The ac power flow problem can be solved efficiently by Newton's method. Only five iterations, each equivalent to about seven of the widely used Gauss-Seidel method, are required for an exact solution. Problem dependent memory and time requirements vary approximately in direct proportion to problem size. Problems of 500 to 1000 nodes can be solved on computers with 32K core memory. The method, introduced in 1961, has been made practical by optimally ordered Gaussian elimination and special programming techniques. Equations, programming details, and examples of solutions of large problems are given.

Power Flow Solution by Newton's Method

A survey is presented on the currently available numerical techniques for power-system load-flow calculation using the digital computer. The review deals with methods that have received widespread practical application, recent attractive developments, and other methods that have interesting or useful characteristics. The analytical bases, computational requirements, and comparative numerical performances of the methods are discussed. Attention is given to the problems and techniques of adjustments in load-flow solutions, and the suitabilities of various methods for modern applications such as security monitoring and optimal load flow are examined.

Review of load-flow calculation methods

The study of power flow analysis for microgrids has gained importance where several methods have been proposed to solve these problems. However, these schemes are complicated and not easy to implement due to the absence of a slack bus as well as the dependence of the power on frequency as a result of the droop characteristics. This paper proposes simple and effective modifications to the conventional method (Newton Raphson) to compute the power flow for microgrids. The presented method provides a simple, easy to implement, and accurate approach to solve the power flow equations for microgrids. The proposed method is applied to two test systems: a 6-bus system and a 38-bus system. The results are compared against simulation results from PSCAD/EMTDC which validate the effectiveness of the developed method. The proposed technique can be easily integrated in current commercially available power system software and can be applied for power system studies.

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A Novel Approach to Solve Power Flow for Islanded Microgrids Using Modified Newton Raphson With Droop Control of DG

This paper describes some computer programing techniques for taking advantage of the sparsity of the admittance matrix. The techniques are based on two main ideas; (1) determination of a sequence of operations. which results in a near minimum of memory and computing, (2) preservation of these operations for repetition. Use of these techniques makes it possible to obtain significant reductions in memory and processing time for many network analysis programs. Claims are substantiated by actual results.

Techniques for Exploiting the Sparsity or the Network Admittance Matrix

In this tutorial paper, the influence of the computer not only on the modus operandi of circuit design, but also on network theory itself, is discussed. The topological properties of linear graphs are reviewed and a matrix-topological formulation of the network problem is described. In addition to the classical mesh, node, and cutset methods, a mixed method of analysis is described which is applicable to dc, ac, and transient problems. Numerical methods of solving linear and nonlinear dc network problems are discussed and a new approach to ac analysis, using the mixed method and a numerical solution of the matrix eigenvalue problem, is described. The extension of this method to the transient analysis of linear networks is also explained. Finally, the problem of instability in the numerical integration of differential equations is discussed and several means of solving the problem are outlined.

Computer methods of network analysis

A new load flow program has been developed which employs the node-impedance matrix of a system. A special input routine was developed that allows the line data to be in any order desired. The program has the capacity to control generator voltages within a specified var (reactive volt-ampere) range, and also to incorporate off-nominal autotransformers. In every system studied using this program, the time for solution was less than that required by the usual nodal branch admittance iterative method.

Power Flow Solution by Impedance Matrix Iterative Method

This paper is an extension of the work by the authors on the Z-matrix load flow. The algorithm originally proposed is derived and further clarified by employing both the matrix equations with reference ground and those with a bus of the system as reference. Test results are reported on the use of the block-iteration process and the axis-reiteration process and the effect of load incorporation on convergence. Refinements in the basic algorithm are also included, with test results shown verifying the theory.

Z-Matrix Algorithms in Load-Flow Programs

This paper presents DC modeling improvements and extensions to include three terminal systems for AC/DC system studies that have been developed and implemented in a large scale stability program. Particular emphasis will be on the representation of DC transmission controls and their effects on dynamic system performance.

The dynamics of AC/DC systems with controlled multiterminal HVDC transmission

A computer program which determines growth patterns and characteristics of secondary distribution systems under the influences of time and load growth is described. New methods of considering the basic load characteristics of customers are employed to determine accurate system costs for future years for all growth paths permitted by specified design changes. Using present worth arithmetic, comparisons of these costs are made to determine the schedules of design changes which will result in greatest economy for the system studied.

Secondary System Distribution Planning for Load Growth

The procIedure of predicting the radio noise (RN) performance of transmission lines, including ultrahigh voltage (UHV) levels, is outlined. The innovations against former publications on this subject are: 1) A complex eigenvalue/eigenvector analysis using Carson's earth correction terms is applied to RN analysis; 2) A new method of treating the phase correlation between modal noise fields is incorporated; 3) The METIFOR weather model is applied, yielding expected radio reception quality in statistical terms.

G. K. Carter

Papers

Power Flow Solution by Impedance Matrix Iterative Method

Z-Matrix Algorithms in Load-Flow Programs

The dynamics of AC/DC systems with controlled multiterminal HVDC transmission

Secondary System Distribution Planning for Load Growth

Calculation of the Radio Interference Statistics of Transmission Lines