This work concerns the formulation and solution of a multi-period security-constrained optimal power flow problem for real-time electricity market operations. The solution of the proposed problem is intended to be part of the core pricing procedure for electricity trading in open markets where real energy, reactive energy, voltages support, and other system resources and services can all be traded in discrete bids and offers. Traditionally, real-time dispatching operations only involve solving single-period security-constrained optimal power flow problems. This work demonstrates the need for solving multi-period security-constrained optimal power flows. The nonsmoothness of the offer/bid-driven optimal power flow problem is studied. Three techniques, namely, a trust-region based augmented Lagrangian method, a step-controlled primal-dual interior point method, and a modified constrained cost variables method, are developed for reliable and efficient computation of large-scale nonsmooth optimal power flows. Numerical studies show that these techniques are reliable and better than some existing ones. To reduce the computational complexity, two decomposition techniques are proposed and studied. In the first one, the auxiliary problem principle method is extended to handle inequality constraints created from generator ramping limits. In the second one, binding time-coupling and contingency-coupling constraints are estimated, ranked, and filtered before the computation is decomposed and parallelized using standard block matrix computation techniques. According to experimental results, the most promising way of solving large-scale multi-period security-constrained optimal power flow problems in real time is to combine the second decomposition method with the modified constrained cost variables method. The optimal power flow formulation and relevant computation techniques proposed in this work balance the needs for: (1) deterministic convergence, (2) accurate computation of nodal prices, (3) support of both smooth and nonsmooth costings of a variety of resources and services, such as real energy, reactive energy, voltage support, etc., (4) full active and reactive power flow modeling of large-scale systems, and (5) satisfactory worst-case performance that meets the real-time dispatching requirement.
