(426f) Towards Gradient-Based Algorithms for the Optimal Design of Hybrid Renewable Energy Systems with Stochastic Generators, Storage, and Discrete Control Logic

Reliable power generation from renewable resources such as wind and solar is difficult because these resources are intermittent and unpredictable. A potential solution to this problem is to combine multiple renewable resources with an array of energy storage options that are complementary in their time-scales of operation, capacities, peak power outputs, and costs. Clearly, the design of such a system (e.g., technology selection, component sizing, etc.) involves a number of complex trade-offs and is highly dependent on the uncertain resource availability and demand. Moreover, with multiple generation and storage units present, operating such a system requires complex control logic that determines when and to what extent each component is used. This is typically called the energy management policy (EMP).

It is well known that designing renewable energy systems according to average resource availabilities leads to highly suboptimal or infeasible designs. In particular, stochasticity during real operation may lead to the violation of operating constraints and the frequent inability to meet demand. Thus, true optimal design of renewable energy systems requires an optimization subject to a detailed stochastic simulation, potentially with discrete events arising from the action of the EMP. Due to the complexity of this problem, it has thus far been treated using heuristic algorithms that view the stochastic simulation as a black-box (e.g., they do no require differentiability or even continuity per se). Unfortunately, these algorithms tend to exhibit slow convergence and are not guaranteed to furnish a local solution or even a KKT point.

In this talk, we consider ‘sequential’ NLP formulations for the above problem and analyze their regularity. For important classes, it is shown that the problem is indeed differentiable. We then undertake the computation of derivatives and assess the utility of applying efficient gradient-based NLP solvers to this class of problems. This approach has the potential for significant efficiency gains over heuristic approaches, and furthermore furnishes true local optima. Since renewable generation and storage technologies remain expensive, overdesigning systems according to suboptimal solutions is very costly and can quickly lead to economic infeasibility of the system. Thus, algorithms that provide higher quality solutions are of great interest for more accurately assessing the value of intermittent renewable resources.