Single site analyses

Of the twelve locations selected for this study, the five wind sites exhibited the highest capacity factors in 2007–2013 (Fig. 2). The three West Texas wind sites each had higher capacity factors than the two South Texas wind sites. The capacity factors for the solar sites were lower and more similar across Texas. This in part results from the fact that potential wind power output varies with the cube of wind speed, while solar output varies linearly with solar irradiance.

Fig. 2 Solar and wind farm capacity factors overall, and during summer and winter peak hours, averaged over 2007–2013. Error bars show the range of annual values Full size image

Next, we computed the average PACP for each site from 2007 to 2013 to assess average outputs during peak load hours (Fig. 2). We compare our calculations of PACP with the factors used by ERCOT in its assessments of resource adequacy. There, ERCOT applies the following factors to wind and solar capacity when tallying their contributions to total resource adequacy: 14% non-coastal wind, 59% coastal wind, and 75% solar for summer resources (ERCOT 2018); and 20%, 42%, and 9.8%, respectively, in winter (ERCOT 2017a, b). ERCOT’s assessments assume that fossil and hydropower resources are fully available to supply peak demand in both seasons.

Tables 1 and 2 show each site’s specific PACP for the summer and winter, respectively. The solar sites had PACPs of 66% during summertime peak hours and 11% during wintertime peak hours. This is roughly in line with the fact that ERCOT applies factors of 75% in summer and 9.8% in winter in its resource adequacy assessments (ERCOT 2018). At individual sites, 2007–2013 average summertime PACP varied from 58.4 to 68.3%, while the interannual range was 12.0–23.5 percentage points. In winter, sites achieved 2007–2013 average PACP of 9.4–13.3% and interannual ranges of 11.2–26.8 percentage points.

Table 1 Peak average capacity percentages for each solar and wind site during each summer Full size table

Table 2 Peak average capacity percentages for each solar and wind site during each winter Full size table

For the three WT wind sites, we computed PACP to average 19% in summertime peak hours and 42% in wintertime peak hours. Note that these levels are substantially higher than the 14% and 20% factors applied by ERCOT in its resource adequacy assessments (ERCOT 2017a, b). PACP ranged from 14.7 to 25.2% across individual sites in the summer, and from 32.4 to 50.0% in winter. For the selected ST wind sites, we find PACPs to average 38% in summer and 48% in winter, compared to ERCOT’s 59% and 42% for summer and winter, respectively. This raises concerns about the seasonality assumed by ERCOT for ST wind sites.

We next examine the monthly and diurnal cycles of power production for each site. Interannual ranges and averages of capacity factors, averaged over each of the three resource types, are shown in Fig. 3. The monthly capacity factors of the highest production WT wind, ST wind, and solar sites for years 2007–2013 are plotted in Fig. 4 and show the general spread of possible production values and the interannual variability of resource availability at these representative locations. Notably, interannual variability of solar production is greatest in the summer, whereas ST wind is variable in summer and winter and WT wind is most variable in spring and autumn.

Fig. 3 Average monthly capacity factors for each resource type over the years 2007–2013. Circles display interannual minima and maxima Full size image

Fig. 4 Monthly capacity factors for representative sites for Buffalo Gap (WT wind, top), Peñascal (ST wind, middle), and Alamo 5 (solar, bottom) Full size image

To assess resource complementarity over the course of a day, aggregate half-hourly production values for each resource were compared for two model days: June 21 (summer solstice) and December 21 (winter solstice) (Fig. 5). The average capacity factor each half-hour over years 2007–2013 is shown in Fig. 5. On June 21, WT wind and solar resources exhibited complementary production patterns over the course of the day, with solar production peaking in the daytime hours and WT wind production peaking at night. ST wind production peaked in the late evening, between the solar and WT wind peak production times, and remained lower than WT wind production for the duration of the day. On December 21, ST wind and solar production values were lower than their summertime levels, while WT wind showed a flatter diurnal profile during winter than in summer.

Fig. 5 Half-hour average capacity factor for each site, 2007–2013, on June 21 (top) and December 21 (bottom) Full size image

The three categories of sites exhibit starkly different diurnal patterns in output. At the WT wind sites, output peaks late at night, around 23:30 CST. By contrast, output from the solar sites peaks just after noon, when the WT wind sites are near their daily lows. Meanwhile, output from ST wind sites peaks in late afternoon, around 16:00 CST, and is lowest early in the morning.

Paired site analyses

While the contrasting temporal patterns described above for individual sites are suggestive of complementarity, paired site analyses allow for complementarity to be probed more directly. One indicator of complementarity of two sites is whether their output is inversely correlated over time, allowing one site to produce more power when the other is unavailable. Table 3 shows the Pearson correlation coefficient for each pair of sites. As expected, pairs of solar sites were strongly correlated, with correlation coefficients ranging from 0.81 to 0.92. Pairs of wind sites were less strongly correlated. In particular, pairing a WT and a ST wind site led to correlation coefficients of just 0.11–0.37 (Table 3). Pairs of WT wind sites had correlation coefficients of 0.44–0.53, and the two ST wind sites had a correlation of 0.75 (Table 3). The lower correlation coefficients across regions illustrate the value of siting wind farms in different parts of the state.

Table 3 Pearson correlation coefficients for each pair of wind and solar resources Full size table

Even better complementarity can be achieved by pairing wind with solar, as each of these pairings had negative correlation coefficients. The average correlation between solar sites and wind sites was − 0.287, suggesting a weak inverse relationship between solar production and wind production. In particular, solar was more inversely correlated with the WT wind sites (− 0.31 to − 0.37) than with the most coastal of the ST wind sites, Peñascal (− 0.12 to − 0.15). Cedro Hill 2 had an intermediate level of inverse correlation with solar.

As explained by Archer and Jacobson (2007), firm capacity provides an additional metric of complementarity by illustrating the minimum amount of power that can be guaranteed for a given percentile of hours per year. We assessed the firm capacity of each pair of sites and illustrate it in Fig. 6 for the pair of sites (Roserock solar and Buffalo Gap wind) that had the greatest firm capacity in 2012 at the 87.5 percentile level considered by Archer and Jacobson (2007). The power duration curves in Fig. 6 are plotted for each site individually and taken together as a pair (in each case with total capacity assumed to be 60 MW), and the vertical line represents the 87.5% threshold. The combination of Roserock solar and Buffalo Gap wind power would output at least 13.2% of its capacity for 87.5% of the hours of the year. By contrast, solar alone has zero firm capacity at this threshold, since it is dark half the time. The Buffalo Gap wind site alone has a firm capacity factor of just 4% at the 87.5% threshold.

Fig. 6 Duration curves of Roserock solar and Buffalo Gap wind sites’ separate and combined hourly power production and firm capacity (out of 60 MW total capacity) at an 87.5% availability threshold Full size image

The highest and lowest ten firm capacities determined for single and paired sites are shown in Table 4. We exclude the solar–solar pairs, which inherently provide zero firm capacity. The highest firm capacities were exhibited by solar and WT wind pairs (specifically with pairs that included the Buffalo Gap wind site) and by WT and ST wind site pairs. Conversely, solar and ST wind pairings and single wind sites produced lower firm capacities, since these sites have both lower capacity factors overall and less negative inverse correlations.

Table 4 Pairs of sites with the ten highest and ten lowest firm capacities, defined here as the amount of capacity (out of 60 MW) available at least 87.5% of the time Full size table

Solar configuration options

All of the analyses above assume single-axis tracking, the most widely used option for utility-scale solar farms. However, it is possible that a mix of alignments could prove complementary or that west-facing arrays could provide power during summer afternoon peak loads. To test how changes in solar array configuration might effect production and complementarity, five solar configurations were considered: fixed-tilt systems with tilt equivalent to latitude pointed south (S), southwest (SW), and west (W); single-axis tracking from west to east; and dual-axis tracking. The highest production solar site, Roserock, was used as the model site in all of the following analyses, and the highest production wind site (Buffalo Gap) was used to measure changes in complementarity between WT wind and solar as the solar array configurations changed.

Production achieved by the different array configurations was measured using capacity factor and PACP (Fig. 7). As expected, capacity factor was largest for the tracking configurations and lowest for the fixed-tilt systems. Additionally, both summer and winter PACPs were higher for dual-axis tracking and single-axis tracking systems, respectively. For fixed-tilt systems, summer PACP rose and winter PACP fell as the system moved from south-facing to west-facing. Overall, the west-facing fixed-tilt system has the lowest total capacity factor of 18%, compared to 32% for the dual-axis tracking system; however, in the summer during peak load hours, the west-facing fixed-tilt system had a PACP of 72%, nearly as high as the 74% for dual-axis tracking. Single-axis tracking costs about $0.15/W AC more than fixed systems (Bolinger et al. 2017), and dual-axis tracking systems are rarely deployed. Thus, the ability of west-facing fixed-tilt systems to achieve such high summertime PACP can be relevant in certain circumstances.

Fig. 7 Capacity factors of various configurations of solar arrays at Roserock for 2012 overall, and during peak load hours of summer and winter Full size image

Next, to measure potential complementarity between solar configurations, correlation coefficients were calculated between half-hourly production for the five array types as well as the Buffalo Gap WT wind location (Table 5). Single-axis tracking followed by the west-facing fixed-tilt array yielded the most strongly negative correlation coefficients with Buffalo Gap, but the differences across the solar configurations were small. The greatest complementarity between two solar array types at the Roserock location was achieved by the west-facing fixed-tilt system combined with the dual-axis tracking system. Pairing a west-facing and south-facing fixed-tilt system also yielded a relatively low correlation coefficient and hence better complementarity than other pairings.

Table 5 Pearson correlation coefficients of half-hourly production between the Buffalo Gap wind site (right column) and five potential configurations of a Roserock solar plant Full size table

Effects of array type on reliable combined production with a WT wind farm were measured with firm capacity (Fig. 8). WT wind alone had the least firm capacity, followed by similar capacity factors for all fixed-tilt systems combined with wind, leaving both single- and dual-axis tracking with similar firm capacities combined with WT wind. The firm capacity percentages followed a similar trend to the farms’ individual capacity factors, suggesting that the differences among solar configurations in complementarity with wind are negligible.