A fast LP approach for enhanced utilization of variable impedance based FACTS devices

Transmission systems are under stress and need to be upgraded. Better utilization of the existing grid provides a fast and cheap alternative to building new transmission. One way to improve the utilization of the transmission network is power flow control via flexible ac transmission system (FACTS) devices. While FACTS devices are used today, the utilization of these devices is limited; traditional dispatch models (e.g., security constrained economic dispatch) assume a fixed, static transmission grid even though it is rather flexible. The primary barrier is the complexity that is added to the power flow problem. The mathematical representation of the DC optimal power flow, with the added modeling of FACTS devices, is a nonlinear program (NLP). This paper presents a method to convert this NLP into a mixed-integer linear program (MILP). The MILP is reformulated as a two-stage linear program, which enforces the same sign for the voltage angle differences for the lines equipped with FACTS. While this approximation does not guarantee optimality, more than 98% of the presented empirical results, based on the IEEE 118-bus and Polish systems, achieved global optimality. In the case of suboptimal solutions, the savings were still significant and the solution time was dramatically reduced.