Determining Disturbance Recovery Conditions by Inverse Sensitivity Minimization

TL;DR

This work defines a recovery boundary in parameter space that separates disturbance scenarios leading to safe recovery from those causing non-recovery, and introduces a safety margin as the distance from a nominal parameter set to this boundary. It builds a theoretical framework using trajectory sensitivities to connect the boundary in parameter space with the RoA boundary in state space, and then develops three algorithms for computing the boundary: pointwise in 1D, continuation-based in 2D, and a least-distance search in higher dimensions, all without requiring prior knowledge of the controlling unstable equilibrium point. The key construct is G(p)=inf_t H(p,t) with H(p,t)=1/||chi(p,t)||_1, so the boundary is G(p)=0, and its gradient DG(p) guides the boundary-search procedures; the approach handles high-dimensional, nonsmooth models by leveraging time-domain simulations and sensitivity information. The methods are demonstrated on the IEEE 39-bus system with up to 86 parameters, revealing nontrivial interactions between load dynamics and controllers and yielding quantified safety margins that are smaller when more parameters are considered, underscoring the value of high-dimensional vulnerability assessment for power systems.

Abstract

Power systems naturally experience disturbances, some of which can damage equipment and disrupt consumers. It is important to quickly assess the likely consequences of credible disturbances and take preventive action, if necessary. However, assessing the impact of potential disturbances is challenging because many of the influential factors, such as loading patterns, controller settings and load dynamics, are not precisely known. To address this issue, the paper introduces the concept of parameter-space recovery regions. For each disturbance, the corresponding recovery region is the region of parameter space for which the system will recover to the desired operating point. The boundary of the recovery region establishes the separation between parameter values that result in trouble-free recovery and those that incur undesirable non-recovery. The safety margin for a given set of parameter values is defined as the smallest distance (in parameter space) between the given values and the recovery boundary. Novel numerical algorithms with theoretical guarantees are presented for efficiently computing recovery boundaries and safety margins. Unlike prior methods, which tend to be overly conservative and restricted to low dimensional parameter space, these methods compute safety margins to arbitrary user-specified accuracy and do so efficiently in high dimensional parameter space. The efficacy of the methods is demonstrated using the IEEE 39-bus benchmark power system, where safety margins are computed for cases that consider up to 86 parameters, and reveal unexpected safety implications that would not have been observed otherwise.

Figures (8)

• Figure 1: Sensitivity of the post-fault frequency to generator mechanical power, as the generator power approaches the recovery boundary.
• Figure 2: The predictor-corrector continuation process for iteratively tracing a sequence of points along a curve.
• Figure 3: IEEE 39-bus benchmark power system.
• Figure 4: $G$ as a function of load scaling factor (blue line). The iterations of the one-dimensional parameter space algorithm are identified by circles and the iterations are labeled.
• Figure 5: The angle of generator 5 relative to generator 2 for the load scaling factor attained at each iteration of the one-dimensional algorithm. These values are shown in Fig. \ref{['fig:single']}.