It characterized with the calculation of active power flows in controlled transmission lines by their expression, using the circuit and operating parameters of the electrical network, as well as taking into account losses without calculation of their derivatives. This paper presents a new algorithm for optimization of modes of power systems taking into account functional constraints in the form of inequality on active power flows in controlled PTL and losses in electrical networks. Therefore, despite the existence of many methods and algorithms for solving of this problem, the issues of their improvement in the direction of increasing the efficiency due to more accurate accounting of limiting and influencing factors remains as an important problem. In general case, it is associated with a large number of different-scale variables, simple and functional constraints in the forms of equality and inequality, the different nature of the initial data on the state of the system and complex dependencies between parameters. The problem of power system mode optimization taking into account losses in electrical networks and constraints on power flows in power transmission lines (PTL) is a complex problem of nonlinear programming.
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