In future power systems, electrical storage will be the key technology for balancing feed-in fluctuations. With increasing share of renewables and reduction of system inertia, the focus of research expands toward short-term grid dynamics and collective phenomena. Against this backdrop, Kuramoto-like power grids have been established as a sound mathematical modeling framework bridging between the simplified models from nonlinear dynamics and the more detailed models used in electrical engineering. However, they have a blind spot concerning grid components, which cannot be modeled by oscillator equations, and hence do not allow one to investigate storage-related issues from scratch. Our aim here is twofold: First, we remove this shortcoming by adopting a standard practice in electrical engineering and bring together Kuramoto-like and algebraic load-flow equations. This is a substantial extension of the current Kuramoto-like framework with arbitrary grid components. Second, we use this concept and demonstrate the implementation of a storage unit in a wind power application with realistic feed-in conditions. We show how to implement basic control strategies from electrical engineering, give insights into their potential with respect to frequency quality improvement, and point out their limitations by maximum capacity and finite-time response. With that, we provide a solid starting point for the integration of flexible storage units into Kuramoto-like grid models enabling to address current problems like smart storage control, optimal siting, and rough cost estimations.
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Electrical engineering literature indicates “power output smoothing” as another major issue with respect to stochastic feed-in.25,27 This is related to frequency quality, as system frequency and power balance are coupled.
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The statistical measures , , and refer to a given time lag ; i.e., strictly speaking, we have , etc. We drop the upper index but specify in the following analysis.
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We define as stationary operation. This is in accordance with real power grids in the sense that, strictly speaking, these are constantly subjected to disturbances and hence never in a stationary state with and .
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2019
Author(s)
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