A Global Solution Algorithm for AC Optimal Power Flow through Linear Constrained Quadratic Programming

We formulate the Alternating Current Optimal Power Flow Problem (ACOPF) as a Linear Constrained Quadratic Program (LCQP) with many negative eigenvalues (r) and linear constraints, making it NP-hard. We propose two algorithms, Feasible Successive Linear Programming (FSLP) and Feasible Branch-and-Bound (FBB), for a global optimal solution. These use optimization strategies like bounded successive linear programming, convex relaxation, initialization, and branch-and-bound to find a globally optimal solution within a predefined ε-tolerance. The complexity of FSLP and FBB is O(N ∏ᵢ₌₁ʳ√r(tᵤⁱ-tₗⁱ)2 √ε), where N is the complexity of solving subproblems at each FBB node. Variables tₗ and tᵤ are the lower and upper bounds of t, respectively, and -|t|² is the negative quadratic component in the ACOPF objective function. We use penalized semidefinite modeling, convex relaxation, and line search to design a globally feasible branch-and-bound algorithm for the LCQP form of ACOPF, finding an optimal solution within ε-tolerance. Initial results show FSLP and FBB can find global optimal solutions for large-scale ACOPF instances, even with large r, and outperform other methods in most PG-lib tests.