FACTS Devices Allocation via Sparse Optimization

Although there are vast potential locations to install FACTS devices in a power system, the actual installation number is very limited due to economical consideration. Therefore the allocation strategy exhibits strong sparsity. This paper formulates FACTS device allocation problem as a general sparsity-constrained OPF problem and employs L
_q
(0 <; q ≤ 1) norms to enforce sparsity on FACTS devices setting values to achieve solutions with desirable device numbers and sites. An algorithm based on alternating direction method of multipliers is proposed to solve the sparsity-constrained OPF problem. The algorithm exploits the separability structure and decomposes the original problem into an NLP subproblem, an L
_q
regularization subproblem, and a simple dual variable update step. The NLP subproblem is solved by the interior point method. The L
_q
regularization subproblem has a closed-form solution expressed by shrinkage-threholding operators. The convergence of the proposed method is theoretically analyzed and discussed. The proposed method is successfully tested on allocation of SVC, TCSC, and TCPS on IEEE 30-, 118-, and 300-bus systems. Case studies are presented and discussed for both single-type and multiple-type FACTS devices allocation problems, which demonstrates the effectiveness and efficiency of the proposed formulation and algorithm.