑎: 𝑡 + 1

- 37 -

If the same timestamp is found across the three phases with spacing greater than 6 (1 minute), it

is recorded as the starting point of an actual tap change. In the voltage profile of 20th January

2020, there are seven tap changes detected by the algorithm. This process is repeated iteratively

on the individual daily profiles of complete days in the season, and their corresponding

timestamps are determined. The timestamps are split further into their time groups 𝑇𝐺1, 𝑇𝐺2, 𝑇𝐺3

and 𝑇𝐺4. See Appendix B – 2.2

Figure 4-9: Changes in voltage according to the algorithm.

The primary substation produces a noticeable voltage reduction at less than 1,3% change. This

could not be added to the tap changes originating from the VRDT in the secondary substation.

Figure 4-10: Voltage profiles 𝑈1, 𝑈2, 𝑈3, 20th Jan. 2020

The voltage patterns observed across the lines are identical at the point of tap change, such that

the number of tap operations on each line on the same day is the same. Figure 4-11(a) represents

a three-phase tap change occurring simultaneously at a given time. Figure 4-11(b) shows a

situation where the tap change does not induce voltage reduction on the three phases

simultaneously. There might be a time delay that prevents any particular phase from registering

a voltage reduction.

TG

1

225V

- 38 -

(a) Corresponding tap change (b) Non-corresponding tap change

Figure 4-11: Voltage profile at tap change timestamps

The time-of-day groups that I focused on were overnight time (𝑇𝐺2 = 22: 00 − 04: 00) and evening

time (𝑇𝐺1 = 16: 00 − 22: 00). They both contain 524 tap operations for three months.

The timestamps were recorded for further evaluation. Daily random timestamps without tap

changes were recorded; it will serve as a benchmark for comparing the results of the CVR factors

during tap change and normal operation. This was done by generating a sample group of random

numbers within the intervals of 𝑇𝐺1 and 𝑇𝐺2. I ensured that no timestamp as an origin of a tap

change occurred 10 points before or after a random point (see Table 4-1). There are 11 random

timestamps for the random samples per day.

Figure 4-12: One-week power demand profile.

The analysis of the active power shows seasonality that roughly describes the consumption

pattern for the loads connected to the ECOTAP. The peak load is 52kW on phase 1.

- 39 -

4.3 Results The CVR factor computation follows a direct method where the voltage, active and reactive power

percentage change magnitudes for each phase on the preselected timestamps are computed. A

second filter was applied at this stage.

Figure 4-13: Process flow for CVR factor evaluation

At the end of the CVR factor evaluation for each timestamp, another day is selected. 𝑇𝐺1 and 𝑇𝐺2

contains 969 and 603 values respectively, were both 𝐶𝑉𝑅𝑓𝑃 and 𝐶𝑉𝑅𝑓𝑄 contains the same number

of values as the total for each time group. An outlier detection and filter function were applied to

the active and reactive power CVR factors using ±10 and ±50, respectively. By filtering, we

eliminate extreme conditions of voltage reduction because of natural changes in consumption

patterns. This set of data will be further evaluated separately. See Appendix B – 2.3.

In Figure 4-14, the average CVR values for active and reactive power are 1,30 and 4,96,

respectively. This means that the CVR effect of 1% change in the voltage could result in a 1,30%

change in the active power and a corresponding 4,96% change in the reactive power. The

magnitude of change in the reactive power is higher because of the total percentage change in

reactive power in our observations. This is a hypothesis drawn from our observations and can be

subject to further verification. The reactive power CVR factors are four times higher than the active

power CVR factors. Similar research in this area has the same observation (Shim et al., 2017).

Statistically, the range of reactive power variation is less than that of the active power; therefore,

it will produce higher percentage changes. The CVR factors were benchmarked against the CVR

factors of the random timestamps because upon evaluation, random timestamps produced zero

active and reactive power CVR factors. Thus, the real CVR effect – the difference between the

voltage changes during normal operations (random sample group) and tap change operations,

was determined as stated.

- 40 -

Figure 4-14: Box plot of the CVR factors

Figure 4-15: Distribution of the CVR factors.

The hypothesis for this comparison is that random samples of voltage have an equal probability

distribution for positive and negative changes in their magnitude. This, in turn, affects the values

of the active and reactive power. The magnitude of random voltage changes is very little, as

shown in the figure below. At the operating point where %∆𝑉 is zero, %∆𝑃 is also zero.

Figure 4-16: Distribution of random samples of voltage and power changes.

- 41 -

The associated CVR factors from this control sample group always have a mean value of zero.

This is the expected observation following the characteristics of the voltage and load variables.

This can be proven further by using the significance testing – z test. This test proves or disproves

a null hypothesis on the distribution of the random CVR factors. The proof is provided in 4.4.2.

The rest of the time groups and seasons of the year produced good and characteristic CVR factors

for active and reactive power that highlights the influence of PV supply in the network. The CVR

factors show a downward trend from nighttime to daytime. The winter period is the least affected

by PV integration. The PV peak production period (𝑇𝐺4) coincides with the period of lowest CVR

factors obtained for the spring, summer, and autumn seasons. During summer, the overnight

period has the least CVR factor because it has the least demand for heating and other seasonal

load demand. The seasonal table of CVR factors can be found in Appendix B – Table 4.

Figure 4-17: Annual CVR factors for active power, 2020

The network operators provided additional measurement data for 2019 for further testing. The

result shows a consistent pattern with 𝑇𝐺1, 𝑇𝐺2, 𝑇𝐺3 and 𝑇𝐺4 having 0,95, 1,06, 0,99 and 0,74

CVR factors respectively. Here we can see that 𝑇𝐺4 has the lowest value as a result of PV

injection. Although the capacity of the PV system is not specified, I expect it to be the same with

2020.

From Figure 4-3, we can observe the presence of a testing station that consumes an average of

1,76% of the total load demand of the network. This station is considered an industrial consumer,

and it also has its PV installation that provides power during its peak output. A different set of data

was obtained, which also contains measurement for active power, reactive power, and voltage.

In December, the CVR factor of the residential consumers increased by 2,91% when the test

station data was removed from the overall network measurement. Therefore, the test field had

little impact on the CVR factors observed on the network. See Appendix B – 2.4.

The overall range of active power 𝐶𝑉𝑅𝑓 is 0,70 to 1,61. The associated savings in power using a

voltage reduction setpoint of 2,5% will be 1,75% to 4,03%. This results in an average of 1,56kW

savings on each phase of the network. Similarly, the average CVR factor during the peak period

(𝑇𝐺1) is 0,97. Therefore, a peak demand reduction of 2,4% can be achieved using the current

setup. This reduction has an economic impact on the overall tariff cost for the consumers.

0.00

0.50

1.00

1.50

2.00

TG1 TG2 TG3 TG4

Annual CVR_f-P

Winter Spring Summer Autumn

- 42 -

4.4 Hypothesis Testing

4.4.1 Evaluation of Outliers.

In the preceding section, I eliminated some outliers from the CVR factors of active and reactive

power. I will evaluate this set of data by extracting their corresponding timestamps and studying

their underlying characteristics. From the formula for CVR factors – equation (4-4), the voltage

divides power simultaneously to obtain its CVR factor. The observed rage of +%∆𝑈 is 1,70 – 4,03

in the month of December. Therefore, the outlier can be said to originate from load changes

across the three phases. I shall focus on some of them and visualize the normal changes in active

power and changes represented by the outliers. With an average CVR factor of 0,94, the average

%∆𝑃 should be between 1,60 – 3,80. In the figure below, the significant rise in power consumption

can be seen from the values of %∆𝑃 below -20%. This is the position of the filter for the CVR

factors associated with active power, with an average voltage change of ±2,0%. Negative

changes in these values represent a rise in power consumption.

(a) box plot of outliers (b) line plot of outliers

Figure 4-18: Changes in randomly sampled active power measurements

The four outliers that can be seen from these images show that they have a different magnitude

from the rest of the changes in power. They occur randomly through the dataset and time sample

groups, but they are more common in 𝑇𝐺1 and 𝑇𝐺4. The noticeable impact of these outliers is that

the mean CVR factors will become zero because the outliers substantially shift the average value

down to the negative interval. One way to mitigate this shift is by having enough sample points of

similar magnitudes in the opposite direction to counter this effect and produce a more statistically

accurate mean value. Therefore, the higher the number of samples, the higher the accuracy of

the mean value estimation. This justifies the reason for removing the outliers and applying the

filter of ±10 to the CVR factors.

4.4.2 Randomized Control Group

Let us consider the randomized control group. A mean CVR factor of zero denotes stationarity in

the trend of a randomized sample group of voltage and power changes. This is the null hypothesis

(𝐻0) we wish to prove. This stationarity originates from an equal distribution of ∆�̅� and ∆�̅� on the

- 43 -

positive and negative real axis ±ℝ. Alternatively, there is an equal probability of obtaining a

positive or negative value from changes in voltage and power. See Appendix B – Figure 11.

𝐻0: 𝑋�̅�(𝑡) = 0, ∀ 𝑖 ∈ {1, … , 𝑛} 𝑎𝑛𝑑 𝑋𝑖 ∈ {−ℝ, … , +ℝ} (4-5)

𝐻0: 𝑋𝑘̅̅̅̅ (𝑡) = 𝑋�̅�(𝑡) ∀ 𝑘 ∈ {1, … , 𝑚} 𝑤𝑖𝑡ℎ 𝑝𝑣𝑎𝑙𝑢𝑒 > 0.05 (4-6)

𝐻𝑎: 𝑋�̅�(𝑡) ≠ 0, 𝑤ℎ𝑒𝑛 𝑝𝑣𝑎𝑙𝑢𝑒 > 0.05 (4-7)

The p-value is the test static that describes the error tolerance of the average value 𝑋�̅�(𝑡). There

are two control groups of the random variables. 𝑛 and 𝑚 are the sample sizes drawn from a

normal distribution of iid random samples. I shall test for stationarity on both sample groups before

proceeding to evaluate the null hypothesis. When equation (4-5) passes with a p-value greater

than 0,05, then we can test equation (4-6). The figure below shows the depth of the changes in

the random sample groups for voltage and power. One can observe that the average value is

around zero.

(a) Voltage changes in the random group (b) Load changes in the random group

Figure 4-19: Stationarity of random voltage and power changes.

From section 3.2, the stationarity test using the ADF and KPSS produced a p-value of 0,047 for

∆𝑈 samples and 0,100 for ∆𝑃 samples. n:m ratio is 7:3 of the total control group. Therefore, ∆𝑈

is stationary while ∆𝑃 is non-stationary. Using the z-test from (Skipper & Perktold, 2010), we can

evaluate the p-values for equation (4.5). ∆�̅� p-value is 0,5897, therefore we can accept the 𝐻0.

∆�̅� p value is 0,2766, we also accept the 𝐻0. Using the same z-test, we can evaluate equation (4-

6). For ∆𝑈𝑖 𝑎𝑛𝑑 ∆𝑈𝑘, the p value is 0,7362 – we accept 𝐻0 while for ∆𝑃𝑖 𝑎𝑛𝑑 ∆𝑃𝑘, the p-value is

0,6249 – we accept 𝐻0. This goes to prove that a random sample group of voltage and power

changes produces zero effects of CVR. See Appendix B – 2.5.

4.4.3 Sensitivity to Averaging Intervals.

The averaging interval for estimating ∆�̅�, ∆�̅� and ∆�̅� was determined in 4.2.1 to be 1 minute. This

section would like to study what effect an interval adjustment (halving and doubling) would have

on the CVR factors. Increasing the number of data points used in determining the averages has

a significant statistical role to play in the final value of the CVR factor and its accuracy. By

extending the interval, there could be an improvement in the accuracy of the average values of

voltage and power if the noise level, degree of randomness, or trend is insignificant. If there is no

- 44 -

significant trend (continuous rise or fall in the time series profile) during a tap change, then it will

be difficult to control the influence of interval adjustment. In our case, the percentage change

during a tap change is equal to or sometimes less than the percentage change outside the period

of the tap changer, thereby resulting in a higher percentage of outliers in the CVR factors. The

lower the CVR factor outliers for a particular averaging interval, the more accurate the estimated

mean factor is. Such observation can be seen in the reactive power profile in Figure 4-20, which

is why this evaluation will focus on the active power profile.

Figure 4-20: Voltage, active, and reactive power profile during a tap change.

However, if you extend the interval to introduce a trend, then natural variations in voltage and

power will begin to influence your results. This is not a problem for a near-stationary profile such

as the reactive power profile. The averaging intervals and corresponding results can be seen in

the table below.

Table 4-2: Averaging intervals, CVR factors, and percentage of outliers

Interval (min.) Datapoint (#) December January February

𝐶𝑉𝑅𝑓 Outlier (%) 𝐶𝑉𝑅𝑓 Outlier (%) 𝐶𝑉𝑅𝑓 Outlier (%)

0,5 3 0,99 6,97 0,74 15,10 0,64 16,59

1,0 6 1,14 9,17 0,86 12,48 0,86 15,07

1,5 9 1,26 12,25 1,08 13,50 0,98 15,22

2,0 12 1,16 12,87 1,26 15,16 0,90 17,81

2,5 15 1,09 14,90 1,39 17,59 0,80 19,33

3,0 18 1,05 15,43 1,39 17,21 0,90 21,16

The table above shows that a rise in the interval size increases the percentage of outliers in the

total CVR factors evaluated. This means that such averaging interval includes natural variations

in the power consumption that is not just attributed to a tap change. Thus, I can conclude that a

1,0 – 1,5-minute interval is adequate for estimating the most accurate CVR factor because the

average CVR factors in the table above can be found between these intervals. This observation

may be peculiar to this dataset.

- 45 -

Energy Savings Evaluation

5.1 Estimation Approach

The need to test the potential of VVO/CVR in the distribution grid is largely supported by the

possibility of achieving energy savings in a continuous framework when it is deployed. Grid

operators and utilities can observe changes during CVR operation and compare the load profile

during this operation to that obtainable during normal operating days. However, considering the

load types and class of consumers (domestic, commercial, or industrial) connected to the grid, a

varying amount of savings can be achieved. Therefore, understanding the kind of load and

consumer types is necessary for weighing the achievement of CVR on the grid.

Industrial customers have a very low potential of producing substantial energy savings from CVR

because of the kind of load classes they have. That is why most research and testing of CVR is

focused on domestic and light commercial consumers. Here it is common to achieve more than

1% energy savings. In a testing campaign conducted by Northwest Energy Efficiency Alliance on

13 utilities in the USA, 1,5% - 2,0% energy savings was achieved (Anderson, 2019).

The financial reward associated with these savings can be estimated by determining the LCOE

within the year of deployment. A 2% reduction in annual demand in Germany can result in about

90kWh savings. With an energy tariff of 29,52ct/kWh (2018), total savings per consumer as a

result of CVR would be 26,57€ (IEA, 2020).

In other to achieve these goals on any pilot project, a good testing framework should be set up, a

proper statistical estimation methodology for load estimation should be defined, and finally, a good

CVR factor should be obtainable from the computation. The difference between the estimated

energy for CVR-off on testing and the measured energy consumption during testing gives you

energy savings (ΔE). As described in section 2.4, it is always challenging to estimate load for

CVR-off during a CVR-on operation.

5.1.1 Continuous Energy Testing Framework

This testing framework is designed to record variations in energy consumption under certain

environmental conditions. The factors that influence energy consumption (2.3) that in turn

determine savings are voltage, temperature (T), humidity (H), solar irradiation (I), wind speed (W),

and PV output. In a continuous framework, CVR is applied once a day at a lower magnitude but

above the upper limits of noise (say 0,85%). In other cases, CVR can be applied continuously

throughout the testing period. Accounting to load mix in the demand side, a suitable ∆𝑈𝑡 would

be 2,0% or more.

The start and end of daily cycles should be placed at 00:00 hours, where there are lesser

variations in consumption so that complete observations can be made during the day without

interruptions. The test days alternates with non-test days for 24 hours duration. Alternatively, a

continuous testing protocol that should last from 3 weeks to one month can be deployed instead.

In this scenario, the historical dataset for further evaluation should hold a strong correlation to the

underlying environmental and behavioral changes in the testing area. A continuous scheme like

this is necessary when the network operator cannot alter voltage setpoints regularly. The purpose

- 46 -

of providing this margin is for us to observe the normal load profile and use this observation to

select suitable historical profiles for estimating the CVR-off load pattern. 𝐶𝑉𝑅𝑓−𝐸 shall be

evaluated hourly for weekdays, for the entire duration of 4 weeks. Measurement resolution is 15

minutes or one hour based on the granularity of the environmental measurement. Three weeks

represents a substantially wide range of weather changes (temperature, humidity, etc.) that could

affect energy consumption.

This evaluation assumes that there is a load growth in the historical load consumption patterns.

Suppose there is a percentage increase in the load consumption due to additional appliances,

network expansion, or the addition of EV. In that case, an annual growth factor will be used to

normalize the measurement before computing energy savings. The baseline data for evaluating

CVR-off during the testing period of 2021 is the 2019 historical data which does not have a taping

operation in April.

A test field in Southern Germany was used as a case study (same as in 4.2.2). The testing period

was the month of April 2021. A voltage reduction from 228V to 222.5V was implemented following

a continuous protocol that lasted for 30 days. That means that the voltage reduction was initiated

on April 1 and was sustained till April 30.

5.1.2 Parameter Definition and Selection

Figure 5-1: Load profiles on test days

The intervals of 𝐿1, 𝐿2, 𝐿3 are set for the testing framework as defined in the figure above. The test

data profile above (𝐷𝑡) is composed of periods: pre-test (𝐿1), testing (𝐿2) and post-testing (𝐿3). A

non-test (historical) profile (𝑋𝑖𝑘) of external parameters is used to build a regression model for

estimating the load 𝑃𝑡𝑒 using current environmental observations (𝑋𝑡𝑒) within 𝐿2. 𝑃𝑡 is load

measurement during CVR-on operation. Following the testing framework (4.1.1, 5.1.1), the total

number of test days (weekdays excluding holidays) in 4 weeks is 14. Historical measurements

will use similar weekdays for the evaluation.

The load profile during 𝐿1, 𝐿2, 𝐿3 are 𝑃𝑡1, 𝑃𝑡2, 𝑃𝑡3 respectively. From 𝑃 we can evaluate hourly

energy (𝐸) consumption in kWh. Our estimation duration, therefore, is within 𝐿2. This means that

𝑃𝑡𝑒, 𝑃𝑡2, 𝐸𝑡2 and 𝐸𝑡𝑒 are the evaluation parameters. Therefore,

- 47 -

%∆𝐸𝑖 = (𝐸𝑡𝑒−𝐸𝑡2)𝑖

𝐸𝑡𝑒× 100 (5-1)

Where 𝑖 = (1,2,3, … , 𝑛). Let 𝛿 be the granularity in hours of 𝑋𝑡, 𝑋𝑡𝑒 such that 24𝛿⁄ = 𝑛. In equation

(5-1) above, 𝑛 =𝐿2

𝛿⁄ . If 𝛿 = 1 hour. Therefore 𝐸𝑡 = 𝑃𝑡. If 𝛿 = 14⁄ hours, 𝐸𝑡 = 𝑚𝑎𝑥(𝑃𝑡)4. The

associated energy savings becomes Ete − Et2.

The CVR factor for energy becomes

𝐶𝑉𝑅𝑓𝐸 =%∆𝐸

%∆𝑉 (5-2)

When we model 𝑃𝑡𝑒 using all equal weights of the environmental parameters 𝑋𝑖, the resultant

estimation error will be higher than that of selected parameters with higher correlation.

𝑃𝑡𝑒 = 𝑓(𝑃𝑖𝑘 , 𝑋𝑖𝑘, 𝑋𝑡𝑒) (5-3)

Where 𝑋 = (𝑇, 𝐻, 𝑊, 𝜌), ambient temperature, humidity, wind speed, and pressure, respectively.

Therefore, 𝑋𝑖𝑘 = (𝑇𝑖𝑘 , 𝐻𝑖𝑘 , 𝑊𝑖𝑘 , 𝜌𝑖𝑘). The best parameter factor shall be defined using the cross-

correlation of 𝑃𝑖𝑘 and 𝑋𝑖𝑘. The higher the magnitude of the weighing function, the higher their

similarity and influence on the regression model. This evaluation is carried out before building the

regression model.

(𝑃𝑖𝑘, 𝑋𝑖𝑘) are points from 0 – 720 in April. Let this range be represented as 𝑃𝑛, 𝑋𝑛. Cross-

correlation defines the degree of correlation between two trending time series.

𝑅𝐾𝐺(𝑡) = 𝐸[𝑃𝑛�̅�𝑛] (5-4)

The parameter E is the weighing parameter or expected value operator for the finite series of 𝑃𝑛

and 𝑋𝑛. However, this parameter will be normalized and be valid within the interval [-1,1]. The

normalization function defined by Pearson’s correlation coefficient is given by.

𝛾𝐾𝐺(𝑡) =𝐸[(𝑃−𝜇𝑃)𝑡(𝑋−𝜇𝑋̅̅ ̅̅ ̅̅ ̅̅ ̅)𝑡]

𝜎𝑃(𝑡)𝜎𝑋(𝑡) (5-5)

Where 𝜇 and 𝜎 are respectively mean and standard deviation of the series. 𝛾𝐾𝐺 = 1 shows perfect

cross-correlation while 𝛾𝐾𝐺 = −1 shows inverse cross-correlation. The 𝑋𝑛 profiles are ranked by

the magnitude of their cross-correlation with 𝑃𝑛 in descending order. When 𝛾𝐾𝐺 > 0,67, that

parameter is selected for modeling. These evaluations can be done using scipy and scikit-learn.

See Appendix C.

5.1.3 Preprocessing and Modeling with MLR

MLR is a simple regression model that uses more than one independent parameter Xik for

estimating the value of the dependent parameter 𝑃𝑖𝑘. Each parameter contributes equally to the

estimation. The characteristic equation of the model is defined by a linear relationship between

the independent and dependent variables. This trend line is the slope or degree of change in the

series of observations. The accuracy of this fitting can be evaluated using the Root Mean Square

Error (RMSE) characteristic.

- 48 -

Given a DataFrame of the selected environmental parameter and power demand, we can

randomize the DataFrame by using a random seed. Then, further split it into a test and train sub-

arrays. The parameters that makeup Xik are numerical variables while the hourly data ℎ𝑖, DoW

and holiday data are categorical variables. The temperature variable will be further divided into

heating degree hours (HDH) and cooling degree hours (CDH). The numerical variable can be

utilized directly for evaluation, while the categorical variables will be decomposed to numerical

variables using a machine learning method called one-hot encoding. This can be achieved using

the sklearn 𝑂𝑛𝑒𝐻𝑜𝑡𝐸𝑛𝑐𝑜𝑑𝑒𝑟() object. This data processing principle is part of a common library

of tools in machine learning. There are 24 categorical values in ℎ𝑖. Therefore, 24 𝑥 1 array will be

decomposed to 24 𝑥 24 arrays where each value of ℎ𝑖 will head each column.

The MLR machine learning model uses a group of data for training and another group for testing,

usually split at 70:30 or 80:20 percent. The training dataset will be used to train the model, while

the testing dataset will be used to test it. During post-processing, the predicted value of the

dependent variable in the test dataset will be compared with the actual independent variable of

the test set using the RMSE characteristic. A test score greater than 95% will be accepted.

Figure 5-2: Multilinear Regression evaluation process for energy savings.

In the figure above, the baseline data represents the April 2019 dataset with a voltage setpoint

of 235V, load profile, and corresponding weather data. The test data is the April 2021 dataset

with a voltage setpoint of 222V, load profile, and corresponding weather data.

- 49 -

5.2 Energy Savings Results

Figure 5-3:Scatter plot of estimated energy to real energy.

The baseline environmental dataset was obtained for April 2019, 2020 and 2021, from Weather

Underground, Hof. There is a reoccurring pattern in the demand profile that shows seasonality.

Figure 6 in Appendix C shows that weekdays have lower cumulative demand than weekends and

public holidays. From section 5.1.2, a cross-correlation of the variables was carried out. The HDH

and humidity parameters were the best correlated numerical variables with total power. (Appendix

C – Table 2). The MLR model was built using predefined conditions. The RMSE value of the

model itself is 16,2953 with a Pearson’s correlation of 0,910. This model was used to further

evaluate 𝐸𝑡𝑒 using the April 2021 environmental parameters as the training dataset that was feed

into the model. The Pearson’s correlation and RMSE values are 0,788 and 21,0322, respectively.

See Appendix C – 3.3. A linear SVR machine learning algorithm was used to model the load and

weather dataset, but its Pearson’s correlation was 0,8715. This has a lower accuracy than the

MLR model. Therefore, the MLR model was chosen as the better model.

Figure 5-4: Estimated and real energy profile for April 2021

The figure above shows the result of the estimation of the MLR model for energy. The difference

between the profiles is the energy savings. There is a low accuracy in the estimation because of

- 50 -

the low correlation between the training features and the target variable. There are not enough

data points for training the model, resulting in a slightly less accurate load estimation.

The CVR factor for energy according to equation (5-2) can be seen below.

Figure 5-5: CVR factor for energy

The average change in voltage from normal operation to a reduced setpoint is 5,25% (Appendix

C – Figure 8). This percentage change is substantial enough to induce power changes on the

consumption side. From Figure 5-5, the mean CVR factor for energy is 0,71 while the median is

0,87, using the same filtering interval for active power in 4.3. Evaluation on a weekday and

weekend basis (Appendix C – Figure 9) gave a CVRf for energy on the weekday of 0,67 (0,87

medians) and the weekend 0,83 (0,88 medians). This goes to show the underlying pattern of

energy consumption in this network. Consumers seem to be more active on the weekend;

therefore, they consume more power compared to the weekday. More CVR benefits can be

achieved in the weekend and holidays where more loads can be expected to be turned on,

therefore, leading to higher energy consumption. However, this is not conclusive evidence, and

the observation can be influenced by model accuracy. The energy savings achieved using this

model in April was 3,69% which corresponds to 1.007,25kWh.

Figure 5-6: CVR factor for energy without PV output.

- 51 -

The isolation of the impact of PV integration in the overall energy demand can be challenging to

evaluate. The simple approach adopted here is to eliminate the time group (TG4) where PV output

is at its peak. The new dataset shall comprise hours ranging from 17:00 to 09:00 of the following

day. The evaluation process was repeated as described above, and a new CVR factor of energy

is computed. The figure above shows the box plot of the energy demand reduction CVR factors.

The CVR factor of 0,48 was obtained as a result. This indicates that there is a lower percentage

savings (2,52%) achievable when normal demand is considered. There is a substantial reduction

in the number of data points used to evaluate this factor. Therefore, this result is not conclusive

and there is significant inaccuracy in the estimation model with a Pearson’s correlation score of

0,84. The cross-correlation of the environmental features with the measured load as shown in

Appendix C – Table 2 is based on the observations derived for the current dataset. This

observation is not conclusive and cannot be substantiated with in this report because of limited

data. However, the process of this evaluation is and can be utilized for estimating energy savings.

5.3 Cost-benefit analysis

One of the value propositions of CVR, as described in 1.2, is the ability of this technique to

minimize energy consumption during the period of its implementation. This is demonstrated by

evaluating the energy savings attributed to this voltage reduction. A suitable weighing parameter

is the LCOE. This is the overall life cycle cost of an energy installation (for example, PV) as a ratio

of the total cost (CAPEX and O&M) and output during its operational life measured in €/kWh. The

total energy consumption of 27,296.75kWh was recorded from the dataset mentioned above. The

average tariff cost + VAT of 29,23€𝑐𝑒𝑛𝑡𝑠/kWh is obtainable across Southern Germany (BDEW,

2017). Therefore, the total tariff cost for this month is 7.978,84€.

Let us assume that the April energy measurement and its corresponding energy savings are the

same for the rest of the months; therefore, we have an annual energy savings of 3,69% with

327,56MWh annual consumption. The LCOE benefits will be compared to that of an equivalent

PV installation – an additional investment to the overall project cost. Annually, the network can

save 3.533€ from CVR protocols and divert the resources to increased PV integration or network

expansion. Considering Southern Germany with a solar irradiance ranging from 1100 – 1180

kWh/m2 and a commercial-scale rooftop PV system, the CAPEX cost is between 800 and 1000

€/kWp. A 100kWp installation with a lifetime of 25 years, adjusted WACC of 2,1%, and O&M of

2,5% CAPEX can yield an average annual output of 111,75MWh. This output was subsequently

adjusted for module degradation of 0,25% annually. Therefore, the CAPEX cost will be 90.000€

(Fraunhofer ISE, 2018).

A lifecycle production of 2816.49MWh at LCC of 165.759,54€ gives an LCOE of 0,058€/kWh. The

associated annual savings from CVR for the same duration will reduce the LCC to 55.901,54€.

- 52 -

Figure 5-7 Energy savings applied to the PV system LCOE.

From the figure above, we can observe that there is a significant reduction in the LCOE

(0,025€/kWh) when these annual savings in energy demand are achieved and applied towards

renewable energy integration. These savings can also be compared to an equivalent amount of

carbon offset from reduced generation from conventional fossil-based sources such as coal.

Therefore, it makes economic sense to deploy CVR on a continuous scheme because it reduces

investment costs into new DG projects and offsets carbon for the primary source of electricity.

This observation is not conclusive because of the underlying assumptions used in its computation.

An annual energy savings of 3,69% (as assumed) might be beyond what is obtainable together

with other economic factors. This computation shows an effective process of estimating energy

savings for a network operator, which can be applied to various networks. More data and testing

periods will be needed to compute real annual energy savings.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

LCOE LCOE+savings

LCO

E (€

/kW

h)

- 53 -

Discussion and Conclusion

6.1 Discussion

The three key evaluations carried out in this report are comprehensive outlines of voltage

measurement and verification followed by a simple methodology of peak and continuous power

demand reduction, and finally, a continuous energy savings estimation.

The determination of voltage noise magnitude in Chapter 3 is necessary when defining the

protocol/scheme for the tapping operation that will induce CVR. The general guide is to define a

protocol where there will be enough tap changes that will produce a statistically accurate

estimation of the CVR factors. Therefore, the lower the number of tap changes within the period

of operation, the lower the accuracy of the estimation following the central limit theorem. Also,

suppose the magnitude of the tap change is equal to the magnitude of the computed voltage

noise. In that case, the natural variations in voltage levels attributed to topological variations and

load responses will swallow the resulting effect of the tap changer. Therefore, no significant

change that is equal to the known magnitude of the initial tap change can be measured. ECOTAP

VPD is capable of producing ±2,5% voltage change for a single tap change. Using an ARIMA

model, we can identify the magnitude of noise in voltage, current, and power of a timeseries

measurement as the interval of change in its residual that is characteristic of white noise. In our

voltage evaluation, this magnitude was found to be ±0,5𝑉. This estimate varies according to the

characteristics of different network areas.

Having an idea of the minimum tap adjustments required for CVR, we can plan a testing protocol

for peak shaving during peak periods following the demand profile of the specific feeder. In

Chapter 4, the observed peak period was from 17:00 to 21:00 on weekdays and weekends. The

period of evaluation is mostly four weeks but depends on the agreement with the network

operator. During peak load, the tap change can occur several times and above a minimum interval

defined statistically according to the central limit theorem of a stochastic process. Section 4.4.3

shows that altering the averaging interval results in higher or lower CVR factors with more or less

percentage of outliers. Therefore, the adequate interval will be the median value. Using the simple

direct method for CVR factor evaluation, the percentage change in voltage, active power, and

reactive power is determined. Prior to this, initial filtration for percentage change in voltage within

the noise interval is removed from the estimation. The mean and median values of the CVR

factors for the various periods (time of day, season, etc.) are computed. The average CVR factor

for active and reactive power are 1,30 and 4,96, respectively. The result of the entire evaluation

shows that the CVR factors are less during peak PV production and more at the peak demand

periods. However, during peak, demand reduction of 2,4% can be achieved for a 2,5% reduction

in voltage using ECOTAP VPD. From section 4.3, it can be observed that PV integration has a

reducing effect on demand; therefore, it produces lesser CVR factors during its peak production.

In energy savings evaluation, the main goal is to reduce the voltage setpoint to the least allowable

level that will not induce voltage limit infringement at the end of the line. This reduced setpoint is

maintained or alternated for the entire testing period. Environmental data (temperature, humidity,

irradiance, wind speed, etc.) is necessary for the energy evaluation because they represent the

conditions that will induce load changes by the consumer, together with the time, season, and

- 54 -

other special events. It is important to note that a strong correlation between these parameters

and the load profile should exist. A historical dataset from the same network is required to build

the representative load model used to estimate the load during normal operations in the CVR on

period. There is a correlation between the estimated energy profile for normal operations during

CVR-on and the measured energy profile during the same testing period. From Chapter 5, a

multilinear regression model was used to estimate the load profile during normal operation in

April. A CVR factor for the energy of 0,71 was obtained with 3,69% energy savings for a 5,25%

reduction in voltage. This result falls within the general interval (2,0% – 5,0%) of energy savings

from previous research. When this saving is applied to a PV integration investment, an LCOE of

0,025€/kWh is feasible. Therefore, there is an economic benefit in deploying CVR using ECOTAP

VPD.

These conclusions on energy savings are limited to the month in question. The accuracy of the

model estimation and the difference between the weekday and weekend CVR factors are mere

hypotheses that will require substantial validation with more datasets and testing scenarios. The

model itself is an accurate and established load estimation process because we constantly

achieved high accuracy. With a reduced number of features for energy demand estimation during

low PV production hours, the model accuracy is reduced. There are other methods of carrying

out energy savings testing. This involves the use of alternate testing days and similar feeders.

Alternate testing days require a reduced voltage setpoint for the first day and normal operation

for the next, alternated. The advantage of this approach is that the baseline weather parameters

used to build the model fall within the same period of the testing. Therefore, there is a higher

chance of improved accuracy. The similar feeders approach ensures that two feeders with the

same characteristics are used for the testing. One feeder runs the CVR, and the other is used as

a baseline feeder. In this case, no baseline load modeling is required because both operations

are running concurrently. Another way to improve accuracy is by increasing the granularity of

measurement intervals of the load profile. Improved granularity ensures that there is enough

dataset for load estimation.

In conclusion, voltage optimization and reduction using CVR are excellent and reliable

approaches to achieving peak shaving and energy savings. By ensuring proper measurements

and accuracy of tap change operations, a CVR factor of power and energy is a good

representation of the associated benefit of tap adjustment using the ECOTAP VPD.

6.2 Challenges and Future Work Direction

Conservation voltage reduction measurement and evaluation require good statistical evaluation

tools to compute, verify, and prove the accuracy of the results. The verification of the key

observations in the computation requires the use of a statistical hypothesis that is difficult to prove.

This could be because there are not enough data points for generating enough control groups for

proof. The testing protocol does not support such intended evaluation because of granularity,

statistical characteristics of the dataset, and measurement accuracy. The result of verification

carried out for a particular variable might not work for another variable. For example, in the

verification of the CVR factors for the random sample group, it was assumed that the null

- 55 -

hypothesis of stationarity would be ascertained for both voltage and power measurements. It was

only proven for the voltage measurements.

Secondly, in other to detect enough tap changes and improve the accuracy of the estimation, one

must scan through a lot of data using an algorithm that is not optimizable for time complexity.

Sometimes, such datasets can contain as many as 3 million data points.

In other to estimate load profiles based on environmental and behavioral patterns, there needs to

be a proper measurement of the environmental parameters within and around the test site. The

further you go from the test site, the lower the correlation of these parameters to your load profiles.

Most weather stations are placed at strategic locations but outside the region of the test field. That

was the case in this project. Therefore, it is challenging to get accurate weather data for baseline

model development. A good model also requires enough data points to be effective. Efficiency

will drastically reduce when you are working with limited historical datasets. No matter the

machine learning model you are using for the evaluation, a limited dataset will produce poor

estimation accuracy.

6.2.1 Future work

The new frontiers in CVR and VVO from an evaluation and technology perspective involve

integrating digital solutions based on machine learning. Machine learning and AI solutions allow

the DNOs to evaluate large datasets with all forms of variables that represent the network

configuration, consumer behavior, and weather changes. Research in this field should also

include demand response management systems. The tools and processes of estimating energy

savings from test field datasets have evolved through the years from simple mathematical

evaluations and curve fittings to advance statistical and machine learning solutions. This is partly

because more variables are being considered for building the best model possible. It will be

worthwhile to discover the best machine learning algorithm and automation tool that can perfectly

process and interpret historical load profiles and forecast future trends that will be relevant in

planning CVR operations in a network. By using an automated process with SCADA integration,

one can properly determine and implement peak shaving in real-time using a cloud-based back-

end process.

A general deterministic approach should be developed and tried on the challenge of noise level

estimation and other errors. This approach should not just account for model error but also

measurement uncertainties, statistical and numerical errors. This will help determine the

magnitude and number of tap changes within a specific period that is sufficient for estimating

average CVR factors. Some research has suggested the use of Monte Carlo simulations.

The sensitivity of reactive power to voltage changes needs to be studied further. This report

discovered that reactive power CVR factors are always four times higher than active power. No

research project has clearly defined the reason for this – most generally skip this parameter in

their evaluation. Perhaps, a larger collection of CVR factors taken from the same testing period,

together with a proper understanding of the load types using an exponential load model, could

explain this observation. A general mathematical principle that will express the relationship

between reactive power changes to the voltage across several feeders can be determined as

well.

- 56 -

This thesis did not consider industrial load response in detail. This would also be a good area to

research further because the kWh value of a percentage energy savings for an industrial

consumer is much higher than the savings of the same percentage for the residential consumer.

Although research has shown that there are limited changes in the load mix within a day or season

for the industrial consumer, it is still significant to evaluate it because of the very high demand.

- 57 -

Reference List An, K., Liu, H., Zhu, H., Dong, Z., & Hur, K. (2016). Evaluation of Conservation Voltage

Reduction with Analytic Hierarchy Process: A Decision Support Framework in Grid

Operations Planning. Energies, 9(12), 1074. Retrieved January 13, 2021, from

https://www.researchgate.net/publication/312436206_Evaluation_of_Conservation_Voltage_

Reduction_with_Analytic_Hierarchy_Process_A_Decision_Support_Framework_in_Grid_Op

erations_Planning.

Anderson, P. (2019). Conservation Voltage Reduction (CVR): Northwest Energy Efficiency

Alliance Distribution Efficiency Initiative Project Final Report.

Andersson, J., & Burberg, M. (2015). Testing for Normality of Censored Data. UPPSALA

University. Retrieved January 03, 2021, from http://uu.diva-

portal.org/smash/get/diva2:816450/FULLTEXT01.pdf.

Arif, A., Wang, Z., Wang, J., Mather, B., Bashualdo, H., & Zhao, D. (2018). Load Modeling—A

Review. IEEE Transactions on Smart Grid, 9(6), 5986–5999. Retrieved April 12, 2021, from

https://ieeexplore.ieee.org/document/7917348.

BDEW (2017). BDEW_Strompreisanalyse in Deutschland_Mai 2017 (Haushalte und Industrie).

Berlin: Bundesverband der Energie- und Wasserwirtschaft e.V. Retrieved June 16, 2021,

from https://www.dieter-

bouse.de/app/download/5810146532/BDEW_Strompreisanalyse+in+Deutschland_Mai+2017

.pdf.

Bechara, C. G. (2017). Utilization of Advanced Conservation Voltage Reduction (CVR) for

Energy Reduction on DoD Installations: ESTCP Final Report ( No. EW-201519). ESTCP.

Retrieved April 11, 2020, from https://apps.dtic.mil/sti/pdfs/AD1052531.pdf.

Castro, M., Moon, A., Elner, L., Roberts, D., & Marshall, B. (2017). The value of conservation

voltage reduction to electricity security of supply. Electric Power Systems Research, 142, 96–

111.

Chen, C.-S., Wu, T.-H., Lee, C.-C., & Tzeng, Y.-M. (1995). The application of load models of

electric appliances to distribution system analysis. IEEE Transactions on Power Systems,

10(3), 1376–1382.

Choi, B.-K., Chiang, H.-D., Li, Y., Li, H., Chen, Y.-T., Huang, D.-H., & Lauby, M. G. (2006).

Measurement-Based Dynamic Load Models: Derivation, Comparison, and Validation. IEEE

Transactions on Power Systems, 21(3), 1276–1283. Retrieved January 15, 2021, from

https://ieeexplore.ieee.org/stampPDF/getPDF.jsp?tp=&arnumber=1664964&ref=aHR0cHM6

Ly9pZWVleHBsb3JlLmllZWUub3JnL2RvY3VtZW50LzE2NjQ5NjQ=.

Delfanti, M., Merlo, M., & Monfredini, G. (2014). Voltage Control on LV Distribution Network:

Local Regulation Strategies for DG Exploitation. Research Journal of Applied Sciences,

Engineering and Technology, 7, 4891–4905, from

https://core.ac.uk/download/pdf/55151525.pdf.

Deutsche Kommission Elektrotechnik Elektronik Informationstechnik in DIN und VDE (2016).

Merkmale der Spannung in öffentlichen Elektrizitätsversorgungsnetzen; Deutsche Fassung

EN 50160:2010/A1:2015: DKE.

El-Shahat, A., Haddad, R. J., Alba-Flores, R., Rios, F., & Helton, Z. (2020). Conservation

Voltage Reduction Case Study. IEEE Access, 8, 55383–55397.

- 58 -

ENWL (2018). Smart Street Closedown Report. Electricity North West. Retrieved November 03,

2021, from https://www.enwl.co.uk/globalassets/innovation/smart-street/smart-street-key-

docs/smart-street-closedown--report.pdf.

Erickson, J., & Gilligan, S. (1982). The Effects of Voltage Reduction on Distribution Circuit

Loads. IEEE Transactions on Power Apparatus and Systems, PAS-101(7), 2014–2018.

Fallon, F., & Hyman, G. (Eds.) (2020). Applied Statistics and Probability for Engineers:

Explorations in philosophy and religious thought (3rd ed.). New York: Oxford University

Press.

FNN (2016). Voltage Regulating Distribution Transformer (VRDT) – Use in Grid Planning and

Operation. Forum Netztechnik/Netzbetrieb im VDE. Retrieved December 12, 2020, from

https://www.vde.com/resource/blob/1570326/c4c73c2670f47f82071b81eab368b85e/downloa

d-englisch-data.pdf.

Fraunhofer ISE (2018). Levelized Cost of Electricity- Renewable Energy Technologies.

Fraunhofer Institue for Solar Energy Systems ISE. Retrieved June 18, 2021, from

https://www.ise.fraunhofer.de/content/dam/ise/en/documents/publications/studies/EN2018_Fr

aunhofer-ISE_LCOE_Renewable_Energy_Technologies.pdf.

Fraunhofer ISE (2021). Recent Facts about Photovoltaics in Germany ( No. 210202). Freiburg,

Germany: Fraunhofer ISE. Retrieved February 13, 2021, from

https://www.ise.fraunhofer.de/en/publications/studies/recent-facts-about-pv-in-ger-many.html.

Hong, T., Wilson, J., & Xie, J. (2014). Long Term Probabilistic Load Forecasting and

Normalization With Hourly Information. IEEE Transactions on Smart Grid, 5(1), 456–462.

Hossan, M. S., & Chowdhury, B. (2017). Time-varying stochastic and analytical assesment of

CVR in DER integrated distribution feeder. In I. Staff (Ed.), 2017 North American Power

Symposium (NAPS) (pp. 1–6). Piscataway: IEEE.

Hyndman, R., & Athanasopoulos, G. (2018). Forecasting: Principles and Practice (2nd ed.).

Melbourne, Australia: OTexts.

IEA (2020). Germany 2020 - Energy Policy Review. International Energy Agency (IEA).

Retrieved January 11, 2021, from

https://www.bmwi.de/Redaktion/DE/Downloads/G/germany-2020-energy-policy-

review.pdf?__blob=publicationFile&v=4.

Draft Standard, IEEE P1885 (2013, June 03): IEEE Standards Association.

Kennedy, B. W., & Fletcher, R. H. (1991). Conservation voltage reduction (CVR) at Snohomish

County PUD. IEEE Transactions on Power Systems, 6(3), 986–998.

Le, B., Canizares, C. A., & Bhattacharya, K. (2015). Incentive Design for Voltage Optimization

Programs for Industrial Loads. IEEE Transactions on Smart Grid, 6(4), 1865–1873. Retrieved

January 20, 2021, from https://ieeexplore.ieee.org/document/7038218.

Lefebvre, S., Gaba, G., Ba, A.-O., Asber, D., Ricard, A., Perreault, C., & Chartrand, D. (2008 -

2008). Measuring the efficiency of voltage reduction at Hydro-Québec distribution. In 2008

IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical

Energy in the 21st Century (pp. 1–7). IEEE.

Liu, H. J., Macwan, R., Alexander, N., & Zhu, H. (2014). A methodology to analyze conservation

voltage reduction performance using field test data. In 2014 IEEE International Conference

on Smart Grid Communications (SmartGridComm 2014). Venice, Italy, 3-6 November 2014

(pp. 529–534). Piscataway NJ: IEEE.

- 59 -

Mokkapaty, S., Weiss, J., Schalow, F., & Declercq, J. (2017). New generation voltage regulation

distribution transformer with an on load tap changer for power quality improvement in the

electrical distribution systems. CIRED - Open Access Proceedings Journal, 2017(1), 784–

787, from www.ietdl.org.

Montgomery, D., Jennings, C., & Kulahci, M. (2008). Introduction to Time Series Analysis and

Forecasting: Wiley Series in Probaility and Statistics. New Jersey: John Wiley & Sons, Inc.

MR (2016). ECOTAP VPD: The Compact Class for Distribution Transformers ( No. F0338803 –

11/19). Maschinenfabrik Reinhausen GmbH. Retrieved December 23, 2020, from

https://www.reinhausen.com/PortalData/1/Resources/mr/products_and_services/pqm/ecotap/

F0338801_pre_ECOTAP_VPD_EN.pdf.

Nam, S.-R., Kang, S.-H., Lee, J.-H., Ahn, S.-J., & Choi, J.-H. (2013a). Evaluation of the Effects

of Nationwide Conservation Voltage Reduction on Peak-Load Shaving Using SOMAS Data.

Energies, 6(12), 6322–6334.

Nam, S.-R., Kang, S.-H., Lee, J.-H., Choi, E.-J., Ahn, S.-J., & Choi, J.-H. (2013b). EMS-Data-

Based Load Modeling to Evaluate the Effect of Conservation Voltage Reduction at a National

Level. Energies, 6(8), 3692–3705. Retrieved December 11, 2020, from

https://res.mdpi.com/d_attachment/energies/energies-06-03692/article_deploy/energies-06-

03692.pdf.

NRECA (2014). Costs and Benefits of Conservation Voltage Reduction ( No. DE-OE0000222).

Virginia: National Rural Electric Cooperative Association. Retrieved May 15, 2021, from

https://www.energy.gov/sites/prod/files/2016/10/f34/NRECA_DOE_Costs_Benefits_of_CVR_

May_2014.pdf.

Oliveira Quevedo, J. de, Cazakevicius, F. E., Beltrame, R. C., Marchesan, T. B., Michels, L.,

Rech, C., & Schuch, L. (2017). Analysis and Design of an Electronic On-Load Tap Changer

Distribution Transformer for Automatic Voltage Regulation. IEEE Transactions on Industrial

Electronics, 64(1), 883–894.

Orloff, J., & Bloom, J. (2014). Null Hypothesis Significance Testing I: 18.05 Introduction to

Probability and Statistics. MIT OpenCourseWare. Retrieved November 29, 2020, from

https://ocw.mit.edu.

Palma, W. (2016). Time Series Analysis. Wiley Series in Probability and Statistics. New Jersey:

John Wiley & Sons, Inc.

Paolella, M. S. (2018). Linear models and time-series analysis: Regression, ANOVA, ARMA and

GARCH. Wiley series in probability and statistics. Hoboken NJ: John Wiley & Sons.

PJM (2021). PJM Manual 13: Emergency Operations. JPM.

Poppen, M., Matrose, C., Schnettler, A., Smolka, T., & Hahulla, P. (2014). Grid Integration

Conformity Testing Procedures for Voltage Regulated Distribution Transformers (VRDT).

CIRED, from

http://www.cired.net/publications/workshop2014/papers/CIRED2014WS_0307_final.pdf.

Renmu, H., Jin, M., & Hill, D. J. (2006). Composite Load Modeling via Measurement Approach.

IEEE Transactions on Power Systems, 21(2), 663–672. Retrieved December 05, 2020, from

https://ieeexplore.ieee.org/stampPDF/getPDF.jsp?tp=&arnumber=1626370&ref=aHR0cHM6

Ly9pZWVleHBsb3JlLmllZWUub3JnL2RvY3VtZW50LzE2MjYzNzA=.

RTF (2015). Standard Savings Estimation Protocol -Voltage Optimization. Regional Technical

Forum. Retrieved January 12, 2021, from https://rtf.nwcouncil.org/decisions?page=3.

- 60 -

Shi, J. H., & Renmu, H. (2003). Measurement-based load modeling - model structure. In 2003

IEEE Bologna Power Tech Conference Proceedings (pp. 631–635). IEEE.

Shim, K.-S., Go, S.-I., Yun, S.-Y., Choi, J.-H., Nam-Koong, W., Shin, C.-H., & Ahn, S.-J. (2017).

Estimation of Conservation Voltage Reduction Factors Using Measurement Data of KEPCO

System. Energies, 10(12), 2148.

Short, T. A., & Mee, R. W. (2012 - 2012). Voltage reduction field trials on distributions circuits. In

PES T&D 2012 (pp. 1–6). IEEE.

Shumway, R. H., & Stoffer, D. S. (2017). Time Series Analysis and Its Applications. Cham:

Springer International Publishing.

Skipper, S., & Perktold, J. (2010). statsmodels: Econometric and statistical modeling with

python.: Proceedings of the 9th Python in Science Conference. Statsmodels.org. Retrieved

December 20, 2020, from https://www.statsmodels.org/stable/index.html#index--page-root.

Sojer, M. (2017). Voltage Regulating Distribution Transformers as new Grid Asset. Procedia

Engineering, 202, 109–120.

Todorovski, M. (2014). Transformer Voltage Regulation—Compact Expression Dependent on

Tap Position and Primary/Secondary Voltage. IEEE Transactions on Power Delivery, 29(3),

1516–1517.

Tran, Q. T., Davies, K., Roose, L., Wiriyakitikun, P., Janjampop, J., Riva Sanseverino, E., &

Zizzo, G. (2020). A Review of Health Assessment Techniques for Distribution Transformers

in Smart Distribution Grids. Applied Sciences, 10(22), 8115.

van Nederpelt, P. (2009). Checklist Quality of Statistical Output. Netherlands: Statistics

Netherlands. Retrieved March 15, 2021, from

https://ec.europa.eu/eurostat/documents/64157/4374310/43_CHECKLIST-QUALITY-

STATISTICAL-OUTPUT-CBS-2009.pdf/2000653a-e8bc-4979-8e13-bb455b5ddc50.

Wang, Z. (2015). Implementation and Assessment of Demand Response and Voltage/Var

Control with Distributed Generators. Dissertation, Georgia Institute of Technology, Georgia.

Retrieved April 11, 2021, from http://hdl.handle.net/1853/53928.

Wang, Z., Begovic, M., & Wang, J. (2014). Analysis of Conservation Voltage Reduction Effects

Based on Multistage SVR and Stochastic Process. IEEE Transactions on Smart Grid, 5(1),

431–439.

Wang, Z., & Wang, J. (2014). Review on Implementation and Assessment of Conservation

Voltage Reduction. IEEE Transactions on Power Systems, 29(3), 1306–1315.

Weather and Climate (2021). Climate in Regensburg (Bavaria), Germany. Retrieved May 02,

2021, from Weathe and Climate: https://weather-and-climate.com/average-monthly-Rainfall-

Temperature-Sunshine,regensburg,Germany.

Xie, Q., Shentu, X., Wu, X., Ding, Y., Hua, Y., & Cui, J. (2019). Coordinated Voltage Regulation

by On-Load Tap Changer Operation and Demand Response Based on Voltage Ranking

Search Algorithm. Energies, 12(10), 1902. Retrieved December 06, 2020, from

https://res.mdpi.com/d_attachment/energies/energies-12-01902/article_deploy/energies-12-

01902.pdf.

Zhang, Y., Huang, T., & Bompard, E. F. (2018). Big data analytics in smart grids: a review.

Energy Informatics, 1(1).

- 61 -

Appendix A This section shall discuss the detailed illustrations they refer to in Chapter 3 – Statistical

Evaluation of Voltage Measurements.

1 Data Analysis and Visualization

The initial time series dataset is ONCOR_A_Ch1

1.1 Description

A -- 0:00:00 -- 23:59:00 -- 9/5/2020 -- 9/13/2020 – 12.960 – 9 days

The dataset comprises a single column of Ch_1 series in a DataFrame with 12.960 entries.

Reshaped this series into nine days profile (9 x 1440).

Table 1: Description of statistical properties

Prop Sat_1 Sun_1 Mon Tue Wed Thr Fri Sat_2 Sun_2

count 1440 1440 1440 1440 1440 1440 1440 1440 1440

mean 120,7098 121,0438 120,5839 120,4744 121,4421 121,1994 121,0594 121,0998 121,8065

std 0,837545 1,076731 1,069531 1,002244 0,802805 0,743145 0,873402 0,789283 0,787405

min 117,5 118,3 117,6 118,3 119,1 119,6 118,5 118,5 119,5

25% 120,2 120,1 119,8 119,6 120,9 120,7 120,4 120,4 121,3

50% 120,9 121,1 120,6 120,4 121,6 121 121 121,2 121,9

75% 121,3 121,9 121,4 121,3 122 121,5 121,8 121,7 122,4

max 122,4 122,9 123 122,4 123,3 123,1 123 122,7 123,4

delta 4,9 4,6 5,4 4,1 4,2 3,5 4,5 4,2 3,9

Table 2: Array of daily voltage measurements

A plot of the daily voltage profiles can be shown in the figure below:

- 62 -

Figure 1: Daily profiles of voltage measurements

- 63 -

1.2 Statistical tests

I tested the linearity and stationarity of the voltage time series. The data shows non-linearity and

non-stationarity, therefore the voltage readings are influenced by the TOD. Carrying out the test

for linearity and stationarity will help confirm this observation. I will use the ordinary list square

OLS method for evaluating linearity and the Augmented Dickey-Fuller test to determine

stationarity

From the file that describes the output, I choose to work on Sat_1, Sun_2, Tuesday

Figure 2: OLS estimation results.

With an r-square value of 0,748, it shows that the TS data is non-linear on the scale of one day.

# Augmented Dickey-Fuller test from statsmodels.tsa.stattools import adfuller

result = adfuller(y) print('ADF Statistic: %f' % result[0]) print('p-value: %f' % result[1]) print('Critical Values:') for key, value in result[4].items(): print('\t%s: %.3f' % (key, value))

# with a p-value > 0,05, we fail to reject the null hypothesis (H0), thus the

time series has a unit root with time dependent structure. # it is non-stationary. This applies to the entire dataset

# ADF Statistic: -1,375883, p-value: 0,593782 Critical Values: 1%: -3,435 5%: -2,864 10%: -2,568

This TS interval is non-stationary because of the p-value from the KPSS test below. Thus it

confirmed that the series is non-stationary at 15min intervals.

- 64 -

# Kwiatkowski-Phillips-Schmidt-Shin test (KPSS) alternative for stationarity

test

from statsmodels.tsa.stattools import kpss

def kpss_test(timeseries): print ('Results of KPSS Test:') kpsstest = kpss(timeseries, regression='c', nlags=96) kpss_output = pd.Series(kpsstest[0:3], index=['Test Statistic', 'p-value','Lags Used']) for key,value in kpsstest[3].items(): kpss_output['Critical Value (%s)'%key] = value print (kpss_output)

kpss_test(y) Results of KPSS Test: Test Statistic 0,414919 p-value 0,070724 Lags Used 96,000000 Critical Value (10%) 0,347000 Critical Value (5%) 0,463000 Critical Value (2.5%) 0,574000 Critical Value (1%) 0,739000 dtype: float64

1.3 ACF and PACF visualizations

Let's determine the ACF of the original Sat_1 voltage readings and further subdivide it into

smaller sample sizes. Then we determine if the sample data set is purely white noise. It should

not be, because the data is AR.

Figure 3. ACF and PACF of Saturday voltage dataset

The ACF and PACF of the reshaped time series (4 x 360) is shown in Figure 3 and 4.

After differencing or demeaning the voltage profile, the ACF and PACF will not correlate along

with the lags as shown in Figure 5 below.

- 65 -

Figure 4. ACF of 4 x 360 reshaped daily profile

- 66 -

Figure 5. PACF of 4 x 360 reshaped daily profile

- 67 -

Figure 6. ACF and PACF of the differenced daily voltage profile.

1.4 ARIMA Modelling

The first modeling was done with ARIMA(19,1,0) on the entire day profile and its residual ACF

and PACF were not white noise.

- 68 -

Figure 7: ACF and PACF of residual values

The last modeling was done with ARIMA(1,0,0) after much iterative reshaping of the data and

with just 45 sample points. The result of this evaluation shows a white noise at the residual.

Figure 8: Residual ACF of the last iteration.

- 69 -

Appendix B This section details the evaluation techniques deployed in CVR factor computation.

2 CVR factor evaluation and validation.

2.1 Voltage and power noise levels

The evaluation of voltage and power noise levels for this new dataset was based on the ARIMA

model in Appendix A. The average magnitude of voltage and power noise in January is ±0,4𝑉

and ±5,15𝑘𝑊 respectively. This means that %∆𝑈𝑒𝑚𝑎𝑥 = 0,35 which is substantial in comparison

with %∆𝑈𝑡 = 2,0. Thus, the tap change of 2,0% is for deploying CVR.

2.2 Tap change detection algorithm

The tap change detection algorithm is based on the voltage profiles of the measurement

dataset. The dataset consists of 10 seconds measurements of voltage, active power, and

reactive power in three phases at the rONT equipped with ECOTAP VPD.

A monthly dataset of the measurement parameters is stored in 12 *csv files, and using the

Pandas DataFrame object, I imported them into the Jupyter Notebook for evaluation while

parsing the time and dates as well. Below is a table of the first few rows of the monthly dataset

with their respective titles.

Table 3: DataFrame of January measurements.

The tap change detection algorithm was built with the following python code:

# Extract the hour (time-of-day) from the date_time column def n_time(index): date_time = t[index] hr = date_time.hour return hr

- 70 -

This function is required for building the time groups 1 – 4, daily and combined to form the

monthly time groups tap changes.

This next function extracts the timestamps where voltage reduction was initiated.

# calculating dV for the entire day def delta_v_index(vlist):

delta_index = [] for i in range(len(vlist)-3): a = abs(vlist[i] - vlist[i+2]) b = abs(vlist[i+1] - vlist[i+3]) if a > 4 or b > 4: if a > b: delta_index.append(i) else: delta_index.append(i+1) else: i+=1

return delta_index

Then I combined the list of timestamps such that each following index is at least 1 minute apart

and that each timestamp is found in all the three voltage datasets.

def combined_index(alist, blist, clist): a = set(alist) & set(blist) & set(clist) index = list(a) remove_index = []

for i in range(len(index)-1): if index[i] == index[i+1]: remove_index.append(i+1) else: i+=1 for k in range(len(index)-1): ch = abs(index[k] - index[k+1]) if ch < 7: remove_index.append(k+1) else: k+=1 for j in sorted(remove_index, reverse=True): del index[j]

return index

Now we can run these functions on the entire month of voltage measurements. Alternatively,

you can run them on daily sub-samples of the monthly data but it will take more time to

evaluate.

dV1 = delta_v_index(U1) dV2 = delta_v_index(U2) dV3 = delta_v_index(U2) com_index = sorted(combined_index(dV1, dV2, dV3), reverse=False) TG1 = [] TG2 = [] TG3 = [] TG4 = []

- 71 -

for d in com_index:

h = n_time(d)

if h>22 or h<4:

TG2.append(d)

elif h>4 and h<10:

TG3.append(d)

elif h>10 and h<16:

TG4.append(d)

else:

TG1.append(d)

print('TG1= {} \nTG2= {} \nTG3= {} \nTG4= {}'.format(TG1, TG2, TG3, TG4)) TG1= [20965, 21174, 24200, 24546, 29739, 29834, 31690, 31691, 32128, 32360, 33454, 33482, 33602, 33603, 33774, 33783, 33845, 58722, 59246, 59310, 59409, 59441, 59598, … TG2= [16937, 16945, 26482, 26591, 26785, 26945, 27079, 34287, 34294, 60394, 60518, 60539, 60850, 61086, 61147, 61340, 86475, 86482, 94725, … TG3= [20529, 20537, 20692, 20823, 27724, 28096, 28410, 28666, 28810, 45366, 45375, 46214, 46324, 55001, 55240, 63118, 63184, 63318, 63427, … TG4= [4604, 5542, 23031, 30425, 30601, 30980, 31015, 31022, 31117, 31594, 38566, 38870, 39177, 39200, 39441, 39487, 39886, 40246, 47263, 47551, 48280, 48890, 64891, 65110, 65470, 65682, 65968, 66106, 73161, 73550, 73623, 73695, 90438, 90495, 90713, 90720, 90728, 90886, …

2.3 Measuring delta U, delta (P, Q)

Each of these parameters is measured for each timestamp across 3 phases as follows.

# voltage change

WINDOW = 6 # the 1 minute interval

def delta_U(tod):

# CONSTANTS

GAP = tod + 2

st = tod - WINDOW

fn = GAP + WINDOW

bf_int = U[st:tod] # from the voltage series for each phase

aft_int = U[GAP:fn] # from the voltage series for each phase

v1 = np.mean(bf_int)

v2 = np.mean(aft_int)

pdv = ((v1-v2)/v1)*100

return pdv

# power change

def delta_PQ(tod, power):

# CONSTANTS

GAP = tod + 2

st = tod - WINDOW

fn = GAP + WINDOW

# form the active power

if power == 'P':

bf_int = P[st:tod]

aft_int = P[GAP:fn]

p1 = np.mean(bf_int)

p2 = np.mean(aft_int)

ch = p1 - p2

if p1 < 0:

pdp = (ch/abs(p1))*100

else:

pdp = (ch/p1)*100

# from the reactive power

if power == 'Q':

bf_int = Q[st:tod]

aft_int = Q[GAP:fn]

q1 = np.mean(bf_int)

q2 = np.mean(aft_int)

ch = q1 - q2

if q1 < 0:

pdq = (ch/abs(q1))*100

else:

pdq = (ch/q1)*100

return pdp, pdq

- 72 -

Thus, the CVR factors for active and reactive powers derived using the equations in section

4.3.1 in the main document were solved below.

# active power CVR factor

def cvrf_P(tod):

volt1 = delta_U(tod)

powr1 = delta_PQ(tod, 'P')

cvr = powr1/volt1

return cvr

# reactive power CVR factor

def cvrf_Q(tod):

volt1 = delta_U(tod)

rctv1 = delta_PQ(tod, 'Q')

cvr = rctv1/volt1

return cvr

Now we can run the evaluation of each time group using these functions as follows.

points = TG1 cvr_val1 = [] cvr_val2 = [] cvr_val3 = [] for i in points: cvr1 = cvrf_p1(i) cvr2 = cvrf_p2(i) cvr3 = cvrf_p3(i) cvr_val1.append(round(cvr1, 4)) cvr_val2.append(round(cvr2, 4)) cvr_val3.append(round(cvr3, 4))

print('{} {} {}'.format(cvr_val1, cvr_val2, cvr_val3)) [7,1656, 5,1855, 6,5184, -0,3282, -5,9241, 2,3125, 13,4897, 12,2916, 1,5989, 0,2798, -1,0223, 8,7947, 0,3597, 0,8479, 2,5864, 5,2, -1,2777, 10,4163, 4,399, -8,666, -7,6803, -3,0132, 0,8488, -4,8851, -4,018, -2,1703, -3,3068, -5,2642, -10,4886, -2,9875, -2,0805, -1,317, 4,5236, -2,9163, -0,8639, 3,9829, 1,0501, -3,0786, -9,4268, 7,5443, -3,6086, 3,1923, 5,4756, 1,699, 0,2716, 0,7351, …]

The complete 12 months dataset contains 3.162.240 data points where were evaluated to

produce the following CVR factors.

Table 4: Seasonal results of CVR factors for 2020

Seasons Time of day

TG1 (16:00 - 22:00) TG2 (22:00 - 04:00) TG3 (04:00 - 10:00) TG4 (10:00 - 16:00)

P Q P Q P Q P Q

Winter µ 0,98 6,09 1,61 3,83 0,47 5,50 1,03 3,72

M 0,98 6,26 1,57 3,03 0,96 4,90 1,16 3,55

Spring µ 0,86 3,57 0,94 4,01 0,89 3,84 0,07 2,45

M 1,12 2,94 1,25 3,30 0,98 3,89 0,25 2,40

Summer µ 0,48 2,46 1,00 2,91 0,88 2,14 0,38 3,09

M 0,56 1,92 0,85 1,90 1,20 0,71 0,76 2,23

Autumn µ 1,56 2,46 1,19 1,50 1,37 3,18 0,63 2,91

M 1,55 1,92 1,25 0,52 1,44 2,40 0,83 2,59

- 73 -

The CVR factors show a downward trend from night to day. The winter period is the least

affected by PV integration. The PV peak production period (10:00 – 16:00) coincides with the

period of lowest CVR factors obtained for the spring, summer, and autumn seasons. The

overnight period during summer has the least CVR factor because it has the least demand for

heating and other seasonal load demand. The reactive power CVR factors are 4,3 times higher

than the active power CVR factors.

2.4 Test field evaluation.

Removing the impact of the test field from the CVR factors of the whole network is important if

you were to consider just the 85 residential households.

Figure 9: Load profile of network area and test field

From the figure above, the test field load consumption is only about 1,75% of the total network

load based on the December measurements. After isolating the test field dataset from the rest

of the network, the CVR factor of mainly the 85 households improved by 2,91% as shown

bellow.

Figure 10(a) Residential network CVR factors

- 74 -

Figure 10(b) Total network CVR factors

2.5 Hypothesis Testing

The control chart is a method of measurement verification that can be used to test the

hypothesis and assumptions introduced in any evaluation where a key parameter is defined with

a particular characteristic. The tests prove the influence of outliers on the dataset, the null

hypothesis of stationarity in the randomized control group, and the sensitivity of the averaging

intervals.

Figure 11 Distribution of voltage, power and CVR factor in the randomized sample group

The standard filtering interval for active power and reactive power CVR factors were determined

by initially analyzing the distribution of the CVR factor dataset. They fall within 95% of a

standard normal distribution of CVR factors. Outliers in the active power measurements were

- 75 -

filtered using the ±10 rule. Where %∆𝑃 > ±20 it will be detected and isolated using its original

timestamp for referencing.

Testing for stationarity can sometimes fail, especially with ADF/KPSS. That is why I introduced

the z-test for evaluating the null hypothesis. Both evaluation approaches are satisfactory

answers to the question of whether we can achieve a zero mean value of CVR factors from the

random sample groups. The following code shows the evaluation.

# test for equation 4.5 from scipy import stats from statsmodels.stats import weightstats as stests

# 0 here is the null hypothesis ztest, pval = stests.ztest(dP, x2=None, value=0) print("Pval = {}".format(float(pval))) Pval = 0,2765

# test for equation 4.6 ztest ,pval1 = stests.ztest(dP1, x2=dP2, value=0,alternative='two-sided') print("Pval = {}".format(float(pval))) if pval<0.05: print("reject null hypothesis") else: print("accept null hypothesis") Pval = 0,6249876944618094 accept null hypothesis

Therefore, I conclude that this null hypothesis is true for all randomized sample groups of

voltage and active power.

Figure 12: Averaging interval effect on CVR factors.

The optimal averaging interval for this evaluation is exactly between 1,0 to 1,5 minutes. This

gives a CVR factor ranging from 0,9 to 1,2. The intervals have little effect on the average CVR

factors obtained (±0,30) but gradually increases the percentage of outliers in the evaluation as

the interval increases.

0.00

10.00

20.00

0.60

0.80

1.00

1.20

1.40

0.50 1.00 1.50 2.00 2.50 3.00

Ou

tlie

r %

CV

Rf

Averaging intervals (min)

December January February

- 76 -

Appendix C 3 Energy savings estimation

In this section, I will outline the steps taken to evaluate the energy savings and CVR factors for

the new datasets. Our entire evaluation shall be based on the April 2019 and 2021

measurements.

3.1 Parameter evaluations

There are two forms and sources of measurement data. Load and voltage measurement data

came from the test field here in Southern Germany. Its granularity is 10 seconds. Known and

operating project site with an NDA. The environmental dataset is an airport weather station

close to the project sight. Its granularity is 1 hour. An annual growth factor of 5,5%/a was

introduced prior to energy savings evaluation. Thus, the measured load consumption of 2021

will be reduced by 5,5%.

The preprocessing of the dataset of April 2019 for the modeling was carried out first. The table

below shows the initial dataset in combination with the total power (kW).

Table 1: Dataset of the April 2019

date cdh hdh hum dow hol w pres hr P_tm

4/1/2019 0 13,56 0,88 1 0 6,437 0,944 1 35,20769

4/1/2019 0 14,11 0,91 1 0 6,437 0,944 2 29,58804

4/1/2019 0 14,67 0,93 1 0 11,265 0,944 3 33,56577

4/1/2019 0 15,22 0,92 1 0 11,265 0,944 4 70,63927

4/1/2019 0 16,33 0,9 1 0 14,484 0,943 5 63,77718

4/1/2019 0 16,33 0,89 1 0 14,484 0,943 6 77,77088

4/1/2019 0 16,33 0,87 1 0 14,484 0,943 7 44,19558

4/1/2019 0 16,33 0,88 1 0 14,484 0,943 8 43,76921

4/1/2019 0 16,33 0,88 1 0 11,265 0,944 9 28,18465

The table above shows only the first nine rows of the 720 rows of data per hour in April. The

numerical variables were correlated to the total power P_tm using Pearson's correlation, and

the results below were obtained.

Table 2: Pearson's correlation results

Target variable Features Correlation

P_tm CDH 0,105

HDH 0,634

Humidity 0,630

Wind gust 0,126

Pressure 0,068

- 77 -

Therefore, the hdh and humidity parameters are the most correlated and will be used as the

numerical variables in the modeling. The independent variables are denoted by X while the

target variable is represented by y. 𝑋 = ℎ𝑑ℎ, ℎ𝑢𝑚, 𝑑𝑜𝑤, ℎ𝑜𝑙, ℎ𝑟 and 𝑦 = 𝑃_𝑡𝑚.

3.2 Modeling

The categorical features (dow, hol, hr) will be decomposed using 𝑂𝑛𝑒𝐻𝑜𝑡𝐸𝑛𝑐𝑜𝑑𝑒𝑟( ) to

transform it from 𝑑𝑜𝑤 = (720𝑥1) to 𝑑𝑜𝑤 = (720𝑥7). Each unique entry in the dow series will be

transformed to a column and filled in a binary form. 0 means no entry while 1 means that there

is an entry. Similarly, ℎ𝑟 = (720𝑥1) will transform to ℎ𝑟 = (720𝑥24).

from sklearn.preprocessing import OneHotEncoder

X = pd.get_dummies(X,prefix=['dow','hol','hr'],

columns = ['dow','hol','hr'], drop_first=False)

ohe = OneHotEncoder()

transformed = ohe.transform(X['dow','hol','hr'].to_numpy().reshape(-1, 1))

ohe_df = pd.DataFrame(transformed, columns=ohe.get_feature_names())

X = pd.concat([X, ohe_df], axis=1).drop(['Profession'], axis=1)

After this, the dataset was randomized using a random state of 100 and split into train and test

set at 80:20 ratio.

Figure 1: MLR model correlation of predicted and test y-variable

The RMSE and Pearson's correlation result were 16,2953 and 0,910 respectively.

The model residuals are normally distributed as shown in the figure below:

- 78 -

Figure 2: Distribution of the model residuals

With this information, we can insert the April 2021 environmental parameters as the testing

dataset after preprocessing.

Isolating the PV peak production hours (10:00 – 16:00) was necessary in other to determine the

usual load variation from the consumers. The MLR model was re-trained with the new dataset

which reduced from 720 to 510, yielding the following results.

Figure 3: MLR correlation of test and predictor datasets with PV isolation.

- 79 -

Figure 4: Distribution of the model residuals

Figure 5: Average CVR factor with PV isolation

3.3 Energy savings

The figure below shows the seasonality in the weekly consumption in the test field. It shows an

average hourly consumption pattern and the difference in the weekday and the weekends. In

the afternoon when PV production is high and demand is low, there is a negative consumption -

generation. There were certain measures put in place to curtail this by the network operators at

the test field.

- 80 -

Figure 6: One-week demand profile.

The Pearson's correlation and RMSE of the predicted energy versus the real energy

measurement are 0,788 and 21,0322 respectively.

Figure 7: Estimated and real energy profiles

From the figure above, we can see that at some time in the day there were no energy savings

because the estimated power is below the CVR power. Whereas in some days, there were

measured energy savings.

- 81 -

Figure 8: Associated voltage reduction from normal to CVR

The figure above shows the difference in the voltage profiles during a normal operation and

during a CVR operation. The average percentage difference is at 5,25%.

The CVRf for energy was further split into weekdays and weekends and their result can be seen

in the following figure.

Figure 9: Weekday (WD) and Weekend (WE) CVR factors for energy.