Statistical Properties of Electricity Generation from a Large System of Wind Plants and Demand for Fast Regulation

Abstract

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.

On minimization of the group variability of intermittent renewable generators

“…It is a well-known problem. For example, after studying the seven-year stream of 5-minute readings of the energy output from an extensive system of wind plants in the north-western USA, the authors of [16] found out that the demand for fast regulation can be expressed as:…”

“…Fig. 10, taken from [16], gives the results of the experimentally derived MReg for the above-mentioned American wind plant system in the whole of the year 2013, together with the curve (2) fitted to the data using the least squares. For example, according to Fig.…”

“…For example, according to Fig. 10, if the operator of the system studied in [16] were willing to accept no more than 2% probability of getting short in the temporarily available flexible regulation reserve, the total flexible capacity held in reserve for the regulation purposes would not have to be less than about one-twentieth of the total installed power of the wind plants. To sum up, when contemplating minimization of the short-term variability, it is better to use some parameter that reflects the short-term changes in the total output of a system of wind plants rather than simple variance or standard deviation.…”

Minimisation of Generation Variability of a Group of Wind Plants

“…The next question to address, as it comes to application of portfolio optimisation theory to wind plants, pertains to the fact that distributions of energy produced by a system of wind plants are notoriously non-Gaussian (Sabolić [18]). Markowitz's theory, on the other hand, relies on an assumption of normal distribution of data.…”

“…The second major objection on Markowitz's theory pertains to assumption of Gaussian distribution of observed data population. There is a lot of evidence that wind production is not at all Gaussian (see for example Sabolić [18]). In Monahan et al [19] probability density function of land surface wind speeds is characterized using a global network of observations, to conclude that it is essentially a Weibull distribution, which is skewed (non-symmetric about expected value).…”