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

This paper proposes a new integrated model for solving the distribution system planning (DSP) problem by implementing distributed generation (DG) as an attractive option in distribution utilities territories. The proposed model integrates a comprehensive optimization model and planner's experience to achieve optimal sizing and siting of distributed generation. This model aims to minimize DG's investment and operating costs, total payments toward compensating for system losses along the planning period, as well as different costs according to the available alternative scenarios. These scenarios vary from expanding of an existing substation and adding new feeders to purchasing power from an existing intertie to meet the load demand growth. Binary decision variables are employed in the proposed optimization model to provide accurate planning decisions. The present worth analysis of different scenarios is carried out to estimate the feasibility of introducing DG as a key element in solving the DSP problem.

An integrated distributed generation optimization model for distribution system planning

In this paper, a new design methodology for determining the size, location, type and number of capacitors to be placed on a radial distribution system is presented. The objective is to minimize the peak power losses and the energy losses in the distribution system considering the capacitor cost. A sensitivity analysis based method is used to select the candidate locations for the capacitors. A new optimization method using a genetic algorithm is proposed to determine the optimal selection of capacitors. Test results have been presented along with the discussion of the algorithm. >

Optimal selection of capacitors for radial distribution systems using a genetic algorithm

The problem of capacitor allocation for loss reduction in electric distribution systems has been extensively researched over the past several decades. This paper describes the evolution of the research and provides an evaluation of the practicality and accuracy of the capacitor placement algorithms in the literature. The intent of this paper is not to provide a complete survey of all the literature in capacitor allocation, but to provide researchers and utility engineers further insight into the choices of available capacitor allocation techniques and their respective merits and shortcomings. Furthermore, this paper serves as a useful and practical guideline to assist in the implementation of an appropriate capacitor allocation technique.

Classification of capacitor allocation techniques

This Paper presents a new approach for the optimal sizing and siting of substations and network routing problem. The solution approach proposed is a nolinear programming approach. The problem has been formulated as a Quadratic Mixed Integer programming (QMIP) problem in terms of the fixed costs of the substations and lines and the present worth of the energy loss costs of the line segments. The solution to this QMIP problem is obtained in two stages. In the first stage the quadratic programming problem is solved following the procedure developed by Wolfe using simplex method and treating all the variables as continuous variables. In the second stage, a procedure has been suggested to integerize the values of the integer variables. The proposed method is validated using a numerical example.

Distribution System Planning through a Quadratic Mixed Integer Programming Approach

This paper presents a method of optimally choosing fixed and switched shunt capacitors on radial distribution feeders, considering load growth, growth in load factor and increase in cost of energy. Mathematical models to represent cost saving due to energy loss reduction taking the growth factors into account, cost saving due to release in systam capacities, capacitor cost and voltage rise during off-peek hours, as a function of capacitive current flows in the feeder sections have been formulated. Cost functions have been defined for optimizing the choice of both fixed and switched capacitors. A direct search technique known as the Method of Local Viariations has been employed for solving the resulting discrete variational problem. The problem has also been solved using Dynamic Programming Approach for comparison. The proposed method has been illustrated through some actual cases of radial feeders existing in an Indian distribution network. The results highlighting the influence of the growth factors have also been discussed in this paper.

Optimal Choice of Fixed and Switched Shunt Capacitors on Radial Distributors by the Method of Local Variations

An optimal conductor gradation procedure for radial distribution feeders is proposed in this paper. Models to represent feeder cost, energy loss cost and voltage regulation as a function of conductor cross-section and an objective function for optimizing the conductor cross-section have been formulated. The problem has been posed as a multistage decision dynamic programming problem, and the optimal conductor cross- sections for the fender segments are obtained by solving the same. The proposed method takes into account the non-uniform distribution of loads along the length of the feeders and also the maximum permissible voltage drop along a feeder. Further, the method takes into account the load growth in future years of the plan period. The results of the design of a typical radial feeder using thp proposed method are presented and discussed.

An Approach to Optimal Distribution System Planning Through Conductor Gradation

Models to represent substation feed area, feeder voltage drop, feeder load distribution, cost of losses in the feeders and transformers are formuleted in terms of the variable system parameters. Based on these models, objective functions are defined which are employed in arriving at optimal substation size, feeder loading limits and conductor sizes. The technique suggested greatly reduces the computational time and effort compared to the methods presently in vogue. The optimal splutions, obtained for typical Secondary and primary distribution systems using the proposed technique are presented. To bring out toe efficiency of the proposed technique, the computational requirements for the proposed method along with the simulation techniques are discussed. The proposed method is highly promising, since it is very fast, simple and easy to program.

Optimal Distribution System Planning

This paper presents an improved second order load flow method in rectangular coordinates which is distinctly superior to the existing second order methods from the point of view of both speed and storage. Further, the proposed method's memory requirement is comparable to that of the Fast Decoupled Load Flow (FULF) method. The new method would be considerably faster than the FOLF method for a number of systems for which the FDLF method requires a large number of iterations to converge. The proposed method is highly reliable and it gives solutions for a number of systems for which the FDLF method fails. In addition a novel procedure for handling generator bus Q limit violations is also presented.

K. S. Prakasa Rao

Papers

Distribution System Planning through a Quadratic Mixed Integer Programming Approach

Optimal Choice of Fixed and Switched Shunt Capacitors on Radial Distributors by the Method of Local Variations

An Approach to Optimal Distribution System Planning Through Conductor Gradation

Optimal Distribution System Planning

An Exact Fast Load Flow Method Including Second Order Terms in Rectangular Coordinates