Equivalent simplification of torsional dynamics in the closely coupled identical turbine-generators

Usually a thermal power station consists of several identical turbine-generators coupled closely. An equivalent simplification approach is developed in the paper to simplify the torsional dynamics analysis of the power system with the identical multi-machine connected radial to a transmission network. The approach is based on the state-space representation of the systems and the principle that the eigenvalues of the similar matrices are the same. By constructing an ingenious similarity transformation, the state matrix of an identical N-machine system can be transformed to a block diagonal matrix with N blocks on the diagonal, in which N-1 blocks are the same. Each block corresponds to one single-machine system. Therefore, torsional dynamics of the identical N-machine system can be simplified into two types of single-machine systems while all the information on the system eigenvalues are preserved. The theoretical analysis and calculated results show the validity and the practicability of the equivalent simplification approach.