An On-Line Distribution Feeder Optimal Reconfiguration Algorithm for Resistive Loss Reduction Using a Multi-Layer Perceptron

E. Gauche J. Coelho R. C. G. Teive Federal University of Santa Catmina - Brazil

e-mail: coelho@gpse.ufsc.br

Abstiract

This paper presents an on-line distribution feeder optimal reconfiguration algorithm fir resistive loss reduction. ArtiJicial neural networks (ANN) were used to assure the application feasibility in real-time. The demand variation used during the ANN training is represented by samplings via Monte Carlo Simulation. A consolidated heuristic algorithm is utilized to obtain the demand topologies. An integer formulation 0-1 is used to guarantee the solution optimality from the initial solution supplied by the ANN. It is also presented the application results to a demonstrative test system, indicating to new applications in real systems where topological alteration are required.

1. Introduction

Distribution systems feeder reconfiguration is performed by changing the openlclosed states of the sectionalizing switches. One of the reconfiguration objectives consist in reducing the overall system power losses, improving the voltage profile along the feeders.

The network configuration problem with minimum line losses, a mixed-integer non-linear optimization problem, has been solved using branch-and-bound method. Even for those cases where convergence is reached for networks of realistic sizes, the computational burden is extremely high and often unfeasible. Consequently, heuristic methods have been suggested for the efficient solution of the network optimal configuration problem. One of the first papers developed in this field was presented by Merlin [l], who developed a heuristic approach, searching for minimizing the search space of the optimal solution. The method of Merlin starts with all network switches closed. Then, the switches are opened one at a time until a new radial configuration is reached. The works of Shirmohammadi [2] and Borozan [3] improve the effectiveness of Merlin method.

0-7803-4122-8/97 $10.00Of.997 IEEE

A simplified formula was presented by Cinvalar [4] to calculate the loss reduction, which is obtained through only one load transference between feeders. The successive application of this formula permits the multiple transference analysis. The optimal topology strategy obtained from multiple transference, was not consideired by Cinvalar. However, Cinvalar permitted the development of other papers with this objective, as it is presented by Baran [5]. There were new works after Baran brying to reduce the computation burden to obtain the optimal topology, searching for its application in real system, like the Goswani [6] and Jasmon [7] papers.

Genetic algorithms [8] and ANNs 19,101 have been used tlo implement the distribution reconfiguration procedure. Kim [9] and Gauche [lo] works provided the solutiorc in appropriate time, but its optimality is not guaranteed.

Few authors have made significant contributions to present new formulations, concentrating efforts in both the load flow effectiveness and the obtainment of heuristic rules. A new formulation using the 0-1 integer programming was developed by Sarma [ 111 to guarantee the optimal solution without considering the computational burden.

This paper proposes a methodology, to solve the on- line distribution feeder optimal reconfiguration problem for resistive loss reduction, taking into account the reduction of computational burden.

2. Methodology

The proposed method is composed by the following steps:

2.1 Step 1: Monte Carlo Simulation

This, work uses the load pattern presented in Table 1 like medium value of a normal load distribution with a 10% standard-deviation. The Monte Carlo Simulation is

179

used to obtain the demand variation necessary to the ANN training (Step 3). If the standard-deviation grows (possible demand variation), the expected number of optimal configurations (obtained during the loss reduction process executed in Step 2) will grow too. The most frequent configuration, rarely presents the minor medium active power loss [12].

2.2 Step 2: Loss Minimization

This step uses the Baran heuristic method [ 5 ] with the significant contribution of Jasmon [7] to obtain the loss optimal configuration, with each initial load condition obtained in Step 1. The distribution initial configuration can be changed using the line L5 presented in Table I , so the optimal topology for each desired load pattern is obtained. The loss minimization algorithm is used so many times as the adopted number of samplings via Monte Carlo Simulation. As it was presented in other works [4,5], the loss minimization improves the voltage profile due to the reduction of the system total load.

2.3 Step 3: ANN training

The implemented ANN multi-layer perceptrons (MLP) is trained using the back-propagation algorithm. This kind of ANN is recommended for input-output non-linear mapping applications [13]. For each one load states obtained in Step 1 , is determined the network configuration with minimum losses in Step 2. So, the ANN input data are the demands and the ANN output data are the optimal configurations. The number of sets input-output is equal to the number of samplings via Monte Carlo Simulation. An ANN is trained for each different optimal configuration obtained in Step 2. Then, this ANNs set will give the optimal configuration to any demand sampled, different or not those used during the training (this ANNs set assimilate the system characteristics). The ANN answer is obtained in a fast time. It is important to note that the first steps are executed in 1-2-3 order, and this set of steps is executed only once, if the initial number choice of samplings via Monte Carlo Simulation is suitable.

2.4 Step 4: Optimality

A formulation based on Sarma [l I ] is used to test the solution optimality given by the ANNs in Step 3. If the initial solution given fast by the ANNs is not the optimal, it is close to the optimal, like presented by Baran [SI. So, in few iterations in this step the optimal solution will be reached.

3. Mathematical Formulation

The Baran heuristic method [SI is based on the formula developed by Cinvalar [4], which determines the loss reduction ARPdue to a load transference between feeders. This reduction between one branch “b” originally open and one branch “m”, originally closed, is obtained using the equation (1).

;€Le$ icRighl

-(Pm2 + e m 2 ) [ C r i ] i E Right U Left

where: Left

Right

m branch to be opened.

the mesh side where will occur the diminution of active power flow; the mesh side where will occur the increment of active power flow,

Jasmon [7] proposed the utilization of the equation (1) only for the branches which the active power flow is closer (up or down) to the optimum active power flow value, decreasing the computational burden of the Baran method.

Sarma [ 1 11 proposed a new 0- 1 integer programming to obtain the optimal solution of the reconfiguration problem. The formulation based on Sarma can be easily assimilated from the Figure 1. At first, the current in each system line is determinated from the line states, so:

il = 12 +(1-L5)(14 + I s ) (2 ) i3 =( l -L5)(14 + 1 5 ) (3 ) i4 = I5 (4) i2 = I 3 + Lg(I4 + Z5) (5) i5 = L5(Z4 +Z5) ( 6 ) L5 LO (7)

where: i line currents, I bus currents.

In the equations (2-6) L5 = O if the line L5 is not being used and L5 = 1 otherwise.

Afterwards, the loss objective function is minimized with the current values above, respecting the constraint of the equation (7).

180

(8) O.F.= min C r k i k .2

k = l , n L where:

nL number of lines, Y line resistance.

the hidden layer and 1 output unit in the output layer. The output layer will indicate how close the ANN solution is of the desired solution.

Table 2 - Obtained Configurations Considering 500 and 1000 Load Patterns

4. Demonstrative Example

The proposed algorithm is applied to a test system, whose diagram is depicted in Figure 1. The system data [12] such as node connections, load at the line ends and line impedances, can be found in Table 1.

Figure 1 - Demonistrative Example

Everytime the line L5 (nodes 3-4) is used, a mesh is formed in the distribution system. This mesh has to be open (in the optimum point) maintaining the system radial characteristic [5]. Two different optimal configurations are obtained with 500 and 1000 samplings, to the different load patterns obtained in Step 1 , as one can observe in Table 2.

Table 1. Example System Characteristics

Node

0.002

I I I I

The Table 2 shows that for 500 and 1000 samplings the system has the same characteristics. This fact indicates the convergence of the Monte Carlo Simulation. Two MLP neural networks are trained with the first set of 500 load patterns. There are 5 load nodes in the system (5 input units are used in the input layer), 3 hidden units in

11 Lineopen I Occurrence I Occurrence 11

Aftelr the training process, one input set (loads) sampled in the same conditions of the training set is submitted to those ANNs. The given answers (on/off line states) by the Baran minimization algorithm [5] and by the ANNs are the same, as can be observed in Table 3.

Table 3. Optimal Topology I Baran Method I ANN I

Finixlly, the optimality is verified using the equations (2-8) based on Sarma i l l ] , with the sampled values of current which are listed below.

12 = 0.3679 , I3 = 0.8560 , I4 = 0.5893 , I 5 = 0.9714

This procedure confirmed the optimality of the solution given by the neural network (Table 3).

5. Conclusions

An efficient algorithm for the optimal reconfiguration of primary distribution network with minimum losses, based on ANNs and integer programming technique, was presented.

This method is not subjected to the initial topological conditions as the most existing algorithms are.

Dule to both the simplicity of the algorithm implementation and the low time of execution, this approach is appropriate for the analysis of realistic large systenis in real-time.

181

Finally, an application package based on the proposed model is under evaluation, using real cases obtained from the CELESC (local distribution company).

6. Acknowledgments

The authors are grateful by the fmancial support of both CNPq and Capes (Brazilian Research Councils).

7. References

[l] A. Merlin and H. Back, “Search for a Minimum-Loss Operational Spanning Tree Configuration in Urban Power Distribution Systems”, Proc. of the Fifth Power System Conference (PSCC) Cambridge U.K. 1975, pp. 1-18.

[2] DShirmohammadi and H. W. Hong, “Reconfiguration of Electric Distribution Networks for Resistive Line Losses Reduction”, IEEE Trans. on PWRD-4 (1989), pp. 1492- 1498.

[3] Borozan V., Rajicic D. and Ackovski R.,“lmproved Method for Loss Minimization in Distribution Networks”, IEEE Trans. on Power Syst. - 10 (1995), pp. 1420-1425.

[4] Civanlar S., Grainger J. J., Yin H., and Lee S. S. H., “Distribution Feeder Weconfiguration for Loss Reduction”, IEEE Trans. on PWRD-3 (1988), pp. 1217- 1223.

[5] M. E. Baran and F. F. Wu, “Network Reconfiguration in Distribution Systems for Loss Reduction and Load Balancing”, IEEE Trans. on PWRD-4 (1989), pp. 1401- 1407.

[6] S. K. Goswami and S. K. Basu, “A New Algorithm for the Reconfiguration of Distribution Feeders for Loss Minimization”, IEEE Trans. on PWRD-7 (1992), pp.

[7] G. B. Jasmon and L. H. Callistus C. Lee, “A Modified Technique for Minimization of Distribution System Losses”, Electric Power System Research - 20 (1991), pp.

[8] K. Nara, A. Shiose, M. Kitagawa and T. Ishibara, “Implementation of Genetic Algorithm for Distribution System Loss Minimum Re-configuration”, IEEE Trans, on PWRD-5 (1992), pp. 1044-1051.

[9] Kim H., KO Y. and Jung K.-H., “Artificial Neural Network Based Feeder Reconfiguration for Loss Reduction in Distribution Systems”, IEEE Trans. on PWRD-8 (1993),

[ 101 E. Gauche and J. Coelho, “Distribution Reconfiguration Considering Demand Variation Using Neural Techniques” (in Portuguese), 30 ELAB - Encontro Euso- Afro-Brasileiro de Planeamento e Explora@o de Redes de Energia, Oporto (1996), Portugal, pager 22.

[l I ] N. D. R. Sarma and K. S. Prakasa Rao, “A New 0-1 Integer Programming Method of Feeder Reconfiguration for Loss Minimization in Distribution Systems”, Electric Power Systems Research - 33 (1995), pp. 125-131.

Algorithm for Minimal Loss Reconfiguration in Distribution Networks”, submitted to the 1996 IEEE Summer Meeting.

[I31 “A Tutorial Course on Artificial Neural Networks with Applications to Power Systems”, IEEE PES 1996.

1484- 1490.

81-88.

pp. 1356-1366.

1121 E. Lbpez, H. Ogazo, P. Pedrero and R. Diaz, “An Efficient

182