Integrating large-scale renewable energy resources into the power grid poses several operational and economic problems due to their inherently stochastic nature. The lack of predictability of renewable outputs deteriorates the power grid’s reliability. The power system operators have recognized this need to account for uncertainty in making operational decisions and forming electricity pricing. In this regard, this dissertation studies three aspects that aid large-scale renewable integration into power systems. 1. We develop a nonparametric change point-based statistical model to generate scenarios that accurately capture the renewable generation stochastic processes; 2. We design new pricing mechanisms derived from alternative stochastic programming formulations of the electricity market clearing problem under uncertainty; 3. We devise a novel approach to coordinate strategic operations of multiple noncooperative system operators.
The current industry practices are based on deterministic models that do not account for the stochasticity of renewable energy. Therefore, the solutions obtained from these deterministic models will not provide accurate measurements. Stochastic programming (SP) can accommodate the stochasticity of renewable energy by considering a set of possible scenarios. However, the reliability of the SP model solution depends on the accuracy of the scenarios. We develop a nonparametric statistical simulation method to develop scenarios for wind generation using wind speed data. In this method, we address the nonstationarity issues that come with wind-speed time-series data using a nonparametric change point detection method. Using this approach, we retain the covariance structure of the original wind-speed time series in all the simulated series.
With an accurate set of scenarios, we develop alternative two-stage SP models for the two-settlement electricity market clearing problem using different representations of the non-anticipativity constraints. Different forms of non-anticipativity constraints reveal different hidden dual information inside the canonical two-stage SP model, which we use to develop new pricing mechanisms. The new pricing mechanisms preserve properties of previously proposed pricing mechanisms, such as revenue adequacy in expectation and cost recovery in expectation. More importantly, our pricing mechanisms can guarantee cost recovery for every scenario. Furthermore, we develop bounds for the price distortion under every scenario instead of the expected distortion bounds. We demonstrate the differences in prices obtained from the alternative mechanisms through numerical experiments.
Finally, we discuss the importance of distributed smart grid operations inside the power grid. We develop an information and electricity exchange system among multiple distribution systems. These distribution systems participate/compete in common markets cohere electricity is exchanged. We develop a standard Nash game treating each distribution system (DS) as an individual player who optimizes their strategies separately. We develop proximal best response (BR) schemes to solve this problem. We present results from numerical experiments conducted on three and six DS settings.
Operations Research and Engineering Management
Prof. Harsha Gangammanavar
Electrical, Electronics Engineering, Mathematics, Applied, Statistics
Number of Pages
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Ariyarathne, Saumya Sakitha Sashrika, "Study Of Stochastic Market Clearing Problems In Power Systems With High Renewable Integration" (2022). Operations Research and Engineering Management Theses and Dissertations. 16.
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