Parallel derivative-free optimization for simulation-based design of behind-the-meter energy systems

In this work, the integrated design and dispatch of behind-the-meter or distributed resources (e.g. stationary battery storage and solar PV generation) is considered. A simulation-based framework is employed, generating high-fidelity results with closed-loop predictive control at a fine resolution, at the expense of high computational cost (several minutes to a few hours per design point). To address this challenge, parallel derivative-free design methods are considered. Four methods are compared, including state-of-the-art surrogate-based methods (Radial-Basis Functions and Gaussian processes) and sampling strategies, an evolutionary-based method, and a simple sequential grid refinement method. As a case study, two types of design problem with increasing complexity are considered, namely, the design of behind-the-meter resources (three design variables) and the inclusion of grid capacity (four design variables). The second yields a constrained design problem for which violations can only be determined after solving the computationally expensive simulation. For the three-dimensional case, all methods present a good performance, achieving a solution within 1% of the optimum after the first iteration, with the sequential grid refinement exhibiting the fastest convergence and achieving the best final objective value. This indicates that the parallel evaluation of multiple sampling points may be more important than the choice of method for small decision spaces. For the four-dimensional constrained case, the Genetic Algorithm presents the best tradeoff between performance and computational effort, while the rough objective function terrain generated by constraint violation penalties reduces the performance of surrogate-based methods. Contour plots with flat regions indicate flexibility in the optimal design and highlight the importance of characterizing the solution space. • A bilayer simulation-based framework is employed for the high-fidelity design of behind-the-meter energy resources, entailing high computational cost for the outer design layer. • Derivative-free optimization methods that exploit parallelization enable the efficient solution of the design problem. • Four parallel algorithms are compared in terms of performance, including direct-search, genetic, and state-of-the-art surrogate-based methods with novel sampling strategies. • Two types of design problems are considered, a classic low-dimensional equipment design problem and a higher-dimensional power capacity-constrained problem • All methods perform well for the unconstrained low-dimensional problem, while the genetic algorithm performs best for the higher-dimensional constrained problem. • Surrogate-based methods show decreased performance under constraints via penalty terms when the optimum is located near the infeasible region.