Modeling Variability and Uncertainty of Photovoltaic Generation: A Hidden State Spatial Statistical Approach

In this paper, we construct, fit, and validate a hidden Markov model for predicting variability and uncertainty in generation from distributed (PV) systems. The model is unique in that it: 1) predicts metrics that are directly related to operational reserves, 2) accounts for the effects of stochastic volatility and geographic autocorrelation, and 3) conditions on latent variables referred to as “volatility states.” We fit and validate the model using 1-min resolution generation data from approximately 100 PV systems in the California Central Valley or the Los Angeles coastal area, and condition the volatility state of each system at each time on 15-min resolution generation data from nearby PV systems (which are available from over 6000 PV systems in our data set). We find that PV variability distributions are roughly Gaussian after conditioning on hidden states. We also propose a method for simulating hidden states that results in a very good upper bound for the probability of extreme events. Therefore, the model can be used as a tool for planning additional reserve capacity requirements to balance solar variability over large and small spatial areas.