Transient Performance of Electric Power Networks under Colored Noise
| Autor: | Tommaso Coletta, Ph. Jacquod, Bassam Bamieh |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
0209 industrial biotechnology
Dynamical systems theory 02 engineering and technology White noise Impulse (physics) 01 natural sciences 010305 fluids & plasmas 020901 industrial engineering & automation Quadratic equation Colors of noise Optimization and Control (math.OC) 0103 physical sciences Time derivative FOS: Mathematics Transient response Statistical physics Laplace operator Mathematics - Optimization and Control Mathematics |
| Zdroj: | CDC |
| DOI: | 10.48550/arxiv.1807.09048 |
| Popis: | New classes of performance measures have been recently introduced to quantify the transient response to external disturbances of coupled dynamical systems on complex networks. These performance measures are time-integrated quadratic forms in the system's coordinates or their time derivative. So far, investigations of these performance measures have been restricted to Dirac-$\delta$ impulse disturbances, in which case they can be alternatively interpreted as giving the long time output variances for stochastic white noise power demand/generation fluctuations. Strictly speaking, the approach is therefore restricted to power fluctuating on time scales shorter than the shortest time scales in the swing equations. To account for power productions from new renewable energy sources, we extend these earlier works to the relevant case of colored noise power fluctuations, with a finite correlation time $\tau > 0$. We calculate a closed-form expression for generic quadratic performance measures. Applied to specific cases, this leads to a spectral representation of performance measures as a sum over the non-zero modes of the network Laplacian. Our results emphasize the competition between inertia, damping and the Laplacian modes, whose balance is determined to a large extent by the noise correlation time scale $\tau$. Comment: Six pages. Final version, published in the proceedings of the 57th IEEE Conference on Decision and Control, CDC 2018 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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