Optimal Power Flow Solutions
TL;DR: A practical method is given for solving the power flow problem with control variables such as real and reactive power and transformer ratios automatically adjusted to minimize instantaneous costs or losses by Newton's method, a gradient adjustment algorithm for obtaining the minimum and penalty functions to account for dependent constraints.
Abstract: A practical method is given for solving the power flow problem with control variables such as real and reactive power and transformer ratios automatically adjusted to minimize instantaneous costs or losses. The solution is feasible with respect to constraints on control variables and dependent variables such as load voltages, reactive sources, and tie line power angles. The method is based on power flow solution by Newton's method, a gradient adjustment algorithm for obtaining the minimum and penalty functions to account for dependent constraints. A test program solves problems of 500 nodes. Only a small extension of the power flow program is required to implement the method.
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TL;DR: In this paper, the authors extend the Dommel-Tinney approach by incorporating exact outage-contingency constraints into the method, to give an optimal steady-state-secure system operating point.
Abstract: The Dommel-Tinney approach to the calculation of optimal power-system load flows has proved to be very powerful and general. This paper extends the problem formulation and solution scheme by incorporating exact outage-contingency constraints into the method, to give an optimal steady-state-secure system operating point. The controllable system quantities in the base-case problem (e.g. generated MW, controlled voltage magnitudes, transformer taps) are optimised within their limits according to some defined objective, so that no limit-violations on other quantities (e. g. generator MVAR and current loadings, transmission-circuit loadings, load-bus voltage magnitudes, angular displacements) occur in either the base-case or contingency-case system operating conditions.
1,487 citations
TL;DR: In this paper, an evolutionary-based approach to solve the optimal power flow (OPF) problem is presented. And the proposed approach has been examined and tested on the standard IEEE 30bus test system with different objectives that reflect fuel cost minimization, voltage profile improvement, and voltage stability enhancement.
1,209 citations
TL;DR: An implementation of an interior point method to the optimal reactive dispatch problem is described in this article, which is based on the primal-dual algorithm and the numerical results in large scale networks (1832 and 3467 bus systems) have shown that this technique can be very effective to some optimal power flow applications.
Abstract: An implementation of an interior point method to the optimal reactive dispatch problem is described. The interior point method used is based on the primal-dual algorithm and the numerical results in large scale networks (1832 and 3467 bus systems) have shown that this technique can be very effective to some optimal power flow applications. >
842 citations
TL;DR: In this paper, a review of literature on optimal power flow tracing progress in this area over from 1962-93 is presented. Part I deals with the application of nonlinear and quadratic programming.
Abstract: The paper presents a review of literature on optimal power flow tracing progress in this area over from 1962-93. Part I deals with the application of nonlinear and quadratic programming.
832 citations
TL;DR: In this paper, a direct simultaneous solution for all of the unknowns in the Lagrangian function on each iteration is proposed, where each iteration minimizes a quadratic approximation of the Lagrangeian.
Abstract: The classical optimal power flow problem with a nonseparable objective function can be solved by an explicit Newton approach. Efficient, robust solutions can be obtained for problems of any practical size or kind. Solution effort is approximately proportional to network size, and is relatively independent of the number of controls or binding inequalities. The key idea is a direct simultaneous solution for all of the unknowns in the Lagrangian function on each iteration. Each iteration minimizes a quadratic approximation of the Lagrangian. For any given set of binding constraints the process converges to the Kuhn-Tucker conditions in a few iterations. The challenge in algorithm development is to efficiently identify the binding inequalities.
817 citations
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TL;DR: A number of theorems are proved to show that it always converges and that it converges rapidly, and this method has been used to solve a system of one hundred non-linear simultaneous equations.
Abstract: © The British Computer Society Issue Section: Articles Download all figures A powerful iterative descent method for finding a local minimum of a function of several variables is described. A number of theorems are proved to show that it always converges and that it converges rapidly. Numerical tests on a variety of functions confirm these theorems. The method has been used to solve a system of one hundred non-linear simultaneous equations. Related articles in Web of Science
4,305 citations
TL;DR: The ac power flow problem can be solved efficiently by Newton's method because only five iterations, each equivalent to about seven of the widely used Gauss-Seidel method are required for an exact solution.
Abstract: The ac power flow problem can be solved efficiently by Newton's method. Only five iterations, each equivalent to about seven of the widely used Gauss-Seidel method, are required for an exact solution. Problem dependent memory and time requirements vary approximately in direct proportion to problem size. Problems of 500 to 1000 nodes can be solved on computers with 32K core memory. The method, introduced in 1961, has been made practical by optimally ordered Gaussian elimination and special programming techniques. Equations, programming details, and examples of solutions of large problems are given.
1,112 citations
01 Nov 1967
TL;DR: With this method, direct solutions are computed from sparse matrix factors instead of from a full inverse matrix, thereby gaining a significant advantage in speed, computer memory requirements, and reduced round-off error.
Abstract: Matrix inversion is very inefficient for computing direct solutions of the large sparse systems of linear equations that arise in many network problems. Optimally ordered triangular factorization of sparse matrices is more efficient and offers other important computational advantages in some applications. With this method, direct solutions are computed from sparse matrix factors instead of from a full inverse matrix, thereby gaining a significant advantage in speed, computer memory requirements, and reduced round-off error. Improvements of tea to one or more in speed and problem size over present applications of the inverse can be achieved in many cases. Details of the method, numerical examples, and the results of a large problem are given.
780 citations
01 Jan 1967
154 citations
TL;DR: In this article, two dominant types of sensitivity relations are defined, namely sensitivity of one electrical variable such as the voltage Vi at node i, with respect to another electrical variable, such as reactive production Qj at node j, and sensitivity of the operating cost F with respect with such electrical variables as the consumption Ci at vertex i and the production Pj at vertex j.
Abstract: Sensitivity is defined as the ratio ?x/?y relating small changes ?x of some dependent variable to small changes ?y of some independent or controllable variable y. In power systems, two dominant types of sensitivity relations are defined, namely 1) sensitivity of one electrical variable, such as the voltage Vi at node i, with respect to another electrical variable, such as reactive production Qj at node j, and 2) sensitivity of the operating cost F with respect to such electrical variables as the consumption Ci at node i and the production Pj at node j.
148 citations