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Center for Nonlinear Studies |
In this talk we describe ongoing work in two directions. First, we describe and motivate modifications to current grid mechanisms, in particular OPF but also secondary control, aimed at reducing stochastic behavior while maintaining near-optimaility. Recent work on stochastic control for e.g. OPF has handled stochasticity by relying on chance constraints, or on enario-based modeling. In these models "risk" is constrained by stipulating that the probability of some undisarable event is low, while for example minimizing the expected operational cost. However, even under this paradigm the system may display high stochasticity and for example cost may vary by a standard deviation or more with high probability -- in other words, variance of system behavior can be very high. We discuss numerical examples and methodologies for computing near-optimal solutions (under the existing constraints) that reduce variance metrics. In the second part of the talk, if time permits, we consider problems related to current "cyber-physical" research. Such work has produced procedures resting on DC-based state estimation, whereby phase angles (possibly computed using AC equations) are inserted into DC equations (using known loads) to recognize events where the topology of the grid has been altered. Instead, we consider the stricter regime where PMU data is used, together with the nonlinear AC equations. Here, the attacker modifies the grid topology (e.g. by disabling lines) and modifies loads. The PMU data reported by the attacker needs to satisfy the AC equations and also needs to reflect grid response to load changes (secondary response). We describe computational procedures that compute sparse attacks that are completely hidden, even though severe line overloads are actually reflected (but, again, completely hidden) in the actual data.
Host: Michael Chertkov