Authors

Abstract

Though the convex optimization has been widely usedin power systems, it still cannot guarantee to yield a tight (accurate) solution to some problems. To mitigate this issue, this paperproposes an ensemble learning based convex approximation foralternating current (AC) power flow equations that differs fromthe existing convex relaxations. The proposed approach is basedon three-phase quadratic power flow equations in rectangularcoordinates. To develop this data-driven convex approximation ofpower flows, the polynomial regression (PR) is first deployed as abasic learner to fit convex relationships between the independentand dependent variables. Then, ensemble learning algorithms suchas gradient boosting (GB) and bagging are introduced to combine learners to boost model performance. Based on the learnedconvex approximation of power flow, optimal power flow (OPF)is formulated as a convex quadratic programming problem. Thesimulation results on IEEE standard cases of both balanced andunbalanced systems show that, in the context of solving OPF,the proposed data-driven convex approximation outperforms theconventional semi-definite programming (SDP) relaxation in bothaccuracy and computational efficiency, especially in the cases thatthe conventional SDP relaxation fails