# A Mathematical Programming Approach for Allocation and Analysis of TCSC in Power Transmission Systems

## Keywords:

Mathematical programming, Reactive power control, Flexible AC transmission systems, Power system control, Optimization## Abstract

In this paper, a mathematical programming approach based on a branch and bound (BB) algorithm is proposed in order to determine the optimal allocation of thyristor-controlled series compensators (TCSC) in electrical power transmission systems, considering line thermal limits. The TCSC modeling is added in the Y-bus matrix, facilitating the computational implementation. BB-Y is the methodology used in this paper aiming to maximize the loading of the system considering a certain quantity of TCSC. In addition, the proposed algorithm is implemented for another test, using a determined number of TCSC, in order to improve the network voltage profile and minimize the total transmission losses. The methodology uses an interior point method to solve the problem relaxed, modeled as a reactive optimal power flow problem. Simulations are performed on the IEEE 118-bus test system, allocating different quantities of TCSC to find the maximum load the system can support. Given a certain number of TCSC, previously defined for a specific load, the TCSC are reallocated considering different objectives. For two TCSC the time for relocation is shorter than 4 seconds. The results also show that from three TCSC onwards, the maximum load increasing is not relevant, being around 0.3%. Therefore, the conclusion is that the algorithm has a low processing time, and conservative solutions allied with the presented methodology can be used in the optimal allocation of TCSC, what the aim is to optimize the systems performance.

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