What day-ahead reserves are needed in electric grids with high levels of wind power?

Day-ahead load and wind power forecasts provide useful information for operational decision making, but they are imperfect and forecast errors must be offset with operational reserves and balancing of (real time) energy. Procurement of these reserves is of great operational and financial importance in integrating large-scale wind power. We present a probabilistic method to determine net load forecast uncertainty for day-ahead wind and load forecasts. Our analysis uses data from two different electric grids in the US with similar levels of installed wind capacity but with large differences in wind and load forecast accuracy, due to geographic characteristics. We demonstrate that the day-ahead capacity requirements can be computed based on forecasts of wind and load. For 95% day-ahead reliability, this required capacity ranges from 2100 to 5700 MW for ERCOT, and 1900 to 4500 MW for MISO (with 10 GW of installed wind capacity), depending on the wind and load forecast values. We also show that for each MW of additional wind power capacity for ERCOT, 0.16–0.30 MW of dispatchable capacity will be used to compensate for wind uncertainty based on day-ahead forecasts. For MISO (with its more accurate forecasts), the requirement is 0.07–0.13 MW of dispatchable capacity for each MW of additional wind capacity.


Introduction
Wind power has experienced substantial growth over the past decade in the US and in Europe. Installed capacity in the US increased more than tenfold from 4.2 GW in 2001 to 60 GW in 2012(AWEA 2013. Electricity generated Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. from wind in the US accounted for under 0.2% of total electricity production in 2001, and now provides over 3% of total electrical energy (EIA 2013). European installed wind capacity increased fivefold in the same time period, from 17.3 to 94 GW, and produces over 6% of the total electrical energy produced (Wilkes et al 2012).
Current levels of wind capacity do not pose a large problem for grid operators in most regions, but future growth will require operational changes in order to ensure a reliable grid (Xie et al 2011). Since wind power is not dispatchable, wind forecasts are used along with load forecasts to make operational decisions ranging from minutes to days in advance (Botterud et al 2010). Because forecasts are not perfect, excess dispatchable generation capacity must be procured to ensure reliability in the operation of the grid. The Electric Reliability Council of Texas (ERCOT) includes net load (load minus wind) forecast uncertainty in its operational reserve procurement decisions. ERCOT procures operational reserve capacity equaling 95% of net load forecast errors 3 (ERCOT 2010). The remaining uncertainty is covered with balancing energy procured in the spot market. The Midcontinent Independent System Operator (MISO), on the other hand, does not rely on operating reserves to correct forecast errors. Instead, it strives to ensure that adequate supply is available in the spot markets to handle forecast uncertainty. However, on a percentage of energy basis, MISO has less wind power than ERCOT (see table 1) and stronger transmission ties to neighboring grids. The cost of balancing wind forecast uncertainty has been estimated in several studies. A review of the literature suggests the range of estimates is from $2.5 (Elektrotek 2003) to $7 (Enernex 2007) per MWh of wind energy generated. Two important points should be made here. First, these estimates include the cost of balancing wind variability over time scales of seconds to minutes along with the costs of balancing longer time scale wind forecast errors. Second, wind forecast uncertainty is balanced with non-spinning reserves which are relatively slower and less costly than other forms of operating reserves such as regulation and spinning reserves. The analysis presented here does not consider economics of wind forecast error balancing.
The growth of wind power creates a need to update unit commitment and operating reserves procurement algorithms. Wang et al (2008) proposed a model to incorporate the uncertainty of wind forecasts in unit commitments. Doherty and O'Malley (2005) presented a reserves procurement model that combines wind forecast uncertainty with load forecast uncertainty and generator forced outage probabilities.
Ortega-Vazquez and Kirschen (2009) and Matos and Bessa (2009) each presented decision analytic frameworks to determine operating reserves in systems with wind power by balancing the cost of reserves and the cost of load curtailments. Bouffard and Galiana (2008) presented an economic dispatch algorithm that accounts for wind forecast uncertainty.
In the work cited above, wind and load forecast errors are generally modeled as normally distributed random variables. The one exception is Matos and Bessa, who used a non-parametric model for wind forecast errors. As shown by Hodge et al (2012), wind forecast errors at the regional level are generally not Gaussian. Lange (2005) and Bludszuweit et al (2008) demonstrated that wind forecast errors have distributions that can be highly skewed when the forecast is for a very low or high value of wind power. Wind forecasts near the middle of the forecast range have more symmetric error distributions (although not necessarily Gaussian). This is important in power system modeling as the representation of wind forecast uncertainty appears to have a significant effect on unit commitment results (Lowery and O'Malley 2012).
Here we focus on net load forecast uncertainty as a function of the forecast quantity of wind generator output. At wind levels where net load uncertainty is dominated by wind forecast uncertainty, operational decisions should be based on a systematic assessment of net load uncertainty reflecting changes in wind forecast levels. Using data from ERCOT and MISO, we show that neither wind nor load forecast errors are normally distributed random variables, and describe the influence of load and wind forecast levels on net load uncertainty. Finally, we estimate dispatchable generation requirements in grids with much higher wind power.

Wind and load data
We use data on wind and load forecasts along with actual values of wind and load from ERCOT and MISO. The ERCOT data consist of hourly wind forecast values for 1-48 h look-ahead times covering 2009 and 2010. AWS Truepower provided actual wind generation values along with estimated uncurtailed wind generation potential. In MISO wind forecast data were obtained from their website, which provides day-ahead wind forecasts and actual wind generation. Our data span February 2011-May 2012. Day-ahead load forecasts and observed loads were also obtained from the Ventyx database. Wind curtailments in MISO were estimated to range from 2% to 6% each month (MISO 2012). Since the curtailments are small and we do not have hourly data on curtailment quantities, we neglect these curtailments in our analysis.
Aggregate wind power in MISO has a significantly lower forecast error than does ERCOT (table 1). During the time covered by our dataset, ERCOT and MISO had similar levels of installed wind capacity (∼10 GW). However, the wind farms in MISO's territory span a much larger area than for ERCOT (figure 1). Large wind power footprints reduce the correlation of wind generation between wind farms, and lower variability in aggregate wind generation (Katzenstein et al 2010, Fertig et al 2012. The accuracy of wind forecasts improves as the variability decreases (Focken et al 2002).

Day-ahead load forecast uncertainty
The data in table 1 show that load forecasts tend to be more accurate than wind power forecasts. Operators compute load forecasts at many time intervals for daily operations. Here we are concerned with the forecasts made one day in advance, which are used to make decisions in unit commitment and operating reserve levels. Figure 2 shows actual hourly load versus forecasted load for ERCOT for one week in January. The bottom line in figure 2 illustrates the forecast error. We define the absolute forecast error as the forecast value minus the actual value.
The distribution of load forecast errors in both ERCOT and MISO is dependent on the load forecasts. Figure 3 shows the hourly load forecast errors plotted against the load forecasts. All data are normalized by the mean load in the respective grid. In our analysis we divided the load forecast data into three forecast bins as shown in figure 3: low load (forecasts less than 90% of mean load), medium load (between 90% and 120% of mean load) and high load (forecasts greater than 120% of mean load). We choose these bins to capture the range of variance of the forecast errors.
We used the @Risk software package to fit parametric distributions to load forecast errors for ERCOT and MISO. Even though no distributions passed a Pearson's chi-squared test, the logistic distribution provided the best fit among the distributions tested, in both sets of load forecast errors, as measured by likelihood values (figure 4). In agreement with Hodge et al (2012), we found that the actual load forecast error distribution has more mass around zero than a normal probability density function (PDF) would predict. Figure 4 shows histograms of the load forecast errors normalized by mean load forecast with fitted logistic distributions for ERCOT and MISO. A separate logistic distribution was fit to each load forecast bin.

Day-ahead wind forecast uncertainty
In comparison to day-ahead load forecasts, day-ahead wind forecasts have much greater relative uncertainty. Wind forecast error distributions also differ from load forecast error distributions in that they become highly skewed for low and high wind forecasts. The plots in figure 5 show hourly  . Load forecast errors for ERCOT (top) and MISO (bottom) with data separated into three different load forecast classes. All values are normalized by the mean load forecast. Low forecasts include all forecasts less than 90% of the mean forecast; medium forecasts are between 90 and 120% of the mean forecast; and high forecasts are greater than 120% of the mean forecast. Histogram bars show the relative frequency of the actual data while solid lines show the fitted logistic distributions.  wind forecast errors plotted against wind forecast values for ERCOT and MISO. All values are shown as a fraction of installed wind capacity. At low wind power forecasts, the errors tend to be more negative while high wind power forecasts produce more positive forecasts.
In order to account for the dependence of wind forecast error distributions on the wind forecast level, we used the logit-normal model to represent wind forecast errors as described in Mauch et al (2013) and briefly in the online supplementary data (available at stacks.iop.org/ERL/ 8/034013/mmedia). This model is illustrated in figure 6 for ERCOT and MISO wind forecast data. Error distributions are negatively skewed at the low forecasts and positively skewed at the high forecasts. The fit at low and medium forecasts is much better due to the lack of samples at the high end of the forecast range.

Day-ahead net load uncertainty
Net load is defined as load (L) minus wind (W) power (1) The actual (subscript A) levels of load and wind subtracted from the forecasted values (subscript F) give the net load forecast errors (2) Rearranging terms gives Load forecast errors and wind forecast errors are commonly assumed to be independent variables (Matos andBessa 2009, Ortega-Vazquez andKirschen 2009). The correlation coefficients of wind and load forecast errors in our data were 0.09 for ERCOT and 0.05 for MISO (both significant at the 95% level). We assume uncorrelated wind and load forecast errors here. However, the empirical data show that the correlation coefficient of wind and load forecast errors varied over a wide range and we discuss the implications of correlation between wind and load forecast errors in the online supplementary data. With uncorrelated variables, the PDF of the net load errors is derived by taking the cross-correlation of the load errors and the negative of the wind errors. The integral was evaluated by numerical integration using the Simpson quadrature.
The cumulative distribution function (CDF) is then the integral of the PDF, which allows one to determine confidence intervals for a desired reliability level.
(6) Figure 7 shows CDFs for the load and net load errors calculated using data from ERCOT for a medium load forecast (90%-120% of the mean load) and wind forecast level of 5000 MW with 10 000 MW of installed wind capacity. Ninety-five per cent of the net load errors range from −4650 to 3850 MW. In order to cover this level of uncertainty, a grid must have 4650 MW of excess dispatchable generation capacity available to cover under forecasts and 3850 MW of down generation capacity to cover over forecasts. Our analysis focuses on under forecast errors, which require additional generation capacity to be brought online quickly. Considering only the errors that result from an under forecast of net load, we compute the probability of the forecast error being less than some given value conditioned on the event that the forecast error is negative.
Using (7), we calculate the value for z that gives a probability of 0.05 to get the generation capacity required to cover 95% of potential under forecast errors.

Results
During the interval our data were collected, ERCOT's installed wind capacity increased from 8.3 to 9.5 GW, and MISO's wind capacity increased from 9.1 to 10.8 GW. We scaled the wind data to simulate an installed wind capacity of 10 GW in both grids and compared dispatchable generation capacity requirements due to wind uncertainty for both grids.
We assume a system operator procures reserves in the form of dispatchable capacity during day-ahead operation planning. The amount of reserves procured at this stage will be augmented with energy traded on the spot market during the dispatch day. We use the ERCOT target of covering 95% of day-ahead forecast errors with operational reserves in our analysis. It should be noted that reserves to balance wind forecast errors can be procured in multiple time horizons other than day-ahead. There is a trade-off between procuring reserves closer to the dispatch interval and ensuring day-ahead reliability that we do not explore in this paper.
We applied the analysis described in the previous section to wind and load forecast data from ERCOT and MISO to plot the dispatchable generation capacity required for 95% of the net load under forecast errors. Figure 8 displays the required levels of dispatchable capacity as a function of the day-ahead wind power forecast for one period during which the load forecast is near the mean value (medium load). The low and high load forecast bins are shown in later graphs. The 95th percentile of load under forecast errors for ERCOT is 3100 and 2200 MW in MISO. Wind forecast uncertainty for ERCOT increases the required capacity to 5300 MW at a wind power forecast of 7500 MW. In MISO the total capacity required to cover 95% of net load errors is 3100 MW at a wind forecast of 6000 MW. The greater accuracy in MISO wind and load forecasts leads to less net load uncertainty compared to ERCOT (table 1).
Wind uncertainty increases the additional dispatchable capacity requirement for ERCOT up to 2200 MW which is equal to the maximum capacity required for net load forecast errors (5300 MW at a wind forecast of 7500 MW) minus the capacity needed to cover load forecast errors (3100 MW). In MISO (with its lower wind forecast uncertainty), the range is 0-900 MW, with the latter occurring at a wind forecast of 6000 MW.
The median wind forecasts during the observation periods were 3100 MW for ERCOT and 3200 MW in MISO so half the time wind uncertainty contributes less than a few hundred MW of dispatchable capacity requirement. The high end of the operating reserve requirement does not indicate Figure 8. Dispatchable generation capacity required to cover 95% of day-ahead net load under forecast errors for ERCOT and MISO when load forecasts are in the range 90%-120% of mean load forecast. Each graph shows the 95th percentile of load forecast errors as a horizontal line. Net load forecast uncertainty converges to load forecast uncertainty at zero wind forecast and also at the maximum wind forecast. Figure 9. Dispatchable generation capacity required to cover 95%-99% of net load forecast errors for ERCOT and MISO for load forecasts in the range 90% and 120% of mean load forecast. Figure 10. Amount of dispatchable generation capacity required to cover 95% of net load under forecast errors as a function of wind forecast level for 10 GW of installed wind capacity for three different load forecast levels. Back-up requirements peak for ERCOT at a wind forecast of 7500 MW and in MISO at 6000 MW. the additional reserves due to wind; it indicates the reserve requirement at maximum wind uncertainty.
We chose the ERCOT day-ahead reliability level of 95%, but some system operators may choose other day-ahead reliability levels, depending on operational policies. Using medium load forecast levels, figure 9 shows the dispatchable generation capacity required to provide day-ahead reliability levels from 95% to 99% as a function of the day-ahead wind forecast. Providing an increase in day-ahead reliability from 95% to 99% for ERCOT requires 1500 MW more dispatchable capacity. In MISO, 1000 MW of additional capacity is required. Figure 10 shows the effect of the forecasted load on the net load uncertainty. At high load forecasts the uncertainty associated with the load forecast increases, and so does the net load forecast uncertainty. Each plot below displays separate curves for three load forecast levels defined in section 3.1. For ERCOT, the three curves are evenly spaced as load uncertainty increased gradually with the load forecast value. The MISO load uncertainty increased more abruptly at high load forecasts.
The graphs in figure 10 show that the 95th percentile of net load under forecasts for ERCOT ranges from 2100 (low load forecast with no wind) to 5700 MW (high load forecast with 7500 MW wind forecast). In MISO the range is from 1900 to 4500 MW depending on the load and wind forecasts for 10 GW of wind capacity. The online supplemental material (available at stacks.iop.org/ERL/8/034013/mmedia) contains more discussion on the difference of net load forecast uncertainty between ERCOT and MISO.
We now consider the operating reserves that will be required to balance additional forecast uncertainty for future levels of installed wind capacity. The distribution of wind forecast errors is the metric of interest for reserve allocation, rather than the mean or root mean square forecast error. We observe from figure 4 that the distribution of wind forecast errors is much narrower for MISO than for ERCOT. Both grids have very close to the same amount of wind. Thus we conclude that the geographic dispersion component accounts for much of the difference in forecast error.
Similarly, Focken et al (2002) showed that the standard deviation of wind forecast errors decreases as a function of the area covered by the wind farms. They found that the installed wind capacity was less important than the area covered. In their results, the 36-h look-ahead forecast error standard deviation decreased roughly 28% when the area doubled (their figure 9). While Focken et al's work was based on German data, Katzenstein et al (2010) found similar results with ERCOT data when analyzing wind output standard deviation.
However, it can also be argued that holding the geographic area constant while increasing the number of wind turbines will decrease the forecast error and narrow the error distribution. While we do not observe this comparing MISO to ERCOT, we account for both possibilities in what follows. As a worst-case scenario, we assume wind is added to the grid in a manner that the wind forecast accuracy stays constant. This assumes future wind farms cluster in the same areas as existing wind farms. As a best-case scenario, we consider adding more wind away from the existing wind farms to spread the wind over a wider area. In this scenario we reduced the wind forecast errors to represent improved forecasts, as described below. Note that in both scenarios the wind forecast error distribution shape is assumed to be the same, only the width changes.
In order to simulate improved forecasts, we used the results of Focken et al for the wind forecast error standard deviation. In the best-case scenario, we assume the geographical area covered by wind farms doubles as installed capacity increases from 10 to 30 GW. The standard deviation of the wind forecast errors decreases by 28% over this range of installed wind capacity. This suggests that the standard deviation of wind forecast errors can be modeled as a function of installed wind capacity as where C is the installed capacity and α and β are constants. The values of the constants are determined with two pairs of values for σ and C. The first pair is the observed standard deviation of the forecast errors and the installed capacity when the data were collected. The second pair is the observed standard deviation reduced by 28% and the observed installed capacity increased by a factor of three. The resulting functions are shown in figure 11. Observed wind forecast errors were scaled by the ratio of the simulated forecast error standard deviation to the observed standard deviation (equation (9)) to achieve modeled forecast errors with the desired standard deviation. The method described here can be applied accurately without regard to these conjectures about how forecast accuracy changes as more wind is added by using the observed forecast accuracy Figure 12. Dispatchable generation capacity requirements for maximum wind forecast uncertainty for installed wind capacity up to 30 GW for ERCOT and MISO. Horizontal lines show the level of capacity required to cover load forecast errors at high load forecasts. Solid lines show operating reserves required for 95% of net load errors with current wind forecast accuracy. Dashed lines show the results with improved wind forecasts as defined above for wind capacity above 10 GW. Maximum wind forecast uncertainty is assumed to occur for wind forecasts of 75% of installed capacity for ERCOT and 60% of installed capacity in MISO. Current wind capacity refers to the time in which the data were collected. at that larger installed capacity. err mod = err obs σ mod σ obs .
Whether wind forecasts will become more accurate is uncertain. MISO wind farms seem to already exhibit close to the maximum geographical dispersal. The ERCOT situation is much different. Wind is highly concentrated in the western section and future wind developments along the Gulf coast may reduce the correlation of output between wind farms (see figure 1).
We estimated the maximum amount of dispatchable generation required to balance wind forecast errors if installed wind capacity is increased to 30 GW (approximately a three-fold increase from current ERCOT or MISO installed wind). To be clear, this does not indicate that new capacity must be built for future wind. Rather a portion of the existing capacity will provide more reserves as wind displaces energy deployments. For a range of wind capacities up to 30 GW, we determined the maximum amount of dispatchable generation required to cover 95% of the net load forecast errors for ERCOT and MISO. For example, from figure 10 the maximum capacity required for net load errors is 5700 MW for ERCOT and 4500 MW in MISO when wind capacity is 10 GW. The curves in figure 12 show the maximum dispatchable generation as a function of the installed wind capacity for the worst-case scenario (wind forecast accuracy remains constant) and the best-case scenario (improved wind forecast leads to forecast errors scaled down). We modeled the worst-case scenario by linearly scaling up the wind forecast data to simulate greater levels of wind capacity. In the best-case scenario with improved forecasts, the wind forecast Figure 13. Additional day-ahead reserve capacity for maximum wind forecast uncertainty for a range of wind penetration values for ERCOT and MISO. In this figure the horizontal axis is the percentage of load served by wind power. Solid lines assume no change in wind forecast accuracy. Dashed lines show the effect of improved forecasts. Maximum wind forecast uncertainty is assumed to occur for wind forecasts of 75% of installed capacity for ERCOT and 60% of installed capacity in MISO. Current wind level refers to the time in which the data were collected.
errors were scaled such that the standard deviation of the normalized forecast errors decreased with higher installed capacity according to figure 11. For ERCOT, day-ahead reserves required with 30 GW of installed capacity range from 8700 to 13 000 MW (4600 to 8900 MW due to wind). Thus, roughly 16%-30% of this capacity would be needed in the form of dispatchable generation to cover wind forecast uncertainty. Load data is held constant. In MISO the values range from 6000 to 7800 MW (2100 to 3900 MW due to wind). Approximately 7%-13% of MISO wind capacity is required in the form of dispatchable generation to cover wind forecast uncertainty. Once again, this does not indicate that new capacity must be built for future wind. Rather a portion of the existing capacity will provide more reserves as wind displaces energy deployments.
Assuming constant wind capacity factors for ERCOT (CF = 0.35) and MISO (CF = 0.33), we calculate day-ahead reserves needed for wind capacity as a function of the proportion of energy produced by wind. In figure 13, the additional dispatchable capacity represents the maximum day-ahead reserves required beyond that which is needed to cover load forecast errors with a high load forecast. For example, for ERCOT with 10 GW of wind capacity nearly 10% of the load is served by wind. At this capacity the maximum value of the 95th percentile for net load is 5700 MW and the 95th percentile for load forecast errors is 4100 MW meaning the wind adds an additional 1600 MW of reserve capacity to cover 95% of day-ahead forecast errors. In MISO, 10 GW of wind serves 5.5% of load and requires an additional 600 MW of reserves beyond that which is needed for load forecast uncertainty. In order to get 30% of the total generation from wind, ERCOT would require just over 30 GW of installed wind capacity while MISO would need 54 GW of installed wind capacity at current load levels. While MISO has tighter wind forecasts, it has a much larger load. These Figure 14. Additional day-ahead reserve capacity for maximum wind forecast uncertainty as a percentage of peak load for a range of wind penetration values for ERCOT and MISO. Maximum wind forecast uncertainty is assumed to occur for wind forecasts of 75% of installed capacity for ERCOT and 60% of installed capacity in MISO. Current wind level refers to the time in which the data were collected.
two factors nearly cancel each other making the additional capacity requirement on a MW basis equal for both grids when compared on a wind percentage basis. Figure 14 presents the additional day-ahead reserves required to compensate for net load forecast errors as a percentage of peak load, again as a function of the penetration of wind power. This figure may provide useful bounds on the reserves that will be required as wind's share of generation increases.
We now compare the results of our model with the analysis performed for ERCOT to determine operational reserves as defined for ERCOT (2010). ERCOT procures day-ahead operating reserves based upon an analysis of forecast uncertainty from forecasts submitted at 4:00 pm before the operating day. Operating reserves are procured such that the sum of regulation up, non-spinning reserves and 500 MW of responsive reserves cover the 95th percentile of negative net load forecast errors. Here, we are concerned with day-ahead uncertainty and, as such, we analyze uncertainty using forecasts submitted at approximately 6:00 am before the operating day.
Additionally, our analysis differs from ERCOT's method in that we assume dynamic procurements each hour based on forecast values whereas ERCOT sets monthly reserve requirements based on an analysis of forecast data for the previous month and the same month of the previous year. Our model estimates the range of reserves based on the 95th percentile of day-ahead wind and load forecast errors would be from 2100 to 5700 MW. Most hours would be at the low end of the range given the ∼35% capacity factor of wind for ERCOT. Maggio (2012) showed that monthly averages for the combination of regulation up and non-spinning procurements ranged from 2100 to 2500 MW during an eleven-month period in 2011 when approximately 9500 MW of installed wind capacity existed for ERCOT. Adding the 500 MW of responsive reserves, the total of ERCOT's procurement was on average 2600-3000 MW to cover the 95th percentile of net load uncertainty. Maggio's analysis also estimated that between 110 and 800 MW of the reserve procurement was attributable to wind forecast uncertainty (monthly averages). These are monthly averages and are influenced by the system wide capacity factor for ERCOT. We estimate that in certain hours wind uncertainty can be much more significant (over 2000 MW). However, as stated above, half of the wind forecast values are less than 3100 MW, which adds less than 1000 MW to the reserve requirements depending on the load forecast level, in good agreement with the reserves ERCOT currently procures.

Conclusion
Proper quantification of wind forecast uncertainty and how it affects net load uncertainty is essential for optimal reserve procurements. Currently, most US grids do not have high enough levels of wind power to make this a major concern, but this situation is likely to change. We used an empirical analysis of wind forecast uncertainty and load forecast uncertainty to develop a method that can be used in making day-ahead procurement decisions.
We present a method based on observed wind and load forecast distributions. Using data from ERCOT and MISO, we calculated the amount of dispatchable generation capacity required to cover the day-ahead wind and load forecast errors at different desired confidence levels. In order to cover 95% of the day-ahead net load under forecast errors, reserve levels ranged from 2100 to 5700 MW for ERCOT and 1900 to 4500 MW for MISO, depending on the load and wind forecasts. Hence, decisions on generation capacity procurement to cover the day-ahead forecast uncertainty must consider the systematic nature of wind and load forecast uncertainty. As wind power uncertainty begins to dominate load uncertainty, system operators will have to adjust decision making to account for the wind uncertainty.
We also simulated future grids with higher levels of wind capacity and estimated that for ERCOT each additional MW of installed wind capacity would require 0.16-0.30 MW of dispatchable capacity to correct day-ahead forecast errors depending on the accuracy of the forecasts (see figure 12). In MISO this range is 0.07 and 0.13 MW.
Our analysis focused solely on the day-ahead uncertainty. However, ERCOT uses a shorter time horizon to determine reserve requirements. As the decision time approaches, more information becomes known and uncertainty is reduced. We chose to analyze day-ahead forecast data because many operating decisions are made in that time frame. However, procuring reserves in a shorter time frame (say 12 or 6 h in advance) would allow reduced reserve requirements. There is a trade-off between look-ahead time and the number of procurement periods a system operator should consider.
Ramp rate requirements are a factor when planning for hourly changes in net load uncertainty. We did not incorporate this aspect of reserve planning, but it is an important issue that requires further investigation. Nor did we consider the economics of ensuring enough dispatchable generation for wind power uncertainty, since this is highly dependent on factors outside the scope of this research. However, we noted that the non-spinning reserves used by ERCOT to balance wind forecast errors are relatively low cost compared to other, faster types of reserves. Recent studies have estimated the operational integration costs of wind power from $2.5 to $7 MWh −1 of wind energy generation which includes balancing variability and forecast uncertainty. Finally, our work did not take into account grid contingencies leading to forced generator outages. This risk is generally required to be covered with reserves equal to the amount of generation loss from the largest potential contingency in the grid.
This work shows that ensuring a particular level of reliability in an electric system with significant levels of wind power capacity requires hourly levels of reserve capacity that depend on the hourly predictions for load and wind power. We quantify these reserve level requirements as a function of the load and wind power prediction.
Wind power is likely to play a larger role in electricity production in future grids. We show that for ERCOT, as installed wind capacity reaches 30 GW, up to 30% of this capacity will need to be matched with dispatchable capacity to cover wind forecast uncertainty. In MISO, up to 13% of the installed wind capacity must be matched with dispatchable capacity. We note, however, that the numeric values are not transferable to other systems but the method presented in this paper can be applied to do system-specific analysis.