Different Decomposition Strategies to Solve Stochastic Hydrothermal Unit Commitment Problems

Solving very-large-scale optimization problems frequently require to decompose them in smaller subproblems, that are iteratively solved to produce useful information. One such approach is the Lagrangian Relaxation (LR), a broad range technique that leads to many different decomposition schemes. The LR supplies a lower bound of the objective function and useful information for heuristics aimed at constructing feasible primal solutions. In this paper, we compare the main LR strategies used so far for Stochastic Hydrothermal Unit Commitment problems, where uncertainty mainly concerns water availability in reservoirs and demand (weather conditions). This problem is customarily modeled as a two-stage mixed-integer optimization problem. We compare different decomposition strategies (unit and scenario schemes) in terms of quality of produced lower bound and running time. The schemes are assessed with various hydrothermal systems, considering different configuration of power plants, in terms of capacity and number of units

Comparing Spatial and Scenario Decomposition for Stochastic Hydrothermal Unit Commitment Problems

Solving very-large-scale optimization problems frequently require to decompose them in smaller subproblems, that are iteratively solved to produce useful information. One such approach is the Lagrangian Relaxation (LR), a general technique that leads to many different decomposition schemes. The LR produces a lower bound of the objective function and useful information for heuristics aimed at constructing feasible primal solutions. In this paper, we compare the main LR strategies used so far for Stochastic Hydrothermal Unit Commitment problems, where uncertainty mainly concerns water availability in reservoirs and demand (weather conditions). The problem is customarily modeled as a two-stage mixed-integer optimization problem. We compare different decomposition strategies (unit and scenario schemes) in terms of quality of produced lower bound and running time. The schemes are assessed with various hydrothermal systems, considering different configuration of power plants, in terms of capacity and number of units

Robust optimization vs. stochastic programming incorporating risk measures for unit commitment with uncertain variable renewable generation

Unit commitment seeks the most cost effective generator commitment schedule for an electric power system to meet net load, defined as the difference between the load and the output of renewable generation, while satisfying the operational constraints on transmission system and generation resources. Stochastic programming and robust optimization are the most widely studied approaches for unit commitment under net load uncertainty. We incorporate risk considerations in these approaches and investigate their comparative performance for a multi-bus power system in terms of economic efficiency as well as the risk associated with the commitment decisions. We explicitly account for risk, via Conditional Value at Risk (CVaR) in the stochastic programming objective function, and by employing a CVaR-based uncertainty set in the robust optimization formulation. The numerical results indicate that the stochastic program with CVaR evaluated in a low-probability tail is able to achieve better cost-risk trade-offs than the robust formulation with less conservative preferences. The CVaR-based uncertainty set with the most conservative parameter settings outperforms an uncertainty set based only on ranges

Bidding Strategy for Networked Microgrids in the Day-Ahead Electricity Market

In recent years, microgrids have drawn increasing attention from both academic and industrial sectors due to their enormous potential benefits to the power systems. Microgrids are essentially highly-customized small-scale power systems. Microgrids’ islanding capability enables microgrids to conduct more flexible and energy-efficient operations. Microgrids have proved to be able to provide reliable and environmental-friendly electricity to quality-sensitive or off-grid consumers. In addition, during the grid-connected operation mode, microgrids can also provide support to the utility grid. World-widely continuous microgrid deployments indicate a paradigm shift from traditional centralized large-scale systems toward more distributed and customized small-scale systems. However, microgrids can cause as many problems as it solves. More efforts are needed to address these problems caused by microgrids integration. Considering there will be multiple microgrids in future power systems, the coordination problems between individual microgrids remain to be solved. Aiming at facilitating the promotion of microgrids, this thesis investigates the system-level modeling methods for coordination between multiple microgrids in the context of participating in the market. Firstly, this thesis reviews the background and recent development of microgrid coordination models. Problems of existing studies are identified. Motivated by these problems, the research objectives and structure of this thesis are presented. Secondly, this thesis examines and compares the most common frameworks for optimization under uncertainty. An improved unit commitment model considering uncertain sub-hour wind power ramp behaviors is presented to illustrate the reformulation and solution method of optimization models with uncertainty. Next, the price-maker bidding strategy for collaborative networked microgrids is presented. Multiple microgrids are coordinated as a single dispatchable entity and participate in the market as a price-maker. The market-clearing process is modeled using system residual supply/demand price-quota curves. Multiple uncertainty sources in the bidding model are mitigated with a hybrid stochastic-robust optimization framework. What’s more, this thesis further considers the privacy concerns of individual microgrids in the coordination process. Therefore a privacy-preserving solution method based on Dantzig-Wolfe decomposition is proposed to solve the bidding problem. Both computational and economic performances of the proposed model are compared with the performances of conventional centralized coordination framework. Lastly, this thesis provides suggestions on future research directions of coordination problems among multiple microgrids