IJCAS

While the Lyapunov exponents used in previous studies require embedded dimensions and/or multiple initial conditions, our previously proposed instantaneous Lyapunov exponent (ILE) and Malthusian parameter estimator (MPE) directly estimate the rate of increase or decrease by time series data in real-time. The MPE uses adaptive control algorithms to estimate the rate of increase or decrease of the system. Our previously proposed MPE tends to have larger errors for fast-varying parameters and requires a PE condition, but the MPE in the case of a stable system does not satisfy the persistency of excitation (PE) condition. In this paper, we apply recently proposed parameter estimation algorithms effective for time-varying parameters to MPE. Moreover, the other MPE using the generalized parameter estimation-based observer (GPEBO) and the energy pumping-and-damping injection construction is proposed, that does not require the PE condition. The proposed methods allow us to monitor the transient stability in real-time. We compare the estimation performance of ILE and four MPE’s by using two power system examples.

Keywords: Instantaneous Lyapunov exponent, Malthusian parameter, phasor measurement unit, rotor angle dynamics, transient stability.