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Center for Nonlinear Studies |
The prevalence of renewables in modern transmission networks has researchers and system operators asking: What happens when the wind changes, and could fluctuations harm the grid? The instanton problem formalizes this question. Although small changes in wind are typically harmless, it is possible for certain patterns of fluctuations across several wind farms to violate one or more network constraints. Out of all such troublesome patterns, the most likely is termed the instanton. Prior work has shown that the instanton may be found by optimizing over a physically accurate AC model of the system. With no guarantee of convergence, this method is unlikely to see use in a real-time operating environment. The DC power flow approximation, on the other hand, yields a convex instanton problem that may be solved quickly and efficiently, albeit with questionable accuracy. The DC approximation makes several assumptions to linearize the system; of these, the most significant is that all voltages are equal to 1 per unit (a “flat†voltage profile). Current work is focused on moving away from this DC approximation by accounting for voltage deviations. This improves accuracy of instanton solutions while maintaining guaranteed convergence. The talk begins with background information on power flow and a derivation of the instanton problem. Next, previous work is discussed, covering both convex and non-convex solution methods. Finally, an approximate AC scheme which accounts for voltages is presented.
Host: Misha Chertkov