Iterative McCormick Relaxation for Joint Impedance Control and Network Topology Optimization

Abstract: Power system operators are increasingly deploying Variable Impedance Devices (VIDs), e.g., Smart Wires, and Network Topology Optimization (NTO) schemes for mitigating operational challenges such as line and transformer congestion, and voltage violations. This work aims to optimize and coordinate the operation of distributed VIDs considering fixed and optimized topologies. This problem is inherently non-linear due to power flow equations as well as bilinear terms introduced due to variable line impedance of VIDs. Furthermore, the topology optimization scheme makes it a mixed integer nonlinear problem. To tackle this, we introduce using McCormick relaxation scheme, which converts the bilinear constraints into a linear set of constraints along with the DC power flow equations. We propose an iterative correction of the McCormick relaxation to enhance its accuracy. The proposed framework is validated on standard IEEE benchmark test systems, and we present a performance comparison of the iterative McCormick method against the non-linear, SOS2 piecewise linear approximation, and original McCormick relaxation.