  Electromagnetic transient (EMT) simulation is a crucial tool for power system
dynamic analysis because of its detailed component modeling and high simulation
accuracy. However, it suffers from computational burdens for large power grids
since a tiny time step is typically required for accuracy. This paper proposes
an efficient and accurate semi-analytical approach for state-space EMT
simulations of power grids. It employs high-order semi-analytical solutions
derived using the differential transformation from the state-space EMT grid
model. The approach incorporates a proposed variable time step strategy based
on equation imbalance, leveraging structural information of the grid model, to
enlarge the time step and accelerate simulations, while high resolution is
maintained by reconstructing detailed fast EMT dynamics through an efficient
dense output mechanism. It also addresses limit-induced switches during large
time steps by using a binary search-enhanced quadratic interpolation algorithm.
Case studies are conducted on EMT models of the IEEE 39-bus system and a
synthetic 390-bus system to demonstrate the merits of the new simulation
approach against traditional methods.
