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. >

Network reconfiguration in distribution systems for loss reduction and load balancing

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. >

Optimal capacitor placement on radial distribution systems

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. >

Optimal sizing of capacitors placed on a radial distribution system

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.

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M.E. Baran

Papers

Optimal capacitor placement on radial distribution systems

Optimal sizing of capacitors placed on a radial distribution system