Distributionally robust building load control to compensate fluctuations in solar power generation

This paper investigates the use of a collection of dispatchable heating, ventilation and air conditioning (HVAC) systems to absorb low-frequency fluctuations in renewable energy sources, especially in solar photo-voltaic (PV) generation. Given the uncertain and time-varying nature of solar PV generation, its probability distribution is difficult to be estimated perfectly, which poses a challenging problem of how to optimally schedule a fleet of HVAC loads to consume as much as local PV generation. We formulate a distributionally robust chance-constrained (DRCC) model to ensure that PV generation is consumed with a desired probability for a family of probability distributions, termed as an ambiguity set, built upon mean and covariance information. We benchmark the DRCC model with a deterministic optimization model and a stochastic programming model in a one-day simulation. We show that the DRCC model achieves constantly good performance to consume most PV generation even in the case with the presence of probability distribution ambiguity.