Stochastic optimization of energy usage with uncertain input data

Abstract:
Energy supply systems require predictive planning of the operation of all energy generation and storage systems to ensure minimal costs. This requires forecasts, for example for solar and wind energy, demand and energy prices, in order to be able to plan all variables in advance. However, these forecasts are usually subject to uncertainties, which makes the optimization considerably more difficult. To achieve the most cost-effective energy supply for the following day, these uncertainties must be modeled and included into the calculations. This contribution examines the various steps of a sto-chastic optimization approach to this problem using a simple energy system and compares the result with a standard deterministic approach that neglects the uncertainties. The energy system used consists of a photovoltaic (PV) plant, an electric consumer and a battery system and is connected to a local grid with a fluctuating electricity price. The first step in the stochastic approach is the analysis of the forecast error distribution. Subsequently the distribution of the forecast error must be discretized using a sampling method. In the next step, error scenarios are created out of the samples, which can then be used for the actual stochastic optimization algorithm. This article compares different methods for the sampling and scenario generation steps before the stochastic optimization model is solved in its extensive form. In addition, a deterministic optimization algorithm is implemented to calculate a purely forecast-based schedule. This allows the im-provement achieved with the stochastic approach to be measured. To better classify the improvement, a schedule is also calculated based on the realized time series and thus represents the best possible schedule. Finally, the costs for the target energy system without battery are calculated to provide further context. In order to make a realistic statement about the effects of the various planning methods, a complete year was predictively optimized and simulatively evaluated on the basis of the actual consumption and generation data.