Inference, estimation, and prediction for stable operation of modern electric power systems

Abstract

To keep pace with social-ecological disruptions and technological progressions, electrical power systems must continually adapt. In order to address the stability-related challenges associated with these adaptations, this thesis develops a set of analytically rigorous yet practically oriented methods for ensuring the continued stability of modern power systems. By leveraging inference, estimation, and predictive modeling techniques, the proposed methods capitalize on the unprecedented amount of real time data emerging from modernizing smart grids. For each method, we provide simulated test results from IEEE benchmark systems. Newly deployed Phasor Measurement Units (PMUs) are observing the presence of detrimental low frequency forced oscillations (FOs) in transmission grid networks. To begin this thesis, we address the problem of locating the unknown sources of these FOs.

To perform source identification, we develop an equivalent circuit transformation which leverages suitably constructed transfer functions of grid elements. Since FO sources appear in this equivalent circuit as independent current injections, a Bayesian framework is applied to locate the most probable source of these injections. Subsequently, we use our equivalent circuit to perform a systematic investigation of energy-based source identification methods. We further leverage this equivalent circuit transformation by developing "plug-and-play" stability standards for microgrid networks that contain uncertain loading configurations. As converter-based technology declines in cost, microgrids are becoming an increasingly feasible option for expanding grid access. Via homotopic parameterization of the instability drivers in these tightly regulated systems, we identify a family of rotational functions which ensure that no eigenmodes can be driven unstable.

Any component which satisfies the resulting standards can be safely added to the network, thus allowing for plug-and-play operability. High-fidelity linearized models are needed to perform both FO source identification and microgrid stability certification. Furthermore, as loss of inertia and real-time observability of grid assets accelerate in tandem, real-time linearized modeling is becoming an increasingly useful tool for grid operators. Accordingly, we develop tools for performing real-time predictive modeling of low frequency power system dynamics in the presence of ambient perturbations. Using PMU data, we develop a black-box modeling procedure, known as Real-Time Vector Fitting (RTVF), that takes explicit account for initial state decay and concurrently active input signals. We then outline a proposed extension, known as stochastic-RTVF, that accounts for the corrupting effects of unobservable stochastic inputs.

The surrogate modeling utilized by vector fitting can also be applied to the steady state power flow problem. Due to an unprecedented deployment of distributed energy resources, operational uncertainty in electrical distribution networks is increasing dramatically. To address this challenge, we develop methodology for speeding up probabilistic power flow and state estimation routines in distribution networks. We do so by exploiting the inherently low-rank nature of the voltage profile in these systems. The associated algorithms dynamically generate a low-dimensional subspace which is used to construct a projection-based reduced order model (ROM) of the full nonlinear system. Future system solves using this ROM are highly efficient.