A Complex-LASSO Approach for Localizing Forced Oscillations in Power Systems

We study the problem of localizing multiple sources of forced oscillations (FOs) and estimating their characteristics, including frequency, phase, and amplitude, using noisy PMU data. We assume sparsity in the number of locations, and for each location, we model the input FO as a sum of a few unknown sinusoids. This allows us to obtain a sparse linear model in the frequency domain that relates measurements and the unknown input locations at frequencies of the unknown sinusoidal terms. We determine these frequencies by thresholding the empirical spectrum of the noisy data. Finally, we cast the location recovery problem as an $\ell_{1}$-regularized least squares problem in the complex domain-i.e., complex-LASSO (linear shrinkage and selection operator). We numerically solve this optimization problem using the complex-valued coordinate descent method and show its efficiency on the IEEE 68-bus, 16 machine and WECC 179-bus, 29-machine systems.