Vector Regularization of Material Flows in Complex Power Systems

Background: There is an analytic solution to the problem of material balances regularization if the definition of a priori information is incorrect, but this solution does not take into account different degrees of determination accuracy of every parameter, and metrological and technological limitations that should be known in practical calculations. Therefore, it is urgent to identify the accuracy of every parameter of the a priori information when correcting material balances. Materials and methods: To formulate and solve the problems of correcting the a priori information the authors suggest using matrix methods of making up material balances and graph theory. The formulated optimization problems are solved by statistical programming methods. Results: Based on the matrix model of flows in complex power systems the authors have formulated the task of vector regularization of material flows taking into account the balance limitations for all or selected sub-systems, in which the regularization parameter is chosen for each parameter of the a priori information with the metrological characteristics of the elements of the monitoring system taken into consideration; the combination of these parameters is presented as a diagonal matrix of regularization parameters. The authors obtained an analytic solution without limitations on the allowed values of a priori information, and a numerical solution using the method of statistical programming that allows taking into account specific limitations or their combination. Conclusions: The authors suggested a generalized method of regulating material flows in complex power systems which takes into consideration various degrees of determination accuracy of a priori information, technological and metrological limitations and can be applied to processing of test results of power equipment and preliminary calculations of actual technical and economic performance of the equipment.