Ensemble Learning Based Convex Approximation of Three-Phase Power Flow
This work addresses the need for more accurate and efficient convex optimization methods in power system operations, particularly for three-phase networks, though it is incremental as it builds on existing convex relaxation techniques.
The paper tackled the problem of inaccurate convex optimization solutions in power systems by proposing an ensemble learning-based convex approximation for AC power flow equations, which outperformed conventional SDP relaxation in accuracy and computational efficiency on IEEE standard cases, especially where SDP fails.
Though the convex optimization has been widely used in power systems, it still cannot guarantee to yield a tight (accurate) solution to some problems. To mitigate this issue, this paper proposes an ensemble learning based convex approximation for AC power flow equations that differs from the existing convex relaxations. The proposed approach is based on quadratic power flow equations in rectangular coordinates and it can be used in both balanced and unbalanced three-phase power networks. To develop this data-driven convex approximation of power flows, the polynomial regression (PR) is first deployed as a basic learner to fit convex relationships between the independent and dependent variables. Then, ensemble learning algorithms such as gradient boosting (GB) and bagging are introduced to combine learners to boost model performance. Based on the learned convex approximation of power flows, optimal power flow (OPF) is formulated as a convex quadratic programming problem. The simulation results on IEEE standard cases show that, in the context of solving OPF, the proposed data-driven convex approximation outperforms the conventional SDP relaxation in both accuracy and computational efficiency, especially in the cases that the conventional SDP relaxation fails.