Multistage scenario trees generation for renewable energy systems optimization

Resumen

The presence of renewables in energy systems optimization have generated a high level of uncertainty in the data, which has led to a need for applying stochastic optimization to modelling problems with this characteristic. The method followed in this thesis is multistage Stochastic Programming (MSP). Central to MSP is the idea of representing uncertainty (which, in this case, is modelled with a stochastic process) using scenario trees. In this thesis, we developed a methodology that starts with available historical data; generates a set of scenarios for each random variable of the MSP model; define individual scenarios that are used to build the initial stochastic process (as a fan or an initial scenario tree); and builds the final scenario trees that are the approximation of the stochastic process. The methodology proposes consists of two phases. In the first phase, we developed a procedure similar to Muñoz et al. (2013), with the difference being that the VAR models are used to predict the next day for each random parameter of the MSP models. In the second phase, we build scenario trees from the Forward Tree Construction Algorithm(FTCA), developed by Heitsch and Römisch (2009a); and an adapted version of DynamicTree Generation with a Flexible Bushiness Algorithm (DTGFBA), developed by Pflugand Pichler (2014, 2015). This methodology was used to generate scenario trees for two MSP models. A first model, Multistage Stochastic Wind Battery Virtual Power Plantmodel (MSWBVPP model) and to a second model, which is the Multistage StochasticOptimal Operation of Distribution Networks model (MSOODN model). We developed extensive computational experiments for the MSWBVPP model and generated scenario trees with real data, which were based on MIBEL prices and wind power generation of the real wind farm called Espina, located in Spain. For the MSOODN model, we obtained scenario trees by also using real data from the power load provided by FEEC-UNICAMP and photovoltaic generation of a distribution grid located in Brazil. The results show that the scenario tree generation methodology proposed in this thesis can obtain suitable scenario trees for each MSP model. In addition, results were obtained for the model using the scenario trees as input data. In the case of the MSWBVPP model, we solved three different case studies corresponding to three different hypotheses on the virtual power plant’s participation in electricity markets. In the case of the MSOODN model, two test cases were solved, with the results indicating that the EDN satisfied the limits imposed for each test case. Furthermore, the BESS case gave good results when taking into account the uncertainty in the model. Finally, the MSWBVPP model was used to study the relative performance of the FTCA and DTGFBA scenario trees, specifically by analyzing the value of the stochastic solution for the 366 daily optimal bidding problems. To this end, a variation of the classical VSS (the so-called “Forecasted Value of the Stochastic Solution”, FVSS) was defined and used together with the classical VSS.