[Paper Review] Ensemble Learning Based Convex Approximation of Three-Phase Power Flow

Ren Hu, Qifeng Li+1 more|arXiv (Cornell University)|Sep 12, 2019

Optimal Power Flow Distribution42 references4 citations

TL;DR

This paper proposes a data-driven convex approximation of three-phase AC power flow using ensemble learning to improve accuracy and efficiency over traditional semidefinite programming (SDP) relaxations. By combining polynomial regression with gradient boosting and bagging on rectangular-coordinate power flow equations, the method formulates optimal power flow as a convex quadratic program, outperforming SDP in both solution quality and speed—especially in cases where SDP fails.

ABSTRACT

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.

Motivation & Objective

• To address the limitations of convex relaxations in power systems, particularly their inability to guarantee tight solutions for complex three-phase networks.
• To develop a data-driven convex approximation method that maintains convexity while enhancing accuracy for both balanced and unbalanced three-phase power systems.
• To improve computational efficiency and solution reliability in optimal power flow (OPF) problems where conventional semidefinite programming (SDP) relaxations fail or are too loose.
• To integrate machine learning techniques—specifically ensemble learning—into power system optimization for better approximation of nonlinear AC power flow equations.

Proposed method

• The method uses quadratic power flow equations in rectangular coordinates as the foundation for modeling three-phase power systems.
• Polynomial regression (PR) is employed as the base learner to fit convex relationships between power injection and voltage variables.
• Ensemble learning techniques, including gradient boosting (GB) and bagging, are applied to combine multiple PR learners and enhance model generalization and accuracy.
• The resulting learned convex approximation enables formulating optimal power flow (OPF) as a convex quadratic programming problem.
• The approach is validated on IEEE standard three-phase test cases, comparing performance against conventional SDP relaxation.

Experimental results

Research questions

• RQ1 Can a data-driven convex approximation method improve the accuracy of power flow solutions in three-phase systems where traditional convex relaxations fail?
• RQ2 How does the integration of ensemble learning with polynomial regression enhance the convex approximation of nonlinear AC power flow equations?
• RQ3 To what extent does the proposed method outperform semidefinite programming (SDP) relaxation in terms of solution accuracy and computational efficiency for three-phase optimal power flow?
• RQ4 Can the proposed method maintain convexity while achieving tighter approximations in both balanced and unbalanced three-phase networks?

Key findings

• The proposed ensemble learning-based convex approximation achieves higher solution accuracy than conventional SDP relaxation in optimal power flow problems.
• In cases where SDP relaxation fails to converge or yields infeasible solutions, the proposed method consistently produces feasible and accurate results.
• The method demonstrates superior computational efficiency, reducing solution time compared to SDP while maintaining high accuracy.
• The integration of gradient boosting and bagging significantly improves model performance over individual polynomial regression learners.