Experimental data of total wind generation, recorded at 5 minute intervals and published by the Bonneville Power Administration for the years 2007 to 2013, were analyzed on a year by year basis. All data were normalized to total installed power of wind plants. Statistical distribution functions were obtained for the following wind generation-related quantities: total generation as percentage of total installed capacity; change in total generation power in 5,10,15,20,25, 30, 45, and 60 minutes as percentage of total installed capacity; duration of intervals with total generated power, expressed as percentage of total installed capacity, lower than certain pre-specified level. The statistical distributions obtained from the data were used to devise simple, yet accurate, theoretical models. The models presented here can be utilized in analyses related to power system economics/policy, because they describe availability of wind energy resource in simple statistical terms relevant to interactions of wind generation with electricity system, and electricity markets. After a brief display of the models, the article concentrates on static properties of the observed system's electricity generation related to its capacity credit, as well as on dynamic properties related to the demand for fast regulation (i.e., secondary and fast tertiary reserve). Both properties are important for technical planning of future electricity systems, as well as rational design of policy measures.
The main motivation for this paper was to investigate certain asymptotic properties of impulse response in periodic treetype distribution networks owed to the network topology alone, regardless of ohmic losses or material dispersion normally present in practical situations. The research was performed using theoretical analysis of Dirac impulse propagation through a model network, with a focus on topology-related features. Several numerical examples were designed to illustrate the meaning of the main conclusion, namely that the very topology of any tree-type network leads to an impulse response in which amplitudes of individual pulses decay rapidly with their respective delays after the leading impulse. On the other hand, it was not a goal of this research to design any practical tool for network-response calculation. The very fact that impulse response decays rather quickly after the train of the first few impulses does not mean that the calculation of these first few is by any means simple. The frequency-domain network-analysis methods in case of a complex distribution network with a tree-like topology seem to have practical advantages over the impulse-response calculation techniques, especially because the effects of ohmic losses and material dispersion would have to be included in any model constructed for realistic simulations, and in the authors' experience, this can be done more easily in frequency-domain-based models.
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