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This work proposes an optimization model for the power dispatch under a pool-bilateral market. In it, all transactions and also the power traded in the spot market are separated into different networks according to the corresponding current injections. Using the superposition principle (SP), a set of network equations is assigned to every transaction and to the power injections related to the pool (spot market). The model comprises all of the network equations and inequalities representing operational limits. A primal-dual interior point method is used for the resolution of the optimization problem. The line currents, complex voltages, and power generations associated with every transaction and spot market are obtained. Results are presented for a 5-bus and the IEEE 118-bus systems. Index Terms--Optimal power dispatch, pool-bilateral markets, primal-dual interior point method, superposition principle.

This paper presents a systematic analysis of the main reasons for the failure of solution algorithms in the general non-linear optimal power flow (OPF) problem. It defines the concept of critical and non-critical OPF problems and identifies and categorizes the main types of such cases. In essence, a non-critical case is one where a small variation in a parameter leads to a small change in the optimum solution. Alternatively, critical cases are such that a small variation in a problem parameter leads to either the loss of local optimality or feasibility. Both of these can result in a sharp discontinuity in the solution. Numerical and theoretical examples illustrate each of these cases. Keywords: Optimal Power Flow; Parameter Variation; Loss of Local Optimality; Loss of Local Feasibility.

This work presents a methodology to calculate a sequence of Optimal Power Flow (OPF) solutions under variable load conditions. The aim is to obtain a set of optimal operating points in the neighborhood of the bounds of the region defined by the load flow equations and a set of operational limits. For this, an algorithm based on the Continuation method and on a Primal-Dual Interior Point optimization method is proposed. Such algorithm consists of two main steps: the predictor step, which uses a linear approximation of the Karush-Kuhn-Tucker (KKT) conditions to estimate a new operating point for an increment in the system load; and the corrector step, which calculates the optimum corresponding to the new load level via a nonlinear Primal-Dual Interior Point method. Indices for critical buses and inequality constraints are a byproduct of the methodology. In addition, sensitivity analysis is performed to calculate the amount of reactive compensation which allows for a pre-specified increase in the system load. Results for realistic test systems are presented. Index Terms--Continuation method, nonlinear interior point method, optimal power flow.

Presents a correction to the study "A Methodology for Optimal Power Dispatch Under a Pool-Bilateral Market," on electric power.