G. Darling

Capacitor placement, replacement and control in large-scale distribution systems by a GA-based two-stage algorithm

This paper presents a two-stage algorithm tailored for capacitor placement, replacement and control of general, large-scale, unbalanced distribution systems. The first stage of the proposed algorithm consists of a GA followed by the second stage which consists of a sensitivity-based heuristic method tailored for the capacitor placement, replacement and control problem. The two-stage algorithm is designed to take advantage of the merits of each technique. The GA is employed to find neighborhoods of high quality solutions and to provide a good initial guess for the sensitivity-based heuristic. The heuristic uses the sensitivity of real power loss to reactive power to quickly and locally improve upon the solution provided by the GA with less computation than by allowing the GA to continue. The two-stage algorithm was implemented in the C programming language and tested for a 292 bus unbalanced system with single, two and three-phase branches and grounded and ungrounded portions of the network with promising results.

An efficient algorithm for real-time network reconfiguration in large scale unbalanced distribution systems

Real-time applications demand fast computation, and this paper proposes an efficient algorithm for real-time network reconfiguration on large unbalanced distribution networks. A novel formulation of the network reconfiguration to achieve loss minimization and load balancing is given. To reduce computational requirements for the solution algorithm, well justified power flow and loss reduction formulae in terms of the on/off status of network switches are proposed for efficient system updating. The algorithm relies only on a few full power flow studies based on system states attained by explicit expressions using backward-forward sweeps for efficient computation of power system states at the critical system operating points. The solution algorithm runs in an amount of time linearly proportional to the number of tie switches and the number of sectionalizing switches in the system. The solution algorithm has been implemented into a software package and tested on unbalanced distribution systems including a system with 292 buses, 76 laterals, 7 transformers, 45 switches and 255 line sections under diverse system conditions.

Optimal capacitor placement, replacement and control in large-scale unbalanced distribution systems: modeling and a new formulation

This paper undertakes the problem of optimal capacitor placement, replacement and control in large-scale unbalanced, radial or loop distribution networks. The problem is how to optimally determine the locations to install (or replace, or remove) capacitors, the types and sizes of capacitors to be installed (or replaced) and, during each load level, the control schemes for each capacitor in the nodes of a general three-phase unbalanced distribution system such that a desired objective function is minimized while the load constraints, network constraints and operational constraints (e.g. the voltage profile) at different load levels are satisfied. The objective function considered consists of two terms: cost for energy loss; and cost related to capacitor purchase, capacitor installation, capacitor replacement and capacitor removal. Comprehensive modelings of different components are presented which include primary power networks, three-phase transformers (different winding connections, off-nominal tap ratio, core and copper losses), cogenerators, voltage sensitive load models for single-phase, two-phase and three-phase loads, shunt capacitors and reactors. The new problem is formulated as a combinatorial optimization problem with a nondifferentiable objective function. The configuration space essential in the design of a annealing-based solution methodology for the new problem is derived. >

Capacitor placement and real time control in large-scale unbalanced distribution systems: loss reduction formula, problem formulation, solution methodology and mathematical justification

A comprehensive study of capacitor placement and real-time control in general unbalanced distribution systems is undertaken. New developments in a loss reduction formula, problem formulations, solution methodology and mathematical justification are presented. The problem is decoupled into two subproblems: the capacitor placement subproblem; and the real-time control subproblem. An effective solution algorithm for placing capacitors and determining their real-time control schemes for general unbalanced distribution systems is proposed. To meet the need for efficient implementation in real-time environments, a fast pseudo gradient-type mechanism for deriving capacitor control settings is incorporated into the solution algorithms. A quadratic integer programming based approach is proposed to determine the number, locations and sizing of capacitors to be placed in the distribution systems. The subproblem of determining capacitor control settings under varying loading conditions is formulated as another quadratic integer programming problem. Mathematical justification is provided to show that the proposed algorithms are guaranteed to yield local optimal solutions.

Capacitor placement and real time control in large-scale unbalanced distribution systems: numerical studies

A novel solution algorithm for capacitor placement and real-time control in real large-scale unbalanced distribution systems is evaluated and implemented to determine the number, locations, sizes, types and control schemes of capacitors to be placed on large-scale unbalanced distribution systems. A detailed numerical study regarding the solution algorithm in large scale unbalanced distribution systems is undertaken. Promising numerical results on both 292 bus and 394 bus real unbalanced distribution systems containing unbalanced loads and phasing and various types of transformers are presented, The computational performance for the capacitor control problem under load variations is encouraging.

Optimal capacitor placement, replacement and control in large-scale unbalanced distribution systems: system solution algorithms and numerical studies

This paper develops an effective and, yet, practical solution methodology for optimal capacitor placement, replacement and control in large-scale unbalanced, general radial or loop distribution systems. The solution methodology can optimally determine (i) the locations to install (or replace, or remove) capacitors, (ii) the types and sizes of capacitors to be installed (or replaced) and, during each load level, (iii) the control schemes for each capacitor in the nodes of a general three-phase unbalanced distribution system such that a desired objective function is minimized while the load constraints, network constraints and operational constraints at different load levels are satisfied. The solution methodology is based on a combination of the simulated annealing technique and the greedy search technique in order to achieve computational speed and high-quality solutions. Both the numerical and implementational aspects of the solution methodology are detailed. Analysis of the computational complexity of the solution algorithm indicates that the algorithm is also effective for large-scale distribution systems in terms of computational efforts. Test, results on a realistic, unbalanced distribution network, a 291-bus with 77 laterals, 305 distribution lines and 6 transformers with varying loading conditions, are presented with promising results. The robustness of the solution methodology under varying loading conditions is also investigated.<<ETX>>