Optimal sizing of capacitors placed on a radial distribution system
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. >
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TL;DR: Accuracy analysis and the test results show that estimation methods can be used in searches to reconfigure a given system even if the system is not well compensated and reconfiguring involves load transfer between different substations.
Abstract: A general formulation of the feeder reconfiguration problem for loss reduction and load balancing is given, and a novel solution method is presented. The solution uses a search over different radial configurations created by considering switchings of the branch exchange type. To guide the search, two different power flow approximation methods with varying degrees of accuracy have been developed and tested. The methods are used to calculate the new power flow in the system after a branch exchange and they make use of the power flow equations developed for radial distribution systems. Both accuracy analysis and the test results show that estimation methods can be used in searches to reconfigure a given system even if the system is not well compensated and reconfiguring involves load transfer between different substations. For load balancing, a load balance index is defined and it is shown that the search and power flow estimation methods developed for power loss reduction can also be used for load balancing since the two problems are similar. >
3,985 citations
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. >
1,832 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: A novel hybrid Genetic Algorithm (GA) / Particle Swarm Optimization (PSO) for solving the problem of optimal location and sizing of DG on distributed systems is presented to minimize network power loss and better voltage regulation in radial distribution systems.
920 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 sizing of capacitors placed..."
...Alternatively, another linear approximation can be formulated by neglecting the losses in the DistFlow model (setting jk = 0 in (3)) to obtain the Linearized DistFlow model [23]:...
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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. >
1,832 citations
TL;DR: In this article, a power flow method is described for solving weakly meshed distribution and transmission networks, using a multiport compensation technique and basic formations of Kirchoff's laws.
Abstract: A power flow method is described for solving weakly meshed distribution and transmission networks, using a multiport compensation technique and basic formations of Kirchoff's laws. This method has excellent convergence characteristics and is robust. A computer program implementing this scheme was developed and successfully applied to several practical distribution and transmission networks with radial and weakly meshed structures. The method can be applied to the solution of both the three-phase (unbalanced) and single-phase (balanced) representation of the network, however, only the single-phase representation is treated in detail. >
1,108 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: 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
TL;DR: In this article, the problem of volt/var control on general radial distribution systems is formulated, simplified and solved, where the objective is to minimize the peak power and energy losses while keeping the voltage within specified limits under varying load conditions.
Abstract: In this paper (Part I) and two companion papers (Part II and Part III) the problem of volt/var control on general radial distribution systems is formulated, simplified and solved. The objective is to minimize the peak power and energy losses while keeping the voltage within specified limits under varying load conditions. The decision variables to be optimally determined are (i) the locations, sizes and the real-time control of the specified number of ON/OFF switched and fixed capacitors and (ii) the locations and real-time control of the minimum number of voltage regulators. It is shown in this paper (Part I) that the regulator (volt) and the capacitor (var) problem may be treated as two decoupled problems. Part II of this set of three papers, conjoined with Part 1. provides the analytical tools by which optimal solutions for both problems may be determined. Application of the theory to representative radial systems is shown in Part III whhich also illustrates the economic benefits and numerical results achievable through both regulation and compensation schemes.
220 citations