A Schur Complement Method for DAE Systems in Power System Simulations

The power system networks in North America and Europe are the largest man-made interconnected systems in the world. Many power system applications rely on time consuming dynamic simulations of large-scale power systems in order to optimize the operation and ensure the reliability of the electricity network. Dynamic simulations of power systems involve the solution of a series of initial value, stiff, hybrid DAE systems over a time window. To achieve this, the time window is discretized and a new DAE system is formed and solved at each time step, with initial values taken from the previous time step solution. At each new time step, the DAE system to be solved can be different because of the discrete variables involved in the formulation (e.g. a differential equation can become algebraic and vice versa). A non-overlapping domain decomposition is proposed to speed up the solution of the DAE system using the Schur Complement Method. The special structure of the physical system helps define the domain partitioning scheme and eliminates the need for a partitioning algorithm. It allows the formulation and solution of the reduced system using sparse, direct solvers to obtain the interface variables. Afterward, the parallel evaluation of the internal subdomain variables is possible and efficient load balancing is achieved. Numerically, the method shows no convergence degradation when compared to the integrated method, which is traditionally used for solving power system DAEs. The aspects of decomposition, solution and optimization of the algorithm for the specific problem are discussed and results from the application of the DDM on realistic power system models are presented.