Optimal Control of Cascading Power Grid Failures with Imperfect Flow Observations

Introduction In a cascading failure of a power transmission system, an initial event that disables a possibly small subset of the grid conspires with the laws of physics to set off a sequence of additional outages that, in the worst case, accelerates until a large subset of the network is inoperative, resulting in a significant loss of served power. The mechanics of the process can be summarized as follows: each time a component of the system fails, a new set of power flows takes hold in the remaining network, following the laws of physics and automatic control actions. Should the new flows, for example, exceed the rating of a given line, then that line will likely fail in the near future. In an adverse scenario this gives rise to a vicious cycle which constitutes the cascade (see e.g., [4, 7]). To protect against a cascade, [6] discusses the design of a robust power transmission system. Control strategies for stopping an ongoing cascade are discussed in [7, 8, 11]. The work in this abstract builds on the model in [5] by incorporating stochastics; in particular, we model real-time measurement errors. We consider algorithms that shed load (demand) and curtail supply (generation) as a function of observations taken in real time, with the goal of arresting the cascade with a minimum of demand lost. As a novel contribution, we explicitly model “noise” that would naturally arise in the collection of real-time data. That task relies on a system termed SCADA (“Supervisory control and data acquisition”) which is physically different from the power transmission system. Under normal operation some of this data is estimated using one of several possible state estimators (see e.g., [9, 12]); in the event of a dangerous cascade, it is quite likely that the measurements conveyed by this system would become susceptible to errors, delays, or loss due to rapidly changing conditions, transients, and possibly even failure of the measurement equipment. Building on work in [5] we focus on control algorithms that are computed soon after the onset of the cascade, and we assume an initially slow-moving cascade so that at the start of the process there is sufficient time (e.g., minutes) to compute an appropriate control algorithm; once computed, the control will be applied as the cascade unfolds. In devising a load-shedding schedule to respond to a potential cascade, one must decide when, where, and by how much demand is to be shed. Our method can be viewed as a data-driven approach for computing such actions – it is data-driven because it relies on the knowledge of the initial event, and on the real-time measurements performed to apply the control. Moreover our algorithm seeks to handle measurement error – we explicitly assume that measurements can be incorrect, and yet we look for a control that minimizes lost demand subject to (effectively) a norm constraint on the errors. To this effect, in this abstract we rely on a method akin to the Sample Average Approximation Method [10] to generate, a priori, an appropriate sample of measurement error sequences, and to optimize a control over that set of sequences.