Iterative McCormick Relaxation for Joint Impedance Control and Network Topology Optimization

A team of researchers has published a new method for optimizing modern power grid operations, addressing the complex challenge of coordinating Variable Impedance Devices (VIDs) like Smart Wires with Network Topology Optimization (NTO). The paper 'Iterative McCormick Relaxation for Joint Impedance Control and Network Topology Optimization' introduces an iterative correction technique to enhance the accuracy of McCormick relaxation schemes, which convert inherently non-linear power flow problems with bilinear terms into more manageable linear constraints.

The technical approach tackles what's known as a mixed integer nonlinear problem (MINLP) - one of the most challenging optimization problems in power systems. By applying iterative McCormick relaxation alongside DC power flow equations, the researchers created a framework that outperforms traditional non-linear methods, SOS2 piecewise linear approximations, and standard McCormick relaxation. The method was validated on standard IEEE benchmark test systems, demonstrating practical applicability for real-world grid operations.

This research matters because power systems are increasingly deploying distributed VIDs and topology optimization schemes to address operational challenges like line congestion, transformer overloads, and voltage violations. Current approaches struggle with the computational complexity of coordinating these elements simultaneously. The proposed iterative method provides grid operators with a more efficient tool for optimizing both device settings and network configuration, potentially leading to more reliable and cost-effective power delivery.