The management of reactive resources, in particular the generation facilities under control of transmission operators, plays an important role in maintaining voltage stability and system reliability. The current practice of reactive management relies on heuristics and operators' judgments to procure reactive services. Consequently, it lacks a transparent market process and assurance that the procurement costs are the lowest. This paper presents a practical, market-based solution for managing reactive services by transmission operators. Three distinct features for the proposed solution are: (1) obligating generation facilities to provide reactive services in proportion to their active power output; (2) optimizing and integrating the reactive procurement with market operation for least-cost solution; and (3) taking into account the interactions of active and reactive powers for accurate calculation of the lost opportunity costs of generators. The proposed solution further simplifies the modeling and settlement aspects of reactive management. A model process of reactive power management is presented for use by independent transmission operators. A numerical example is also given to illustrate the application of the proposed solution.

A reactive power management proposal for transmission operators

Optimal power flow (OPF) is one of the key tools for optimal operation and planning of modern power systems. Due to the high complexity with continuous and discrete control variables, modern heuristic optimization algorithms (HOAs) have been widely employed for the solution of OPF. This paper provides an overview of the latest applications of advanced HOAs in OPF problems. The most frequently applied HOAs for solving the OPF problem in recent years are covered and briefly introduced, including genetic algorithm (GA), differential evolution (DE), particle swarm optimization (PSO), and evolutionary programming (EP), etc.

https://link.springer.com/content/pdf/10.1007%2Fs40565-014-0089-4.pdf

A review on applications of heuristic optimization algorithms for optimal power flow in modern power systems

This article introduces a method for local sensitivity analysis of practical interest. A theorem is given that provides a general and neat manner to obtain all sensitivities of a general nonlinear programming problem (around a local minimum) with respect to any parameter irrespective of it being a right-hand side, objective function or constraint constant. The method is based on the well-known duality property of mathematical programming, which states that the partial derivatives of the primal objective function with respect to the constraints' right-hand side parameters are the optimal values of the dual problem variables. For the parameters or data for which sensitivities are sought to appear on the right-hand side, they are converted into artificial variables and set to their actual values, thus obtaining the desired constraints. If the problem is degenerated and partial derivatives do not exist, the method also permits obtaining the right, left, and also directional derivatives, if they exist. In addi...

A closed formula for local sensitivity analysis in mathematical programming

Mathematically, an optimal power flow (OPF) is in general a non-linear, non-convex and large-scale problem with both continuous and discrete control variables. This paper approaches the OPF problem using a modified Artificial Immune System (AIS). The AIS optimization methodology uses, among others, two major immunological principles: hypermutation, which is responsible for local search, and receptor edition to explore different areas in the solution space. The proposed method enhances the original AIS by combining it with a gradient vector. This concept is used to provide valuable information during the hypermutation process, decreasing the number of generations and clones, and, consequently, speeding up the convergence process while reducing the computational time. Two applications illustrate the performance of the proposed method.

A gradient-based artificial immune system applied to optimal power flow problems

Nonconvexity induced by the nonlinear AC power flow equations challenges solution algorithms for AC optimal power flow (OPF) problems. While significant research efforts have focused on reliably computing high-quality OPF solutions, it is not always clear that there exists a feasible path to reach the desired operating point. Transitioning between operating points while avoiding constraint violations can be challenging since the feasible space of the OPF problem is nonconvex and potentially disconnected. To address this problem, we propose an algorithm that computes a provably feasible path from an initial operating point to a desired operating point. Given an initial feasible point, the algorithm solves a sequence of convex quadratically constrained optimization problems over conservative convex inner approximations of the OPF feasible space. In each iteration, we obtain a new, improved operating point and a feasible transition from the operating point in the previous iteration. In addition to computing a feasible path to a known desired operating point, this algorithm can also be used to improve the operating point locally. Extensive numerical studies on a variety of test cases demonstrate the algorithm and the ability to arrive at a high-quality solution in few iterations.

Feasible Path Identification in Optimal Power Flow With Sequential Convex Restriction

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 an 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.

K.C. Almeida

Papers

Optimal power flow solutions under variable load conditions