A Markov-Switching Vector Autoregressive Stochastic Wind Generator for Multiple Spatial and Temporal Scales

Abstract

Despite recent efforts to record wind at finer spatial and temporal scales, stochastic realizations of wind are still important for many purposes and particularly for wind energy grid integration and reliability studies. Most instances of wind generation in the literature focus on simulating only wind speed, or power, or only the wind vector at a particular location and sampling frequency. In this work, we introduce a Markov-switching vector autoregressive (MSVAR) model, and we demonstrate its flexibility in simulating wind vectors for 10-min, hourly and daily time series and for individual, locally-averaged and regionally-averaged time series. In addition, we demonstrate how the model can be used to simulate wind vectors at multiple locations simultaneously for an hourly time step. The parameter estimation and simulation algorithm are presented along with a validation of the important statistical properties of each simulation scenario. We find the MSVAR to be very flexible in characterizing a wide range of properties in the wind vector, and we conclude with a discussion of extensions of this model and modeling choices that may be investigated for further improvements.

The role of regimes in short‐term wind speed forecasting at multiple wind farms

“…Geometrically, the underlying densities are ellipsoidal in shape and vary in size; however, their orientations are fixed parallel to the coordinate axes. Hering et al () use the GMM( Σ r ) method to identify regimes for a stochastic wind generation model, but the more parsimonious GMM( Λ r ) approach was shown to perform well in Kazor and Hering () for identifying wind regimes, so we use it here.…”

“…Movie maps the 20 tower locations labelled by acronym, with full names provided in Table . The general wind patterns of this area of the Pacific Northwest are well documented and have been exploited in many wind forecasting studies (Gneiting et al ; Hering and Genton, ; Yoder et al ; Zhu et al ; Zhu et al ; Hering et al ; Kazor and Hering, ). Substantial east–west pressure gradients develop across the Cascade Mountains and drive wind flows along the Columbia River Gorge (Sharp and Mass, ).…”

“…(These will stream automatically when the pdf is downloaded, or viewed within Internet Explorer 8, but not in some other browsers.) wind forecasting studies (Gneiting et al, 2006;Hering & Genton, 2010;Yoder et al, 2014;Zhu et al, 2014a;Zhu et al, 2014b;Hering et al, 2015;. Substantial east-west pressure gradients develop across the Cascade Mountains and drive wind flows along the Columbia River Gorge (Sharp & Mass, 2004).…”

A Non‐Gaussian Spatio‐Temporal Model for Daily Wind Speeds Based on a Multi‐Variate Skew‐t Distribution

“…Environmental data often exhibit departures from Gaussianity, such as skewness and heavy tails. Traditionally, to continue exploiting the appealing properties of the normal distribution and the well‐developed theory of Gaussian processes, a transformation is usually applied to the data; for example, a square root transformation (Gneiting, ), a power transformation (Ailliot et al ; Bessac et al ) or a Gaussian copula (Hering et al ). Only recently have there been studies that exploit the flexibility of skew‐elliptical distributions, of which the skew‐ t (Azzalini and Capitanio, ) and the skew‐normal (Azzalini, ) distributions are special cases that directly address the skewness and excess kurtosis that are commonly found in wind data.…”

A Spliced Gamma-Generalized Pareto Model for Short-Term Extreme Wind Speed Probabilistic Forecasting

“…The random effect f 2 (w(t)) represents the sub-daily variation of wind speeds, and is similar in spirit to the semiparametric splines of Hering et al (2015). It is assumed to be described by a cyclic Gaussian random walk of second order with precision τ s,2 > 0, defined over each of the 24 hours within a day (Rue and Held, 2005, Ch. 3).…”