Optimal planning of distribution substation locations and sizes — model and algorithm

0142-0615(95)00064-X

Electrical Power & Energy Systems, Vol. 18, No. 6, pp. 353-357, 1996 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights rewved 0142-0615/96/$15.00+0.00

Optimalplanningof distribution substationlocationsand sizesmodeland algorithm Dai Hongwei, Yu Yixin, Huang Chunhua, Wang Chengshan and Ge Shaoyun Department Automation,

of Electric:al Power Engineering and Tianjin University, Tianjin 300072, PRC

Xiao Jian, Zhou Yi and Xin Rui Tianjin

Electric Power Bureau, Tianjin

300070,

PRC

and capacities of future MV distribution substations (generally 110 kV/lO kV, 35 kV/lO kV), which act not only as source points of the LV system, but also load points of the HV system. A large number of factors will be involved in such studies, and the wide range of alternatives usually open to power system planners makes the determination of an optimal plan very difficult. Especially in recent years, rising growth rates, high load densities, ecological considerations, and the scarcity of available land in urban areas have thrust the problem of optimal substation placement beyond the resolving power of the unaided human mind. During the last two decades a number of computerized technique&’ ’ have been developed that can assist in producing optimal distribution substation plans. Many of these techniques contribute measurably to planning efforts. They differ from each other due to the representation of more or fewer problem characteristics and the use of various solution algorithms. However to the authors’ knowledge, there has been no technique developed that does not require the candidate substation locations. Almost all techniques treat the set of potential locations for building distribution substations in the planning period as input data. But in fact, there are so many substation potential locations in the service area of a power distribution system that it is very difficult to accurately define the set of candidate substation locations. In order to overcome this, the authors describe a new model, which can automatically select the optimal sizing and location of distribution substations without requiring any candidate substation locations. In Section II, the distribution substation planning problem model is fully explained. Based on this model, a solution algorithm is shown in Section III. Section IV shows an example that proves the validity and effectiveness of the algorithm.

A new method is presented in this paper to solve the optimal planning problem of distribution substations. The procedure proposed here does not require candidate substation locations and can automatically select the optimal sizes, locations (and service areas of substations in power distribution systems. In addition, an efective solution algorithm is also presented. Copyright 0 1996 Elsevier Science Ltd. Keywords:

expansion planning,

distribution expansion,

mathematical programming

I. Introduction It is the primary concern of power distribution system expansion planning to ‘determine the number, locations and sizes of future distribution substations. In almost all urban areas in China, there are three voltage levels of electric power system (HV system, MV system and LV system) to distribute power to customers. The determination of locations and sizes of HV substations (generally 220kV/110kV,220kV/35kV,500kV/110kV,...),which are source nodes of the whole urban power system, will not be discussed in this paper, as they mainly depend on factors associated with .the power transmission network. The LV substations (generally 10 kV/380 V) are source nodes of the customers, and load nodes of the MV power distribution system. Owing to the large number of LV substations and the difliculty of exactly forecasting the locations and amount of 380V customer loads, the determination of their locations and sizes will not be discussed in this paper either. The problem discussed in this paper is the determination of the number, locations Received 31 May 1994; accepted 1 June 1995

353

Optimal planning of distribution

354

II. Distribution substation planning model What is required of distribution planners is to determine the load magnitude and its geographic location; then the distribution substations must be placed and sized in such a way as to serve the load at maximum cost effectiveness by minimizing feeder losses and construction costs while considering the constraint of service reliability. In this paper, the service area of the power distribution system is divided into a grid of small squares called ‘sectors’, each having a load point in its centre. The load magnitude of each sector is the product of the load density and the area of the sector. From each distribution substation, several feeders distribute power to load points. A substation’s service area is defined by the area covered by its feeders. It is assumed that there is a feeder between the substation and a load point served by it. Thus, the general substation locating and sizing problem is formulated as follows: minC=Ci+Cz s.t

c iGi

(1)

Wj 5 Si e(Si)cosp

i= 1,2,...,N

substations:

Dai Hongwei

After the area of each sector has been adjusted so that the load magnitude in each sector is roughly equal, function C, can be linearized to:

Thus, the optimization problem (1) can be formulated as follows: min C = cfi

Wjdq

(Si) + 7 F, r

i=l

i=l

jEJi

s.t. CWj
i=1,2,...,N

As Si is a discrete variable, n is an integer a set, and xi and yi are both continuous optimization problem (2) is so complicated be solved. In order to simplify the problem, is assumed. cw-CP +IT (1)

variable, Ji is variables, the that it cannot the following

cos Cp

C W = the total amount of loads CP = the total active power capacity of existing substations IT = a positive integer constant

is the investment cost and operational substations,

cost of future

E Q} (2) Smin = n$n{SilS, I where Q is the set of proposed substation capacities to be built in the planning period. (3) K={SiISi~QorSi=O,i=1,2

is the cost of energy losses on the feeders Si = e(SJ = n= m = N = M = g(Si) = u(SJ = Wj = Ji = r. = LY= dii =

(e)

jCJ,

zhzresmin

where

et al.

capacity of substation i loading coefficient of transformers in substation i number of future substations expected economic life of substations (years) total number of existing and future substations total number of load points investment cost of future substation i operational cost of future substation i load magnitude of load point j set of load points which is served by substation i annual interest rate cost coefficient d(xi - Xj)2 + (vi - Y~)~]is the distance between substation i and load point j.

,..., nt}

Thus, the optimization problem can be expressed abstractly as: from set K, to find a subset T which is a combination that is subject to the constraint (e) and minimizes the objective function. This process can be divided into two sub-processes, namely: the combining process and the locating process. (1) Combining process This process can be expressed as: from set K, try to find a proper combination T” = {SI, S,, . . . , S,,,} which obeys constraint (e) and minimizes the objective functionf( Ti). It can be formulated as:

(2) Locating process For every unique subset Ti E K, the expressions

Let

fl(Si) = idsi)

eh(SJ

f-0(1+ roY cl

+

ro)~

_

1

+

UC&j

the function Ct can be expressed as: Cl

=

-&fled i=l

Meanwhile, it can be assumed that:

and

&*e(&).coscp,i=

in equation (2) can be determined and will be expressed as CONSTl and CONST2 respectively in the following equation (3). Therefore, the problem in the locating process is to calculate the sites of future substations for every subset Ti. This can be formulated as follows: minC=

CONSTl +yFy,

Wjdv=:f(Ti)

i=l

W=eWj/M, i=l

+f=CKW.

1,2,...,N

i=l

s.t.

c jcJi

Wj 5 CONST2

jcJi

i= 1,2,...,N

(3)

Optimal planning of distribution substations: Dai Hongwei et al.

In the combining process, the heuristic combination optimization algorithm14 is employed, and the multi-source locating algorithm’s is used in the locating process. By these means, the complex original process can be decomposed into many simple processes, which reduce the computational burden considerably. All these algorithms will be described in Section III.

III. Solution algoirithm Based on the solution strategy described in Section II, an algorithm developed in this paper is illustrated in Figure 1. Note that this algorithm is made up of three parts as follows. I I I .l Heuristic combination optimization algorithm

This algorithm is used in the combining process presented in Section II. It involves the following steps.

(1) Form a feasible solution T, which subjects to the constraint. (2) Update some elernents in set T, i.e. while some elements x1, x2, . . . , xk in Set T are ‘unavailable’ or update T with a feasible set ‘unsatisfactory’, T’ = b71,~2,. . . ,~itr . . .}, which is found from set (K-T) and is subject to the constraint (e). (3) If a feasible set T’ can be found and f( T’)
Forming

the

lritiai

Feasible

I

piiz+m

I I I I

I I

Solution

I

-1

Figure 1. The solution algorithm

355

assumed that: n2 =

(CW

-

~~)I&,,

COS cp),

where s max= m;xWS,

E Q).

I

Thus the number of future substations n should be 1125 n 5 ni, then the initial feasible solution can be obtained as follows Set n = n2. Set the capacity of each future substation to S,,. Calculate the location of each future substation with the multi-source locating algorithm. Calculate the sum of the loads’ magnitude in each future substation’s service area XLi, i = 1,2,. . . , n. Then determine the capacity of each future substation as follows:

s.t.sk >xLk/cosp

i= 1,2 ,..., n

then (5) Calculate the objective function f, if f < fmin fmin = f,otherwise go to step (6). (6) Set n = n + 1, if n > q, then stop, otherwise go to step (2). Thus the set T = { S1, S2, . . . , S,}, which corresponds to the objective function fmin, is the initial feasible solution obtained in this procedure. III.3 Multi-source locating algorithm This algorithm is used in the locating process described in Section II, in which it is assumed that each set . , S,,} is known. Thus the locating process T={S,,S2,.. can be formulated as follows: min C’ = 2 i=l

C

Wjdq

jEJi

s.t.CWj
i=1,2

,..., N

jcJi

Obviously, the problem (4) is a constrained multi-source locating problem13, in which not only the locations of future substations should be calculated, but also loads should be distributed to the ‘nearest’ substations and subject to the constraint. In order to solve this problem, the SDA (siting and distributing alternatively)13 method is adopted, which is divided into the following two processes

(1) Distributing process Suppose that locations of substation (xi,&), i= 1,2,... , N, are already known, the remaining variables that should be determined in this process aresetsJj,i= 1,2,... N. That is to say, distributing loads to the ‘nearest’ substations. (2) Siting process Suppose that sets Ji, i = 1,2,. . . , N are already known, the remaining variables that should be determined in this process are the locations of the substation i, i.e. (xf+‘,#‘), each is the central point of loads set Ji, Both the distributing process and siting process are iterated until the solution of the problem converges.

356

Figure 2. Overview

Optimal planning

of distribution

of the supply area

substations:

Dai Hongwei

et al.

Figure 4. Plot of automation

plan

The distributing process which is a’typical transportation problem, can be solved by the general transportation algorithm. IV. Test results Based on the model and algorithm presented in this paper,. a complete planning package has been developed by Tianjin University and Tianjin Electric Power Bureau as a part of the City Network Planning Package CNP. This software has been used for planning several actual distribution substations in China. Owing to space limitations, only one example will be selected to illustrate the effectiveness of the procedure. Figure 2 shows an overview of the supply area of a power distribution system which covers about 500 km2. The city, which lies east of a river and between a mountain and another river, is supplied by 220 kV infeeding substations. The urban district will cover 162 km2 with about one million people in the year 2000. For regional distribution networks, 1lO/lO kV-substations are used to supply LV (10 kV) distribution systems. The load density in this city in the year 2000, with the peak value of 58.8 MW/km2, is shown in Figure 3. It can be found that some new substations must be constructed in the planning period to cope with the increase of power demand. Therefore,

Figure 5. Plot of manual plan

the software CNP has been adopted and the results of a 110 kV distribution substation expansion plan (named the automation plan) are shown in Figure 4. To compare this expansion plan, Figure 5 shows another plan made by an experienced planner (named the manual plan). Table 1 describes Ci , C2 and C in equation (1) for both plans. Comparison shows that the plan made by manpower is more expensive than that given by the software. It is worth noting that the automation plan has been approved by many planning engineers. Some substations from that plan are being constructed in the power distribution system. V. Conclusion A new model is presented here to select automatically

the optimal size and location of substations in the power distribution system, which does not require the candidate substation locations. The solution method is based on the decomposition of the original problem. The software based on this model is one part of the City Network Planning Package CNP. However it can be used independently as a separate planning tool, even though it is based on spatial electric load forecasting. An example is presented to show the effectiveness of the algorithm. It should be remarked that the model presented in this paper considers the period of the study only at a single Table 1. Costs of both plans (lo4 Yuan)

Figure 3. Plot of load delivery

Automation plan Manual plan

Cl

C?

C

726.76 836.97

588.91 949.5

1315.67 1786.47

Optima/planning

of distribution

stage. Based on the pseudo dynamic methodology*, the algorithm can be used 1.0design the number, location and size of future distribution substations in a horizon year which is called the ‘Horizon Year Static Optimal System’. Owing to the scope of this paper, the topic concerning how to transform the base year design to horizon year design in an optimal, or near-optimal manner is not discussed here. A paper will be presented when this extended work is finish.ed.

VI.

References

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substations:

Dai Hongwei

et al.

357

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of sources

locating

problems’

Magazine of the Operation Research Vol 4 No 1 (1985)

pp 4-11 (in Chinese) 14 Chen Lizhou Optimization methodfor engineering design on discrete variables: principles and applications The Mechanical Industry Press (1989) (in Chinese)