Strategic Investment in Energy Markets using Bayesian optimization

As electricity markets become more involved, strategic investment defined as the task of sizing and siting new generation units on a power system becomes increasingly computationally taxing. Adding new units in a market influences generation schedules and prices in a manner that may not be profitable for the investor overall. Strategic investment can be formulated as a mixed-integer linear program, which may not scale gracefully in larger networks and/or an increased number of stochastic scenarios. We tackle strategic investment using Bayesian optimization (BO), a machine-learning approach for minimizing hard-to-evaluate functions. BO builds a surrogate Gaussian process (GP) model for the investment cost function using function evaluations at judiciously selected points. Minimizing the surrogate cost is faster than minimizing the actual cost. By leveraging the multiparametric programming structure of strategic investment, we further expedite the standard BO approach on two fronts. First, the investment cost and its gradient with respect to the investment decision variable are evaluated more efficiently. Second, incorporating gradient information into the GP surrogate model improves its accuracy. Extensive tests on the IEEE 118-bus system corroborate the computational advantages of the BO approach over competing alternatives.