Algorithm for power systems mode optimization taking into account the frequency change in terms of probablistic nature of initial information

Abstract

The task of power systems mode optimization relates to the complex tasks of non-linear mathematical programming. Despite the development over the past few decades many methods and algorithms for solving this problem, questions of their improvement taking into account the current operating conditions of energy systems remain an important task. This article proposes a new algorithm for the optimization of short-term modes of power systems, taking into account frequency changes in terms of the probabilistic nature of initial information. A distinctive feature of the algorithm is associated with the elimination of the need to choose the single slack bus with balancing power plant in calculations, which is typical for many existing methods. It is shown that taking into account frequency change in the optimization of power system mode in terms of probabilistic nature of initial information can introduce significant changes in the calculation results and lead to a corresponding increase in the resulting economic effect.

Taking into account the constraints in power system mode optimization by genetic algorithms

“…In the problems of power system short-term modes optimization, the initial information about loads of buses in some cases may have a probabilistic or partially indefinite nature. The algorithm described here can be effectively used to solve such a problem based on the use of the procedures described in [17][18][19][20][21].…”

Algorithm for optimization of power system short-term mode in conditions of partial uncertainty of initial information taking into account the frequency change

“…The optimal solutions obtained at this stage forms conditionally optimal plans for the problem. Then, at these conditionally optimal plans and corresponding loads of electric consumers the values of objective function which form the diagonal elements of the "payment matrix" Bii, i = 1, 2, ..., n are calculated as in optimization under conditions of probabilistic nature of initial information [17].…”

“…3) The choice of the best plan among conditionally optimal plans in basis of the use of received payment matrix is carried out by additional criterion of minimax risk, which proceeds from the assumption that no matter what plan we accept, the risk from its implementation will necessarily be the worst [17,21,22 ].…”

Mathematical model of the problem of accounting for losses in electrical networks when optimizing the loads of electrical consumers

“…-lots of PL, in which power flows are controlled; -power i-th TPS and j-th electric consumer in t-м regulation cycle interval; -total losses of active power in electrical networks в t-м regulation cycle interval; fuel cost i-th THES at its load in t-м regulation cycle interval ; functions of active power imbalances in t-м interval and electricity -th consumer for the regulation cycle T, respectively [3][4].…”

“…The described problem can be reduced to minimization of the following function (7) where t, j -indefinite Lagrange multipliers to take into account the limitation in the form of the balance of active power in the power system in t -м regulation cycle interval (2) and electricity for j-th consumer for a cycle of regulation (3); -penalty function introduced when the flow restriction is violated l -th PL in t-м regulation cycle interval. In the described mathematical model of the problem, it is assumed that the calculated HPS are taken into account based on the selection of the corresponding Lagrange multipliers λ and their reduction, in the calculated sense, into the category of equivalent TPS as in [1][2][3][4]. And TPS with a limited fuel supply for the planned period are taken into account by the algorithm proposed in Chapter 3 of this work.…”