Optimization-Based Study On Unit Commitment Problems In Power System

The electric power industry is a representative energy industry. It is not only a big energy producer, but also a big energy consumer. Therefore, it is beneficial for both the optimal allocation of power and the rational use of energy to manage the operation of the electric power industry scientifically. The unit commitment problem is an important part in the operational management of the electric power industry. Its main task is to determine the on/off status of the units and the associated output level according to the power demand and the physical characteristics of the units so as to minimize the generating cost. A scientific unit commitment scheduling can not only ensure the stable operation of the power system, but also help the generating company to utilize the resource efficiently, save energy and reduce emissions, lower the operating cost of the system, raise the service quality of the power supply, and thus enhance its market competitiveness. With the rapid development of the electric power industry and the increasing challenges of energy shortage, it has become a common concern focused by both industry and academia to study the modeling and the optimization methods of the unit commitment problem.In this dissertation, a problem-oriented classification method is proposed and a review on the unit commitment problem is presented first. Both the modeling and the optimization methods of the unit commitment problems with different features are then investigated. The investigations are performed from the perspectives of system security operation, reaction to the unforeseen unit breakdown, environment friendliness, coordinated pricing considering market and consumer behavior, respectively. Finally, by taking the iron and steel industry with high energy consumption as the background, a production planning problem with nonlinear energy consumption cost is also investigated from the perspective of energy conservation. The main contents are summarized as follows.1) A heuristic algorithm to the ramp rate and system security-constrained unit commitment problemThe ramp rate constraint means that the change of the output level in the adjacent periods should be within a certain limit, while the system security constraint means that the amount of power flow through each transmission line should be within the prescriptive limit in order to insure the security operation of the system. In this dissertation, a model-based two-stage heuristic algorithm is proposed for the unit commitment problem with both the ramp rate constraint and the system security constraint. In the first stage, the feasibility of the on/off status of the units is judged by using the associated economic dispatch model. If the on/off status of the units is infeasible, construct a relaxation model of the studied problem by approximating the objective function linearly and relaxing some constraints and take the relaxation model to make the on/off status of the units feasible. In the second stage, determine the output level of the units by solving the associated economic dispatch model. The test based on a118-bus system indicates the effectiveness and robustness of the proposed heuristic method.2) A corrective unit commitment problem to an unforeseen unit breakdownCorrective unit commitment refers to the timely correction to the original unit commitment scheduling when an unforeseen unit breakdown occurs. For this problem, we use a scenario tree to depict the stochastic breakdown duration and the deviation of the corrective schedule from the original one to express the impact caused by the breakdown. Taking the objective of minimizing the expected generating cost and the deviation from the original schedule, we formulate the problem as a mixed integer nonlinear programming model. The proposed variable splitting-based Lagrangian relaxation algorithm decomposes the problem into multiple single-unit subproblems and an artificial variable subproblem. Each single-unit subproblem is solved by a two-stage optimal algorithm combined with a pre-processing technique, while the artificial variable subproblem is solved by using the linear programming solver. The Lagrangian dual problem is solved by a bundle method to improve the performance of the algorithm. Numerical results on a39-bus system indicate the effectiveness of the proposed algorithm.3) A unit commitment problem with CO2emission penalty in the electricity market In this unit commitment problem, both the electricty price and CO2emission penalty are considered. The objective is to maximize the generating profits, which are determined by the electricity selling revenue, generating cost, and emission penalty. For this problem, we take a piecewise linear penalty function to formulate the different penalty modes corresponding to different range of the amount of emissions. By presenting an effective mathematical expression to the penalty function, we establish a mixed integer nonlinear programming model. A variable splitting-based Lagrangian relaxation algorithm is developed for solving the problem where the relaxed problem is solved by a two-stage optimal algorithm and a linear programming solver. The proposed adaptive frequency strategy accelerates the speed of the algorithm. Numerical experiments on test cases of different sizes demonstrate the good performance of the proposed algorithm. The emission reduction effects of different penalty methods are also compared.4) A stochastic unit commitment with CO2emissions trading in the electricity marketIn this unit commitment problem, not only the electricity price, but also the emission constraint and the emissions trading are taken into account. The objective is to maximize the expected total profits, which are determined by the electricity selling revenue, the generating cost, and the emissions trading cost. For this problem, we depict the stochastic electricity price, the emissions trading price, and the electricity demand by a scenario tree and formulate the problem as a large-scale mixed integer nonlinear programming model. A Lagrangian relaxation-based heuristic algorithm is developed. Numerical results on test cases generated randomly indicate the effectiveness of the proposed algorithm.5) A stochastic unit commitment problem with pricing coordinationIn this unit commitment problem, the unit commitment schedule and the electricity price are decided simultaneously. The stochastic relationship coefficients are depicted by a scenario tree. Taking the expected generating profits determined by both the electricity selling revenue and the generating cost, we formulate the problem as a mixed integer nonlinear programming model. A Lagrangian relaxation-based heuristic algorithm is developed according to the characteristics of the model. Numerical results on test cases of different sizes show the effectiveness of the proposed algorithm. 6) A stochastic steel production planning problem with nonlinear costIn this problem, we take the production process from the heat furnace to hot rolling as the background and investigate a production planning problem with stochastic production demands and energy consumption. The energy consumption cost is described by a nonlinear function and the stochastic production demands are depicted by a scenario tree. Taking the expected cost, including the energy consumption cost of the heat furnace, the production cost of hot rolling, and the inventory holding cost, as the objective function, we establish a mixed integer nonlinear programming model for the problem. A stepwise Lagrangian relaxation heuristic for the problem is proposed where variable splitting is introduced during Lagrangian relaxation. In the algorithm, the original model is approximated as a mixed integer linear programming model by a piecewise linear approxiamtion method. The obtained approximation model is solved by a variable splitting-based Lagrangian relaxation algorithm. The approxiamtion error can be improved by adjusting the linearization ranges effectively. The experiment is based on a large set of test cases, which are generated randomly according to the actual production data. Numerical results indicate the effectiveness of the proposed algorithm. The impact of demand uncertainty on the solution is also discussed.