Tabu Search Based Topology Modification for Power Systems Hwachang Song1 1 Dept. of Electrical and Information Engineering, Seoul National Univ. of Science and Technology, 232 Gongneung-ro, Nowon-gu, 139-743 Seoul, Republic of Korea
[email protected]
Abstract. The paper presents a method for topology optimization of power systems as countermeasures against excessive fault current level. By the method, the magnitudes of Thevenin impedances at the critical locations would be increased for the reduction of fault current levels. In this paper, a Tabu search on the solution space with binary variables was adopted as the solution technique. Keywords: Fault level security, Tabu search, topology optimization, power systems.
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Introduction
This paper mainly discusses applicable remedial actions to the excessive fault current problem. In the system planning stage, the usually accepted countermeasure is to install new circuit breakers with higher short-circuit capacity enough to cover the excessive fault currents, but this measure requires an amount of investment costs. As in [1], there are several other measures applicable for the purpose. Of them, bus splitting and line opening can be adopted in the operational planning stage. If properly chosen, these actions can successfully lessen fault current levels at critical locations by increasing the magnitudes of Thevenin impedances; however, system static security might be severely deteriorated in terms of voltage and thermal limits. For adequate section of locations for the two remedial actions, the two aspects of reducing fault current and maintaining static security should be considered. This paper describes a method for determining power system topology modification to reduce the fault current levels at critical locations. For the topology change, this paper covers bus splitting and line opening. The locations of the topology changing actions are assumed to be chosen in advance. For bus splitting, there are several ways to apply for a bus, if a number of incoming and outgoing branches is connected to the bus. To solve the problem with binary variables of whether the remedial actions are conducted or not, this paper adopts a Tabu search [2], searching the solution space with an extended objective function. This paper includes an illustrative example applying the Tabu search based topology modification algorithm to 23-bus test system. AST 2013, ASTL Vol. 20, pp. 1- 4, 2013 © SERSC 2013
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Proceedings, The 5th International Conference on Advanced Science and Technology
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Topology Modification
The main purpose of the topology modification algorithm is to reduce fault current levels at critical locations. After the long-term planning is completed, system operators (SO) need to check whether the corresponding system satisfies security criteria for the real-time operation. In power system operation, there are several security issues, but this paper concentrates on fault current related security. The fault current, IF, which the load side bus experiences when a 3-phase short circuit is applied, is a function of VTh and ZTh, as follows:
IF =
VTh Z Th
(1)
For transfer capability enhancement, the reduction of |ZTh| is desirable, but it deteriorates fault level security. If the circuit breaker at the corresponding location has less short-circuit capacity than the fault current level, the fault might not be isolated in an adequate period of time and hence then it can be spread through the system. Moreover, it can result in second faults and the damage of the circuit breakers. 2.1
Problem Formulation
Consider that bus-splitting is applied to a busbar. There are many incoming and outgoing lines or transformers connected to an EHV (extra high voltage) substation. Thus several combinations are available even for a substation, but system operators may have a certain strategy to determine the adequate bus splitting. In this paper, it is assumed that the bus splitting method was predetermined. Thus, the decision variables of the problem can be expressed as binary variables representing whether to apply bus splitting or line opening at the corresponding location or not. For determining remedial actions of bus splitting and line opening at the given places, this paper adopts the following formulation: N RA
min ∑ wi bi i =1
s.t.
Vi ≤ I i max , i ∈ S F Z Fii
(2)
Vi min ≤ Vi ≤ Vi max , i = 1,..., N B S k ≤ S k max , i = 1,..., N BR Z Tii ≤ 1 − M T , i = 1,..., N L Z Li where bi is the decision variable for i-th remedial action and wi is the weighting factor for bi. In (2), NRA is the number of remedial actions considered; |Vi| stands for voltage magnitude at bus i; ZFii and ZTii denote (i, i) component of Z bus impedance matrix for fault and transfer capability analysis, respectively; ZLi represents the equivalent load impedance at load bus i; Vimin and Vimax are the lower and upper limits of voltage
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Tabu Search Based Topology Modification for Power Systems
magnitude at bus i; Sk and Skmax are complex power flow for branch k and its maximum thermal rating; NB, NBR and NL are the number of buses, branches and loads, respective; MT describes the margin of the index, which is less than 1. 2.2
Application of Tabu Search
To use Tabu search for the problem of this paper, the original formulation of (2) needs to be modified such a way that the objective function is extended using the penalty terms applied for those constraints violated. The extended objective function is described as follows: N RA
min ∑ wi bi + c F i =1
NB
N BR
i =1
k =1
∑ PFi + cV ∑ PVi + cS ∑ PSk
i∈S F
(3)
NT
+ cT ∑ PTi i =1
Vi 0 ≤ I i max Z Fii PFi ≡ Vi Vi − I > I i max i max Z Fii Z Fii Vi min ≤ Vi ≤ Vi max 0 PVi ≡ Vi min − Vi Vi min > Vi V Vi < Vi max i max − Vi 0 S k ≤ S k max PSk ≡ S k − S k max S k > S k max Z Tii 0 ≤ 1− M T Z Li PTi ≡ Z Tii Z Tii − 1 + M > 1− MT T Z Li Z Li where cF, cV, cS and cT are the weighting factors for the penalty terms. The search methed employed in this paper is based on a local search with Tabu list from an arbitrarily chosen initial solution in the space consisting of the binary decision variables. For the problem with small number of decision variables, the method can easily provide acceptable solution in a small number of iteration. As the solution dimension gets large, however, final solutions might not achieve dramatic changes even though it performs several independent runs of searching from different starting solutions, due to the fact that local minima tend to be clustered. The search of this paper is to move the current solution to the best one obtained by evaluating the extended objective function value with (3) for the k-level neighborhood in a random manner within the maximum number of searched neighbors.
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Proceedings, The 5th International Conference on Advanced Science and Technology
The algorithm indeed takes a random initialization procedure and the search starts from the initial solution. Thus, the performance of applying the method depends on the initial solution. Fig. 1 shows the change in the extended objective function value for a case with one of worst starting points. By examining the k-level neighborhood in a random manner, the algorithm might have more chance to improve the solution quicklier.
Fig. 1. Extended objective function values at each searching iteration when applying the proposed method
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Conclusion
This paper presents a Tabu search based topology modification algorithm for electrical networks. The algorithm is for the problem of reducing fault current level, and the solution needs to satisfy system operating limits that need be considered in the operational planning stage. This paper adopts a search method with Tabu list to determine the solution's next position by examining the k-level neighborhood in a random manner within the maximum number of objective function evaluation.
References 1. Khorrami, M., Nader, M.S., Nejhad, N.K.: Short Circuit Current Level Control and its Effects on Circuit Breakers Transient Studies. Journal of Electrical Engineering: Theory and Application 1, 4--17 (2010) 2. Glover, F.W., Laguna, M.: Tabu Search, Kluwer, Norwell (1998)
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