Power System Mode optimization by piecewise-linear approximation of energy characteristics of Power Plants

Abstract

The issues of improving of methods and algorithms for power system short-term mode optimal planning are considered. The main disadvantages and calculation difficulties typical for traditional algorithms are described. An effective algorithm for power system mode optimization based on a piecewise- linear approximation of nonlinear dependencies is proposed. Application of the proposed algorithm can effectively increase the accuracy and overcome many calculation difficulties associated with discontinuity of energy characteristics of power plants and various constraints in the form of equality and inequality.

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

“…-according to the balance of electricity for a control cycle for each of the calculated electricity consumers (3) -by the limiting capacities of design power plants and electricity consumers (4) (5)…”

“…-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.…”

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

“…At present, methods of taking into account various constraints in optimization of power system modes by traditional algorithms based on methods of gradient [11,12], reduced gradient [12], Newton [13], Lagrange [14,15], linear programming [16,17], etc. are well researched.…”

Optimization of Electrical Networks Modes on Transformation Coefficients of Transformers

“…To date, as the results of the work of many scientists and specialists around the world, many methods and algorithms for solving the problem under consideration have been developed. They effectively use various approaches and optimization methods, such as classical [1,2,13,14], heuristic [3,4], artificial intelligence [5,6,7], etc.…”