Homogeneous generation period method for the analysis of wind generation variation Arturas Klementavicius a,⇑ , Virginijus Radziukynas a , Neringa Radziukyniene a , Gediminas Pukys b a Lithuanian Energy Institute, Breslaujos str. 3, LT-44403 Kaunas, Lithuania b Vilnius University, Universiteto str. 3, LT-01513 Vilnius, Lithuania article info Article history: Received 4 December 2013 Accepted 25 April 2014 Keywords: Wind generation variation Generation gradient Homogeneous generation period Power system operator Homogeneity Ramp abstract The paper presents a novel method for statistical quantification of wind power variation based on a new concept of homogeneous generation periods (HGPs). It starts with the state-of-the-art review of approaches addressing the quantification of wind power variation. The suggested method is based on identification of (a) wind generation gradients (positive, negative, insignificant and ineligible) for the time steps and (b) HGPs (increasing, decreasing, constant and null-generation). In result, the method provides a statistical evaluation on variation of wind generation process in observation period in terms of statistical characteristics of HGPs. The validation of method is performed on a numerical set-up representing Lithuanian wind power cluster in a windy 13-day period. The validation results point to the effectiveness of the suggested method for the ex-post quantification of wind generation variation in a short-term time span. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction The wind speed and related wind generation are random parameters and their temporal variation (also called variability, fluctuation, intermittency, volatility) are intrinsic features of the respective stochastic processes. The uncertainties in wind speed/ generation forecasts and fluctuations around the forecasted mean values complicate the balancing, control and even stability of power systems [1,2]. Here an aggravating circumstance is the real- ity of power systems since the late 1990s when they were pushed close to operational limits due to the increased loading [3]. On the other side, the wind power industry expresses its own variation-related concerns, and one of the biggest troubles is how to secure the over-the-schedule generation when wind provides it in real time, without generation curtailments for system balanc- ing or protection reasons [4,5]. Absorption of over-the-schedule generation by controllable loads, e.g. electrical vehicle charging systems, would be a good solution [6]. To mitigate the impacts of variation, both sides need adequate information support. The rationale for such a support is to use statistical wind speed/generation data to develop stochastic wind speed/generation forecasting and behaviour models [7,8]. None- theless, the quantitative assessment of wind generation variation seems to lack the characteristic metrics and indicators, particularly those specifying the uniformity (or intermittency) of generation over the time period. Here the capacity factor of a wind plant is often used [9–13] which points to the output variation from mean value to rated value, but does not reflect the frequency and size of output changes. The variation of wind generation output and wind speeds is conventionally defined by probability density distributions and their statistical characteristics. The probability density distribu- tions are derived from the time series data and their distributional parameters are identified, with Weibull and Rayleigh distributions found as best fitting [14]. The distributional parameters, i.e. those obtained from the distributions, are required to assess the suitabil- ity of the functions. Such distributional parameters are the parameters of the function itself (as parameters of the Weibull function), the wind energy output and the correlation coefficient of the probability density distributions. Additional parameters http://dx.doi.org/10.1016/j.enconman.2014.04.082 0196-8904/Ó 2014 Elsevier Ltd. All rights reserved. Abbreviations: HGP, homogeneous generation period; PSO, power system operator; p.u., per unit, i.e. quantities as fractions of a defined base unit quantity; G min , minimum eligible generation of wind power cluster; G nom , nominal capacity of wind power cluster; G WT , wind turbine nominal capacity; k fluc , fluctuation rate; M r , number of time steps in r-th HGP; N inc , number of increasing HGPs; N ob , number of time steps in observation period; N ob 1-min , number of 1-min time steps in observation period; P HG r , length of r-th HGP; S ob 30-min , set of 30-min gradients (30- min time steps); T ob , wind generation observation period; DG HGP r , generation ramp of r-th HGP; x, gradient significance threshold; f hom , wind generation homogeneity rate; r, standard deviation. ⇑ Corresponding author. Tel.: +370 37 401937; fax: +370 37 351271. E-mail address: arklemen@mail.lei.lt (A. Klementavicius). Energy Conversion and Management 86 (2014) 165–174 Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman