Uncertainty quantification of photovoltaic power generation

Environmental concerns and global energy crises have caused a rapid proliferation of renewable energy sources worldwide. For Singapore, due to its geographical location within the tropical Sun Belt, PV energy is the most propitious kind of renewables that can be deployed. Two important issues related to intermittency of PV generation are variability and uncertainty. Variable power with uncertain nature has several consequences in power systems such as the need for rising ancillary service, increase in voltage and frequency fluctuations and adverse effects on power quality and economics. What exacerbates the situation is the lack of inertia in PV systems which leads to abrupt changes in voltages and power outputs. Improving PV forecasting methods, as an indispensable approach to mitigate PV power intermittency, has attracted researchers recently. Forecasts can be done as point or probabilistic predictions. Nearly all previous works focused on single-valued (or point) forecasts, similar to the case of wind power forecasting. However, point forecasts can only be helpful when no significant uncertainty is involved, since it fails to dispense a full picture of all potential future outcomes. On the other hand, the aim of probabilistic predictions is to provide decision-making under uncertainty with the full information. In recent years, there has been a surge of interest in stochastic optimization approaches to cover different uncertainties in power systems. It is often assumed that the random variables involved have known parametric distributions. However, even in cases where observations form a known and well-behaved marginal distribution, there is no guarantee that conditional predictive densities (or distributions of forecast errors) follow that same distribution. Wrong distributional assumptions may directly yield biases in analyses and results. Stochastic optimization therefore calls for a thorough design and evaluation of probabilistic forecasting approaches. Although valuable studies have been conducted on probabilistic wind forecasting, one can hardly find published investigations on probabilistic solar energy forecasts. In spite of the similarities in wind and PV power forecasts, there are significant differences such as the influential variables and the relationship between meteorological variables and the available PV power which may result in different statistical features. This, indeed, necessitates a more focused research on solar power statistics. This thesis aims at providing practical methods for both point and probabilistic forecasts of PV generation. If probabilistic forecasts are properly employed, they can serve as a decision-aiding tool to alleviate challenges attached to stochastic generation. However, despite of the benefits of probabilistic forecasts over point forecasts, they fail to capture development of forecast errors through successive lead-times, interdependent generation in contiguous locations or negatively correlated generation levels in diverse geographic areas. The reason is that they treat random variables for each lead-time and each location individually and separately while PV generations are stochastic processes with spatially spread and time interdependent infeeds. Therefore, in multi-stage decision-making problems such as unit-commitment or optimal power flow, it is an integral requirement to estimate aggregated uncertainties in the system and model space-time stochasticity of intermittent resources. This issue is addressed here by analysing and capturing spatio-temporal dependencies in PV generation. Multivariate predictive distributions are modelled and space-time trajectories describing the potential evolution of forecast errors through successive lead-times and locations are generated.Doctor of Philosophy (EEE