A unified mathematical model of the power flow in a system containing a reactive component compensator consisting of capacitor banks connected in series to a thyristor control reactor is presented. The application of the FACTS (Flexible Alternative Current Transmission System - Controlled flexible DC power transmission) technology is shown to reduce the gap between the controlled and unmanaged modes of operation of the electric power system (EPS), presenting dispatching personnel with additional degrees of freedom in the management of power flows and voltages in excess and deficit areas of the electric network. The main objectives of the FACTS technology application are studied: increasing the transmission line capacity to the thermal limit; optimizing power flows in a complex heterogeneous network; increasing the static and dynamic stability of the electric power system. To assess the action of the new generation of regulators of the power system, two alternative models of power flow in the electric power system are considered. In the first model, the concept of alternating series reactance is used as a state variable. In the second model, the characteristic of the advance angle is used, given in the form of a nonlinear dependence in the problem of calculating the power flow using the Newton-Raphson method. Conclusions are made on the presented models of power flow allowing to estimate possibilities of the serial capacitor with thyristor control TCSC (Thyristor Controlled Series Capacitor), as FACTS device, on improvement of modes of functioning of electric power system.

A mathematical model is presented for optimizing power flows in an electric network with a flexible controlled alternating current power transmission device - FACTS. The range of questions on the problem of optimizing the power flow in electric networks with one of the FACTS devices, the SVC static power factor compensator, has been expanded and investigated. The Lagrange function for the SVC device is proposed, which serves as the basis for obtaining a linearized equation and determining the optimum of the objective function. The method and algorithm of the optimization problem in the electric power system containing devices of the FACTS technology have been synthesized. The mathematical model allows for flexible and reliable optimization of the electrical power system. Flexibility is explained by the universality of the model, and reliability is explained by the high convergence rate of the Newton method used.