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The transience and unpredictability of processes in electric power systems (EPS) determine complexity of its control. This problem is especially relevant for EPS with renewable energy sources and flexible alternating current transmission systems technologies. Automatic control systems simplify the solution of this problem. Despite this, many issues related to EPS state control are solved by power system operators. Decision support systems (DSS) are applying to increase efficiency of operators work. However, existing algorithms in practice are inoperable in some cases: unrealizable decisions are formed, or decision cannot be found at all, etc. Another important problem is impossibility to preliminarily verify the proposed solution. In this regard, operators can additionally use EPS simulators, which are usually limited either by the size of simulated scheme or by the details of equipment mathematical models. The limitations are a consequence of numerical methods using, which are badly applicable for large-scale power systems simulation. In this article, a novel DSS has been developed based on a hybrid approach to EPS modeling combining properties and capabilities of several simulation techniques: analog, physical and digital. The implicit integration of differential equations in analog way makes possible modeling faster than real time. Such opportunity allows operator to verify more decisions and select the most effective ones. The algorithm for DSS application has been developed and described in the article. The properties and capabilities of the developed DSS are confirmed by experimental studies and tests in a real EPS. [ABSTRACT FROM AUTHOR]