Stepwise Restoration of Distribution Network under Cold Load Pickup: A New Approach

Vishal Kumar1, Rohith Kumar H.C., I. Gupta, and H.O. Gupta

Department of Electrical Engineering, Indian Institute of Technology, Roorkee, India.

Abstract—An approach for stepwise restoration of a power distribution network under

cold load pickup (CLPU) is presented in this paper. The steps used in restoration process

are evaluated from the distributed load-points considered on the CLPU profile. For each

of these steps, optimal locations for load restoration are determined, and hence resulting

in the optimal switching sequence for entire network restoration. The optimization is

performed to achieve multiple objectives of maximum utilization of the existing system

and minimum switching operations subjected to the satisfaction of system constraints.

Genetic algorithm has been adopted for searching the optimum solution. The approach

has been successfully applied to two networks with different topologies, including a

practical distribution network.

Keywords—Cold Load Pickup, Distribution system restoration

NOMENCLATURE α Time constant for CLPU model STotal Total connected load

∆T Delay in the delayed exponent model STVTransformer maximum loading-limit violation

σi Decision variables ( 1=ON and 0=OFF) SU Un-diversified value of a load in p.u. aij Participation factor of Lj at step i SW Number of switching operations at a step

IVSum of the ratios of branch-current violations to their thermal limit {SW(Lj)} Set of load locations restored at step j

KTM Transformer maximum loading factor Tm0 Initiation of restoration in CLPU model

m Total number of distinct load-points considered on CLPU profile Tm1

Time instant for start of diversity in CLPU model

NbrTotal no. of branches in the network, and {.} is the set of branches Ti Time instance of step i

NbuTotal no. of buses in the network, and {.} is the set of buses u(t) Unit step function

Ri Total restored load up to ith step VVSum of the ratios of bus-voltage violations to the voltage limit

S(t) Load demand for time t ≥ Tm0 as per CLPU model WIV Weight for IV

Lj Total load restored (diversified) in step j WLoadWeight for ratio of un-restored load to connected load

SD Diversified value of a load in p.u. WSW Weight for SW SUnrestored Load un-restored during current step WTV Weight for STV

1 Corresponding author and; presently, is with EED, IET Lucknow, India- 226 021.

ST Substation transformer rating WVV Weight for VV NP Population size [A](m x m) Participation factor matrix for aij

Pc Crossover probability [R](m x 1) Matrix for Ri Pm Mutation probability [L](m x 1) Matrix for Lj

I. INTRODUCTION

Prolonged outages cause severe problems during restoration of the power

distribution network. The key cause for this severity is the loss of diversity among the

connected loads [1]-[2], as it leads to additional power demand from the system. This

condition arises due to presence of thermostatically controlled load, and is known as Cold

Load Pickup (CLPU). The significant rise in the amount of thermostatically connected

loads has elevated the CLPU problem, owing to the fact that these loads lose their

diversity, leading to heavy loading condition during the post outage restoration period.

The types of load connected, duration of outage, local weather conditions and users living

habits affect the severity of CLPU condition. As evident from literature [3]-[6], CLPU

condition is characterized by a transient stage followed by an enduring stage. Transient

stage is primarily due to the inrush current in motors and transformer magnetization

current, hence it vanishes within few seconds. However, the enduring stage is largely due

to the loss of load diversity and extends for much longer duration causing excessive

loading on the network interconnecting elements. The permissible loading limits of one

or more interconnecting elements will be reached even if a portion of total load is

restored [7]-[10]. Further hindrance in the restoration is caused due to the violation of

steady state operational limits (i.e. permissible voltage and current limits of buses and

branches respectively) during enduring stage. Therefore utilities prefer to sub-divide the

entire network into sections and restore it in steps, because the network gradually regains

its diversity with time.

The consideration of CLPU problem dates back to 1952, and researchers

considered it be an inrush phenomenon and suggested remedies such as change of relay

settings, and usage of very inverse type relays [11]-[12]. However, in recent years the

dominant load behavior has forced the researchers to recommend better techniques to

tackle CLPU problem. Usage of adaptive relaying scheme and optimal designing of the

network to accommodate CLPU are the few eminent ones of these suggestions [2], [6],

[9], [10], [13], [14]. However, a clear insight into the literature reveals that CLPU is site

specific and is more likely an operational problem than a design problem. Therefore for

an already operational system, picking up of loads in steps/sections becomes the only

viable solution [5], [7].

Literature reveals several distinctive efforts of researchers to restore the network

optimally. Optimal sequence for restoration of sections was determined by Ucak and

Pahwa [7] such that total restoration time gets minimized, besides minimizing customer

interruption duration. Further refinement of work was done by using the adjacent pair-

wise method to minimize Customer Average Interruption Duration Index (CAIDI) [8].

Wakilesh and Pahwa [9] dealt the CLPU problem from the design point of view and

performed a minimization of total annual cost function comprising cost of transformer,

energy interruption, sectionalizing switches and transformer overloading. Further they

extended the work by applying Genetic Algorithms (GA) to a compensated real-life

distribution feeder [10]. Researchers have also utilized GA [3] and ant algorithms [15]

proficiently to determine the sequence of switching for restoration under CLPU

condition. In a recent paper by Gupta and Pahwa [14], authors have exploited voltage

drop based approach to optimally design and expand the network. Consequently, it is

evident that extensive amount of work has been carried out for optimally designing the

network. However, steady state operational constraints need further attention as CLPU

problem introduces severe voltage violations in the network. Further, in the section-wise

restoration, the precedence constraint has been used by the researchers [3],[7]-

[10],[14],[15] to determine the optimal placement and operation of the sectionalizing

switches, however this constraint limits the total load getting restored owing to

subsequent loading effects. In the proposed approach the load-wise restoration has been

performed which means loads restored at a step may not be in the form of a section of the

network instead these may be at dispersed locations i.e. free from precedence constraint.

The initial concept for restoration of distribution network with the use of proposed

approach has been given in [16]. Certain assumptions were made in [16] these are:

participation factors for loads switched ON at different steps were neglected and delays

associated to CLPU model were not considered in steps beyond staring step. However,

the present paper proposes a realistic approach of step-wise restoration using optimal

sequencing of operation of load-switches to achieve maximum utilization of the existing

system. The approach selects several distinct load-points on the CLPU load profile as per

CLPU model [17], and discrete time steps corresponding to these load-points are

determined. The load corresponding to these steps are evaluated, and are used in

determining the switching locations. The GA is applied at each of these steps to

determine the optimal set of loads to be restored; consequently the optimal sequence of

restoration is obtained. The applicability of the proposed approach is illustrated on a 33-

bus system taken from literature [18], and also on 41-bus practical distribution system

[19].

II. METHODOLOGY FOR SELECTION OF STEPS

Numerous varieties of CLPU model are available in the literature [20]-[25].

However, most of these models can be characterized equivalent to a delayed exponential

model for the sake of mathematical and analytical simplicity [17]. Mathematically, such a

model can be synthesized as (1), [14].

1

1 1

- ( - )( ) [ ( - ) ] ( - )+ [1- ( - )] ( -

t TmD U D m U m mS t S S S e u t T S u t T u t T

α= +

0) (1)

Few assumptions are made in the proposed approach these are listed below:

1. The network is operating in normal condition at the given load for a long

duration; therefore load diversity is well established before occurrence of outage.

2. All loads in the network follow similar CLPU model [17] at their restoration

following an extended outage.

A. Load-point evaluation

In the proposed approach several distinct load-points are considered on the CLPU

load profile. These points are used as steps for stepwise restoration. The loads that can be

restored at each of this point are determined for step-by-step restoration. Since all the

loads follow the same CLPU model, loading produced by loads restored in different steps

would be different. However, the restored load and expected load at each of load-points

and their subsequent time instants can be evaluated and is done as follows:

From (1) after shifting origin:

( )( ) [ ( ) ] ( ), 1...T Ti ni D U DS T S S S S e u t T n mα− −∆= = + − −∆ ∀ ≥ (2)

From (2) 1 ln , 1...

iD

iU D

S ST TS Sα

⎡ ⎤⎛ ⎞−= − + ∆ ∀ ≥⎢ ⎥⎜ ⎟−⎢ ⎥⎝ ⎠⎣ ⎦

n m (3)

The discrete time instants Ti, determined from (3), are timing corresponding to

load-point i and these are used as steps during restoration process. The restored load Li at

a step i is given by the summation of loads restored at that particular step i. Consequently

as per assumption-2, loads restored at different steps contribute to the total load

depending on their step of restoration. This contribution is referred as participation factor

a (i.e. ratio of load at a step to its diversified value). The aij explains the contribution of

each load restored at step j in the total restored load Ri at step i, and set {SW(Li)} gives

the load locations of restored loads at step i. Therefore evaluation of participation factors

for various step-points needs to be performed, and is done as follows.

The restored load (R0) corresponding to {SW (L0)} at the initiation of restoration of

network (i.e. step-0) is given by (4).

0

0 *U

D

S 000R L a L

S= = (4)

Similarly, for an ith step (i.e. at Ti instant), the set of loads restored up to this step is given

by (5) and the total load restored up to this step is given by (6).

(5) 0 1{ ( )} { ( )} ... { ( )}iSW L SW L SW L⎡ ⎤∪ ∪ ∪⎣ ⎦

(6) 0 1

0 1 ... ii i i iiR a L a L a L⎡= + + +⎣ ⎤⎦

From (6) 0

ij

i ij

jR a L=

= ∑ (7)

Therefore, the total restored load sequence for m such steps can be expressed in matrix

form as [R](m+1) x1 and is formulated as in (8).

[ ] [ ] [ ]( 1 ) ( ) ( 1 )m m m

R A L× ×

=m ×

(8)

Participation matrix A gives the contribution of each set of load at step i which

was restored at step j. Since the loads at load-locations {SW (Lj)} restored at step j follow

the considered delayed exponent model, the contribution of these loads at step i can be

calculated from (1) by applying the appropriate value of time instants. However, the

contribution of a load will always be zero before it is restored, hence [A] is a lower

triangular matrix and rest of the elements of [A] can be determined from (9).

( )1 1 1... 1

0 1,...

i jT T TUD

Uij

D

S e jSSa S

i

i j

j i m

α⎧ ⎡ ⎤− − −∆⎛ ⎞ ⎢ ⎥⎪ ⎣ ⎦⎜ ⎟⎪ ⎜ ⎟⎝ ⎠⎪

⎪⎪⎨⎪⎪⎪⎪⎪⎩

+ − ∀ = −

=

∀ > +

=

jj L

(9)

The [L] is a column matrix with each element representing the load restored at the

corresponding step. A set of evaluated timing instances of switching along with their

corresponding participation matrix for six step-points used during this research work has

been presented in Table A-I.

The total expected load at a step is the total load in case if all the un-restored loads

prior to that step get restored at that step, and is given by (10).

0

iEi i

j

R a=

= ∑ (10)

,

, - before 1

ji j L is total load restored in step jji j L is total load remained un restored step j

∀ ≠

∀ = −

III. PROPOSED APPROACH

Most of the previous methods are cost based optimizations [7]-[10], and they do

not take into account the utility voltage limits and feeder thermal constraints. On the

other hand here an approach for step-wise restoration through consideration of load-

points on CLPU profile is proposed. The optimization in this proposed approach aims at

maximally utilizing the existing capacities with all the operational constraints being met.

In this load-point based approach evaluation of sufficient number of load-points (m) is

carried out initially, and corresponding to each of these load-points, discrete time steps

are determined. At each of these steps GA is applied to determine the optimal load for

restoration with no considered network constraint being violated. Consequently

application of GA for all such steps yields the entire sequence of restoration in step-by-

step manner.

A. Problem Formulation

The objective of utilizing GA for search is to obtain best utilization of the existing

system while meeting all network constraints. Therefore entire search is oriented towards

finding the minimum load rejection along with minimum switching operation. The

problem under study is a case of non-linear multi-objective constrained optimization.

This multi-objective problem is converted into a single objective problem form with

suitable penalties as to reflect the relative importance of associated elements, and this

given in (11).

= × + + + +LoadUnrestored

IV V VV V TV TV SWTotal

SMin f W W I W V W S W SWS (11)

Where, 1

σ==∑

Nbu

Unrestored i ii

S S

S

(12)

(13) 1

==∑

Nbu

Total ii

S

Objective function (11) is subjected to system operational constraints and they all need to

be satisfied. These constraints are given as follows:

1) Thermal constraint

{ } r a te di iI I i N b r≤ ∀ ∈ (14)

Where, Ii is the current in the branch i, Iirated is the rated current of branch i.

2) Bus Voltage constraint

Bus voltage at all buses of the network must be within permissible limit.

{ }min max iV V V i N≤ ≤ ∀ ∈ bu (15)

3) Substation transformer loading constraint

Total demand supplied by substation transformer has to be within maximum

loading limit of transformer for short durations so that there is no additional loss of

transformer life (16).

Maximum Transformer Loading: (16) MAXT TS K≤ TS

Loading limit of the forced air-cooled transformer corresponding for a delayed

exponential CLPU model for different outage-duration, and pre-outage and post-outage

loading conditions has been presented in [7]. The maximum supplying limits for one-

hour outage with different pre and post outage load conditions have also been determined

[7], [26].

4) Power flow constraint

The network power flow equations must be satisfied to ensure a stable steady

state operation.

B. Proposed Algorithm

Computational steps involved in determination of the optimal restoration

sequence of network using the participation factor approach is given following the next

sub-section. In this algorithm binary decision variables are used as the chromosome, and

they represent the status of the load connected at each of the bus. The fitness value

evaluated for each of this chromosome represents superiority of these probable candidate

solutions.

C. Genetic Algorithm

GA is a stochastic search technique based on the principle of natural evolution

[27]. GA works with a set of probable solutions/candidates rather than a single point and

is believed to acquire more likely a global optimum point. The fitness function acts as a

measure of evaluation of quality of the solution. The genetic operators such as crossover

and mutation are applied on these set of probable candidates, thereby allowing candidate

solutions to explore further in the search space. The binary encoded GA with each bit

representing the status of load connected to that bus is employed. GA here comprises an

elite preserving mechanism with two point crossover and swap type mutation to optimize

(11).

≤

U00

D

bu

j

i

Step 1:- S

Input m,a =S

set j = 0,LC = N ;

Generate: random population P ;

Step 2:- Evaluate: T (3);

Step 3:- if j m Then compute participation fact

;

for i = 0 to m by

k

ors of

{SW(L (9); set i = 1; Else network is not restored in 'm' steps;Step 4:- if j = 0 //Initiation of restoration Then go to next step;

)} for k = 0 to m using

k

ij

ij

ij

Else retain all{SW(L in

chromosomes of P ;

Step 5:-

Evaluate: fitness of each chromosome in P

using (11);Step 6:-

Apply : genetic operators P

)} for k = 0 to j-1

; set i = i

≤

∑

MAX

jk

k=0

Step 7:- if i Ge // End of step j Then go to Step 4 Else

LC = LC -

Step 8:- if LC = 0; //Restoration compl

+1;

;

No. ofelements of{SW(L )} ;

ete Then output the switching sequence; Else j = j+ 1 and go to Step 3;

Computational flow of the proposed approach.

IV. RESULTS AND DISCUSSIONS

The proposed approach is applied to two different network topologies including a

real network to demonstrate the effectiveness of the approach. The computation utilizes

following parameters, α= 1 hr-1, ∆T = 30 minutes= 0.5 hours and SU = 2.5 p.u., SD = 1

p.u.. The outage duration is considered as more than one hour, hence KTM=1.50 was

selected with no additional transformer loss of life. The number of steps m=6 (i.e. steps 0-

5) is used and corresponding time instances and participation matrix is presented in Table

A-I. The set of penalties/weights in the objective function for the present case-studies

[16], and the GA parameters used during the search for all the systems are given below.

Weights GA parameters

WLoad : 75.0 NP : 100

WIV : 500.0 Pc : 0.8

WVV : 10000.0 Pm : 0.05

WTV : 50.0 GeMAX : 100

WSW : 10.0

A. Test System-1

A 33-bus, 12.66 kV, capacitor compensated test system with an assumed sub-

station transformer capacity of 5.0 MVA was extracted from [18], [28]. The network

details and single line diagram of the distribution system is made available in Table A-II

and Fig. A3 respectively. Even though the network is optimally compensated, it faces

severe under-voltage problems during CLPU condition. The buses from 4 to 18 and 23 to

33 are severely affected by under-voltage problem during CLPU condition. Therefore to

utilize the available permissible voltage limit the sub-station voltage is raised to 1.045

p.u. However, even after elevating the sub-station voltage, buses 6 to 18 and 26 to 33

continued to violate under-voltage permissible limit. Hence the simultaneous restoration

of network gets restricted largely due to voltage limit violation. Conversely, during step-

wise restoration of the network with the proposed approach a minimum voltage of

0.9531p.u. was observed, with a network loading of 7.1294 MVA at step-0. The Table I

summarizes few of the above mentioned findings.

TABLE I Minimum voltage and percentage power loss in network during CLPU

Tail end voltage in p.u. (i.e. V18)

Percentage power loss

1. Sub-station voltage of 1.p.u. 0.7766 15.63

2. Sub-station voltage of 1.045p.u. 0.8364 13.71

3. Sub-station voltage of 1.045p.u. and at step-0 of restoration.

0.9531 5.72

The total restored load at each step and hence the entire restoration sequence is

presented in Table-II. The graphical view of such a stepwise restoration approach is

presented in Fig. 1. The entire network gets restored at step-5, with total restoration

duration of 234.07 minutes (i.e. ≈ 3 hr 54 minutes). Since, the capacitors are installed in

the network for reactive power compensation, the network was also tested against the

light loading condition for over-voltages, but no violations were observed.

TABLE II Stepwise restoration sequence of 33-bus system

Step i

Total Expected Load in MVA up to

step i

Total Restored Load in MVA up

to step i

Loads to be restored after step i

Switches operated at step

i

0 10.1321 7.1294 7,8,12,13,17,18,31-33 9 1 8.5819 6.8216 12,13,17,18,31-33 2 2 6.9298 5.7676 12,17,18,32 3 3 5.8184 4.9879 18,32 2 4 4.9220 4.8092 18 1 5 4.5026 4.5026 None 1

0

2

4

6

8

10

12

-20 30 80 130 180 230Time in Minutes

Load

in M

VA

Expected Load

Restored Load

Step 1 Step 2 Step 3 Step 4 Step 5

Fig. 1. Stepwise restoration of 33-bus network.

B. Test System-2

Finally the proposed approach has been illustrated on a 33kV, 41-bus real

network of a part of Bhopal city, India [19] with sub-station transformer rated capacity of

30.0 MVA is considered for illustration of the proposed approach. All calculations were

carried out at a load factor of 40%. The restoration sequence and the restored load at each

of the steps are presented in Table-III. The network gets restored at step-4 with a total

restoration period of 192.48 minutes (i.e. ≈ 3 hr 13 minutes). Fig. 2 illustrates step-by-

step restoration corresponding to this network.

TABLE III Stepwise restoration sequence of 41-bus system

Step i

Total Expected

Load in MVA up to step i

Total Restored Load in MVA up

to step i

Loads to be restored after

step i

Switches operated at

step i

0 35.456 27.957 7,16,30,32,41 5 1 29.838 23.535 7,41 3 2 24.125 19.351 41 1 3 21.039 16.106 41 0 4 18.577 18.577 None 1

0

5

10

15

20

25

30

35

40

-20 30 80 130 180Time in minutes

Loa

d in

MV

A

Expected Load

Restored Load

Step 1 Step 2 Step 3 Step 4

Fig. 2. Stepwise restoration of 41-bus real network.

C. Summary

The proposed approach has been demonstrated on two networks including a real

network. A brief summary of test systems is presented in Table-IV. Apparently major

portion of total load is restored during initial step of restoration; however the delay in

restoration is largely due to violation of operational voltage limits. In the proposed

approach, precedence constraint was relaxed and this leads to a higher percentage of load

restoration at the restarting of network. The GA convergence curve for test systems

during initial step (i.e. Step-0) of restoration is presented in Fig. A2.

TABLE IV Summary of the test systems

Test System

No. of steps for

restoration

Total restoration

time in minutes

Percentage of restored load in the initial step

Total no. of switching operations

33-Bus 5 234.07 70.364 18

41-Bus 4 192.48 78.916 10

Since, the existing methods of stepwise restoration of network do not consider all the

constraints which have been incorporated in the proposed approach and none of the

methods performs dispersed loads switching, hence no direct comparison can be made

between the two.

V. CONCLUSION

The proposed approach presents a scheme for stepwise restoration of distribution

network through optimal sequence of restoration under CLPU condition. The load-points

based stepwise restoration methodology presented here utilizes the system capacity more

efficiently than restoring the network in terms of section. The methodology effectively

exploits the load-wise switching of the network rather than section-wise switching.

The issue presented in this paper is of high relevance to distribution companies

striving to improve the reliability in energy deficient countries through effective

utilization of existing system. The simplicity of the proposed approach would attract

attention from distribution companies.

APPENDIX The time instances and their corresponding participation factor evaluated using

(3) and (9) for six step (0-5) restoration of network is given in Table A-I. The parameters

used during the evaluation are given in section-IV. The CLPU curve used for the

assessment of participation factors at different steps is given in Fig. A1.

TABLE A-I

Sample time instances and corresponding participation factors Participation factor for {SW(Lj)} restored at jth

instance Step (i)

Time instance

(Ti) j=0 j=1 j=2 j=3 j=4 j=5 0 0 2.50 0 0 0 0 0 1 54.33 2.00 2.50 0 0 0 0 2 95.92 1.50 2.24 2.50 0 0 0 3 137.51 1.25 1.62 2.24 2.50 0 0 4 192.48 1.10 1.25 1.50 1.99 2.50 0 5 234.07 1.05 1.12 1.25 1.50 2.24 2.50

SD

SU

Load

S(T

n) w

ith lo

ad-p

oint

s

Time (Steps)

1.25

1.5

2.0

T0 T1 T2 T3

1.101.05

T4 T5

T∆

ToutOutageoccurs

Initiation ofrestoration

Fig. A1. Evaluation of timing of steps and participation factors.

0 10 20 30 40 50 60 70 80 90 10010

15

20

25

30

35

40

45

No. of Generations --------->

Fitn

ess v

alue

----

----

>

33-Bus system41-Bus system

Fig. A2. GA convergence curve for the test systems at the initial restoration step.

Table A-II Line and Loading details of 33-Bus, 12.66kV system (Base MVA=1 MVA)

Line No

From Bus No

To Bus No

Resistance in ohm

Reactance in ohm Bus No Pload in

MVA Qload in

MVA

Capacitors added in

MVA 1 1 2 0.0922 0.047 1 0.000 0.000 0 2 2 3 0.493 0.2511 2 0.100 0.060 0 3 3 4 0.366 0.1864 3 0.090 0.040 0 4 4 5 0.3811 0.1941 4 0.120 0.080 0 5 5 6 0.819 0.707 5 0.060 0.030 0 6 6 7 0.1872 0.6188 6 0.060 0.020 0 7 7 8 0.7114 0.2351 7 0.200 0.100 0 8 8 9 1.03 0.74 8 0.200 0.100 0 9 9 10 1.04 0.74 9 0.060 0.020 0.100

10 10 11 0.196 0.065 10 0.060 0.020 0 11 11 12 0.3744 0.1238 11 0.045 0.030 0 12 12 13 1.468 1.155 12 0.060 0.035 0 13 13 14 0.5416 0.7129 13 0.060 0.035 0 14 14 15 0.591 0.526 14 0.120 0.080 0.300 15 15 16 0.7463 0.545 15 0.060 0.010 0 16 16 17 1.289 1.721 16 0.060 0.020 0 17 17 18 0.732 0.574 17 0.060 0.020 0 18 2 19 0.164 0.1565 18 0.090 0.040 0 19 19 20 1.5042 1.3554 19 0.090 0.040 0.100 20 20 21 0.4095 0.4784 20 0.090 0.040 0 21 21 22 0.7089 0.9373 21 0.090 0.040 0.100 22 3 23 0.4512 0.3083 22 0.090 0.040 0 23 23 24 0.898 0.7091 23 0.090 0.050 0.100 24 24 25 0.896 0.7011 24 0.420 0.200 0.100 25 6 26 0.203 0.1034 25 0.420 0.200 0.100

Line No

From Bus No

To Bus No

Resistance in ohm

Reactance in ohm Bus No Pload in

MVA Qload in

MVA

Capacitors added in

MVA 26 26 27 0.2842 0.1447 26 0.060 0.025 0 27 27 28 1.059 0.9337 27 0.060 0.025 0 28 28 29 0.8042 0.7006 28 0.060 0.020 0 29 29 30 0.5075 0.2585 29 0.120 0.070 0.200 30 30 31 0.9744 0.963 30 0.200 0.600 0.500 31 31 32 0.3105 0.3619 31 0.150 0.070 0.100 32 32 33 0.341 0.5302 32 0.210 0.100 0

33 0.060 0.040 0

Total Load in MVA

3.715

2.3

1.700

1 110

33

32

31

30

29

28

27

26

25

24

23

2221

20

19

98765432

18

17

16

15

14

13

12

1Sub-station

Fig. A3. Single line diagram of 33-bus distribution network.

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