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Electric Power Systems Research 42 (1997) 165 172
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Optimal SVC placement for voltage stability reinforcement C.S. Chang *, J.S. Huang Department of Electrical Engineering, National University of" Singapore, 10 Kent Ridge Crescent, Singapore 116260, Singapore Received 8 November 1996
Abstract
This paper presents a scheme of hybrid optimization using the simulated annealing and Lagrange multiplier techniques for optimal SVC planning and voltage stability enhancement. It also proposes a 4-step procedure for synthesizing the optimal reactive reinforcement. The hybrid optimization is formulated into a constrained problem with non-differentiable objective function in both continuous and discrete variables. By decomposing the optimization into two subproblems, an optimal SVC placement is obtained and the reactive margin is maximized. ,~ 1997 Elsevier Science S.A. Keywords: Static var compensator placement; Voltage stability enhancement; Reactive margin; Lagrange multiplier; Simulated annealing
1. Introduction
Static var compensators (SVCs) have been extensively used in electric power systems for reactive power support and voltage stability enhancement. SVC planning, therefore, has long been a major concern of power industry. According to the objectives of installing SVCs, such as increasing operation efficiency, ensuring a certain security level, and improving service quality, SVC planning can be formulated into an optimization problem. This type of optimization problem may have non-linear and non-differentiable objective functions and constraints, and may contain both continuous and discrete variables. Ref. [2] proposed a two-stage optimization method using an expert system and a simulated annealing algorithm to solve the SVC planning for maximum system security and minimum cost in operation. Ref. [6] developed a computer package based on the simulated annealing techniques for multiple-objective SVC planning of large scale power systems. The multiple-objective optimization problem was transformed into single-objective by employing the e,-constraint method to achieve good tradeoffs among different subobjectives. In ref. [7], a hierarchical approach was presented for var optimization in system
*
Corresponding author. E-mail:
[email protected] 0378-7796/97/$17.00 ,~G 1997 Elsevier Science S.A. All rights reserved. PII S 0 3 7 8 - 7 7 9 6 ( 9 6 ) 0 120 1- 1
planning. The approach sought optimal var placement through solving two subproblems iteratively, namely: vat dispatch in system operation and var allocation in system planning. In the above methods, attention has been focused upon power loss, voltage deviation, and expenditure. Relatively little effort has been directly involved with voltage stability improvement. One conceptually simple method of SVC planning for voltage stability enhancement is based on modal analysis around a critical operating point of the power system. With this method, eigenvalue analysis of the system Jacobean matrix near the critical point is exploited to identify the buses vulnerable to voltage collapse and the buses best located for reactive power injection [1]. Obviously this method depends upon the critical mode selection and can meet difficulties in capacity apportionment for multiple SVC placement. It is known that voltage collapse and other instability problems can be regarded as phenomena associated with inability of power systems to meet reactive demands [8]. When SVCs are used for voltage stability reinforcement, optimal placement can be obtained by seeking a compensation scheme which maximizes the system reactive margin. Several algorithms have been developed for such a scheme [3-5]. In these references, participating factors were adopted to determine the load increasing directions when stressing power systems. Nonlinear programming techniques were used to calculate the reactive margins [3,5]. By introducing one
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more variable (the power factor) to constrain the real and reactive demands for each busbar, Ref. [4] solved the apparent power margin of power systems. For a practical and reliable estimation, these methods took into account system constraints, such as generator reactive limits, allowable voltage deviation ranges, and lower and upper bounds of transformer taps. Apart from maximizing the system reactive margin, this paper proposes an approach which also seeks the optimal SVC placement. The approach is hybrid with two recursive optimization blocks. In the first optimization block (the SVC placement subproblem), the method of parallel simulated annealing is used for best utilization of a given SVC overall capacity by evaluating: (a) the number of SVCs, (b) the locations of these SVCs, and (c) the apportionment of the compensation. In the second optimization block (the reactive margin subproblem), the Lagrange multiplier method is used to maximize the reactive demand margin of the power system for each configuration of the SVC reinforcement as generated from the main subproblem. To assess effects of the reactive reinforcement on voltage stability, the worst contingency should be identified and studied in order to determine whether the reactive reinforcement is stretched beyond its limit during adverse conditions. The worst contingency is affected by different operating modes of the system, and can be treated as an optimization problem. In this paper, an approach of synthesizing the reactive reinforcement is proposed with the use of the hybrid optimization. The is basically a 4-step procedure: 1. identification of the worst contingency which can either be a process of successive contingency analysis or optimization; 2. choice of the design configuration which can either be the worst-contingency or some other configuration; 3. evaluation of reactive margin and optimal SVC placement for the design configuration with the use of the proposed hybrid optimization; 4. performance assessment of the above reactive reinforcement using other system configurations. The paper is organized as follows. Section 2 outlines the hybrid scheme of SVC placement and reactive margin optimization. Section 3 defines and formulates the reactive margin for a power system. According to the formulation, Section 4 presents the reactive margin subproblem, and Section 5 describes the SVC placement subproblem. Numeric simulations and discussions are given in Section 6. The above approach for synthesizing the optimal reactive reinforcement is applied to the IEEE 14-bus system, and two of the case studies performed are presented. Section 7 contains the concluding remarks of the paper.
2. Overall algorithmic layout for optimal SVC
placement In this paper, the objective of planning a SVC reinforcement scheme is to enhance voltage stability. Traditionally, SVCs are installed in heavily loaded areas and at the weakest buses to alleviate stressed power systems. On such a basis, the SVC planning is reduced to a problem of assigning the appropriate capacity to certain busbars in a chosen area of the power system. In many cases, however, placing SVCs simply according to the strength of the node voltage does not result in an optimal reactive reinforcement for the benefits of voltage stability. The effectiveness of each proposed SVC reinforcement scheme should be assessed by how much it increases the system reactive margin. Thus the SVC compensation should be planned more intelligently in order to maximize the system reactive margin. The system reactive margin is defined as the maximum amount of extra reactive demand to be supplied by the system, before it reaches a critical point and encounters problems in maintaining voltage stability.
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C.S. Chang, J.S. Huang/Electric Power Systems Research 42 (1997) 165-172
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The algorithm for the optimal SVC placement is formulated into an optimal search problem with a main subproblem and a subproblem for evaluating the system reactive margin• Without an intelligent scheme as shown in Fig. 1, the computational costs involved are prohibitively high, as this would involve an optimal search over a large number of SVC placement schemes and operating states. In the subproblem for evaluating the system reactive margin, the Lagrange multiplier (LM) method is adopted to maximize the extra reactive demand to be supplied by the system while maintaining voltage stability. At the beginning of the planning exercise, various constraints of the SVC placement such as the number, the characteristics and the overall capacity of the SVC compensators are established. In the main subproblem, the simulated annealing technique is employed to search among SVC placements, each of which is described by the number of SVC nodes, the locations, and the capacity apportionment, so as to maximize the reactive demand margin of the study system. Apart from the voltage stability enhancement, the SVC planning is also related to other factors, such as the costs and environment impacts. For cost effectiveness, it is necessary to limit the number of SVC units, as well as to aim for a high reactive demand margin.
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