Improving the Accuracy of Second-Order Cone AC Optimal Power Flow by Convex Approximations

We propose three convex approximation methods to improve the performance of second-order cone AC optimal power flow (SOC-ACOPF) model. These methods are formulated in the proposed SOC-ACOPF models, correspondingly, ConicLA, ConicRe, and ConicTA. The principle is to drop the original assumptions of the SOC-ACOPF model by using improved approximation methods. The nonconvex constraints in ACOPF are expressed by using quadratic equivalence. These quadratic constraints are then approximated in two different ways: ConicLA uses controllable tangent lines as linear approximations; ConicRe uses rotated cones. Furthermore, the assumption of small voltage phase angle difference (along each line) which is used in many power flow models is dropped in the ConicTA model. ConicTA approximates sinusoidal function by its expanded Taylor series and then re-applies approximation methods developed in ConicLA and ConicRe. The advantages of our approximation methods are that the proposed SOC-ACOPF models are convex and more accurate. Using Power System Analysis Toolbox (PSAT) as the benchmark, numerical results from various IEEE test cases show that our models outperform the original SOC-ACOPF model prominently especially for power distribution networks.