A Learning-boosted Quasi-Newton Method for AC Optimal Power Flow

Despite being at the heart of many optimal power flow solvers, Newton-Raphson can suffer from slow and numerically unstable Jacobian matrix inversions at each iteration. To reduce the computational burden associated with calculating the full Jacobian and its inverse, many Quasi-Newton methods attempt to find a solution to the optimality conditions by leveraging an approximate Jacobian matrix. In this paper, a Quasi-Newton method based on machine learning is presented which performs iterative updates for candidate optimal solutions without having to calculate a Jacobian or approximate Jacobian matrix. The resulting learning-based algorithm utilizes a deep neural network with feedback. With proper choice of weights and activation functions, the model becomes a contraction mapping and convergence can be guaranteed. Results demonstrated on networks up to 1,354 buses indicate the proposed method is capable of finding approximate solutions to AC OPF faster than Newton-Raphson, but can suffer from infeasibile solutions in large networks.