Optimal Network Reconfiguration Of Electrical Distribution Systems

Optimal Network Reconfiguration of Electrical Distribution Systems Bhoomesh Radha, Robert T. F. Ah King and Harry C. S. Rughooputh University of Mauritius Reduit, Mauritius [email protected]

Abstract- Distribution systems are critical links between the utility and customer, in which sectionalizing switches a r e utilized for both protection and configuration management. Usually, distribution systems a r e designed.to be most efficient a t peak load demand. Obviously, the network can be made more efficient by reconfiguring it according to the variation in load demand. This paper surveys the methods that have been proposed to solve the network reconfiguration problem and presents a n integration of two algorithms: a network-topology-based three-phase distribution power flow algorithm and an algorithm for determining power loss of a radial configuration for a power distribution network Simulation results of the proposed method on a 22 kV Bramsthan section of the CEB network of Mauritius are presented.

investigate methods for network reconfiguration. The objective of network reconfiguration is to reduce power losses and improve reliability of power supply by changing the status of existing sectionalizing switches and ties. This paper surveys the methods that have been proposed to solve the network reconfiguration problem and presents an integration of two algorithms: a network-topology-based three-phase distribution power flow algorithm and an algorithm for determining power loss of a radial configuration for a power distribution network. Simulation results for the 22 kV Bramsthan section of the CEB network of Mauritius are presented.

2 Survey Methods

Network

Reconfiguration

Under normal operating conditions, distribution feeders may b e frequently reconfigured by opening and closing switches to reduce line losses, improve feeder voltage profile and increase network reliability while meeting all load requirements and maintaining a radial network. These requirements result in a very complicated non-linear integer optimization problem. The exact optimal solution of such a problem may be obtained only by enumeratively examining all possible switch options, requiring prohibitively long computational time because the number of switch options is usually very large in a practical distribution network. This problem is not easily solvable by standard optimization methods and yet its accurate solution can result in vast savings for electricity utilities.

1 Introduction Every electrical utility in the world has a vast network of distribution systems to supply power to its consumers. The average line losses in the transmission and distribution system in Mauritius are found to be in the region of 12%, which is high compared to corresponding values (7 to 9%) io advanced countries like the USA, France, Sweden and Japan, etc. These losses have to be brought down to a reasonable level in order to improve the efficiency of distribution system. Furthermore, in the present days of energy crises and with increasing concern for environmental pollution, energy conservation should be a priority.

Different algorithms have been previously used to solve the recoofiguration problem and each method has involved one or more difficulties such as: (1) The high computational time for medium and large scale systems may be prohibitive, (2) Reliance on heuristics, hence sub optimal solutions, (3) Difficulty in obtaining feasible solutions.

Power losses in the distribution system at the time of peak load condition increase the requirement of generating capacity, while the energy over that required by the system load increases. In other words, payload of the system decreases. No doubt, the line losses cannot altogether be avoided, due to inherent resistance of distribution lines; however these can be reduced to a reasonable low value by taking suitable measures.

Sarfi et al [l] survey a variety of approaches to the network reconfiguration problem. This survey begins by stating, “The generalized reconfiguration problem presents a considerable computational burden for a distribution system of even moderate proportions.” This assumed computational burden follows 6om the observation that “the nonlinear nature of the distribution system necessitates that at each iteration of an optimization algorithm a load flow operation be performed to determine a new system operating point.” If this is correct, it follows that a direct or exhaustive solution is infeasible, so that a practical solution

Distribution systems are critical links between the utility and customer, in which sectionalizing 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 12% of the total power generated is wasted in the form of line loss at distribution level. Hence, it is of great benefit to

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must employ some heuristic search method, possibly guided by a simplified optimization procedure. This is the approach taken by most of the methods surveyed. 2.1 Discrete Branch And Bound Method Merlin and Back [ 2 ] presented one of the frst works reported to reduce losses in a distribution network. It presents an integer-mixed non-linear optimization model that is solved through the discrete branch and bound method. Its solution scheme starts with a meshed network by initially closing all switches in the network. The switches are then opened one at a time until a new radial configuration is reached. An equivalent linear resistive network model is used to determine the switches to be opened. Due to the combinatorial nature of the problem, it requires checking a great number of configurations for a real-sized system.

developed to obtain the optimal switch plan with m i n i u m switch operations to accomplish the transition 60m the initial Configuration to the optimal configuration. This optimal switch plan is obtained by eliminating those unnecessary switch operations suggested during the iterative solution procedures of the single-loop optimization approach.

In [7], Baran and Wu developed search techniques based on the idea of branch exchange for the reconfiguration of balanced distribution systems. To assist in the search, two methods are proposed for the computation of load flows for radial networks with different degrees of accuracy: the approximate power flow and backward-forward methods. In addition, an algebraic expression is proposed that allows estimating the loss reduction and load-balincing index for a given topological change. Rudnick et 01 [SI modified the solution methodology proposed by Baran and Wu [7]. To obtain a solution, that methodology requires fulfilling a large amount of load flow calculations, and due to the great computational effort involved for a real sized distribution system, it turns out to be impractical. As a solution to this difficulty, a simplified non-iterative calculation method is proposed that allows calculating the power flows and the voltages of the buses of the system with reasonable accuracy, drastically reducing the computational effort.

Shirmohammadi and Wong [3] used the same heuristic procedure exposed in [ 2 ] . They share its advantages and prevent its main disadvantages. The solution scheme also starts by closing all the network switches, which are then opened one after another by determining the optimum flow pattern in the network. 2.2 Switch Exchange Type Heuristic Method In [4], Civanlar ef al suggested a switch exchange type heuristic method, where a computationally effective formula was presented for determination of the loss change due to a switch exchange. Goswami and Basu [ 5 ] extended the method of Civanlar ef al in an intuitative way by simply limiting the switch exchange operation within a single loop each time. An improved configuration is obtained by successively conducting the single-loop switch exchange until no further improvement can be obtained. This singleloop optimization approach is superior to other heuristic algorithms since it provides implementation simplicity, computation efficiency, solution feasibility and optimality.

All of the proposed methods described above employ a heuristic search and thus they converge to a local optimum solution, that is convergence to the global optimum is not guaranteed. 2.3 Exhaustive Search Algorithm

Morton and Mareels [9]proposed a more efficient solution to the network reconfiguration problem. They suggested a method for determining a minimal-loss radial configuration for a power distribution network, using an exhaustive search algorithm. Despite being exhaustive, the method used is highly efficient, deriving its efficiency from the use of graph-theoretic techniques involving semi-sparse transformations of a current sensitivity matrix. The algorithm can be applied to networks of moderate size and has advantages over existing algorithms for network reconfiguration in that it guarantees a globally optimal solution (under appropriate modelling assumptions), and is easily extended to take account of phase imbalance and network operation constraints.

Fan ef a/ [6] presented an analytical description and a systematic understanding about the single-loop optimization approach via qualitative analysis. The problem of network reconfiguration for minimum loss is formulated as an integer optimization problem with a quadratic objective function, &1 type state variables and a linear constraint equation with state dependent formulas. This nonlinear integer-programming problem, if linearized could be approximately represented by an integer LP (Linear Programming) problem. This understanding leads to the consideration of applying the concept of simplex method normally used for solving LP problems, which, in turn leads to the direct derivation of the single loop optimization approach. This fact indicates that single-loop optimization approach actually originates from the same technical principle as the simplex method. In addition, a simple and efficient scheme is used to calculate the load flow and loss change in the network after a switch exchange in a loop. A heuristic procedure is then

2.4 Simulated Annealing

At present, new methods based on artificial intelligence have been used in DNRC [IO, 111. Chiang and JeanJumeau [ l 11 presented a simulated annealing (SA) method to solve the DNRC problem, in which the SA was very time-consuming. It requires an improved SA with high speed to handle the DNRC problem.

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Theorem 1 191: Let G be the graph of a distribution

2.5. Genetic Algorithm

One of the fust studies where genetic algorithm (CA) is applied to the global optimal solution of DNRC is discussed in [IO]. This study shows that GA rather than the SA approach obtained a better performance. Zhu [12] further refines the GA method by modifying the string structure and fitness function. In [lo], the string used in GA describes all the switch positions and their " o d o f f states. The string can be very long and it grows in proportion with the number of switches. For large distribution systems, GA. cannot effectively search such long strings. In [12], the string is shortened. To reduce computational burden, approximate fitness functions were used in GA to represent the system power loss [lo]. It may affect the accuracy and effectiveness of GA. GAS are essentially unconstrained search procedures within the given represented space. All information should be fully represented in the fitness function. An over-approximated fitness function would lead directly to unreliable solution. In [12], a precise fitness function is used.

network, let T c G be a tree and let an

elementary

tree

c r , c q E G . Let S of the tree networks the To

Y.l

transformation

k )be

involving

arcs

and SI be the sensitivity matrices and T / respectively, in which

T

'row corresponds to the arc cy, respectively cy, -

and other rows correspond to like arcs. Let rIE GI , -

12s

Gz be the nodes incident with c, , and let G = 1 if -

-

cr is directed from ri to rz , and -lothenvise. Then 1)

I S,k=

2)

I Smk=

if

SyI-

Sy,=

I

Slk=

0 if

0

OTSmk=

0

,

GrSmr2Smk

If sIrI- slrrf 0 and

3) then

SJk

SIk#

Smk#

0 ,othenvise

0 , with j

#

m ,

/ SJk= S J ' I - S J ? ~

3 Network-Topology-based Three-phase Load Flow

The following results are used, the proof of which can be found in [9]: 1) Let T c G be a tree. Then )is a tree if and

A network-topology-based three-phase distribution power

onlyif C,E T and cjEK,b"

flow algorithm featuring robustness and computer economy has been developed by Teng [13]. This method fully exploits the special topology of a distribution network to obtain a direct solution. Two matrices: the bus-injection to branch-current matrix (or current sensitivity matrix), BIBC and the branch-current to bus-voltage matrix BCBV are sufficient to obtain the power flow solution. The traditional Newton-Raphson and Gauss implicit Z matrix algorithms, which need LU decomposition and fonvardlbackward substitution of the Jacobian matrix or the Y admittance matrix are not required.

T,,]k

2) Trees TI and TZ in G are related by an elementary tree transformation in G if and only if d 3 ) LetTi , Tz he any trees in G . If d

bt, Tz)=k

.

, then

For a new configuration, the sensitivity matrix is modified row by row; whenever a row of the matrix changes, the corresponding cable current is recalculated and the losses perturbed by the difference between the squares of the old and new currents, multiplied by the appropriate cable resistance:

Network Morton and Mareels [9] have suggested a method for determining power loss of a radial configuration for a power distribution network. This method is highly efficient, deriving its efficiency from the use of graph-theoretic techniques involving semi-sparse transformations of a ,

(TI, T z k l

Tz can be obtained from through a sequence of exactly k elementary tree transformations.

4 Power Losses of Radial Power Distribution

current sensitivity matrix, S

1.

In the case of the row corresponding to the arc being substituted, the magnitude of the current is unchanged, and the loss need only be altered to take account of the physical cable substitution:

The algorithm can he

applied to any networks and has advantages over other existing algorithms for network reconfiguration in that it is easily extended to take account of phase imbalance and network operation constraints. The algorithm developed can be used with any search algorithm for the solution of the network reconfiguration problem. Theorem 1 [9] describes the effect of an elementary tree transformation on the sensitivity matrix for a tree network.

doSF P,oss+(rr-rq)lid2

(2)

Based on Theorem 1 [9] and the network-topologybased three-phase distribution power flow algorithm [13], the flowchart representing the implementation of the above procedure to calculate the network losses using constantpower loads is given in Fig. 1. In the case of constant-

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current loads, the calculation of the power loss does not involve the network-topology-based three-phase load flow.

NO I

I

I

I

Input the reduced incidence matrix

A ,21 and s k for initial tree Tu. Input

.

the tie switch numbers of t e e Compute sensitivity matrix

TI

so fur tree T o

Modify S'according to Theorem 1 to obtain the sensitivity of the new spanning tree TI

Modify Z J to incorporate the impedances oithe new tree.

NI8 (C34)

I

(A

Fig. 2: Node numbering scheme of Bramsthan distribution network

A

5 Application of Network Reconfiguration to Distribution Systems of Mauritius The 22 kV Bramsthan section of the CEB network of Mauritius is selected for reconfiguration purposes. The test system shown in Fig. 2 comprises a cable network 'G having N = 33 nodes (or buses), C = 36 cable segments and nullity v =4. To fit in our framework, the supply bus 0 is relabelled as 33, and is taken as datum node. The cable network topology and impedances are given in Table A in the Appendix. The 32 load circuits can be assumed to have either constant power characteristic or constant current characteristic whose real and imaginary parts are provided in Table A, next to the data for the fust 32 cable segments. Cable segments 32 through 36 are tie lines. The system base is V=22 kV and S= IO MVA. Power factor is assumed to be 0.8 (lagging). The active and reactive powers of the loads at the sink nodes (customer load point) are obtained by multiply the rating of connected transformers with their respective demand factors (at 19:OO). The total system load is 21.39975 MW.

Compute

U Calculate network l o s s ~ z j l j

Return rcsu11 for configuration

TI

Fig. 1: Flowchart showing implementation of algorithm to calculate network losses of any tree of a distribution network using constant-power loads

In order to get a precise branch current and system power loss, the network-topology-based three-phase load flow described in the previous section is used. As the sub69

.t.

Radial nework Open switcher

I Power loss (MW)

I

Initial network Switch 33 Switch 34 Switch35

Switch36 1.2333

I

I

reconfiguration for system loss reduction,” Electric PowerSystems Research, vol. 31, pp. 61-70, 1994. A. Merlin and H. Back, “Search for a Minimum-Loss Operating Spanning Tree Configuration for an Urban Power Distribution System,” Proc. Of 5“ Power Systems Comp. Con., Cambridge, UK., Sept. 1-5, 1975. H. W. Hong, D. Shirmohammadi and “Reconfiguration of Electric Distribution Networks for Resistive Line Losses Reduction,” IEEE Transactions on Power Delivery, vol. 4, No. 2, pp. 1492-1498, April 1989. S . Civanlar, J. 1. Grainger, H. Yin and S. S . H. Lee, “Distribution Feeder Reconfiguration for Loss Reduction,” IEEE Transactions on Power Delivery, vol. 3,No. 3,pp. 1217-1223, July 1988. S. K. Goswami and S. K. Basu, “A New Algorithm for The Reconfiguration of Distribution Feeders for Loss Minimization,” IEEE Transactions on Power Delivery, vol. 7,No. 3, pp. 1482-1491, July 1992. J. Y. Fan, L. Zhang and J. D. McDonald, “Distribution Network Reconfiguration: Single Loop Optimization”, IEEE Transactions on Power Delivery, vol. 1 I , No. 3, pp. 1643-1647, August 1996. M. E. Baran and F. F. Wu, “Network reconfiguration in distribution systems for loss reduction and load balancing,” IEEE Transactions on Power Delivery, vol. 4,No. 2,pp. 1401-1407, April 1989. H. Rudnick, I. Hamisch and R. Sanhueza, “Reconfiguration of Electric Distribution Systems”, Faculty of Engineering, U.T.A. (Chile), Vo1.4, 1997 A. B. Morton and I. M. Y. Mareels, “An Efficient Brute-Force Solution to the Network Reconfiguration Problem”, IEEE Transactions on Power Delivery, vol. 15. No. 3. DD. 996-1000.,~ Julv 2000. [IO] K. Nara, A. Shiose, M. Kitagawa and T. Ishihara, “Implementation of genetic algorithms for distribution systems loss minimum reconfiguration”, IEEE Transactions on Power System, vol. 7, No. 3, pp. 1643-1647, August 1992. [ 111 H.-D. Chiang and R. Jean-Jumeau, “Optimal Network Reconfigurations in Distribution Systems: Part 1: A New Formulation and A Solution Methodology”, IEEE Transactions on Power Delivery, Vol. 5, No. 4, pp. 1902-1909, November 1994. [I21 J. Z. Zhu, “Optimal reconfiguration of electrical distribution network using the refmed genetic algorithm”, Electric Power Systems Research 62 (2002) 37-42. [I31 J.-H. Teng, “A network-topology-based three-phase load flow for distribution systems”, Proc. Nutl. Sci. Counc. ROC@). Vo1.24, No. 4,2000. pp. 259-264. [I41 R. T. F. Ah King, B. Radha and H. C. S. Rughooputh, “A Real-Parameter Genetic Algorithm for Optimal Network, Reconfiguration”, to be presented at International Conference on Industrial Technology ICIT’03, Maribor, Slovenia, 10 - 12 December 2003.

Genetic algorithm Switch 33 Switch 34 Switch 21 Switch 36 1.1759

The system real power loss is about 5.76% (1.2333 MW). Although the percentage of real power loss may seem low, loss reduction is always desirable (if possible). By applying genetic atgorithm, the optimal network reconfiguration is attained after five generations [14]. A reduction of 0.0574 MW has been achieved due to network reconfiguration. The percentage of real power loss for optimal network configuration is around 5.49%. This shows that a further reduction in real power loss is achieved. The tie lines before and after network The results reconfiguration are listed in Table 1. correspond to closing one of the four tie lines and opening one switch of the original network to maintain the radial structure. From the optimised network, it is observed that the current on the individual cable segments and the node voltages are within the operational limits. Thus, we have been able to fmd a new radial operating structure that minimises the system power loss while satisfying operating constraints.

I

6 Conclusions Using a constant-power load model, the feeder currents, network node voltages and network losses can be calculated using the network-topology-based three-phase load flow presented. Graph theoretic techniques that involve semi-sparse transformations of a current sensitivity matrix are used in the network-topology-based three-phase load flow to calculate the power loss, current through each line segments and voltage profile of the network. Consequently, the algorithms take into account operational limits, such as maximum current, power transfer limits on individual cable segments and node voltage constraints. These checks for such limits are incorporated into the algorithm and any particular configuration that fails to satisfy these checks are rejected. In this paper, a practical Mauritian distribution is used for reconfiguration purpose. Numerical results for the case study have been presented to illustrate the performance and applicability ofthe method.

References [I]

R. 1. Sarfi, M. M. A. Salama and A. Y. Chikhani, “A survey of the state of the art in distribution system

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I . .

Appendix

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