A Time–Power Series-Based Semi-Analytical Approach for Power System Simulation

Time-domain simulation is the basis of dynamic security assessment for power systems. Traditionally, numerical integration methods are adopted by simulation software to solve nonlinear power system dynamics for any given contingency under a specific operating condition. An alternative simulation approach promising for online applications is to offline derive a semi-analytical solution (SAS) for power system differential equations and then online evaluate the SAS over consecutive time windows regarding the operating condition and contingency until the simulation result over a desired period is obtained. This paper proposes a general semi-analytical approach that derives and evaluates an SAS in the form of a power series in time to approximate the true solution. This paper provides an error-rate upper bound of the SAS for reliable use of adaptive time windows in evaluation of the SAS. To extend the semi-analytical approach for solving general power system differential-algebraic equations, this paper also proposes a dynamic bus method to efficiently link the SAS for dynamic components with the numerical solution of the network algebraic equations. Case studies on the New England 39-bus system and the Polish 2383-bus system test the performance of the proposed approach, compare it with other methods, and show the potentials of the proposed semi-analytical approach for online simulation.