Optimal capacitor placement on radial distribution systems
TL;DR: In this article, the problem of capacitors placement on a radial distribution system is formulated and a solution algorithm is proposed, where the location, type, and size of the capacitors, voltage constraints, and load variations are considered.
Abstract: The problem of capacitor placement on a radial distribution system is formulated and a solution algorithm is proposed. The location, type, and size of capacitors, voltage constraints, and load variations are considered. The objective of capacitor placement is peak power and energy loss reduction, taking into account the cost of the capacitors. The problem is formulated as a mixed integer programming problem. The power flows in the system are explicitly represented, and the voltage constraints are incorporated. A solution method has been implemented that decomposes the problem into a master problem and a slave problem. The master problem is used to determine the location of the capacitors. The slave problem is used by the master problem to determine the type and size of the capacitors placed on the system. In solving the slave problem, and efficient phase I-phase II algorithm is used. >
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TL;DR: In this paper, a nonlinear programming problem for capacitors placed on a radial distribution system is formulated and a solution algorithm is developed to find the optimal size of capacitors so that the power losses will be minimized for a given load profile while considering the cost of the capacitors.
Abstract: A capacitor sizing problem for capacitors placed on a radial distribution system is formulated as a nonlinear programming problem, and a solution algorithm is developed. The object is to find the optimal size of the capacitors so that the power losses will be minimized for a given load profile while considering the cost of the capacitors. The formulation also incorporates the AC power flow model for the system and the voltage constraints. The solution algorithm developed for the capacitor sizing problem is based on a Phase I-Phase II feasible directions approach. Novel power flow equations and a solution method, called DistFlow, for radial distribution systems are introduced. The method is computationally efficient and numerically robust, especially for distribution systems with large r/x ratio branches. DistFlow is used repeatedly as a subroutine in the optimization algorithm for the capacitor sizing problem. The test results for the algorithm indicate that the method is computationally efficient and has good convergence characteristics. >
1,391 citations
TL;DR: It is proved that convexification requires phase shifters only outside a spanning tree of the network and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints.
Abstract: We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we prove that both relaxation steps are always exact, provided there are no upper bounds on loads. For mesh networks, the conic relaxation is always exact but the angle relaxation may not be exact, and we provide a simple way to determine if a relaxed solution is globally optimal. We propose convexification of mesh networks using phase shifters so that OPF for the convexified network can always be solved efficiently for an optimal solution. We prove that convexification requires phase shifters only outside a spanning tree of the network and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints. Part I introduces our branch flow model, explains the two relaxation steps, and proves the conditions for exact relaxation. Part II describes convexification of mesh networks, and presents simulation results.
983 citations
TL;DR: This paper reviews distributed algorithms for offline solution of optimal power flow (OPF) problems as well as online algorithms for real-time solution of OPF, optimal frequency control, optimal voltage control, and optimal wide-area control problems.
Abstract: Historically, centrally computed algorithms have been the primary means of power system optimization and control. With increasing penetrations of distributed energy resources requiring optimization and control of power systems with many controllable devices, distributed algorithms have been the subject of significant research interest. This paper surveys the literature of distributed algorithms with applications to optimization and control of power systems. In particular, this paper reviews distributed algorithms for offline solution of optimal power flow (OPF) problems as well as online algorithms for real-time solution of OPF, optimal frequency control, optimal voltage control, and optimal wide-area control problems.
800 citations
Cites methods from "Optimal capacitor placement on radi..."
...As an alternative to (2), balanced radial distribution networks can be represented using the DistFlow model [13]....
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TL;DR: This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms.
Abstract: This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations in each model, and proves equivalence relationships among them. Part II presents sufficient conditions under which the convex relaxations are exact.
796 citations
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16 May 2011
TL;DR: In this article, the authors discuss and compare via simulation various design options for control systems to manage the reactive power generated by these inverters, and find that local control schemes are able to maintain voltage within acceptable bounds.
Abstract: High-penetration levels of distributed photovoltaic (PV) generation on an electrical distribution circuit present several challenges and opportunities for distribution utilities. Rapidly varying irradiance conditions may cause voltage sags and swells that cannot be compensated by slowly responding utility equipment resulting in a degradation of power quality. Although not permitted under current standards for interconnection of distributed generation, fast-reacting, VAR-capable PV inverters may provide the necessary reactive power injection or consumption to maintain voltage regulation under difficult transient conditions. As side benefit, the control of reactive power injection at each PV inverter provides an opportunity and a new tool for distribution utilities to optimize the performance of distribution circuits, e.g., by minimizing thermal losses. We discuss and compare via simulation various design options for control systems to manage the reactive power generated by these inverters. An important design decision that weighs on the speed and quality of communication required is whether the control should be centralized or distributed (i.e., local). In general, we find that local control schemes are able to maintain voltage within acceptable bounds. We consider the benefits of choosing different local variables on which to control and how the control system can be continuously tuned between robust voltage control, suitable for daytime operation when circuit conditions can change rapidly, and loss minimization better suited for nighttime operation.
707 citations
References
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TL;DR: In this paper, the extremal value of the linear program as a function of the parameterizing vector and the set of values of the parametric vector for which the program is feasible were derived using linear programming duality theory.
Abstract: J. F. Benders devised a clever approach for exploiting the structure of mathematical programming problems withcomplicating variables (variables which, when temporarily fixed, render the remaining optimization problem considerably more tractable). For the class of problems specifically considered by Benders, fixing the values of the complicating variables reduces the given problem to an ordinary linear program, parameterized, of course, by the value of the complicating variables vector. The algorithm he proposed for finding the optimal value of this vector employs a cutting-plane approach for building up adequate representations of (i) the extremal value of the linear program as a function of the parameterizing vector and (ii) the set of values of the parameterizing vector for which the linear program is feasible. Linear programming duality theory was employed to derive the natural families ofcuts characterizing these representations, and the parameterized linear program itself is used to generate what are usuallydeepest cuts for building up the representations.
2,133 citations
TL;DR: In this paper, a nonlinear programming problem for capacitors placed on a radial distribution system is formulated and a solution algorithm is developed to find the optimal size of capacitors so that the power losses will be minimized for a given load profile while considering the cost of the capacitors.
Abstract: A capacitor sizing problem for capacitors placed on a radial distribution system is formulated as a nonlinear programming problem, and a solution algorithm is developed. The object is to find the optimal size of the capacitors so that the power losses will be minimized for a given load profile while considering the cost of the capacitors. The formulation also incorporates the AC power flow model for the system and the voltage constraints. The solution algorithm developed for the capacitor sizing problem is based on a Phase I-Phase II feasible directions approach. Novel power flow equations and a solution method, called DistFlow, for radial distribution systems are introduced. The method is computationally efficient and numerically robust, especially for distribution systems with large r/x ratio branches. DistFlow is used repeatedly as a subroutine in the optimization algorithm for the capacitor sizing problem. The test results for the algorithm indicate that the method is computationally efficient and has good convergence characteristics. >
1,391 citations
TL;DR: In this paper, the Equal Area Criterion (EACC) was used to optimize the net savings associated with reduction of power and energy losses through shunt capacitor placement on primary distribution feeders.
Abstract: New generalized procedures are developed for optimizing the net savings associated with reduction of power and energy losses through shunt capacitor placement on primary distribution feeders. These procedures are applied to realistic problems to facilitate their immediate use by the electric utility distribution system designer. It is shown that a basic principle, called here "The Equal Area Criterion", offers significant computational and physical insight into numerous problems outside the bounds of studies previously reported and widely accepted in industry
377 citations
TL;DR: A framework of concepts is developed which helps to unify a substantial portion of the literature on large-scale mathematical programming and comprises problem manipulations that can be used to derive what are often referred to as “master” problems; the principal manipulations discussed are Projection, Inner Linearization, and Outer Linearization.
Abstract: A framework of concepts is developed which helps to unify a substantial portion of the literature on large-scale mathematical programming. These concepts fall into two categories. The first category consists of problem manipulations that can be used to derive what are often referred to as “master” problems; the principal manipulations discussed are Projection, Inner Linearization, and Outer Linearization. The second category consists of solution strategies that can be used to solve the master problems, often with the result that “subproblems” arise which can then be solved by specialized algorithms. The Piecewise, Restriction, and Relaxation strategies are the principal ones discussed. Numerous algorithms found in the literature are classified according to the manipulation/strategy pattern they can be viewed as using, and the usefulness of the framework is demonstrated by using it see Part II of this paper to rederive a representative selection of algorithms.
The material presented is listed in the following order: The first section is introductory in nature, and discusses types of large-scale problems, the scope of discussion and the literature, and the notation used. The second section, entitled “Problem Manipulations: Source of 'Master' Problems” covers the subjects of projection, inner linearization and outer linearization. The third section, “Solution Strategies: Source of 'Subproblems',” discusses piecewise strategy, restriction and relaxation. The fourth section is entitled “Synthesizing Known Algorithms from Manipulations and Strategies,” and is followed by a concluding section and an extensive bibliography.
237 citations
TL;DR: In this paper, a new method is described which determines the optimum number, location, and size of shunt capacitors in a radial distribution feeder with discrete lumped loads so as to maximize overall savings, including the cost of capacitors.
Abstract: A new method is described which determines the optimum number, location, and size of shunt capacitors in a radial distribution feeder with discrete lumped loads so as to maximize overall savings, including the cost of capacitors. The method also determines when capacitors are not economically justified. Dynamic programming techniques are used and several algorithms developed to obtain the optimal solution by regarding the optimization process as a multistage decision process with the desired Markovian property. Special cases are studied and solutions obtained when no capacitor cost, cost proportional to installed capacity, and cost proportional to installed capacity plus a fixed cost per installed bank are considered. The methods are suitable for efficient solution in a digital computer.
236 citations