On the Numerical Stability and Accuracy of One-Step Delay Approximations

The One-Step Delay Approximation (OSDA) technique consists in delaying certain variables of a power system model with time delays of magnitude equal to the step size of the Time Domain Integration (TDI). The objective of the OSDA is to reduce the mutual coupling of the system's equations and the density of the Jacobian matrix that needs to be factorized at each step of the TDI. In turn, the OSDA leads to a simulation speedup but may worsen the accuracy of the results. This paper provides a novel matrix-pencil based approach to assess the OSDA technique in terms of its impact on the accuracy and numerical stability of the TDI of power systems. The case study illustrates the proposed approach through the WSCC 9-bus benchmark system.