Delay-based numerical stability of the partitioned-solution approach

This paper proposes a technique to evaluate the numerical stability and accuracy of the Partitioned-Solution Method (PSA) for the time domain integration of the Differential Algebraic Equations (DAEs) that are used for power system angle and voltage stability analyses. The partitioned approach consists in solving differential equations and algebraic constraints separately. While efficient, this technique introduces a “mismatch” between state and algebraic variables. The paper states the formal analogy of such a mismatch with a time delay of algebraic variables. Then a Small-signal Stability Analysis (SSSA) for Delay Differential Algebraic Equation (DDAE) is applied to define the numerical stability of the PSA as a function of the integration time step. Results are tested using the IEEE 14-bus system as well as a 1,479-bus model of the all-island Irish system.