Using Hybridizing Harmony Search Algorithm for Network Reconfiguration to Reduce the Losses and Improve Voltage Profile

Using Hybridizing Harmony Search Algorithm for Network Reconfiguration to Reduce the Losses and Improve Voltage Profile

M. Sai Phaneendra P. Jayakar,

Department of Electrical Engineering Department of Electrical Engineering Chebrolu Engineering College, Chebrolu Engineering College,

Guntur,A.P,India Guntur,A.P,India

Ch. Hari Babu, Department of Electrical Engineering

Chebrolu Engineering College, Guntur,A.P,India

Abstract: This paper presents an harmony search algorithm for loss-minimization reconfiguration in large-scale distribution systems. Electrical distribution network reconfiguration is a complex combinatorial optimization process aimed at finding a radial operating structure that minimizes the system power loss while satisfying operating constraints. The Hybridizing Harmony search algorithm is a recently developed algorithm which is conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In order to validate the proposed algorithm, simulations are carried out on 33 and results are compared with other approaches available in literature. It is observed that the proposed method outperformed the other methods in terms of the quality of solution.

Keywords: Distribution system, Network reconfiguration, Loss reduction, Harmony Search Algorithm.

1. INTRODUCTION

   Power distribution networks are built as interconnected meshed networks; however, they are arranged to be radial in operation to simplify over-current protection. The configuration may be varied with switching operations to transfer loads among the feeders. Under normal operating conditions, optimization of network configuration is the process of changing the topology of distribution systems by altering the open/closed status of switches so as to find a radial operating structure that minimizes the system real power loss while satisfying operating constraints.

   Feeder reconfiguration entails altering the topological structure of distribution feeders by changing the open/close status of the switches under both normal and abnormal operating conditions. Since many candidate-switching combinations are possible in a distribution system, finding the operating network reconfiguration becomes a complicated combinatorial, non- differentiable constrained optimization problem. Distribution system reconfiguration for loss reduction was first proposed

   by Merlin et al [1]. They employed a blend of optimization and heuristics to determine the minimal-loss operating configuration for the distribution system represented by a spanning tree structure at a specific load condition. A branch and bound type heuristic algorithm was suggested by Civanlar et al. [2], where a simple formula was developed for determination of change in power loss due to a branch exchange. In [3][5], the authors suggested to employ a power flow method-based heuristic algorithm (PFBHA) for determining the minimum loss configuration of radial distribution networks. In [6,7,8], the authors proposed a solution procedure employing simulated annealing (SA) to search an acceptable non-inferior solution. Nara et al. [9] presented an implementation using a genetic algorithm (GA) to look for the minimum loss configuration. Das [10] presents an algorithm based on the heuristic rules and fuzzy multi- objective approach for optimizing network configuration.

   In this paper, improvements developed to make HHSA algorithm more effective and more efficient for loss- minimum reconfigu-ration in large-scale distribution systems. The proposed method is tested on 33 and results obtained are very encouraging.

   The rest of this paper is organized as follows: Section II gives the problem formulation. Section III provides an overview of Harmony Search Algorithm. Section IV describes applicationof HSA algorithm for the network reconfiguration problem. Section V presents computational results and section VI outlines conclusions.

2. PROBLEM FORMULATION

   The network reconfiguration problem in a distribution system is to find a best configuration of radial network that gives minimum power loss while the imposed certain operating constraints. Which are voltage profile of the system, current capacity of the feeder and radial structure of the distribution system. The objective function for the minimization of power loss is described as:

   Minimize f min( P )

   (1)

   ( P2 Q'2 )

   PLoss( k ,k 1 ) rk . k k

   (7)

   V

   T ,Loss 2

   k

   Subjected to

   Vmin

   Vi

   Vmax

   (2)

   The total power loss of the feeder, PT,Loss, may then be determined by summing up the losses of all line sections of the feeder, which is given as

   where

   Ii Ii,max

   (3)

   PT ,Loss PLoss( k ,k 1 )

   n

   k 1

   (8)

   PT ,Loss is the total real power loss of the system;

   where n is the total number of lines sections in the system.

   Vi Voltage magnitude of bus i;

   Vmin ,Vmax are bus minimum and maximum voltage limits respectively;

3. OVERVIEW OF HARMONY SEARCH ALGORITHM

   The Harmony Search Algorithm (HSA) is a new

   Ii , Ii,max

   are current magnitude and maximum current limit of branch i respectively;

   metaheuristic population search algorithm proposed by Geem

   et al [12]. HSA was derived from the natural phenomena of musicians behavior when they collectively play their musical

   The power flows are computed by the following set of simplified recursive equations [11] derived from the single- line diagram shown in Fig. 1.

   Sending End Receiving End

   instruments (population members) to come up with a pleasing harmony (global optimal solution). This state is determined by an aesthetic standard (fitness function). The HS algorithm, is simple in concept, few in parameters, and easy in implementation, has been successfully applied to various

   Pk jQ'

   k

   V0 Vk Vk+1

   P + jQ rk + jxk P

   k k

   Vn

   • jQ

   P jQ

   benchmarking, and real-world problems like traveling salesman problem [13]. The main steps of HS are as follows [12]:

   k k

   Yk1 Yk2

   k 1

   PLk 1 jQLk 1

   k 1 n

   n Step 1: Initialize the problem and algorithm parameters.

   Step 2: Initialize the harmony memory. Step 3: Improvise a new harmony.

   Step 4: Update the harmony memory. Step 5: Check the termination criterion.

   Fig. 1 Single-line diagram of a main feeder

   Pk 1 Pk PLoss,k PLk 1

   P rk P2 ( Q Y V 2 )2 P

   (4)

   These steps are described in the next ve subsections.

   1. Initialize the problem and algorithm parameters

      V

      k 2 k

      k

      k k k

      Lk 1

      The general optimization problem is specied as follows:

      V

      Qk 1 Qk QLoss,k QLk 1

      Qk

      • xk

      2

      Vk

      P 2 ( Qk

      k

      2

      • Yk 1 Vk

        2 )2 Y 2

        (5)

        Minimize

        f(x)

        (9)

        k 1

        k

        • Yk 2 Vk 1

          • QLk 1

            Subject to x

            X ,

            i 1,2,………….N

            i

            2 2 r 2 x 2

            Vk 1

            Vk

            • k k

            P 2 Q' 2

          • 2 rk Pk xk Q'

          V

          2 k k

          k

          k

          where f(x) is an objective function; x is the set of each

          2

          Vk k k Pk

          2 r 2 x 2 2

          ( Qk

          Y V 2 )2

          (6)

          decision variable xi; N is the number of decision variables, Xi

          is the set of the possible range of values for each decision

          • 2 rk Pk xk ( Qk Yk Vk

          )

          L

          i

          i

          U

          i

          L

          i

          U

          i

          2

          k k

          Vk

          variable, that is x X x and x and x are the

          where Pk and Qk are the real and reactive powers flowing out of bus k, and PLk+1 and QLk+1 are the real and reactive load powers at bus k+1. The shunt admittance is denoted by Ykl at any bus k to ground. The resistance and reactance of the line section between buses k and k+1 are denoted by rk and xk, respectively.

          The power loss of the line section connecting buses k and

          k+1 may be computed as

          lower and upper bounds for each decision variable. The HS algorithm parameters are also specied in this step. These are the Harmony Memory Size (HMS), or the number of solution vectors in the harmony memory; Harmony Memory Considering Rate (HMCR); Pitch Adjusting Rate (PAR); and the number of improvisations (NI), or stopping criterion. The harmony memory (HM) is a memory location where all the solution vectors (sets of decision variables) are stored. Here, HMCR and PAR are parameters that are used to improve the solution vector. which are dened in Step 3.

   2. Initialize the harmony memory

      where rand( ) is a uniform random number between 0 and 1 and Xi is the set of the possible range of values for each

      decision variable, that is L xi X i U xi . For example, an

      In this step, the HM matrix is filled with as many randomly generated solution vectors as the HMS

      HMCR of 0.85 indicates that HSA will choose decision variable value from historically stored values in HM with

      85% probability or from the entire possible range with (100-

      x

      1

      1

      x

      2

      1

      HM

      1 ..

      x

      x

      2

      2

      2 ..

      1

      x

      x

      N 1 2

      N 1

      1

      x

      N 85) % probability. Every component obtained with memory

      x

      2 consideration is examined to determine if pitch is to be

      N adjusted. This operation uses the rate of pitch adjustment as a

      parameter as shown below:

      x HMS 1 x HMS 1

      .. x HMS 1

      x HMS 1

      1 2

      N 1

      N if

      rand ( ) PAR

      x HMS x HMS

      .. x HMS

      x HMS

      1 2

      N 1

      N

      (10)

      x x rand () bw

      There is a possibility of infeasible solutions which violate the constraints. However, the algorithm forces the search towards feasible solution area. Static penalty functions are used to calculate the penalty cost for an infeasible solution. The total

      i i

      else

      (13)

      cost for each solution vector is evaluated using:

      xi xi

      M

      fitness( X ) f ( X ) (min[ 0, g ( x )] 2

      end

      i i

      i1

      P

      2

      (11)

      where bw, is an arbitrary distance bandwidth. In order to improve the performance of the HSA and eliminate the

      j 1

      j (min[ 0,h j ( x )]

      drawbacks associated with fixed values of PAR and bw [14], a variable values of PAR and bw are used in improvisation step. The dynamically changed values of PAR and bw with

      where i and j are the penalty coecients. Generally, it is

      dicult to nd a specic rule to determine the values of the

      generation number is expressed as shown below:

      penalty coecients and hence these parameters remain problem-dependent.

   3. Improvise a new harmony

      PAR( gn ) PAR

      min

      • PARmax PARmin gn (14)

      NI

      where PAR( gn ) is the pitch adjusting rate for each

      A New Harmony vector x' x1 ,x2 ,…….xN , is

      generation,

      PARmin , PARmax

      are the minimum and

      generated based on three criteria: (1) Memory consideration

      (2) Pitch adjustment (3) Random selection. Generating a new harmony is called improvisation. According to memory

      consideration, ith variable x =( x1 xHMS ) . The HMCR,

      maximum pitch adjusting rates respectively and gn is the generation number, NI is number of iterations.

      bwgn bwmax expc.gn

      i 1 1

      which varies between 0 and 1, is the rate of choosing one value from the historical values stored in the HM, while (1- HMCR) is the rate of randomly selecting one value from the possible range of values, as shown in eq.(12).

      ln bwmin

      c

      bwmax

      NI

      (15)

      if rand(

      ) HMCR

      where

      bwgnthe bandwidth is for each generation,

      i i i i 1

      x' x' x1 , x 2 ,…..x HMS

      else

      (12)

      bwmax is the maximum bandwidth.

   4. Update harmony memory

      x' x' X

      If the new harmony vector

      x' x ,x ,…….x , has better

      i i i 1 2 N

      end

      fitness function than the worst harmony in the HM, the new harmony is included in the HM and the existing worst harmony is excluded from the HM.

   5. Check termination criterion

The HSA is terminated when the termination criterion (e.g. maximum number of improvisations) has been met. Otherwise, steps 3 and 4 are repeated.

In order to demonstrate the convergence capability of harmony search, let us consider the harmony memory with the following parameters: the size of HM = M,

the number of instruments (variables) = N,

the number of possible notes (values) of instruments = L, the number of optimal note (value) of instrument i in HM

= Hi,

harmony memory considering rate = Hr, and

Hi

the optimal harmony (optimal vector) = (X, Y, Z). The probability to find the optimal harmony, Pr (H) is

V. APPLICATION OF HSA FOR NETWORK RECONFIGURATION PROBLEM

The optimum distribution network is obtained by first generating all possible radial structures of the given network (without violating the constraints) and subsequently evaluating the objective function. However, real distribution systems contain many nodes, branches, and trees. Conventional optimization methods are ineffective and impractical, because of dimensionality. In this paper HHSA is proven to be an effective and useful approach for the network reconfiguration problem.

In general, the structure of solution vector [15] for a radial distribution system is expressed by Arc No.(i ) and SW. No.(i ) for each switch i . Arc No.(i ) identifies the arc (branch) number that contains the ith open switch, and SW. No.(i ) identifies the switch that is normally open on Arc

r

Pr( H ) N H

i1

M ( 1 H r )

1

L (16)

No.(i ). For large distribution networks, it is not efficient to represent every arc in the string, since its length will be very long. In fact, the number of open switch positions is identical to keep the system radial once the topology of the distribution

where the pitch adjusting rate is not considered because it is an optional operator. Initially, the HM is stuffed with random harmonies. If there is no optimal note of all instruments in the HM,

H1 H2 ……. H N 0

1

networks is fixed, even if the open switch positions are changed. Therefore, to memorize the radial configuration, it is enough to number only the open switch positions. Fig. 2 shows a 33-bus [15] distribution network with five switches that are normally open.

The open switches in the loops L1 to L5 for the network given in fig. 2(a) are given as 33, 34, 35, 36, and 37. Similarly other radial topology is generated randomly with the open

and

Pr( H ) ( 1 H

) 1 N

r L

switches 19, 13, 21, 30, and 24 as shown in fig. 2(b) and open status of these switches satisfy the radial topology without any isolated node in the system. Therefore, in order to

This means the probability Pr(H) is very low. Consider a solution vector (X, Y, Z). However, if the schema of optimal harmony such as (*, Y, Z), (X, *, Z), (X, Y, *) have better fitness (better evaluation) than other ones, the number of optimal notes of instrument i in the HM, Hi will be increased iteration by iteration. Consequently, the probability of finding the optimal harmony, Pr(H) will increase.

It is observed that, by nature, the Harmony Search incorporates, the structure of existing heuristic methods. It preserves the history of past vectors (Harmony Memory) similar to TS, and is able to vary the adaptation rate (Harmony Memory Considering Rate) from the beginning to the end of computation resembling SA, and manages several vectors simultaneously in a manner similar to GA. However, the major difference between GA and HS is that HS makes a new vector from all the existing vectors (all harmonies in the Harmony Memory), while GA makes the new vector only from two of the existing vectors (the parents). In addition, HS can independently consider each component variable in a vector while it generates a new vector, where as GA cannot since it has to maintain the structure of a gene.

represent an optimum network topology, only positions of the open switches in the distribution network need to be known. Suppose the number of normally open switches (tie switches) is N, then the length of a solution vector is N.

The solution vectors for fig. 2(a) and fig. 2(b) are represented as follows:

The solution vector for fig. 2(a):

HW1= [33 34 35 36 37]

The solution vector for fig. 2(b):

HW2= [19 13 21 30 24]

In the similar way all other possible solution vectors of fig. 2 are generated without violating the radial structure or islanding any load in the network. The total number of solution vectors (HMS) generated are less than or equal to highest numbers of switches in any individual loop. The total Harmony Matrix generated randomly with objective function values sorted in ascending order is shown below.

01

7

02

7

19 03

20 04 23

21 L1 05 L5 24

6

22 06 25 6

138.54 141.32

145.11

07 26

08 27

28

L3

09

10 29

11 30

152.23

7 155.75

7 157.31

12 L2 31

13 32

HM 20

170.57

14 33

15

20

178.41

16 L4

19

182.13

17

18

(a)

01

02

19 03

04 23

19

19

20

33

192.37

194.55

198.87

202.71

20

L1 05 L5 24

06 25

21 07 26

08 27

L3

09 28

22

10 29

11 30

12 L2

Read the system data and Specify decision variable (Tie Switches), harmony memory size (HMS)(possible candidate switches in each loop), harmony memory considering rate (HMCR), pitch adjusting rate (PAR), termination criterion (maximum number of iterations)

13

Start

Initialization of harmony memory (HM): Generate initial harmony memory randomly [solution vector] (as many as HMS)

14 31

15 32

16 L4 33

17

18

Evaluate the objective function (Power Loss) and sort it in ascending order

(b)

Improvisation of a new harmony from HM based on three rules: Memory Consideration, Pitch Adjustment, Random Choice

Fig. 2. 33Bus radial distribution system

Is new harmony is better than a stored harmony in HM?

Yes

Update HM

No

No Termination

condition satisfied?

Yes

Stop

Fig. 3. Flow chart of Harmony Search Algorithm

The new solution vectors are updated by using equation (12). Using the new solution vectors, the worst vectors of previous iteration will be eliminated with a new random vectors selected from the population that has less objective function value.

This procedure is repeated until termination criteria is satisfied. The flow chart of the proposed algorithm is shown in Fig. 3.

V. TEST RESULTS

The proposed method is tested on 33-bus [15] and 119- bus [19] radial distribution systems and results are obtained to evaluate its effectiveness. For all these systems, the substation voltage is considered as 1 p.u. and all tie and sectionalizing switches are considered as candidate switches for reconfiguration problem. The algorithm was developed in MATLAB, and the simulations were done on a computer with Pentium IV, 3.0 GHz, 1GB RAM.

Test Case I – 33-Bus System: The first example system is a 33bus, 12.66 kV, radial distribution system [15] as shown in fig. 2. It consists of five tie lines and 32 sectionalize switches. The normally open switches are 33 to 37 and the normally closed switches are 1 to 32. The line and load data of the network is obtained from reference [15] and the total real and reactive power loads on the system are 3715 kW and 2300 kVAr. The initial power loss of this system is 202.771 kW. The lowest bus bar voltage limit is 0.9131 p.u which occurs at node 18.

TABLE I

PARAMETERS OF THE HS ALGORITHM

The parameters of Hybridizing HS algorithm used in the simulation of the network are shown in Table I. The optimal configuration obtained by the proposed algorithm is 7,10,14,37,36, which has a real power loss of 138.067 kW. This amounts to a reduction of 31.89 % in total power loss. The minimum node voltage of the system after reconfiguration improved to 0.9342 p.u (node 33).

The voltage profile of the system is as shown in Fig. 4.

This shows feeder are relieved from the overloading and makes it possible to load the feeders further. The power loss in each branch is also shown in Fig. 5. It is observed that the losses in almost every branches is drastically reduced except at 18, 19, 20, 21, 33, 34, and 35 where the losses are increased a little because of shifting of loads on to these feeders.

Before Reconfiguration After Reconfiguration

60 Pow er Losses for 33-bus System

Power Lss at each branch

50

40

30

20

10

0

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37

Num ber of Branches

Fig. 5. Losses in the system before and after reonfiguration

The results of the proposed algorithm are compared with Genetic Algorithms [16], Refined Genetic Algorithms

TABLE IV

SIMULATION RESULTS OF 33-BUS SYSTEM

.

1

SYSTEM BUS VOLTAGE in PER UNIT

0.99

0.98

0.97

0.96

0.95

0.94

0.93

" BUS VOLTAGE " Versus " BUS NUMBER "

AFTER

From the results, it is observed that the optimal power loss obtained by the proposed method is 4% less than GA and 2% less than RGA and PGSA. The convergence characteristics of the proposed HHSA algorithm for 33-bus system are shown in Fig.6. Simulations are carried out for 250 iterations and optimum solution is obtained after 160 iterations. The CPU time taken by the processor to carry out the simulations for 250 iterations is 6.8 sec.

0.92

0.91

BEFORE 0 5 10 15 20 25 30 35

SYSTEM BUS NUMBER

Fig. 4. Voltage Profile of 33-bus system

Fig. 6. Convergence characteristics of HHSA for 33-bus system

V. CONCLUSIONS

A recently developed Hybridizing Harmony Search Algorithm is successfully applied for optimizing the large scale radial distribution systems to reduce I2R loss. The Hybridizing Harmony Search Algorithm is mathematically quite simple concept, easy for implementation as is uses few parameters and effective in finding the solutions of combinatorial optimization problems. It neither needs initial starting values for the variables nor a population of candidate solutions of the problem. Moreover, Hybridizing Harmony Search Algorithm uses a stochastic random search based on the harmony memory considering rate (HMCR) and pitch adjusting rate (PAR), which effectively guide a global search rather than a gradient search, so that derivative information is unnecessary. Furthermore, HHSA generates a new vector after considering all of the existing vectors based on the HMCR and the PAR, rather than considering only two (parents) as in genetic algorithms. These features increase the flexibility of the HHSA and produce better solutions.

Simulations are carried on a medium (33-bus) and results are compared with other methods like GA,RGA,PGSA.Results show that the proposed algorithm can converge to optimum solution with higher accuracy in comparison with other methods mentioned.

REFERENCES

1. A. Merlin, H. Back, Search for a minimal-loss operating spanning tree configuration in an urban power distribution system Proceedings of 5th Power System Computation Conference (PSCC), Cambridge, UK, 1975, pp. 1-18.

2. S. Civanlar, J. Grainger, H. Yin, and S. Lee, Distribution feeder reconfiguration for loss reduction, IEEE Trans. Power Del., vol. 3, no. 3, pp. 12171223, Jul. 1988.

3. D. Shirmohammadi and H.W. Hong, Reconfiguration of electric distribution networks for resistive line losses reduction, IEEE Trans. Power Del., vol. 4, no. 2, pp. 14921498, Apr. 1989.

4. T. P. Wagner, A. Y. Chikhani, and R. Hackam, Feeder reconfiguration for loss reduction: an application of distribution automation, IEEE Trans. Power Del., vol. 6, no. 4, pp. 19221931, Oct. 1991.

5. S. Goswami and S. Basu, A new for the reconfiguration of distribution feeders for loss minimization, IEEE Trans. Power Del., vol. 7, no. 3, pp. 14841491, Jul. 1992.

6. H. C. Cheng and C. C. Kou, Network reconfiguration in distribution systems using simulated annealing, Elect. Power Syst. Res., vol. 29, pp. 227238, May 1994.

7. H. D. Chiang and J. J. Rene, Optimal network reconfiguration in distribution systems: part 1: a new formulation and a solution methodology, IEEE Trans. Power Del., vol. 5, no. 4, pp. 19021908, Oct. 1990.

8. H. D. Chiang and J. J. Rene, Optimal network reconfiguration in distribution systems: part 2: solution algorithms and numerical results, IEEE Trans. Power Del., vol. 5, no. 3, pp. 15681574, Jul. 1992.

9. K. Nara, A. Shiose, M. Kitagawoa, and T. Ishihara, Implementation of genetic algorithm for distribution systems loss minimum reconfiguration, IEEE Trans. Power Syst., vol. 7, no. 3, pp. 1044 1051, Aug. 1992.

10. D. Das, A fuzzy multi-objective approach for network reconfiguration of distribution systems, IEEE Trans. Power Del., vol. 21, no. 1, pp. 202209, Jan. 2006.

11. Smarajit Ghosh and Karma Sonam Sherpa, An Efficient method for Load-Flow Solution of Radial Distribution Networks, International Journal of Electrical Power and Energy Systems Engineering, vol. 1, no. 2, pp. 108-115, 2008.

12. Z. W. Geem, J. H. Kim, and G. V. Loganathan, A new heuristic optimization algorithm: harmony search, Simulation, vol. 76, no. 2, pp. 6068, 2001.

13. Z.W. Geem, C. Tseng, and Y. Park, Harmony search for generalized orienteering problem: best touring in China, Springer Lecture Notes Comput. Sci., 3412 (2005) 741750.

14. M. Mahdavi, M. Fesanghary, and E. Damangir, An improved harmony search algorithm for solving optimization problems, Applied Mathematics and Computation, vol. 188, no. 2, pp. 1567 1579, 2007.

15. M. E. Baran and F.Wu, Network reconfiguration in distribution system for loss reduction and load balancing, IEEE Trans. Power Del., 4(2), 1989, 14011407.

16. Y. Y. Hong and S. Y. Ho, Determination of network configuration considering multi-objective in distribution systems using genetic algorithms, IEEE Trans. Power Syst., vol. 20, no. 2, pp. 10621069, May 2005.

17. J. Z. Zhu, Optimal reconfiguration of electrical distribution network using the refined genetic algorithm, Elect. Power Syst. Res., vol. 62, pp. 3742, 2002.

18. Chun Wang and Hao Zhong Cheng, Optimization of Network Configuration in Large Distribution Systems Using Plant Growth Simulation Algorithm, IEEE Transactions on Power Systems, Vol. 23, No. 1, February 2008.

19. D. Zhang, Z. Fu, L. Zhang, An improved TS algorithm for loss- minimum reconfiguration in large-scale distribution systems, Electric Power Systems Research, Vol. 77, pp. 685694, 2007.