Optimization of Short-term Modes of Hydrothermal Power System

Abstract

Optimal planning of short-term modes of power systems is a complex nonlinear programming problem with many simple, functional and integral constraints in the form of equalities and inequalities. Especially, the presence of integral constraints causes significant difficulties in solving of such problem. Since, under such constraints, the modes of power system in separate time intervals of the considered planning period become dependent on the values of the parameters in other intervals. Accordingly, it becomes impossible to obtain the optimal mode plan as the results of separate optimization for individual time intervals of the period under consideration. And the simultaneous solution of the problem for all time intervals of the planning period in the conditions of large power systems is associated with additional difficulties in ensuring the reliability of convergence of the iterative computational process. In this regard, the issues of improving the methods and algorithms for optimization of short-term modes of power systems containing thermal and large hydroelectric power plants with reservoirs, in which water consumption is regulated in the short-term planning period, remains as an important task. In this paper, we propose the effective algorithm for solving the problem under consideration, which makes it possible to quickly and reliably determine the optimal operating modes of the power system for the planned period. The results of research of effectiveness of this algorithm are presented on the example of optimal planning of daily mode of the power system, which contains two thermal and three hydraulic power plants..

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

“…Taking into account losses in electrical networks and the corresponding network factor in the optimal planning of short-term modes of power systems with control of the load of electrical consumers, in the general case, can lead to a significant change in the load schedules of regulated electrical consumers and the redistribution of the total load of the power system between the calculated power plants. Here, optimization is carried out by reducing the total fuel costs in the power system by reducing losses as a result of choosing the optimal load schedules for power consumers and power plants participating in the optimization [1][2].…”

“…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.…”