| This dissertation presents a fundamental study of the stochastic optimal power flow (OPF) problem. The conventional OPF is formulated with perfect knowledge of parameters of electric power systems. It does not reflect the existence of uncertainty in power systems. Stochastic OPF is proposed to model the uncertainty in OPF problems, including the uncertainties associated with power supply unavailability, load demand, energy price and line outages. From the process of optimization and operational handling of uncertainty in power systems, the recourse model of stochastic OPF is proposed and corrective controls are introduced with associated costs so that the constraints of the power system operation are satisfied and the operational cost is minimized. Further, stochastic OPF with linear power flow constraints is derived. Its accuracy is discussed theoretically and numerically. It is concluded that the linear AC power flow model induces small errors when it is applied to study the power flow after a single outage.; Numerical techniques are introduced to solve the problem of stochastic OPF with linear power flow constraints efficiently. The random variables are approximated by a set of discrete representative random variables. Decomposition method is applied to solve the stochastic OPF with linear power flow constraints. The computation efficiency is improved in two aspects, the decomposition algorithm and the construction of scenario space. The scenario screening techniques are proposed to select the critical scenarios based on engineering experience. A stochastic OPF solver is implemented with functions of deterministic OPF, contingency analysis, matrix modification and decomposition algorithm. The significance of stochastic OPF model is reflected in solutions of the optimal dispatch with various uncertainties. All solutions show the dependence on costs of corrective controls and probability of scenarios. This is true in reality but not reflected in solutions of the conventional OPF model. Applications of stochastic OPF are extended to many aspects of power system operation and planning. |
