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Contract No. DE-AC36-08GO28308

A Solar Reserve Methodology 

for Renewable Energy 

Integration Studies Based on 

Sub-Hourly Variability Analysis 

Preprint

E. Ibanez, G. Brinkman, M. Hummon, 

and D. Lew

To be presented at the 2nd Annual International Workshop on 

Integration of Solar Power into Power Systems Conference

Lisbon, Portugal

November 12–13, 2012

Conference Paper

NREL/CP-5500-56169

August 2012
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1 

A Solar Reserve Methodology for 

Renewable Energy Integration Studies 

Based on Sub-Hourly Variability Analysis 

Eduardo Ibanez, Gregory Brinkman, Marissa Hummon, and Debra Lew

National Renewable Energy Laboratory

Golden, CO 80401; USA

Abstract—Increasing penetrations of wind and solar energy are 

raising concerns among electric system operators because of the 

variability and uncertainty associated with the power sources. 

Previous work focused on the quantification of reserves for systems 

with wind power. This paper presents a new methodology that 

allows the determination of necessary reserves for high penetrations 

of photovoltaic power and compares it to the wind-based 

methodology. The solar reserve methodology was applied to Phase 2 

of the Western Wind and Solar Integration Study. A summary of 

the results is included.

Keywords—photovoltaic, power system operations, reserves, solar 

power, wind power

I. NOMENCLATURE

• P: actual power generated

• PCS: clear-sky power, or hypothetical power generated in 

the absence of clouds

• PF: power forecast

• SPI: solar power index, which is the ratio P/PCS

• ΔP: difference in power output between two time steps

• Δt: time step

II. INTRODUCTION

One of the main concerns with the integration of high

penetrations of wind and solar generation is the effect their 

variable nature can have on the system. To hedge against this 

variability, system operators can hold additional reserves so that 

the system can economically respond to unexpected events. A 

reserve methodology was developed for wind power in the 

Eastern Wind Integration and Transmission Study (EWITS) [1], 

but currently a counterpart does not exist for solar power.

The objective of this paper is to analyze sub-hourly 

photovoltaic (PV) data series, which have been recently 

synthesized based on observed measurements and satellite 

imagery [2]. Based on this analysis, a robust (yet simple to 

implement) reserves methodology was created to inform the 

commitment and economic dispatch of electrical systems with 

high penetrations of solar data. Unlike wind, PV power has a 

predictable daily component (represented by the clear-sky output) 

that adds complexity to the problem. Our methodology is able to 

successfully extract this component and minimize the need for 

reserves, which leads to lower production costs. This method is 

also able to capture variations in daily and seasonal trends.

The methodology was applied to the Western Wind and Solar 

Integration Study Phase 2 (WWSIS2) [3]. This study presents 

scenarios with high penetrations of renewable energy. In 

particular, the high-solar scenario considered 25% of solar 

penetration and 8% of wind in the Western Interconnection (WI). 

The operation of each scenario was modeled using PLEXOS and 

the reserve methodology was subsequently validated through the 

5-min dispatch in [4]. 

The remainder of this paper is organized as follows: 

Section III introduces the concept of operating reserves and the 

wind reserve methodology; Section IV introduces WWSIS2; 

Section V presents the new solar reserve methodology, along 

with its validation; and Section VI concludes.

III. RESERVES AND WIND POWER

A. Operating Reserves

Operations of power systems occur at a range of time scales 

that can be summarized, from longer to shorter, as shown in 

Fig. 1 [5]. Unit commitment and scheduling are performed over 

days to economically commit the units in the system to meet 

forecasted load and other system requirements. During shorter 

periods of time (minutes to hours), the system re-dispatches its 

units to counteract deviations from the schedule through load

following. Similarly, traditional units are re-dispatched to perform 

regulation, which is the fast response of generators to changes 

that range from seconds to minutes.

Through these steps, the power system operator is able to 

maximize the use of cheap base load units (e.g., nuclear or coalfired generators) while utilizing fast-response units (e.g., natural 

gas combustion turbines) to maintain system stability and 

reliability.

Operating reserves are required by the operator so the system

can positively respond to forecast errors and events that cannot 

The authors are with the National Renewable Energy Laboratory, Golden, 

CO 80401; USA. (email: eduardo.ibanez@nrel.gov, 

gregory.brinkman@nrel.gov, marissa.hummon@nrel.gov, debra.lew@nrel.gov) 
2 

Figure 1 Power system time scales 

be accounted for in the scheduling process. In the United States, 

the most common are regulation reserves, although load 

following, or flexible, reserves are becoming more popular. Both 

are designed to account for the system’s variability (random but 

expected changes in the system) and uncertainty (unexpected 

changes). Both load and conventional generators affect the 

variability and uncertainty through forecast errors and unexpected 

outages, respectively.

Nonconventional renewable generation, such as wind and PV 

solar, are variable and uncertain in nature because their output 

depends on ever-changing wind speeds and solar irradiance that

cannot be completely predicted ahead of time. Thus, high 

penetrations of these resources lead to an increase in reserves 

necessary in the system. These requirements are especially

critical in long-term integration studies, such as EWITS or the 

Western Wind and Solar Integration Study, which simulate

higher renewable energy penetrations than in today’s systems.

B. Wind Reserve Methodology

Previous work [3, 5] has been able to quantify the uncertainty 

of wind power. Because short-term variations in wind power 

output are hard to predict, persistence forecasts are used to 

calculate uncertainty. For instance, for an economic dispatch 

model run in 5-min intervals, 10-min-ahead forecasts would be 

used. The forecast errors can be calculated by comparing the 

forecasted and the actual power output.

Fig. 2 shows forecast errors represented against the actual 

power output. The plot corresponds to the entire WI footprint for

the high-solar scenario for WWSIS2, which is introduced in more 

detail in the following section. The general trend that can be 

observed is that forecast error variability is highest around the 

50% production level. It is expected that changes can go up and 

down and also that the turbine power conversion is the steepest at 

that point.

Figure 2. Wind 10-min forecast errors versus power output,

along with 95% confidence interval bands

Figure 3. Wind power production and dynamic reserve

requirements for the WI

Confidence intervals (represented as red and blue lines) were 

used to determine up and down reserve requirements so that a 

certain percentage of occurrences were covered by the reserves. 

In Fig. 2, the confidence intervals covered 95% of forecast errors. 

The result was a dynamic determination of reserve requirements, 

as represented in Fig. 3. Similar plots and time series can be 

produced for other time steps, such as 30 min or 1 hour, to 

calculate flexibility reserve requirements.

IV. PHASE 2 OF THE WESTERN WIND AND SOLAR 

INTEGRATION STUDY

The solar reserve methodology in this paper has been 

developed based on data from WWSIS2. WWSIS2 examined

three scenarios with 33% energy penetration of renewables and a 

reference scenario for the WI. The reference scenario and 

conventional generation fleet were consistent with other studies 

performed by the Western Electricity Coordinating Council’s 

Transmission Expansion Planning Policy Committee [6]. 
3 

Table I summarizes the breakdown of variable generation 

between wind and solar for these scenarios. Although the 

reference and high-solar scenarios had the same wind penetration, 

the location of wind generators to achieve the 8% energy 

penetration varied slightly, leading to slightly different amounts 

of installed capacity. Although solar refers to both PV and 

concentrated solar power (CSP), only PV was considered in this 

analysis. The reason is that in Phase 1 of the Western Wind and 

Solar Integration Study, CSP presented several hours of storage; 

thus, it can be dispatched to a certain degree.

TABLE I. BREAKDOWN OF WWSIS2 SCENARIOS

Scenario Wind 

Penetration

Solar 

Penetration

Wind 

Capacity 

(GW)

Solar 

Capacity 

(GW)

Reference 8% 3% 27.9 11.4

High Wind 25% 8% 66.2 34.6

High Mix 16.5% 16.5% 43.8 54.9

High Solar 8% 25% 23.4 81.7

Load time series data from 2006 was chosen from the Ventyx 

Velocity Suite [6] and was increased to represent the load in 

2020, the focus year. The wind data set was derived from the 

large wind speed and power database [7] developed by 3TIER 

using a Numerical Weather Prediction model applied to the West. 

Because the model allows for the re-creation of the weather at 

any time and space, wind speed data was sampled at 

representative hub heights for modern wind turbines every 10 

min for a 3-yr period on a 2-km spatial resolution. The resulting 

data set was then used to construct the 2006 time series, which 

was paired with the 2006 load data time series to preserve the 

consistency of common weather impacts. Solar data was 

produced by the National Renewable Energy Laboratory [9] 

based on the satellite-derived irradiance generated by the State 

University of New York/Clean Power Research [10], which is 

available on a 10-km grid at an hourly resolution. Sub-hourly 

data were interpolated as described in [2].

V. SOLAR RESERVE METHODOLOGY

The proposed solar reserve methodology builds upon the 

wind methods previously presented. Some adjustments were 

necessary to take into account solar daily patterns that occur, but 

the process followed three distinct steps: (a) definition of forecast 

error; (b) use of explanatory variables to group similar patterns; 

and (c) application of the reserve requirements based on the 

explanatory variables.

With this formalized framework in mind, the wind forecast 

errors were calculated based on persistence forecasts. Power 

output was used as an explanatory variable to find reserve 

requirements (Fig. 3) and to create the dynamic reserve 

requirements (Fig. 4). The following subsections develop similar 

concepts for PV power.

A. Solar Forecast Errors 

Solar-based generation presents clear patterns because of its 

dependency on the sun. These patterns are best captured with 

clear-sky simulations, which calculate the power output in the 

absence of clouds. The top panel in Fig. 4 represents the actual 

and clear-sky power outputs in the WI during three summer days 

in the high-solar scenario. The bottom panel in Fig. 4 represents

the 10-min ramps in the same time scale.

If the same power-persistence forecast used for wind was 

applied in this case, we would have consistently seen the largest 

demand for reserves occurring around sunrise and sunset. 

However, it is clear from the graph that the power deltas could be 

decomposed into the contribution from the clear-sky power and a 

smaller, high-frequency variation. In other words, if the clear-sky 

trends were removed from the power deltas, the reserve 

requirements would be smaller.

Figure 4. Power and clear-sky power output and ramps

The first step in the creation of the short-term solar forecast 

was the definition of the solar power index (SPI), which 

represents the ratio between actual power, P, and clear-sky 

power, PCS. The index can take values between 0 and 1, as shown 

in (1), and is undefined when PCS is 0. 

SPI = min (P/PCS, 1) (1)

With this index, we defined the power forecast, PF, for a time 

step Δt that utilized known quantities at time t, plus the expected 

clear-sky power output, which could be pre-calculated for any 

time of the year based on the location of the sun:

PF(t+Δt) = P(t) + SPI(t) × [PCS(t+Δt) – PCS(t)] (2)

Graphically, (2) can be represented as shown in Fig. 5. The 

forecast was based on the persistence of SPI. Thus, to obtain the 

forecast, we added the clear-sky ramp scaled by the SPI to the 

current power output. The forecast error could then be calculated:

Error = ΔP(t) – P(t) + SPI(t) × ΔPCS(t)] (3)

B. Explanatory Variables

The challenge of determining suitable explanatory variables 

was finding the balance between the overall minimization of 

reserve requirements and simplicity. We found that the following 

two variables were especially effective at fulfilling this goal:

• SPI, as defined in the previous subsection, which 

effectively separated “cloudy” and “sunny” days

• Clear-sky ramps, which separated the different times of 

the day (positive in the morning, close to 0 at midday, 

and negative toward sunset)
4 

For WWSIS2, the reserves were calculated based on 5-min 

time series. The first step was to create ten divisions; 

subsequently, 100 groups were formed by the combination of 

both variables. For each group, reserves were calculated by 

taking the appropriate percentiles (e.g., 2.5% and 97.5% to create 

95% confidence intervals). To avoid the reserves being 

dominated by outliers, reserves were not calculated for a group if 

it presented less than 20 members. In that case, the reserves for 

the closest group were used instead.

Figure 5. Graphical representation of short-term forecast for solar

This method was applied to all scenarios in WWSIS2. The 

regulation reserves were calculated using 10-min time and 

95% confidence intervals for the entire footprint. The results are 

represented in Fig. 6. Flexibility reserves were calculated for 

different subregions using hourly time steps and 70% confidence 

intervals. Fig. 7 shows the down ramp requirements for Southern 

California Edison (SCE), the region with the highest PV 

penetration.

Both figures suggest that reserve requirements depend on the 

combination of both variables. The highest down reserves 

requirements were usually located on the top right corner, which 

corresponded to sunrises where SPI was close to 1. In such 

occasions, the calculation of SPI was highly unstable given that 

the denominator in (1) was very small. At times, the forecast 

called for a “sunny” sunrise, and the clear-sky correction was 

heavily weighted in (2). The inability to produce a good forecast 

at these particular instances created the high reserve 

requirements. The graphs also show that reserves were higher in 

the middle of days (clear-sky ramps close to 0) that were partly 

cloudy (SPI around 50%). For particularly sunny days (SPI close 

to 1), requirements were much smaller.

C. Application of Reserve Requirements

After the reserve requirements were determined, they could 

be applied to the time series by finding the combination of the 

explanatory variables that best fit each point in time. Fig. 8 and 9 

represent the resulting requirements for regulation reserves in the 

WI and flexibility reserves in SCE, respectively.

Most of the time, regulation reserves for the high-penetration 

scenarios stayed below 1% of the nameplate capacity; whereas 

the reference case could reach 1.5%, as shown in Fig. 10. This 

reflects the increasing geographical diversity across the 

interconnections.

Figure 6. Regulation reserve requirements by scenario

for the entire WI

Figure 7. Flexibility requirements by scenario for SCE

Flexibility reserve distributions for SCE were relatively 

constant across scenarios (Fig. 11).

D. Validation

A 5-min dispatch of the WI using PLEXOS was performed in 

[4] to test the methodology presented here. A much simpler 

method can be done to check how often the forecast errors violate 

the reserve requirements.

First, the 5-min regulation requirements were compared to the 

forecast errors; the results are summarized in Table II. Overall, 

the confidence intervals were well maintained. Interestingly, the 

down-ramp violations were generally more frequent than the upramp violations. Table III summarizes the results for flexibility 

reserve violations in SCE and showed the same trends. 
5 

Figure 8. Dynamic regulation reserve requirements for the WI by scenario

Figure 9. Flexibility reserves for SCE by scenario

Figure 10. Distribution of regulation down reserves

relative to installed capacity for the WI

Figure 11. Distribution of flexibility down reserves

relative to installed capacity for the WI
6 

TABLE II. FREQUENCY OF REGULATION RESERVE VIOLATIONS

Scenario Up (%) Down (%) Both (%)

Reference 2.6 2.7 5.3

High Wind 1.9 3.2 5.1

High Mix 1.8 3.3 5.1

High Solar 1.9 3.4 5.2

TABLE III. FREQUENCY OF FLEXIBILITY RESERVE

VIOLATIONS IN SCE 

Scenario Up (%) Down (%) Both (%)

Reference 13.1 18.2 31.2

High Wind 11.6 17.8 29.4

High Mix 11.9 16.8 28.8

High Solar 12.0 16.4 28.4

These statistics were calculated for the hours in which there is 

potential solar production. If hours of darkness were included, the 

percentage of violations would drop to 3.2% and 14.8% on 

average for regulation and flexibility reserves, respectively.

VI. CONCLUSIONS

This paper presented a new methodology for the estimation of 

solar reserves. It generalized a previous method for wind power 

reserves. The method includes the determination of a short-term 

solar forecast based on the solar power index and the use of two 

explanatory variables, which reduce overall reserve requirements. 

The method was applied to the scenarios considered in WWSIS2,

and graphical representations were included. Finally, the 

frequency of violations was checked to successfully validate the 

reserves created.

ACKNOWLEDGMENT

This work was supported by the U.S. Department of Energy 

under Contract No. DE-AC36-08-GO28308 with the National 

Renewable Energy Laboratory.

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Golden, CO: National Renewable Energy Laboratory, 2010, 

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into Power Systems, Lisbon, Portugal, November 2012. 

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