Modeling Loss in an Electrical Grid with Usage Apparatus Gram-Schmidt and on Distribution Coefficients

Abstract

The problem of accurate determination of the energy losses in electric networks. To ensure this goal with the existing heterogeneity in the network loads are presenting them as a product of the mean values of the relevant operating parameters (power, current) for the period T and time functions, the averages for the time interval [0, T] is equal to one. Retrieves a universal model, which characterizes the nodal operational parameters, in the space of an orthogonal basis. The mathematical model for determining the loss of electricity and based on effective approach using the distribution coefficients. Advantages of the matrix coefficients of distribution at various regime parameters (nodal capacity, currents) for the development of the theory of methods for determining the energy losses, is in its universality as a matrix of generalized parameters, the formation of which is possible with the use of other matrices, such as the centers of resistance, contour conductivities and elements of graph theory, numerical methods, etc. The application of these models allow us to replace the dominant hitherto cumbersome ways and methods to integrate power and energy losses based on complex iterative procedures more simple and accurate. Analysis of data obtained with significant loads node network diagrams, determination of losses in the space orthogonalization of the basis of the problem is accurate and has a systematic error, which was confirmed by calculating the summation of losses on the hourly charts levels of nodal operation parameters design of the electrical network.

 Keywords: distribution coefficients matrix, power and energy losses, orthogonal basis.