A new algorithm for power distribution system planning

A new algorithm for power distribution system planning

Rakesh Ranjan a,*, B. Venkatesh a, D. Das b

a FET, Multimedia University, Ayer Keroh Lama, 75450 Melaka, Malaysiab Electrical Engineering Department, IIT Kharagpur, Kharagpur 721302, India

Received 3 August 2001; received in revised form 10 January 2002; accepted 25 January 2002

Abstract

In this paper, an attempt has been made to develop a new algorithm for distribution system planning. The proposed algorithm

does not require prior knowledge of candidate substation location and can automatically select location of a substation, the optimal

feeder configuration and the optimal sizes of branch conductors while satisfying constraints such as current capacity, voltage drop

and heuristic rules. Several algorithms are proposed for distribution systems planning. A generalized algorithm is developed for

obtaining the optimal feeder path and the optimal location of substation on minimum loss criterion. Heuristic rules are incorporated

in the above algorithm. Another algorithm is for branch conductor optimizations. Modified load flow method is also presented in

the paper, which can handle composite load models. The load flow algorithm is used for solving radial distribution networks (RDN)

and branch conductor optimization algorithm. The load flow algorithm and branch conductor optimization techniques are used as

subroutine in the generalized distribution systems planning algorithm. Through numerical example the validity of proposed method

is verified. # 2002 Elsevier Science B.V. All rights reserved.

Keywords: Distribution systems; Load flow; Conductor optimization; Expert system

1. Introduction

The problem of distribution system planning is to find

the optimum location of the substation and the opti-

mum feeder configuration to connect the loads to the

substation. Many approaches to solve the distribution

system planning have been proposed [1�/9] but they

assume that new installation candidates are known

before hand. However, the assumption of the known

candidate locations of feeder or substation may simplify

the problem but can not give the optimum solution. Few

other methods [10�/12] have also been reported to find

optimum distribution system plan. All these methods

are based on mathematical programming techniques

such as branch and bound technique and mixed integer

programming method. For a given forecasted load,

these methods can yield feeder configuration and

substation location. However, all these methods fail to

incorporate heuristic rules. For distribution systems

planning or feeder expansion in the urban area it is

very difficult to find the space for substation and feeder.

Therefore, finding the optimal candidate location itself

will not suffice to solve the problem, heuristic rules need

to be incorporated for a feasible optimal distribution

system planning. Some researchers have made an

attempt to develop expert system for distribution

systems planning. Wong and Cheng [13] have proposed

artificial intelligence approach for load allocation in

distribution system. Hsu and Chen [14] have proposed

knowledge based expert system for distribution systems

planning. Braunner and Zobel [15] have also proposed

distribution systems planning using expert systems.

In the present work a generalized distribution systems

planning algorithm has been developed. Three algo-

rithms are presented for generalized distribution systems

planning. The first algorithm determines the optimal

feeder configuration. Second algorithm finds optimum

location of substation. A third algorithm optimally

selects branch conductor sizes. A load flow algorithm

that can handle composite load models is also presented

in the paper. Load flow algorithm is highly useful for

optimal feeder configurations, branch conductor opti-

mizations and system solutions.* Corresponding author. Fax: �/606-231-6552.

E-mail address: [email protected] (R. Ranjan).

Electric Power Systems Research 62 (2002) 55�/65

www.elsevier.com/locate/epsr

0378-7796/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 3 7 8 - 7 7 9 6 ( 0 2 ) 0 0 0 4 4 - 5

mailto:[email protected]

2. Modified load flow method

Load Flow algorithm developed by Das et al. [16] is

modified to incorporate composite load model. Theconvergence criterion is such that if, the difference of

voltage at every node in successive iterations is less than

0.0001 p.u. the algorithm has then converged. The

modified load flow algorithm does not require any

specific branch and node numbering scheme, however,

a simplified numbering scheme, which can be easily

understood, is used and discussed in Section 2.3.

2.1. Circuit model

In this section, a circuit model of Radial Distribution

Network (RDN) is presented. It is assumed that three-

phase RDN is balanced and can be represented by

equivalent single line diagram. Line shunt capacitance at

distribution voltage level is negligibly small. Fig. 1

shows the single line diagram of a sample RDN, andthe electrical equivalent of one branch of RDN is shown

in Fig. 2

2.2. Mathematical model of radial distribution networks

Mathematical model of RDNs can easily be derived

from Fig. 2 [16]:

I(j)�½V (m1)½ � d(m1) � ½V (m2)½ � d(m2)

Z(j)(1)

and,

P(m2)� jQ(m2)�V�(m2)I(j) (2)

where Z (j)�/R (j)�/jX(j), m1 and m2, the sending and

receiving end nodes, respectively; P(m2), sum of the real

power loads of all the nodes beyond node m2 plus the

real power load of the node m2 itself plus sum of the real

power losses of all the branches beyond node m2;

Q (m2), sum of the reactive power loads of all the nodes

beyond node m2 plus the reactive power load of thenode m2 itself plus sum of the reactive power losses of

all the branches beyond node m2.

From Eqs. (1) and (2) we can get:

½V (m2)½�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiB(j)�A(j)

p(3)

where

A(j)�P(m2)R(j)�Q(m2)X (j)�0:5½V (m1)½2 (4)

B(j)�A2(j)�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZ2(j)(P2(m2)�Q2(m2))

p(5)

Real and reactive power losses in the branch j are:

LP(j)�R(j)(P2(m2) � Q2(m2))

½V (m2)½2(6)

and

LQ(j)�X (j)(P2(m2) � Q2(m2))

½V (m2)½2(7)

Since in this paper composite load modeling is

considered for the systems, therefore, flat voltage start(jV (i)j�/1.0 p.u. for i�/1. . .NB) is incorporated in the

algorithm. Using Eq. (3) voltage at each receiving end

node is computed. The new voltage is compared with the

old voltage in each iteration, and if the difference is less

than 0.0001 p.u. for each node the algorithm is assumed

to have converged.

½V (m2)�V (m2)?½B0:0001 p:u: for m2�1 . . . NB (8)

2.3. Node and branch numbering scheme

No systematic numbering scheme of laterals, sublat-erals, branches and nodes is required for the proposed

load flow solution of RDN. The numbering scheme does

not affect the convergence of algorithm or its computa-

tional efficiency. However, the numbering scheme

adopted for the program is presented considering Fig.

3 as test system. First, the nodes in the main feeder

(feeder starting from substation node 1) are numbered.

As it is seen in Fig. 3, these nodes are numbered 1, 2, 3,4, 5 and (1), (2), (3), (4) are branch numbers. The node

numbering and branch numbering starts from substa-

Fig. 1. Radial distribution networks.

Fig. 2. Equivalent of Fig. 1.

Fig. 3. Numbering scheme of RDN.

R. Ranjan et al. / Electric Power Systems Research 62 (2002) 55�/6556

tion that is assigned node number 1. Thereafter, the

nodes on the main feeder other than substation are

explored for the laterals. In Fig. 3 node 2 is having a

lateral. Then, node numbers and branch numbers areassigned starting from the parent node {node 2} of the

lateral 6, 7 and 8 are node number of the first lateral

from the substation and (5), (6) and (7) are the branch

numbers. Further, lateral under consideration is ex-

plored for the sublaterals, it is seen that node 7 is having

sublateral. Number is assigned for the sublateral node

starting from child node (node 7) as 9 and branch

number as (8). Again the main feeder is investigated forthe laterals and node 3 is observed to have lateral. Node

numbers 10 and 11 are assigned to the nodes ahead of

parent node (node 3) and branch numbers are (9) and

(10), respectively. There is no sublateral seen. So other

nodes of main feeder is examined and it is found that

process of node numbering is complete as there is no

further lateral emerging from the main feeder.

2.4. Load modeling

The balanced loads can be represented either asconstant power, constant current, and constant impe-

dance or as exponential load. The exponential loads are

basically combination of these based on proportion of

the type of consumer loads. At each node of the

distribution network the proposed algorithm is capable

of performing load flow calculations considering either

of load or combinations of all the above said loads. The

loads are modeled as:

P0(m2)�P(m2)(a0�a1V�a2V 2�a3V e1) (9)

Q0(m2)�Q(m2)(b0�b1V 2�b2V 2�b3V e2) (10)

In the algorithm e1�/1.38 and e2�/3.22 are consid-

ered for exponential load [17]. The first term of Eqs. (9)

and (10) represents constant power load, second term

represents constant current load and subsequent terms

represent constant impedance and exponential load.P (m2) and Q (m2) is the total real and reactive load at

the receiving node m2. For all the cases loads are

modeled such that:

a0�a1�a2�a3�1:0 (11)

b0�b1�b2�b3�1:0 (12)

2.5. Load flow calculation

The first step of load flow calculation is to find P (m2)

and Q (m2). A computer algorithm is developed tocompute it internally. Considering m2�/2 mathematical

expression for P (m2) and Q (m2) computation is given

below:

P(2)�XNB

i�2

PL(i)�XNB�1

i�2

LP(i) (13)

Q(2)�XNB

i�2

QL(i)�XNB�1

i�2

LQ(i) (14)

Once P (m2) and Q (m2) is computed, they are

updated for the composite load model by Eqs. (9) and

(10). Initially constant voltage for all the nodes is

assumed and real and reactive losses are set to zero.

After that, voltage at each node is calculated using Eq.

(3) and real and reactive power loss is calculated. Afterthe new voltage jV (i)?j of all the nodes (i�/1. . .NB) are

computed, convergence of the solution is checked from

Eq. (8). If it does not converge whole process is repeated

with the new set of voltages until convergence criterion

is satisfied.

3. Optimal branch conductor selection algorithm

Selection of optimal branch conductor size is extre-mely important in distribution system planning. The aim

of optimal conductor size selection is to design a feeder

so as to minimize an objective function, which is sum of

capital investment and capitalized energy loss costs for

the feeders. Optimal size of the branch conductor is

obtained using the load flow technique described in

Section 2.

3.1. Objective function

The basic problem is that of selecting a conductor

type for each branch of radial distribution feeder such

that the sum of the cost of capital investment and cost of

real power losses are minimized while maintaining an

acceptable voltage level.

The Levelized annual cost for the real power loss in

branch j can be calculated by:

c(j)�Kp�LP(j)�LP(j)�KE�T�Lsf (15)

where, LP(j) is real power loss in branch j ; Kp, levelized

annual demand cost of losses (Rs/kW); KE, energy cost

of losses (Rs/kWh); T�/8760 h and Lsf is loss factor.

While computing the annual cost by Eq. (15) load

growth is considered as:

Load�(1�g)n

where, g�/7% annual growth rate and n is the number

of years.

The levelized annual cost of capital investment for

branch j is:

z(j)�a�A(j)C�LEN(j) (16)

where, C is cost of the line (Rs/mm2 per Km); A (j ), the

R. Ranjan et al. / Electric Power Systems Research 62 (2002) 55�/65 57

cross sectional area of branch j (mm2); LEN(j ), length

of branch j and a is the carrying charge rates (feeder).

The objective function of branch j can be:

j(c; z)�c(j)�z(j) (17)

3.2. Constraints

1) Voltage: The voltage at every node in the RDN

must be above the acceptable voltage level i.e.

½V (i)½�Vmin for all i

2) Maximum current carrying capacity: Current flow-

ing through branch j with k type of conductor

should be less than the maximum current carrying

capacity of k type conductor. i.e. jI(j , k )jB/

CMAX(k ).

Optimal selection of conductor is obtained by branch

wise minimization technique using load flow algorithmdescribed earlier. Here all necessary steps for optimal

conductor selections are summarize for branch j :

1) Compute P (m2) and Q (m2) using Eqs. (13) and

(14).

2) Obtain P0(m2) and Q0(m2) using Eqs. (9) and (10)

for different load models.

3) Change the variables P (m2)�/P0(m2) and

Q (m2)�/Q0(m2).

4) Compute A (j) and B (j) using Eqs. (4) and (5) andthen compute jV (m2)j using Eq. (3) for all types of

conductor.

5) Compute real and reactive power loss LP(j ) and

LQ(j) using Eqs. (6) and (7) for all type of

conductors.

6) Compute c (j ) and z (j) using Eqs. (15) and (16) and

then compute j (c , z ) using Eq. (17) for all types of

conductor and store the values in the name ofvariablej j (j , k ) for k�/1, 2. . .

7) First find the minimum value of j j (j , k ) and check

whether voltage and current constraints are satisfied

or not. If constraints are satisfied then choose the

corresponding type of conductor. Otherwise next

lowest value of j j (j , k ) should be considered to

satisfy the constraints and so on till optimal branch

conductor is chosen optimally. This process isrepeated for all branches.

4. Expert system

Fig. 4 shows the architecture of proposed expert

system. It comprises rule base and database. Databaseincludes the load data, location of load points and

obstacles. Rule base includes the heuristic rules. Infer-

ence machine is designed to reach a proper distribution

network plan based on the data and rules in the

knowledge base.

5. Optimum location of substation

Total KVA load fed through a particular node is

TKVA (i) for i�/2. . .NB. TKVA (i) is always available

from the load flow computation. Optimal location of

substation is computed through an iterative algorithm.It is worth mentioning here that substation is chosen as

node 1 (i.e. S�/1). By minimizing real power loss, the

optimal location of substation {X (s ), Y (s )} for substa-

tion S , can be computed through the following iterative

algorithm [14,18]:

X (s)�

XNB

i�2

W (i)X (i)

XNB

i�2

W (i)

; Y (s)�

XNB

i�2

W (i)Y (i)

XNB

i�2

W (i)

(18)

where X (i), Y (i)�/X and Y coordinates of the load

point for i�/2. . .NB.

W (i)�TKVA(i)R(KT)

(½V (i)½2Ds(i)(19)

KT�/K (i�/1) stores optimum type of branch conductor

for i�/2. . .NB, which is obtained using load flow and

optimal branch conductor algorithm as described in

Sections 2 and 3.

Ds(i)�f(X (s)�X (i))2�(Y (s)�Y (i))2g1=2(20)

New initial location of the substation is chosen as:

X (s)�

XNB

i�2

X (i)P(i)

XNB

i�2

P(i)

; Y (s)�

XNB

i�2

Y (i)Q(i)

XNB

i�2

Q(i)

(21)

6. Description of the algorithm for optimal feeder path

For simplicity, only the investment costs of feeder are

compared for each distribution system plan. As the

investment cost is proportional to the feeder length, the

problem of minimizing investment cost reduces to that

of minimizing feeder length. Minimal path algorithm is

extremely suitable for distribution system planning.Taking nine load points shown in Fig. 5 as an example

whose X , Y coordinates are known it is logical to start

computation with new substation.


6.1. Single feeder case

For single feeder case it is assumed that only one

feeder is emerging from the new substation. The set of

‘connected nodes’ S contains one node (new substation)

initially. All the other load points are in set of

unconnected nodes, i.e. S̄ :/

S�/{new substation}.

/S̄/�/{all the load points}.

The distance from any node in S̄ to the node in S is

computed and the one with shortest distance is added to

S . Let load point 5 be this node. Connect new

substation to node 5, the new set S and S̄/ will be:

S�/{new substation, 5}.

/S̄/�/{1, 2, 3, 4, 6, 7, 8, 9}.

A new feeder connecting the new substation and node

5 is implied in this process. Now compare the distancefrom any node in S̄ to any node in S . The node in S̄/ with

the shortest distance is added to S . Let load point 4 be

the node. Connect node 5 to 4. The set S & S̄/ will be:

S�/{new substation, 5, 4}.

/S̄/�/{1, 2, 3, 6, 7, 8, 9}.

Again compare the distance from any node in S̄ to

any node in S and find the minimum distance. Say

shortest distance exists between node 5 and 9. Therefore,

connect node 5 to 9. Now,

S�/{new substation, 5, 4, 9};

/S̄/�/{1, 2, 3, 6, 7, 8}.

This procedure is repeated until all the load points are

connected i.e. all the nodes are in S and S̄/ � /f (null). Itis worth mentioning here that through out the procedure

all the heuristic rules are satisfied.

6.2. Two feeder case

For this case it is assumed that only two feeders are

emerging from the new substation. The distance from

any node in S̄ to the node in S is computed and the two

nodes, which are close to the new substation (two

shortest distances), are added to S i.e. for two feedercase:

S�/{new substation, new substation}.

And say two nodes that are close to substation are 4

and 5, respectively.

Therefore,

S�/{(new substation, 4), (new substation, 5)};

Or S�/{S1, S2}.

where,

Fig. 4. Knowledge based expert system.

Fig. 5. Distribution system load points location (Taken as an

example).


S1�/{new substation, 4};S2�/{new substation, 5}.

Connect new substation to node 4 and new substation

to node 5. Thus:

/S̄/�/{1, 2, 3, 6, 7, 8, 9}.

Now compare the distances from any node in S1 and

S2 to any node in S̄ and find out the shortest distances,

say node 3 is nearest to node 4 (i.e. shortest distance is

D43) and node 9 is nearest to node 5 (i.e. shortest

distance is D59). Now find out minimum of D43 and

D59. Say D59 is minimum, so node 5 belongs to set

S2.Therefore,

S1�/{new substation, 4};

S2�/{new substation, 5, 9}.

Now connect node 5 to 9.Thus:

/S̄/�/{1, 2, 3, 6, 7, 8}.

Again compare the distances from any node in S1 and

S2 to any node in S̄/and find out the shortest distances.

Say node 3 is nearest to node 4 (i.e. shortest distance is

D43) and node 7 is nearest to node 9 (D79) and node 2 is

nearest to node 5 (D25). Find out minimum of the D43,

D79 and D25. Say D43 is minimum; connect node 4 to

3. Now node 4 belongs to set S1. Therefore,

S1�/{new substation, 4, 3};S2�/{new substation, 5, 9}.

and

/S̄/�/{1, 2, 6, 7, 8}.

This process is repeated until all load points areconnected, i.e. all the load points are in S and S̄/ � /f

(null). Through out the process all the heuristic rules are

checked.

Based on the procedure described above a generalized

algorithm for optimal feeder path has been developed

which can handle any number of feeder emerging from a

new substation and which also satisfies all the heuristic

rules.

7. Heuristic rules for distribution system planning

Following heuristic rules have been used for present

study:

. Distribution line is curved or discarded if there is a

big pond between two load points.

. If the line passes through cotton industries, it iscurved or discarded.

. If the line passes through commercial plantation area,

it is curved or discarded.

Fig. 6. Load points location (S/S not shown).


Fig. 7. Optimal feeder configuration (Single Feeder Case).

Fig. 8. Optimal feeder configuration (Double Feeder Case).


. If the line passes through commercial complex, it is

curved or discarded.

. If the line passes through the residential area, it is

curved or discarded.

. Substation location is discarded if the land is too

expensive.. Substation location is discarded if it creates social

and environmental problem.

. Substation location is discarded if it falls near to

school; children play ground or boarding.

. Substation location is discarded if it falls nearer to the

shopping mall.

. Substation is discarded for any geographical installa-

tion restrictions.

8. Complete algorithm for distribution system planning

All necessary steps for the distribution systems

planning are summarized below:

1) Assume any initial location of substation.

2) Obtain optimal feeder path using optimal feeder

path algorithm.

3) Obtain load flow solution and optimum branch

conductors using load flow and optimum branch

conductor selection algorithm. Also compute total

real power loss {TP (1)}.

4) IT�/1.

5) Calculate substation location using Eq. (18).

6) Obtain optimal feeder path using optimal feeder

algorithm.

7) Obtain load flow solution and optimum branch

conductors using load flow and optimum branch

conductor selection algorithms and compute {TP

(IT�/1)}.

8) DIF�/jTP (IT�/1)�/TP (IT)j.9) IF DIFB/o go to Step-11.

10) IT�/IT�/1, go to Step-5.

11) Check whether heuristic rules for substation loca-

tion are violated or not? If rules are violated then

Fig. 9. Optimal feeder configuration (Three Feeder Case).

Table 1

Comparative results of single, double and three feeder configurations

Total length of feeder (km) Real power loss (kW) Reactive power loss (kVAr) jVminj in the feeder

Single feeder 97.63 173.50 125.06 jV33j�0.84916

Two feeder 99.00 56.18 37.49 jV33j�0.95282

Three feeder 100.67 50.12 31.43 jV33j�0.96081


Fig. 10. Sub-optimal feeder configuration (Three Feeder Case).

Fig. 11. Optimal feeder configuration considering load growth after Vth year (Three Feeder Case).


compute new initial location of substation using

Eq. (21) and go to Step-2 otherwise go to Step-12.

12) Final Distribution plan is obtained.

9. Example

A study system of 54 nodes is considered. The

substation is numbered as node-1. Whole service area

is divided into several service squares and their X �/Y

coordinates are known. Load points data are given in

Appendix A. Fig. 6 shows the location of load points.

For the study four different types of conductor Squirrel,Weasel, Rabbit and Raccoon are considered. Computer

simulation has been carried out for single feeder, two

feeder and three feeder configurations of RDNs. It is

mentioned that for all the calculation constant power

loads are considered. Figs. 7�/9 shows the single, double

and three feeder radial distribution systems obtained by

the proposed algorithm. A comparison of results is given

in Table 1.Comparing the results it is observed that utility

should use two or three feeder configurations, since

power losses and total length of the feeder improves

significantly. Two and three feeder configuration shows

close competition as losses and voltage profile improves

but total feeder length increases. However, for over all

reliability considerations three feeder configurations are

finally selected as optimum planned radial distributionsystem. One of the suboptimal results is also presented

in Fig. 10 as reference for comparative study. After

incorporation of load growth of 7% in the algorithm the

simulation results indicate no change in the planned

distribution systems until fourth year. However, in the

fifth year due to load growth some of the feeder

capacities becomes inadequate and thus replacement of

those feeders by conductors of higher ratings is sug-gested in Fig. 11.

10. Conclusions

In this paper an attempt has been made to develop a

generalized algorithm for distribution system planning.

Novel algorithm has been developed for optimum feederpath configuration and optimum location of substation

based on minimum loss criterion. Proposed method is

able to determine the least cost plan by searching

through all the possible candidate locations and it also

satisfies constraints such as current capacity, voltage

drops and heuristic rules. Inference machine has been

developed to reach feasible distribution plan based on

data and heuristic rules in the knowledge base. Modifiedload flow algorithm incorporating composite load

model is developed; the load flow method is repeatedly

used to find optimum conductor size of branches and

optimum location of the substation. Three different

algorithms namely optimum location of substation,

optimal feeder path and optimal branch conductor

selection has been developed for the proposed methodof distribution system planning. Load growth is also

incorporated in the algorithm to compute future repla-

cement/reinforcement of line due to inadequate size of

conductors. The developed algorithm has been imple-

mented on PIII in C�/�/ and several realistic problems

have been tested. From the numerical results it is

verified that the proposed algorithm obtains an accep-

table distribution plan that satisfies current and voltageconstraints and the heuristic rules.

Appendix A: Data for load points

Node num-

ber

X coordinate Y coordi-

nate

Load

(kVA)

1 (substa-

tion)

To be obtained

from the proposedalgorithm

2 1.00 2.00 25.0

3 2.00 15.00 25.0

4 3.00 4.00 25.0

5 4.00 12.00 50.00

6 5.00 11.50 63.00

7 6.00 10.00 63.00

8 7.00 7.00 50.009 1.50 5.50 25.00

10 11.50 13.50 16.00

11 7.50 17.50 16.00

12 8.50 15.50 25.00

13 12.50 10.50 50.00

14 11.00 17.50 63.00

15 8.00 7.50 63.00

16 11.00 6.00 25.0017 5.50 5.50 16.00

18 3.50 8.50 16.00

19 13.00 8.00 16.00

20 14.00 13.00 63.00

21 16.50 14.00 25.00

22 5.50 17.00 25.00

23 20.50 12.00 50.00

24 8.00 9.00 100.0025 5.00 7.00 100.00

26 8.00 5.50 100.00

27 10.50 8.00 50.00

28 10.50 15.00 50.00

29 9.00 19.00 25.00

30 7.50 19.50 63.00

31 5.50 19.50 63.00

32 3.00 17.50 25.0033 13.00 15.50 50.00

34 14.00 16.50 50.00

35 12.50 19.00 25.00


36 11.00 20.00 25.00

37 5.00 15.50 50.00

38 2.00 10.50 50.00

39 3.00 3.50 63.0040 6.00 4.00 25.00

41 9.00 4.50 25.00

42 14.00 11.50 50.00

43 15.00 10.00 50.00

44 15.00 14.50 25.00

45 15.50 12.50 25.00

46 12.00 12.00 63.00

47 14.50 7.50 63.0048 13.50 6.00 25.00

49 13.00 4.50 16.00

50 13.50 18.00 16.00

51 4.00 5.00 25.00

52 9.50 6.50 16.00

53 9.50 17.00 25.00

54 12.00 2.50 50.00

Power factor of the load 0.75Demand factor 1.00

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A new algorithm for power distribution system planning

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