  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 differential-algebraic equations about
any given contingency under a specific operating condition. An alternative
approach promising for online simulation is to offline derive a semi-analytical
solution (SAS) and then online evaluate the SAS over consecutive time windows
regarding the operating condition and contingency until obtaining the
simulation result over a desired period. This paper proposes a general
semi-analytical approach that derives and evaluates an SAS in the form of power
series in time to approximate the solutions of power system differential
equations. An error-rate upper bound of the SAS is also proposed to guarantee
the reliable use of adaptive time windows for evaluation of the SAS. A dynamic
bus method is proposed to extend the semi-analytical approach for solving
general power system DAEs by efficiently linking the SASs for dynamic
components through the numerical solution of the network algebraic equations.
Case studies performed on the New England 39-bus system and the Polish 2383-bus
system test the performance of the proposed semi-analytical approach and
compare to existing methods. The results show that the SAS based approach has
potentials for online simulations.
