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
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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
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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
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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.
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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.
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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)
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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.
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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).
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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.
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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.
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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)
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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 -
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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:
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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.
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# 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.
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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.
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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
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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
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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.
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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.
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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.
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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.
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