Load Curtailment Strategy in Distribution Network with Dispersed Generations

Ardiaty Arief, Muhammad Bachtiar Nappu School of Information Technology and Electrical

Engineering, University of Queensland St. Lucia, Brisbane, Australia e-mail:ardiaty@itee.uq.edu.au

bachtiar@ieee.org

Zhao Yang Dong EA Centre of Excellence of Intelligent

Electricity Networks School of Electrical Engineering and

Computer Science The University of Newcastle, Australia

E-mail: zydong@ieee.org

Muhammad Arief Dept. of Electrical Engineering

Hasanuddin University Makassar, Indonesia

e-mail: aarief@ft.unhas.ac.id

Abstract—Nowadays, large-scale penetration of dispersed generations (DGs) in the distribution systems has changed the structure of power system hence may create technical as well as safety problems. DGs have a large effect on real-time operation and planning for power systems by boosting the complicatedness of control, maintenance and protection of the distribution system network. Nevertheless, in the catastrophe following outage, the installation of DGs in the distribution system can provide local load reliability to be used during emergency and supply the required spinning reserve to maintain power system stability. However, the local voltage stability must be kept during emergency operation, therefore when voltage instability occurs in the distribution system, some load curtailments may be needed. Therefore this paper presents a new strategy of load curtailment in a distribution system with DGs. The proposed strategy is based on well-known static voltage stability approach; the modal analysis that involves eigenvalue and eigenvectors techniques. Numerical example on a 34-bus distribution network is given to illustrate the effectiveness of the proposed method. The analysis compare different load curtailment scheme with or without DGs.

Keywords- dispersed generations; distribution systems; load curtailment; load shedding; voltage stability.

I. INTRODUCTION Due to the fast technological developments of dispersed

generations as well as economic and environmental issues regarding to conventional electricity generations, dispersed generations have grown rapidly in electricity industry [1, 2]. Nowadays, the use of dispersed generation (DG) has risen as a clean renewable energy alternative generation because of its benefit regarding to the exhaustion fossil fuels and global warming problems [3]. It is expected to hold a crucial task in the electricity industry infrastructure and market. Therefore, the topic of dispersed generations has attracted attention of power engineer researchers to conduct various investigations concerning DGs.

Large-scale penetration of dispersed generation (DG) in the distribution systems has changed the structure of power system and may create technical also safety problems. DGs have a large effect on real-time operation and planning for power systems by boosting the complicatedness of control, maintenance and protection of the distribution system network. Nevertheless, in the catastrophe following outage, the

installation of DG in the distribution system can provide local load reliability to be used during emergency and supply the required spinning reserve to maintain power system stability. However, the local voltage stability must be kept during emergency operation, therefore when voltage instability occurs in the distribution system, some load may need to be curtailed. Nonetheless, more DGs installed in the distribution system create more challenges in the load curtailment problems.

Different methodologies have been proposed to provide solution for effective load curtailment in distribution system. References [4, 5] employ genetic algorithm (GA) in their load curtailment design. In [4], the GA is implemented to obtain the optimal load curtailment strategy considering DGs in the case of constant and variable modeling whereas in [5], initially utilizes voltage stability index to find location for load curtailment then optimized their design with GA. Authors in [6] formulate a new method to determine amount and timing of load curtailment combining non linear mathematical computation with discrete differential-algebraic power system formulation. In [7], the authors propose load curtailment in power system with DGs subjected to system, operation and security constraints. A load shedding scheme is proposed in [8] under intentional islanding condition. Reference [9] analyses the Portuguese Electrical System and design load curtailment scheme by categorizing substation feeders. Studies in [10, 11] develop load curtailment method to improve both system voltage and frequency stability after being subjected to perturbation which is determined with swing equation. The authors in [12] design a strategy of load curtailment based on frequency information, rate of change of frequency, willingness of customers to pay and load demand records. In [13], two load curtailment schemes are presented using response-based and combination between response-based and event-based where both of these techniques occupy voltage and frequency to determine amount of load curtailment. Reference [14] develops a method of load curtailment to reduce areas affected by load shedding where the system is optimized with nonlinear optimization then the system’s model is sorted out using the binary particle swarm optimization (BPSO).

In load curtailment, there are two main objectives to be achieved: maintaining power supply to essential loads and minimizing detriment caused by load shedding. Nonetheless, there are two main problems of load curtailment are

(1)

determining proper amount of load curtailment and finding appropriate location for load curtailment. This paper proposes strategy of load curtailment in distribution system with/without DGs that fulfilling the objectives and considering problems in load curtailment. The aim of this paper is to provide the minimum disruption to customer as well as to maintain the voltage stability by measuring minimum amount of load curtailment and determination of the most suitable location load curtailment in distribution system with dispersed generations. The proposed strategy is based on well-known static voltage stability approach; the modal analysis that involves eigenvalue and eigenvectors techniques. The voltage stability is evaluated by calculating the eigenvalues. In the load curtailment design, the eigenvalues are incorporated in determination the amount of load curtailment. Then the eigenvectors are calculated to determine the modal participation factor. Bus participation factor in modal analysis indicates the contribution of the bus to the V-Q sensitivity at the weak bus. Buses with high participation factor are the firstly priority for the location of load curtailment. Numerical example on a 34-bus distribution network is given to illustrate the effectiveness of the proposed method. The analysis compare different load curtailment scheme with or without DGs.

The structure of this paper is as follow. Section II explains about dispersed generations. Section III reviews about load curtailment considering DGs. Proposed methodology is elaborated in Section IV. Then, Section V presents results and analysis, lastly Section VI gives conclusions.

II. DISPERSED GENERATIONS Dispersed generations are defined as the development

electric power sources connected directly on the customer site of the meter or at the distribution system network [15, 16]. Since dispersed generations are installed within the local distribution system network or at a customer’s site, they deliver power directly to the local distribution network.

The integration of dispersed generations into electric power system has brought many benefits. It has positive effects on the voltage profile at the distribution system as well as power quality. Benefits of dispersed generations in the power system operation are [17-19]:

1. Improve the voltage profile by reducing power flow inside the transmission system,

2. Reduce power losses at distribution system by delivering power for some load demand at the distribution,

3. Improve system’s reliability and efficiency by diminishing thermal stresses caused by loaded substations, transformers and feeders,

4. Postpone infrastructure upgrades since they provide transmission capacity release,

5. Decrease expenses related to transmission and distribution,

6. Help in “peak load shaving” and load management programs,

7. Provide local load reliability which can be used as on-site standby to supply power during emergency and system outages,

8. Supply the required spinning reserve thus maintain power system stability,

9. Eliminate or lessen emission.

III. LOAD CURTAILMENT CONSIDERING DGS Load curtailment refers to the process of disconnecting

some system load following perturbations to prevent the power system from possible jeopardy [20, 21]. A power system may go into emergency situation, hence load curtailment as control action in urgent condition need to be taken to ensure power still distributed to imperative loads. In the normal system operating condition, DGs supply power to the system based on the energy availability, production cost, etc [22], therefore during emergency condition, it is important to recognize how far the DGs can provide electricity supply after being subjected to disturbance [23]. Throughout the power outage state, DGs continue supplying power, however, the system voltage may still drop below its nominal values depending on the power disparity between total generation and demand. When the voltage fall below certain value, the power supplied by DGs and from the system do not satisfy the demand, hence load curtailment may still be conducted to maintain the power equilibrium and power system voltage and frequency stability.

There are three states of emergency condition following disturbance [7]. Firstly, the main disturbance takes place in the transmission system. The distribution network provider may be asked to remove some load. Secondly, the key disturbance occurs in dispersed generations then resulting in losing of one or some DGs. In this condition, load curtailment is necessary to maintain the system stability. Thirdly, the core disturbance arises in the system interconnection. In this urgent situation, some areas of the power system with DGs may be separated from the main system.

Load curtailment in all of the three emergency conditions above can be executed in two approaches. First approach is that the DGs are still connected to the system and the main operators keep monitoring the system voltage and frequency stability. The second approach, the DGs are separated from the main system hence forming an unintentional islanding system. Nonetheless, there are several issues that should be considering hence limiting the islanding operation, such as personnel safety, the risk of insufficient fault levels on relays, difficulties in maintaining tolerable voltage and frequency levels and the risk of out-of-synchronous re-closure [2].

Hence, in power systems with several dispersed generations, it is essential to formulate a purpose function to minimize the total load curtailment cost after being perturbed while maintaining power supply to important loads. The objective function can be written as,

min ∆

Where m is the number of loads to be disconnected and is the expense of each load. In addition, to ensure the power

(4)

supply to important loads, so there are some loads that cannot be shed. This will add the following constraint, (2)

Where is the quantity of the rest of load after load curtailment at bus i and is the quantity of load that cannot be curtailed at bus i.

Because the dispersed generations are installed at the distribution systems which are usually radial system, there is more constraint due to the limitation of protection system which do not allow the reverse power, thus 0 (3)

is the active power flow from bus i to bus j.

Other constraints are power flow equations and the frequency, voltage and line flow should be maintained in certain limit, thus

| | cos 0 min max (5)

(6)

(7)

IV. PROPOSED METHODOLOGY In this paper, load curtailment strategies are reviewed for

each different conditions, without DG, with one DG and with 2 DGs. Amount and location of load curtailment are assessed. In our previous study as in [24, 25], bus modal participation factor has been proven to be effective in finding location of load curtailment. The assessment in these studies suggest the conclusion that load curtailment at weak buses can signify for the best solution for improving stability and the modal bus participation factor gives essential information of mechanism to determine the most appropriate location for load curtailment. The next section briefly reviewed the proposed method.

A. Modal Analysis Method Modal analysis is introduced in reference [26] which

involves eigenvalue techniques and the associated eigenvectors of reduced Jacobian matrix. The focus of using the reduced Jacobian matrix instead of system state matrix is on voltage and reactive power characteristic. It provides accurate estimation of proximity to voltage instability as well as information of mechanism of voltage instability (power system part contributing to instability (critical load buses, branches and generators)). Proximity is measured by the magnitude of eigenvalues. The eigenvalues recognize different modes through which the system could be unstable. On the other hand, information of mechanism of voltage instability is provided by the eigenvectors.

Power system is modeled as follow,

∆∆ ∆∆ ∆∆ ∆∆ (8)

where, ∆ is variations in bus real power ∆ is variations in bus reactive power injection ∆ is variations in bus voltage angle ∆ is variations in bus voltage magnitude J is the Jacobian matrix of partial derivatives

Critical bus recognition is accomplished by applying modal analysis method on the system Jacobian matrix, hence (9)

Where, JR is the reduced Jacobian matrix. The modes of power network can be acquired by the eigenvalues and eigenvectors of the reduced Jacobian matrix JR, thus Λ (10)

Where,

is the right eigenvector matrix of JR is the left eigenvector matrix of JR Λ is the diagonal eigenvector matrix of JR

B. System eigenvalue The eigenvalue analysis method has been proven to be

effective in evaluating the steady-state stability of a system. The smallest system eigenvalue λ value is exercised to measure the voltage stability of the system. It also becomes an index to voltage stability measurement.

Eq. (10) can be extended into

0 00 000 0 0

(11)

If > 0, it shows that the system is stable. On the other hand, if < 0, the system is unstable. When = 0, the ith modal voltage collapses. Any reactive power change in that modal will cause infinite variation of modal voltage. The magnitude of each modal voltage change equals to the magnitude of the modal reactive power change times the inverse of . The magnitude of determines the degree of stability of the ith modal voltage.

C. Modal Bus Participation Factor The relative bus participation factor of the kth bus to the ith

mode is provided by the left and right eigenvectors correlating to the system critical modes and can be given as, (12)

Load buses with large participation factor have more influence in contributing to the voltage instability. Consequently these buses become the best candidate buses for determining the location of load curtailment to enhance system voltage stability.

V. RESULTS AND ANALYSIS This study simulates a distribution network performance

after perturbation occurs in the transmission system causing decrease supply to the distribution with and without DGs. Suppose the power flow to the distribution network following main disturbance in the transmission system has reduced 2 pu.

Figure 1. 34-bus distribution network test system [27]

There are 3 cases observed for this condition in this study: No DGs, 1 DG installed at bus 26 and 2 DGs at buses 9 and 26.

A. Case 1: No DG installed When no DG installed, the overall voltages across buses 6-

11 and 16-33 in distribution network system decrease below voltage stability limit as can be seen in Fig. 2 (blue line). Therefore, load curtailment is necessary to reinstate the voltage to its stability limit. From the first iteration participation factor calculation, bus 26 has the highest value (Fig. 3), hence this bus become the best option for load curtailment. But load shedding in this bus cannot stabilize the bring the voltage, therefore more load curtailment is needed at other buses. At the second and third calculation, bus 33 and 11 have the highest participation factor, thus selected as location of load curtailment. Total amount of load shedding in these 3 buses are 1.521+j1.001 pu. In addition, as can be seen in Fig. 6, the system eigenvalue increases from 1.569 (before load curtailment) to 1.624 (after load curtailment).

Figure 2. Voltage magnitude in case without DG installed

Figure 3. Bus modal participation factor for Case 1

B. Case 2: 1 DG installed at bus 26 In this case, we consider one DG unit is installed at bus 26

with total generation 0.8 pu. However, even though with DG installed, the total supply from the system and DGs cannot compensate the load, hence the voltage profile still drop below its voltage stability limit and load curtailment is also needed in this case. However, since there are additional supply from the DG, the amount of load curtailment is less than in Case 1. From the calculation of bus participation factor, in the first iteration, it is shown that bus 33 has the highest contribution to the instability in the distribution network and become the location for load curtailment. The in the second iteration it is bus 11 with the highest participation factor. In this case, load curtailment is performed in this 2 buses with total load being disconnected are 0.78+j0.585 pu. After being disturbed, the eigenvalue drops to 1.5988, but then rises to 1.63 after load shedding.

Figure 4. Voltage magnitude in case with 1 DG installed

C. Case 3: 2 DGs Installed at bus 9 and 26 In case 3, 2 DGs are installed in this distribution network

with total generation of 1.5 pu. In this instance, even though after the transmission system being perturbed that caused reduction of power supply to this distribution, the voltages at the distribution system are still stable, hence no load

0.7

0.75

0.8

0.85

0.9

0.95

1

0 10 20 30

Vol

tage

mag

nitu

de (p

u)

Bus

Before load curtailment After load curtailment

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33

Bus

Part

icip

atio

n Fa

ctor

Bus

1st iteration 2nd iteration 3rd iteration

0.7

0.75

0.8

0.85

0.9

0.95

1

0 5 10 15 20 25 30

Vol

tage

mag

nitu

de (p

u)

Bus

Before load curtailment After load curtailment

33

1 2 3 4

5 6

7 8

9 10 11

23 22 21

26 24

16 17

18 19

20

25

3031

32

0

15 14

13

12

29

28

27

curtailment is needed. The voltage stabilitythis case can be seen in Fig. 5. The edistribution system after being perturbed is 1.

Eigenvalue as voltage stability index befcurtailment at each case is shown in Fig. 6. Famount of load curtailment for each case theactive and reactive power losses at eachcurtailment. Table I provides results summary

Figure 5. Voltage magnitude in case with 2 D

Figure 6. System eigenvalue

Figure 7. Amount of load curtailm

0.7

0.75

0.8

0.85

0.9

0.95

1

0 10 20

Vol

tage

mag

nitu

de (p

u)

Bus

1.52

1.54

1.56

1.58

1.6

1.62

1.64

Case 1 Case 2

1.569

1.5988

1.6241.63

Syst

em e

igen

valu

e

Before load curtailment After load

0

0.5

1

1.5

2

Case 1Case 2

1.521

0.78

1.001

0.585

Load

Cur

tailm

ent (

pu)

P shedding Q shedding

y performance for eigenvalue at the .638.

fore and after load Fig. 7 illustrates the en Fig. 8 describes h case after load y of this study.

DGs installed

ment

Figure 8. Active and

TABLE I. R

Case Number of DGs 0

Total DGs Generation 0

DGs Location -- Amount of load curtailment (pu) 1.521+j1

Location of load curtailment 11, 26 an

Eigenvalue before load curtailment 1.569

Eigenvalue after load curtailment 1.624

Losses at stable condition (pu)

0.3108j0.081

From these three cases obintegration of DGs into distribustructure thus gives more diffiincluding load curtailment schethe DGs provide local load emergency and supply the maintain power system stabilityto consumers and location of loon the network structure, henDGs into the system, the loadmodified.

VI. CON

In load curtailment, there achieved as well as two main objectives are to maintain powminimize damage by load curare determining proper amountappropriate location for load cuaims to design load curtailmenwith/without DGs that fulfillingproblems in load curtailmentknown static voltage stability ainvolves eigenvalue and eigenvis reliable in assessing voltage s

30

Case 3

1.638 1.638

d curtailment

Case 3

0

0

00.050.1

0.150.2

0.250.3

0.35

Case 1C

0.31086

0.08166

Loss

es (p

u)

P loss

d reactive power losses

RESULTS SUMMARY

1 Case 2 Case 3 1 2

0.8 pu 1.5 pu

26 9 and 26

1.001 0.78+j0.585 --

nd 33 11 and 33 --

9 1.5988 1.638

4 1.63 1.638

86+ 66

0.29961+ J0.07853

0.23466+ J0.05853

served, it can be seen that, the ution system changes its network ficulty in control and protection eme. Nonetheless, during outage,

reliability to be used during required spinning reserve to

y. The amount of load disrupted oad shedding heavily depending

nce with the integration of new d curtailment design need to be

NCLUSIONS are two main objectives to be problems to be considered. The

wer supply to essential loads and rtailment, whereas the problems t of load curtailment and finding urtailment. Therefore, this paper nt scheme in distribution system g the objectives and considering t. This study employs a well-analysis; the modal analysis that vectors techniques. This method stability.

Case 2Case 3

0.29961

0.23466

0.078530.05853

Q loss

This study evaluates a distribution network performance with/without DGs after perturbation occurs in the transmission system causing decrease supply to the distribution. This study provides a basis for load curtailment scheme design considering size and location of DGs. This study observes 3 conditions: No DGs, 1 DG installed at bus 26 and 2 DGs at buses 9 and 26. It is shown that the load curtailment plan should be different for all different scenarios. The simulation results also confirm the integration of DGs into distribution network bring positive impact in minimizing quantity of load shedding.

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