Identifying useful statistical indicators of proximity to instability in stochastic power systems

Abstract

Abstract-Prior research has shown that autocorrelation and variance in voltage measurements tend to increase as power systems approach instability. This paper seeks to identify the conditions under which these statistical indicators provide reliable early warning of instability in power systems. First, the paper derives and validates a semi-analytical method for quickly calculating the expected variance and autocorrelation of all voltages and currents in an arbitrary power system model. Building on this approach, the paper describes the conditions under which filtering can be used to detect these signs in the presence of measurement noise. Finally, several experiments show which types of measurements are good indicators of proximity to instability for particular types of state changes. For example, increased variance in voltages can reliably indicate the location of increased stress, while growth of autocorrelation in certain line currents is a reliable indicator of system-wide instability.

Online Learning of Power Transmission Dynamics

“…We see that for both algorithms we don't see any clear plateau in ε(∆t) dependence even for small ∆t. This is due to the increasing with ∆t error in the first-order approximation (7) of the fine-grained dynamics and hence to the level of validity of (12). Nevertheless, we see that for both estimators ε is growing slowly with ∆t, and the error seen for ∆t = 3 cycles is very close to the one realized when the finest possible discretization ∆t = 1 is taken, although the algorithms use three times less samples in the former case.…”

“…An accurate estimation of the dynamic state matrix has a large number of applications that have been well explored in the literature [10], [11], including model validation and parameter calibration [3], [4], probing the proximity to instability and helping in design of the corresponding emergency control actions [12], [13], optimization and resource allocation [14], [15], as well as identification and analysis of forced oscillations in the system [16]. The potential ability to use the learned dynamic parameters to simultaneously perform a purely measurement-based state estimation of deviations in power consumption from nominal values represents another attractive feature of our framework.…”

Investigating the Impacts of Stochastic Load Fluctuation on Dynamic Voltage Stability Margin using Bifurcation Theory

“…The maximum value λP 0 before the SNB occurs corresponds to the voltage stability margin. As a result, the stochastic power system model (5) can be represented by:u = G(u, p(εt)) + σBξ (14) We aim to study the impact of the intensity of the stochastic perturbation σ and the load power increasing speed ε on SNB of the model (14) and thus on the voltage stability margin of power systems.…”

Spatiotemporal Big Data Analysis for Smart Grids Based on Random Matrix Theory

“…t ∈ R, m and p are the sample time, number of system variables and bus, respectively. The model-based stability estimators [51,52] focus on linearization of nonlinear DAEs in (1) and (2) which gives…”