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A reduced-order power-system dynamical model and applications in design and monitoring of power systems Chen, Bo


The widespread integration of distributed energy resources (DERs) in the future power system is likely to cause large and frequent excursions from its steady state. Such circumstances call for systematic methods to design DER controllers toward system-level goals and to estimate unexpected changes. We address these challenges via the development of a reduced-order power system dynamical model in this thesis. First, we develop a reduced second-order power-system dynamical model that accounts for locational effects of load disturbances on system frequency. The locational aspects are retained in the proposed model by incorporating linearized power-flow balance into differential equations that describe synchronous-generator dynamics. Individual synchronous-generator frequency dynamics are then combined into a single aggregate frequency state via weighting factors that can be tuned to maximize the accuracy of the reduced-order model. The proposed reduced-order model is general in the sense that its parameters are related to those of the original full-order model in analytical closed form, so that it can be constructed easily for different systems. Time-domain simulations demonstrate the accuracy of the reduced-order model with various choices of weighting factors and highlight the effect of load disturbance location on aggregate-frequency dynamics. The reduced-order model offers the basic foundation on which DER controllers can be systematically designed to meet grid-level aims. Via a transfer-function representation of the reduced-order model, we relate, in analytical closed form, DER controller parameters to system steady-state and dynamic frequency response. Furthermore, time-domain simulations demonstrate that we can design DER controller parameter in order to meet system frequency-response performance requirements. By leveraging the reduced-order power system dynamical model developed earlier, we propose an optimization-based method to detect the occurrence, estimate the magnitude, and identify the location of load changes. The proposed method relies on measurements of only frequency at the output of synchronous generators along with the reduced-order model that captures locational effects of load disturbances on generator frequency dynamics. The sparsity structure of load-change disturbances is leveraged so that fewer measurements are needed to estimate load changes. Furthermore, a convex relaxation of the problem ensures that it can be solved online in a computationally efficient manner.

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