A statistical learning approach to determine optimal sizing & investment timing of commercial-scale distributed energy resources

Abstract

The problem of optimal sizing and investment timing for a portfolio of gas-fired and photovoltaic (PV) generation is presented and solved using an optimization- classification technique. It is assumed that the demand, the prices of natural gas, and PV technology are stochastic processes. Our methodology takes advantage of decomposing the problem into two sub-problems. First, the optimal sizing problem is solved using dynamic programming and most likely solutions are identified as clusters. Then, the Investment time problem is formulated as a Real Option for each cluster to determine optimal timing. Although the two-step optimization approach can successfully close the loop between operational dynamics and investment decisions, we are also interested in discovering patterns in a multidimensional space of input parameters that make a certain combination of assets optimal among dozens of discrete choices. On that note, by applying Recursive Partitioning algorithm, decision trees are developed to estimate the structure of solutions rendered from optimization models by a rule-based system. Despite the high level of accuracy, the initial model is biased in favor of highly frequent clusters, and discards the optimal clusters resulted from extreme market behaviors. Value at Risk (VaR) is employed as a risk measure to demonstrate the enhancement risk performance. Finally, in order to investigate the robustness of the results, we conduct extensive sensitivity analysis over different parameter settings. The proposed model can be thought of as a statistically optimal summarizer of optimization models that enables decision makers to have an insight into optimal investment strategies according to characteristics of the building and the long-term energy market outlook.