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Distributed flexible AC transmission systems (D-FACTS) has become increasingly popular in recent years. Among all types of D-FACTS devices, variable-impedance D-FACTS is the most cost-effective. However, integration of these devices within an optimal power flow problem introduces nonlinearities that are computationally challenging. In this study, a computationally efficient stochastic optimization model is proposed to optimally allocate variable-impedance D-FACTS considering the randomness of wind power output and load variation. The optimal locations and economic benefits of D-FACTS are compared with those of conventional FACTS. The results show that D-FACTS devices are more cost-effective than conventional FACTS, considering complex operation conditions in a transmission network. The economic benefits will increase if periodical redeployment of D-FACTS is allowed. 

Distributed flexible AC transmission systems (D-FACTS) is an attractive power flow control technology, featuring low cost and flexibility for re-deployment. Optimal allocation of D-FACTS and the mutual influence between existing FACTS and newly planned D-FACTS are challenging but important issues that need to be addressed. This paper proposes a co-optimization model of FACTS and D-FACTS based on stochastic optimization, considering the uncertainties caused by fluctuating load and renewable energy generation. Using this model, the location and set points of FACTS and D-FACTS can be co-optimized; in a system with existing FACTS, the locations of FACTS can be predetermined and the locations of D-FACTS can be optimized. The study shows that existing FACTS affects the optimal locations of D-FACTS and adding D-FACTS into the system affects the optimal set points of existing FACTS. Thus, it is essential to co-optimize the two technologies to maximize their economic benefits.