A stochastic, contingency-based security-constrained optimal power flow for the procurement of energy and distributed reserve

a r t i c l e i n f o It is widely agreed that optimal procurement of reserves, with explicit consideration of system contingencies, can improve reliability and economic efficiency in power systems. With increasing penetration of uncertain generation resources, this optimal allocation is becoming even more crucial. Herein, a problem formulation is developed to solve the day-ahead energy and reserve market allocation and pricing problem that explicitly considers the redispatch set required by the occurrence of contingencies and the corresponding optimal power flow, static and dynamic security constraints. Costs and benefits, including those arising from eventual demand deviation and contingency-originated redispatch and shedding, are weighted by the contingency probabilities, resulting in a scheme that contracts the optimal amount of resources in a stochastic day-ahead procurement setting. Furthermore , the usual assumption that the day-ahead contracted quantities correspond to some base case dispatch is removed, resulting in an optimal procurement as opposed to an optimal dispatch. Inherent in the formulation are mechanisms for rescheduling and pricing dispatch deviations arising from realized demand fluctuations and contingencies. Because the formulation involves a single, one stage, comprehensive mathematical program, the Lagrange multipliers obtained at the solution are consistent with shadow prices and can be used to clear the day-ahead and spot markets of the different commodities involved. This work combines several standard problems found in systems operation and planning in a single mathematical programming framework. The advantages of this formulation are found in greater clarity with respect to the underlying problem to be solved, and for ease of extraction of sensitivity information from the solution. The problems herein considered are • The optimal power flow problem with a full AC nonlinear network model and constraints; • The N − 1 contingency security problem with both static (post-contingency voltage and MVA limits) and dynamic (generator ramp rate limits; voltage angle difference limits; post-contingency load pickup governed by participation factors) constraints; • The problem of procuring an adequate supply of both active and reactive power and corresponding geographically adequate distributed reserves in a day-ahead market scenario in light of the uncertainty of the actual realized demand and the occurrence of specific contingencies , while taking into account the costs and constraints on the corresponding post-contingency flows; • The problem of setting the price for the day-ahead contracts for power and reserve; and • A consistent mechanism for re-dispatching and pricing the next day …