Evolutionary Approach To Distribution Network Reconfiguration For Energy Saving

5.33.1 EVOLUTIONARY APPROACH TO DISTXIBVTION NETWORK RECOFWIGURATION FOR ENERGY SAVING

Y H Song G S Wang A T Johns University of Bath, Bath BA2 7AY, UK P Y Wang Electric Power Research Institute, Beijing, China Abstract: Network reconfiguration for loss reduction in distribution systems is a very important way to save energy. However, due to its nature it is an inherently difficult optimization problem. In this paper, a new type of evolutionary search technique, evolutionary programming (EP), has been adapted and improved for this particular application. In order to improve the performance of EP, a fuzzy controlled EP (FCEP), based on heuristic information, is first proposed. The mutation fuzzy controller adaptively adjusts the mutation rate during the simulated evolutionary process. The status of each switch in distribution systems is naturally represented by a binary control parameter 0 or 1. The length of string is much shorter than that proposed by others. A chain-table and combined depth-first and breath-first search strategy is employed to further speed up the optimisation process. The equality and inequality constraints are imbedded into the fitness function by penalty factors which guarantee the optimal solutions searched by the FCEP are feasible. The implementation of the proposed FCEP for feeder reconfiguration is described in detail. Numerical results are presented to illustrate the feasibility of the proposed FCEP.

I. INTRODUCTION Distribution systems are critical links between the utility and customer, in which sectionalising switches are used for both protection and configuration management. Usually, distribution systems are designed to be most efficient at peak load demand. Obviously, the network can be made more efficient by reconfiguring it according to the variation in load demand. Recent studies indicate that up to 13% of the total power generation is wasted in

the form of line loss at the distribution level [ 11. Hence, it is of great benefit to investigate methods for network reconfiguration.The objectiveof network reconfiguration is to reduce power losses and improve the reliability of power supply by changing the status of existing sectionalising switches and ties. Distribution system reconfiguration for loss reduction was first proposed by Merlin et a1 [2]. They employed a blend of optimisation and heuristics to determine the minimal loss operating configuration for the distribution system represented by a spanning tree structure at a specific load condition. Since then, many techniques have been proposed. Ref [3] provides a survey of the state of the art in distribution system reconfiguration for system loss reduction. These methods can be classified into two grolups: (1) Heuristics methods and Mathematical optimization techniques or combinations [4-131. The use of heuristics was justified by the need to reduce the search space of the reconfiguration problem. Optimization tcchniques include linear programming, dynamic programming and simulated annealing; (2) AI based approaches[14-16], including expert systems and neural networks. More recently, genetic algorithms have been proposed for distribution reconfiguration for loss reduction [17, 181. The results are very encouraging. The characteristics of genetic algorithms make them particularly suited to ill-structured optimizationproblems [19-201. This is because GAS use pay-off (fitness or objective function) directly for the search direction, so no mathematical assumption is needed and GA searching from a population of points can discover global opti” very rapidly. However, as discussed in ref [17], crossover operation has the danger of generating individuals which violate radiality constraints by swapping string of two parent networks. Although techniques cain be introduced to get rid of those bad individuals, this will inevitably increase the computation dramatically. In addition, the encoding and decoding used in ref 1181 is very complicated which slows down

ClRED 97,2-5 June 1997, Conference Publication No. 438, 0 IEE, 1997

5.33.2

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I I I

~

the speed of the algorithm. Thus in this paper, a new type of evolutionary search technique, evolutionary programming (EP), has been employed. b o n g other differences with GAS, there two major ones: (1) EP uses control parameters, not their codings; (2) the generation selection procedure of EP is mutation and competition, not the reproduction, crossover and mutation of GA. GAS emphasize on genetic operators, while mutational transformations play a crucial role in EP. The study in [21,22] shows that EP outperforms GAS in a number of applications. In simple EP, the mutation rate is fixed which has some shortcomings. In order to improve the performance of EP for our particular problem, a fuzzy controlled EP (FCEP), based on some heuristic information, is first proposed. The designed mutation fuzzy controller adaptively adjusts the mutation rate during evolutionaryprocess. The status of each switch in distribution systems is naturally represented by a binary control parameter 0 or 1. The length of string is much shorter than the one used in ref [17]. In addition, a chain-table and depth-width search strategy is employed to fuaher speed up the optisation process. The equality and inequality constraints are imbedded into the fitness function by some penalty factors to guarantee the optimal solutions searched by the FCEP are feasible. The implementation of the proposed FCEP for feed reconfiguration is described in detail. Numerical results are presented to illustrate the feasibility of the proposed FCEP. 11. PROBLEM FORMULATION

Power flow at each node must be kept balance, power flow at each branch must be less than or equal to its maximum capacity and the operating voltage at each node must be in its safety range. Namely,

se*= s, + s,

(i= 1,2,...,n)

(2)

s, c. si-

(i= 1,2,...,n)

(3)

(i= O,l, ...,n)

(4)

Vp.

5

vi 5 vi-

Where S=P+jQ. Therefore, first of all, the power flow must be calculated. Normally, distribution system are operated as radial network. Although reconfiguration of the distribution system changes the states of some sectionalking switches, the radial characteristics of its network is still kept. Thus, the simplified power flow equations can be adopted [7]. Besides the constraints in equations (2), (3) and (4), some more constraints must be satisfied. For instance, the load centres must not be shed: the connection inside a feeder and disconnection between feeders must be simultaneously satisfied. Hence, the constraints equations (5) and (6) are needed.

N

ZLy=l

(j=l,%..Jr)

I=1

2.1 Objective function of network reconfiguration The objective function of network reconfiguration is to minimise the total power losses in the distribution system as the load demand changes. Supposing the number of feeders and of load centres in a distribution system are respectively N and K, then the number of trees is also N. Hence the objective function of network reconfiguration can be expressed by equation (1).

Where n, is number of nodes in the i-th feeder (tree) except its root, rij is the resistance, Pi and Qi are the power flow, Vi is the voltage. 2.2 Constraints in radial networks

The constraints consist of power flow constraints, node voltage constraints, and line thermal constraints etc..

(6) Where Lij stands for load centre. If loadj belongs to feederi, Lij =1, otherwise Lij =O. Equation (5) means that loa4 belongs to feeder, and can only belong to one feeder. Equation (6) meam that all load centres must be supplied. 111. FUZZY CONTROLLED EVOLUTIONARY PROGRAMMING FOR FEEDER RECONFIGURATION

The implementation of fuzzy controlled evolutionary programming for feed reconfiguration involves the following steps:

3.1 Describing switch status If the number of switches in a distribution systeni is M, then the length of chromosome is defined as M. The

5.33.3 status of each switch is ~ t u r a l l yrepresented by a binary control parameter 0 or 1. If the status of a switch is 0, foe example, then it indicaiss that the switch is open otherwise the switch is closed. Every chromosome represents one configuration of the distribution system.

3.2 Generating initial populations The initial populations are generated randomly. The length of a chromosome equals to the number of sectionalising switches and ties in a distribution system. Thus, each chromosome string corresponds to an initial network. To speed up the convergence of FCEP, the constraints described in section 2.2 should be satisfied as much as possible in the initial populations. If the number of the closed switches in the original distribution network is K,, the number of 1 in the initial chromosome should be K,,and the root of one tree can never become a leaf of another tree.

3.3 Formulating new network The data structure of a new network is described by branch nodes and branch status. If the bits in a chromosome are 1, then their corresponding branches are added into a new network and the status of the branches are set to 1 otherwise the branch nodes and branch status are set to zero. 3.4 Describing the data structure of distribution system The data structure of a distribution system is represented by a group of chains. Each consists of : { branch-nodes[head, e n d ] , branch-parameters[resistance, r e a c t a n c e , end-node-realgower, end-ode-reactiveqower, end-node-voltage] , switch-no } For a given branch, the small branch node number is its head and the bigger one is its end. The initial node voltages in the original distribution system are their actual data. After the status of sectionalising switches have been changed, the initial node voltages in a new network are taken the value 1.0 at every node to meet the voltage quality. 3.5 Searching for feeders After the status of sectionalising switches has been changed, i.e. the bits in a chromosome have been changed, the new network is easy to be formulated in terms of the bits in a chromosome as stated above, but the memberships of all load centres could be totally

changed. Hence, we need to search for which feeder a given load centre belongs to. The blend searching technique is employed. In the first place, the search begins with the root of a tree. After the branches linked to the root are searched, their status will be set to zero, and their end nodes will be automatically recorded and will be again used as a new starting point to search for the other branches and nodes until the searching space is traversed. After that we can further determine whether a load centre has been shed through checking the status of the branches. If the status of a branch is not zero, it shows that the branch has never been searched and a load shedding could1 occur. Therefore the branch is needed to be added to a corresponding feeder. The reason for this is that when the searching is running into the problem of nonconsistence, the branch needs to swap its head and end. Of course the end node power sink must be simultaneously changed. For example, if a new network consists of the following branches {(3,13,1), (13,14,1), (10,14,1), (14,15,1), (15,16.1)} and supposing node 3 is the root of the tree. After searching for the tree (feeder), every branch except for (10,14,1) can be addled into the tree and their status are set to zero. If we chleck the status of all the branches in the new network, it is easy to find that the status of the branch (10,14,1) is 1, which shows that the branch has never been searched. The branch is not added into the tree, and the load centre 10 has been shed. After swapping the head and end of the branch, the load centre 10 can be added into the feeder (tree). In order to accelerate the searclling process, chain-tables are used and all feeders can be searched in parallel at the same time. The structure of the chain-table is shown in Fig. 1.

I

I

I

leaves 0

Fig. 1 The structure of a chain-table Taking the chain-table as shown in Fig.2 (a) as an example, its corresponding tree is as shown in Fig.:! (b). Obviously, each chain-table stands for one tree, and the power losses of the tree can be easily computed from leaves to root in terms of the chain-table.

5.33.4

Where S, is the injected power at the root of the i-th feeder and S," is its corresponding maximum capacity. Then the fitness function can be represented by equation (10).

Fig.2 A typical chain-table and its corresponding tree 3.6 Competition based on fitness function

In equation (lo), C is a given big positive real number.

An appropriate fitness hnction is essential to speed up the convergence of the FCEP. In network reconfiguration, the fitness function should consider the objective function of equation (1) and constraints of equations (3-4). The constraints (5-6) have already be considered by searching for feeders of section 3.5. The constraint (2) is embedded into the calculation procedure of network losses.

3.7 Implementation of the fuzzy controlled mutation The procedures to design the mutation fuzzy logic controller, shown in Fig.3, are as follows:

The voltage constraint (3) is rearranged as equations (7) and (8). If Vi > Vi -, then

5-

a,=(-)

Fig.3 Structure of fuzzy mutation controller

2

v, (7)

If Vi < Vi &, then a,=(-)* 5*

vi

Generally, V,, takes the value of 0.95 p.u. and V, takes the value of 1.05 P.u.. In the proposed technique, the search is from the root to the leaves of a tree, but the power losses are calculated from the leaves to the root of the tree. Hence the capacity constraints can be taken into account by equation (9). If Si,

> Sam, then

(1) Choose inputs and output for the mutation fuzzy logic controller.

As a general rule, the changes in fitness Af(t) and A2f(t) are chosen as the inputs to the fuzzy controller and the change in mutation Am(t) as its output. Where, Af(t) = f(t) - f(t-1)

(1 1)

A'f(t) = Af(t) - Af(t-1)

(12)

(2) Define the universes of discourse for Af(t), A2f(t) and Am(t).

In this study, the universes of discourse of Af(t), Azf(t) and Am(t) are respectively defined as [-1.0, 1.01, [-0.5, 0.51 and [-0.1, 0.11. Tlien, all inputs to the fuzzy controller will be standardised into their corresponding universes of discourse.

4.33.5 (3) Respectively define a group of fuzzy subsets to cover their own universes of discourse.

Table 1 Fuzzy inference rules

Define the linguistic value sets of the fuzzy variables Af(t), A2f(t) and Am(t) as equations (13), (14) and (15), and let the membership functions of all fuzzy subsets take triangular distributions as shown in Fig.4. T(Af(t)) = (NL, NR, NS, NM, ZE, PS, PM, PR, PL) T(A2f(t)) = (NL, NS, NM, ZE, PS, PM, PL} T(Am(t)) = {NL, NR, NS, NM, ZE, PS, PM, PR, PL}

(13) (14) (15)

Where NL - Negative Larger, NR - Negative Large, NS - Negative Small, NM - Negative Medium, ZE - Zero, PS - Positive Small, PM - Positive Medium, PR Positive Large, PL - Positive Larger.

P I

(5) Determine the output of the fuzzy controller For any inputs to the mutation fuzzy logic controller, its output is computed. as equation (16) based on the Cuter of Gravity. This method computes the centre of gravity of the final fuzzy control space and produces a result which is sensitive to all the rules executed. Hence, the results tend to move smoothly across the control surface.

Finally, the mutation rate is computed by equation (17). -1 0

-08

-06

-04

-02

0

0.2

04

06

08

1.0

Wt)

m(t+ 1) = m(t) f Am(t)

lif(t) -05

-03

-01

0

01

03

NL NR NS NM

1ZE PS P M

-Om

0

05

PR

(17)

The mutation in a chromosome must be camed out in pairs, i.e., if a bit of the chromosome is mutated from 1 to 0, then anolher bit with binary number 0 must be simultaneously mutated to 1, vice versa. That is to say, if a open switch is closed then its neighbour closed switch must be open, and if a closed switch is open then the neighbouring open switch must be closed. The mutation cannot undermine the radial characteristics of the network and cannot shed the load centres. The FCEP is then programmed in Turbo C+ + on a PC486.

PL

IV. CASE STUDY -01

-006

404 6 0 1

002

OM

006

OW

01

A typical distribution system, as shown in Fig.5, which was studied by Civanlar et a1 [4] is taken as a case study

Fig.4 Membership functions of Af(t), A2f(t) and Am(t) (4) Set inference rules.

The inference rules are defined based upon a series of tests and experience as shown in Table 1.

to test the performance of the FCEP. This systeni consists of 3 feeders, 13 normally closed sectionalising switches, 3 normally open tie-switches and 13 load centres. Feeder section impedance, system loads, arid busbar voltages are given in Table 2.

5.33.6

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System status

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0.991/-0.596

0.12 Status of the sectionalising switches and ties

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Power losses ocw)

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SO-Sl-S2-S3-S4-S5-S6-S7-S8-S9-SlO-Sll-S 12-S 13-S 14-S 15 network

-1 \1 \1 \1 -1 -1 -1 -1 -1-1 \1 -1 -1 $ 4 -1

947.047

0.000

-1 -1 -1 -1 -1 \1 \1 -1 -1-1 -1 .l, -1 -1-1 .l,

882.736

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Status of the sectionalising switches and ties

Power losses ocw)

1 1 1 1 0 1 1

1 1 1 0 1

1 1 1 0

SO-S l-S2-S3-S4-S5-S6-S7-SS-S9-S 10-S 1 l-S12-S13-S14-S15

System status Original network

SO-S l-S2-S3-S4-S5-S6-S7-SS-S9-S 10-S11-S 12-S 13-S 14-S 15

Optimal network

so-s1-s2-s3-s4-s5-s6-s7-s8-s9-s lo-Sl l-s 12-Sl3-Sl4-Sl5 .1 -1 -1 -1 -1 -1 -1 -1 -1-1 -1 -1 -1 -1-1 -1

-1 -1 -1 -1 -1 -1 -1 -1 4-1-1 -1 -1 -1-1 -1 1 1

1 1

1 1 0 1 1

1 1

1 1 0

1 1 1 0 1

1 0 1 1 1

loss reduction

("/.I

834.511

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1 1 1 0 1

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losses

Original network

SO-S l-S2-S3-S4-S5-S6-S7-SS-S9-S 10-S11-S 1 2 413-S 14-S 15

Optimal

SO-S l-S2-S3-S4-S5-S6-S7-S8-S9-SlO-S11-S 12-S 13-S14-S 15

-1 -1 -1 -1 -1 -1 -1 -1 & - 1 -1 -1 & J-1 -1 1 1

netwrk

1 1 0 1 1

1 1 1 0 1

1

ocw)

reduction (%)

837.073

0.000

736.863

11.972%

1 1 1 0

-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 \1 -1 -1 -1 -1 -1

5.33.7 described in detail. The proposed FCEP is applied to a typical example. Applications to larger distribution systems and real systems are underway. This will be reported in a future paper. VI. REFERENCES

Q

"CENTER

__ FEED= SECTION WlTH CLOSED SWITCH FEHlER SEETION WITH OPEN SWITCH

---

Fig.5 Three feeder distribution system The parameters used in FCEP are as follows: Population size = 100; Chromosome length = 16; Initial mutation rate = 0.1; Desired generations = 100. The optimisation results are tabulated in Table 3 (case l), which are achieved after 3 generations. If we reduce the load at the load centre 12 from 4.5+j2.0 to 3.5+jl.O, then the optimal network searched by the FCEP is shown in Table 4 (case 2), which is attained after 2 generations. It can be seen that the optimal network is unchanged if the fluctuation of load is small. In the third case, when the loads at the load center 12 and 15 are reduced to 3.5+j1.0 and 0.5+j0.4 respectively, and the load at 6 is increased to 2,.5 +jl.3, the optimal network searched by the FCEP is shown in Table 5 (case 3), which is attained after 4 generations.

V. CONCLUSIONS

In thk paper, an improved evolutionary programming technique has been proposed for distribution loss minimum reconfiguration. A mutation fuzzy logic controller is developed to speed up the evolutionary process by adaptively adjusting the mutation rate. The status of each switch in distribution systems is naturally represented by a binary control parameter 0 or 1. The length of the string is much shorter than that proposed by others. A chain-table and combined depth-first and breath-first search strategy is employed to further speed up the optimisation process. The equality and inequality c.onstraints are imbedded into the fitness function by penalty factors to guarantee the optimal solutions searched by the FCEP are feasible. The implenientation of the proposed FCEP for feeder reconfiguration is

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5.33.8 IEEE Trans Power Delivery, 1990, pp. 1902-1909 [I21 Hong-Chan Chang and ChengChien Kuo, “Network reconfiguration in distribution systems using simulated annealing, ” Electric Power Systems Research, 29(1994), pp. 227-238. [I31 C. S. Chen, M. Y. Cho, ”Energy loss reduction by critical switches”, IEEE Trans Power Delivery, 1993, pp. 1246-1253 [I41 G. Chang, J. Zrida, J. D. Birdwell, “Knowledgebased distribution system analysis and reconfiguration”, IEEE Trans Power Syst., 1990, pp.239-246 [I51 Derrick Bouchard and Aziz Chikhani, V. I. John and M. M. A. Salama, “Applications of Hopfield neural networks to distribution feeder reconfiguration, Proceedings of the Second International Forum on Applications of Neural Networks to Power Systems, April, 1993, Yokohama, Japan, pp, 311-316. [I61 Hoyong Kim, Yunseok KO and Kyung-Hee J u g , “Artificial neural-network based feeder reconfiguration for loss reduction in distribution systems,” IEEE Transactions on Power Delivery, Vol. 8, No. 3 July 1993, pp. 1357-1367. [17] Koichi Nara,Atsushi Shiose, Minoru Kitagawa and ToshihisaI s b a , “Implementationof genetic algorithm for distribution systems loss minimum reconfiguration,” IEEE Transactions on Power Systems, Vol. 7, August 1992, pp. 1044-1051. [18] M. Kitayama, K. Matsumoto, “An optimization method for distribution system configuration based on genetic algorithm“, Proc IEE APSCQM, 1995, pp.614619 1191 F. Li, Y. H. Song, R. Morgan, D, T. Cheng, ”Genetic algorithms in electric power system optimization“,Proc Adaptive Computing in Engineering Design and Control, 1994, 77-83 [20] D. Srinivasan, F. Wen, C. S . Chang. A. C . Liew, “A survey of applications of eovlutionary computing to power systems“, ISAP’96, 1996 [21] D. B. Fogel, “System identification through simulated evolution: a machine learning approach to modelling“, IEEE Press, 1995 [22] D. B. Fogel, ”A comparison of evolutionary programming and genetic algorithms on selected constrained optimzation problems“, Simulation, 1995, pp.397-404

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