Generation and Evaluation of Space-Time Trajectories of Photovoltaic Power

In the probabilistic energy forecasting literature, emphasis is mainly placed on deriving marginal predictive densities for which each random variable is dealt with individually. Such marginals description is sufficient for power systems related operational problems if and only if optimal decisions are to be made for each lead-time and each location independently of each other. However, many of these operational processes are temporally and spatially coupled, while uncertainty in photovoltaic (PV) generation is strongly dependent in time and in space. 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. Discrimination ability of the relevant scoring rules on performance assessment of space-time trajectories of PV generation is also studied. Finally, the advantage of taking into account space-time correlations over probabilistic and point forecasts is investigated. The empirical investigation is based on the solar PV dataset of the Global Energy Forecasting Competition (GEFCom) 2014.Comment: 33 pages, 11 Figure

Polyhedral Predictive Regions For Power System Applications

Despite substantial improvement in the development of forecasting approaches, conditional and dynamic uncertainty estimates ought to be accommodated in decision-making in power system operation and market, in order to yield either cost-optimal decisions in expectation, or decision with probabilistic guarantees. The representation of uncertainty serves as an interface between forecasting and decision-making problems, with different approaches handling various objects and their parameterization as input. Following substantial developments based on scenario-based stochastic methods, robust and chance-constrained optimization approaches have gained increasing attention. These often rely on polyhedra as a representation of the convex envelope of uncertainty. In the work, we aim to bridge the gap between the probabilistic forecasting literature and such optimization approaches by generating forecasts in the form of polyhedra with probabilistic guarantees. For that, we see polyhedra as parameterized objects under alternative definitions (under $L_1$ and $L_\infty$ norms), the parameters of which may be modelled and predicted. We additionally discuss assessing the predictive skill of such multivariate probabilistic forecasts. An application and related empirical investigation results allow us to verify probabilistic calibration and predictive skills of our polyhedra.Comment: 8 page

Ellipsoidal Prediction Regions for Multivariate Uncertainty Characterization

While substantial advances are observed in probabilistic forecasting for power system operation and electricity market applications, most approaches are still developed in a univariate framework. This prevents from informing about the interdependence structure among locations, lead times and variables of interest. Such dependencies are key in a large share of operational problems involving renewable power generation, load and electricity prices for instance. The few methods that account for dependencies translate to sampling scenarios based on given marginals and dependence structures. However, for classes of decision-making problems based on robust, interval chance-constrained optimization, necessary inputs take the form of polyhedra or ellipsoids. Consequently, we propose a systematic framework to readily generate and evaluate ellipsoidal prediction regions, with predefined probability and minimum volume. A skill score is proposed for quantitative assessment of the quality of prediction ellipsoids. A set of experiments is used to illustrate the discrimination ability of the proposed scoring rule for misspecification of ellipsoidal prediction regions. Application results based on three datasets with wind, PV power and electricity prices, allow us to assess the skill of the resulting ellipsoidal prediction regions, in terms of calibration, sharpness and overall skill.Comment: 8 pages, 7 Figures, Submitted to IEEE Transactions on Power System

An ensemble framework for day-ahead forecast of PV output in smart grids

The uncertainty associated with solar output power is a big challenge to design, manage and implement effective demand response and management strategies. Therefore, a precise PV output power forecast is an utmost importance to allow seamless integration and higher level of penetration. In this research, a neural network ensemble (NNE) scheme is proposed, which is based on particle swarm optimization (PSO) trained feedforward neural network (FNN). Five different FFN structures with 20 FNN in each structure with varying network parameters are used to achieve the diverse and accurate forecast results. These results are combined using trim aggregation after removing the upper and lower forecast error extremes. Correlated variables namely wavelet transformed output power of PV, solar irradiance, wind speed, temperature and humidity are applied as inputs of multivariate NNE. Clearness index is used to classify days into clear, cloudy and partially cloudy days. The forecast results demonstrate that the proposed framework improves the forecast accuracy significantly in comparison with individual and benchmark models