Variability of interconnected wind plants: correlation length and its dependence on variability time scale

Abstract

The variability in wind-generated electricity complicates the integration of this electricity into the electrical grid. This challenge steepens as the percentage of renewably-generated electricity on the grid grows, but variability can be reduced by exploiting geographic diversity: correlations between wind farms decrease as the separation between wind farms increases. But how far is far enough to reduce variability? Grid management requires balancing production on various timescales, and so consideration of correlations reflective of those timescales can guide the appropriate spatial scales of geographic diversity grid integration. To answer 'how far is far enough,' we investigate the universal behavior of geographic diversity by exploring wind-speed correlations using three extensive datasets spanning continents, durations and time resolution. First, one year of five-minute wind power generation data from 29 wind farms span 1270 km across Southeastern Australia (Australian Energy Market Operator). Second, 45 years of hourly 10 m wind-speeds from 117 stations span 5000 km across Canada (National Climate Data Archive of Environment Canada). Finally, four years of fiveminute wind-speeds from 14 meteorological towers span 350 km of the Northwestern US (Bonneville Power Administration). After removing diurnal cycles and seasonal trends from all datasets, we investigate dependence of correlation length on time scale by digitally high-pass filtering the data on 0.25-2000 h timescales and calculating correlations between sites for each high-pass filter cut-off. Correlations fall to zero with increasing station separation distance, but the characteristic correlation length varies with the high-pass filter applied: the higher the cut-off frequency, the smaller the station separation required to achieve de-correlation. Remarkable similarities between these three datasets reveal behavior that, if universal, could be particularly useful for grid management. For high-pass filter time constants shorter than about τ = 38 h, all datasets exhibit a correlation length ξ that falls at least as fast as τ −1 . Since the inter-site separation needed for statistical independence falls for shorter time scales, higher-rate fluctuations can be effectively smoothed by aggregating wind plants over areas smaller than otherwise estimated.

Cost-optimal design of a simplified highly renewable Chinese electricity network

“…Therefore the total capital investments for wind and solar power, shown in blue and yellow respectively, become smaller. At the same time, we also see a more than 50% decrease of backup energy, which can be credited to the smoothing effect caused by smaller correlations among high generation provinces, having a relatively large distance among them [29]. On the other hand, higher transmission costs emerge with larger β values.…”

Correlation and coherence of mesoscale wind speeds over the sea

“…St. Martin et al () show an overview of publications dealing with the correlation of wind speed and wind power measurements as a function of the measurement site distance. Most publications use an exponential function to describe the decay of the correlation coefficient with distance and agree with our results.…”

“…However, the correlation coefficient does not reach zero, probably because of the impact of the annual cycle. St. Martin et al (2015) show an overview of publications dealing with the correlation of wind speed and wind power measurements as a function of the measurement site distance.…”

Simulating effects of a wind‐turbine array using LES and RANS

“…However, some investigators have also used these models to estimate power output [e.g., Jim enez et al, 2015], and they can be particularly useful for large-scale problems such as grid balancing [Archer and Jacobson, 2007;St. Martin et al, 2015] and exploring interactions between wind farms [Kaffine and Worley, 2010;Nygaard, 2014].…”