A Linear Model for Distributed Flexibility Markets and DLMPs: A Comparison with the SOCP Formulation

This paper examines the performance trade-offs between an introduced linear flexibility market model for congestion management and a benchmark second-order cone programming (SOCP) formulation. The linear market model incorporates voltage magnitudes and reactive powers, while providing a simpler formulation than the SOCP model, which enables its practical implementation. The paper provides a structured comparison of the two formulations relying on developed deterministic and statistical Monte Carlo case analyses using two distribution test systems (the Matpower 69-bus and 141-bus systems). The case analyses show that with the increasing spread of offered flexibility throughout the system, the linear formulation increasingly preserves the reliability of the computed system variables as compared to the SOCP formulation, while more lenient imposed voltage limits can improve the approximation of prices and power flows at the expense of a less accurate computation of voltage magnitudes.