The Influence of Load Characteristics on Early Warning Signs in Power Systems

Abstract

Critical infrastructure systems like the power system are in danger of abrupt transitions into unstable and oftentimes catastrophic regimes. These critical transitions occur due to the modification of certain control parameters or an external forcing acting on the dynamical system. Bifurcation analysis can help to characterize the critical threshold beyond which systems become unstable. Moreover, some systems emit early warning signs prior to the critical transition, detectable from small-scale signal fluctuations triggered by the stochasticity of the external forcing. We present here our analysis of a time-domain dynamical power system model subjected to an increasing load level and small-scale stochastic load perturbations. We confirm previous findings from other literature that the autocorrelation of system signals increases, as the load level approaches a critical threshold characterized by a Hopf bifurcation point. Furthermore, we analyze the effects of load homogeneity and load connectivity on early warning signs. We assert that load connectivity does not influence autocorrelation coefficients. In addition, we show that changes in load homogeneity shift the location of the critical threshold.

Appendix

Since this analysis deals with discrete signals, an estimate of the autocorrelation for lag k of a signal with length N is obtained from [29]

$$\begin{aligned} \hat{R}\left[ k\right] = \frac{1}{N-k} \frac{\sum _{i=1}^{N-k}\left( x_i - \bar{x}\right) \left( x_{i+k} - \bar{x}\right) }{s^2} \end{aligned}$$

(8)

where $\bar{x}$ is the sample mean of the signal and $s^2$ is the unbiased sample variance.

Table 1. Maximum turbine output for 10-machine 39-bus New England test case. The following control variables are equal for all generators: Droop ($R = 0.04$ p.u.), Minimum turbine output ($p^{\mathrm {min}} = 0.0$ p.u.), Governor time constant ($T_S = 0.5$ s), Transient gain time constant ($T_3 = 3.0$ s)