Security-Constrained MIP Formulation of Topology Control Using Loss-Adjusted Shift Factors

Following up on our previous work, we formulate a linear, loss-adjusted, shift factor mixed integer program (MIP) to co-optimize generation and network topology. While both the Bθ and shift factor topology control (TC) formulations lead to production cost saving, we showed that the shift factor formulation performs better for small to medium switch able sets. In this paper we extend the original TC shift factor formulation to include marginal losses. We derive loss-adjusted shift factors and show that both losses and flows can be updated linearly with a change in topology by taking advantage of flow-canceling transactions (FCTs). The marginal loss formulation we present in this paper closely resembles that of most market engines. In doing so, we aim to better approximate the AC power flow and to generate topologies leading to production cost savings while maintaining feasibility subject to AC security constrained power flow (SCOPF) constraints.