The stochastic unit commitment problem: A chance constrained programming approach considering extreme multivariate tail probabilities

Reliable power production is critical to the profitability of electricity utilities. Power generators (units) need to be scheduled efficiently to meet electricity demand (load). This dissertation develops a solution method to schedule units for producing electricity while determining the estimated amount of surplus power each unit should produce taking into consideration the stochasticity of the load and its correlation structure. This scheduling problem is known as the unit commitment problem in the power industry. The solution method developed to solve this problem can handle the presence of wind power plants, which creates additional uncertainty.; In this problem it is assumed that the system under consideration is an isolated one such that it does not have access to an electricity market. In such a system the utility needs to specify the probability level the system should operate under. This is taken into consideration by solving a chance constrained program. Instead of using a set level of energy reserve, the chance constrained model determines the level probabilistically which is superior to using an arbitrary approximation.; In this dissertation, the Lagrangian relaxation technique is used to separate the master problem into its subproblems, where a subgradient method is employed in updating the Lagrange multipliers. To achieve this a computer program is developed that solves the optimization problem which includes a forward recursion dynamic program for the unit subproblems. A program developed externally is used to evaluate high dimensional multivariate normal probabilities. To solve the quadratic programs of the period subproblems an optimization software is employed.; The results obtained indicate that the load correlation is significant and cannot be ignored while determining a schedule for the pool of units a utility possesses. It is also concluded that it is very risky to choose an arbitrary level of energy reserve when solving the unit commitment problem. To verify the effectiveness of the optimum unit commitment schedules provided by the chance constrained optimization algorithm and to determine the expected operation costs, Monte Carlo simulations are used where the simulation generates the realized load according to the assumed multivariate normal distribution with a specific correlation structure.