LOLP and Related Metrics

LOLP and related methods, first introduced by Calabrese^[22], are well‐known and are described by Billinton and Allen^[23]. The emerging standard approach to estimating the capacity value of wind energy is based on these and related metrics. In this section, we describe the analysis method in more detail.

LOLP is calculated by a suitable convolution algorithm or Monte Carlo analysis using generator capacity and forced outage data along with demand. A typical application involves calculating LOLP on an hourly or daily basis, although it is possible to use alternative time steps. For example, if we wish to calculate a daily value, LOLP is thus

where P = probability, C_i = capacity available during day i, and L_i = load/demand at day i. If suitable adjustments are made to the demand data, this basic calculation can be performed hourly.

There exists a family of reliability metrics that are related to LOLP. As a probability, LOLP is necessarily 0 ≤ LOLP ≤ 1. However, it is sometimes more convenient to represent an expected value, LOLE, in days per year, hours per year, etc. Thus, a daily LOLE can be calculated as

where P, C_i, and L_i = are defined as before, and N = number of days in the year. An estimate of loss of load hours (LOLHs) can be calculated by adapting the equation by applying the summation across all hours of the year.

Modern power systems are generally combinations of networks that are interconnected. This means that if one balancing region experiences shortfalls in generation, this may not result in disconnecting load but could induce an unplanned import from a neighboring system as inertial and governor responses increase output from units responding to frequency drops. In other cases, a given system may be short on capacity but has made plans to import capacity from a neighboring system. A situation such as this would likely be handled by including the import in the LOLP calculation, but the implication of these points is that LOLP may not necessarily refer to disconnecting load but may mean that some combination of the following occur^[1]: operating reserve margins are not maintained^[2], neighboring capacity is planned to alleviate shortfalls, or^[3] unanticipated imports may occur. For the purposes of this chapter, we do not distinguish between these potential events so that we can focus on the underlying issue addressed by LOLP, which is the level of resource adequacy. There are, however, some methods developed considering multiarea reliability, which we list in the Role of Transmission Interconnections section.

The capacity value (sometimes called capacity credit) of a resource is the MW level that the resource contributes to the reliability target, and it is illustrated in Figure 22.2. The original reliability curve shifts to the right as a new resource is added to the mix. This means that a higher level of peak demand can be supplied at the same reliability level as before. Using the target of 1 day/10 years, the diagram shows an increase in the demand that can be served as 400 MW. This is the ELCC of the plant in question.

The concept of ELCC can also be applied to the power system as a whole. Using the example in Figure 22.2, the generation mix originally has an ELCC of about 10 020 MW. Once the additional resource is added to the system, the overall generation mix ELCC increases to about 10 420 MW. When discussing system ELCC, it is important to distinguish between the ELCC level that results in a given LOLE level and the actual ELCC of the system as given. For example, the actual ELCC of a given power system may be 8000 MW, but the level ELCC needed to achieve 1 day/10 years may be 9000 MW. Thus, actual ELCC is 8000 MW, but desired ELCC is 9000 MW, resulting in an ELCC shortage of 1000 MW.

It is important to note that if a system is extremely reliable, with LOLE ≅0, then virtually no generator will have any meaningful capacity value. This is because there is essentially no LOLE, and thus, there is no way that any generator could meaningfully contribute to lowering LOLE. In many systems, LOLH is 0 for most hours of the year, becoming significantly greater than 0 for a relatively small number of days or hours. The specific days/hours of potential reliability shortfall is dependent on the reliability target that is chosen. It is therefore common to adjust demand or other system parameters so that the LOLE represents a desired target level. An example of this type of adjustment can be found in Ref.^[24]. Amelin^[25] shows that the capacity value of a resource is dependent on the initial system reliability level. A target LOLE level of 1 day/10 years is often used. This is a common target used in the models to get reasonable results, but other targets can also be adopted.

Several academic and industry task forces have recommended the use of LOLP methods for wind capacity value calculations, including the IEEE Wind Power Coordinating Committee^[2], NERC^[4], and the IEA Wind Task 25^{[1, 5, 26]}. This literature recommends using time‐synchronized wind and load data and cautions against the use of simplified methods unless they have been suitably benchmarked. We discuss both of these issues further in later sections of this chapter. NERC suggests that alternative metrics such as LOLH and expected unserved energy (EUE) be compared to the traditional daily LOLE value because of the variable nature of wind and solar energy and the possibility that the daily approach may miss reliability events. NERC also recommends transparency in the way interconnected systems are treated in the assessment because of the potentially significant impact this can have on the reliability calculations and results. We also address the issues of alternative metrics and transmission impacts below.

Methodological Considerations for Variable Generation – Wind Power

The growing presence of variable generation, such as wind power, in power systems results in additional considerations for these traditional probabilistic methods, both from a planning and operation standpoint. Such considerations include properly accounting for^[1] the uncertainty of load and variable generation^[2], the variability of wind and solar, and^[3] operational issues. Historically, the variability of wind was deterministically included in LOLP calculations by using the net load (load minus wind plant output) as the system load value. Numerous studies have now incorporated the long‐term uncertainty in the evolution of load or wind power^{[27, 28]}. This typically involves an exogenous statistical characterization of the uncertainty using, for example, sequential Monte Carlo approaches, time‐series models, or Markov models, and then convolving the resulting profiles and probabilities into the capacity outage probability table. Similarly, the variability of wind can be incorporated into the capacity outage probability table through a multipoint convolution method with a chronological sliding window approach^[29]. However, fewer studies have investigated the joint distributions of load and wind profiles and/or their uncertainty to capture their important correlations^{[30, 31]}. Operational issues include the treatment of noncommitted units, transmission congestion, energy‐constrained generation, time‐coupling constraints of generators (startup and shutdown times, ramping, etc.) that limit their availability, and flexible load resources such as storage. Studies are beginning to account for these impacts^{[31, 32]}; other related methods could also apply to operational decisions, such as the allocation of reserves due to wind forecasting errors (Milligan^[33] used an adaptation of Strbac and Kirschen^[34]).

Interest in these additional considerations has primarily been contained within the academic world, and the resulting methods have not yet been widely adopted by industry. Many of the proposed stochastic methods are not only related to reliability and wind capacity value analyses, but as discussed in a recent Integration of Variable Generation Task Force (IVGTF) report, there may be many other fruitful applications of these methods for factors with high levels of uncertainty, such as fuel prices, generator retirements, extreme meteorological conditions, policies and regulations, and unforeseen economic stagnation or growth^[10].

Reliability Metric Comparison

One of the recommendations in NERC^[4] was to further investigate the impact of using alternative metrics that are based on LOLE analysis but represent different ways of capturing the risk of inadequacy. Examples of such metrics include LOLH and EUE. LOLH improves on the daily LOLE metric because it evaluates LOLP at every hour of the year, discarding those hours during which there is zero LOLP. Daily LOLE is based on the single peak hour of the day. Although the traditional approach prior to the advent of significant wind and solar energy has been to focus on peak demand, some analysis of wind/solar has focused on the peak net demand (demand less wind and solar generation). An often‐used reliability target for daily LOLE is 1 day/10 years, whereas there has been little if any development of similar LOLH targets or characterizations of the relationship between these metrics for systems with significant wind and solar energy.

Ibanez and Milligan^{[35, 36]} undertook some analysis to shed light on the use of LOLH and EUE using models of the U.S. Western Interconnection, shown in Figure 22.3. These analyses were based on either the Western Wind and Solar Integration Study Phase 2 (WWSIS‐2) reference case with 8% wind and 3% solar energy penetration^[36] or the Western Electricity Coordinating Council's (WECC's) Transmission Expansion Planning Policy Committee (TEPPC) 2024 data set with roughly 9% wind and 5% solar capacity penetration^[35].

Modeling runs were performed to establish the relationship between LOLE and LOLH and also between LOLE and EUE. These modeling runs calculated all reliability metrics so that the relationship between pairs of metrics – e.g. EUE and LOLH – could be investigated. For alternative values of LOLE, the reliability model was run, and a trace was developed to show how LOLH or EUE varied as a function of LOLE. This was performed for several balancing authority areas, subregions, and the entire interconnection. In all cases, the relationship between LOLH or EUE and LOLE is log‐linear, with parallel curves for all regions^[35]. The differences among the regions depend both on the number and size of the generators (smaller areas tend to have larger slopes), as well as the net load shape (profiles that show higher relative peaks tend to have larger slopes)^[36].

Related work by Ibanez and Milligan^[36] also calculated the ELCC of the system with and without wind and solar to determine the impact of these same reliability metrics on capacity value, using equivalent levels of reliability for each metric. They analyzed alternative wind/solar build‐outs in the West that were taken from the WWSIS‐2^[37]. A reference case had 8% annual energy from wind and 3% from solar (29 GW of installed wind and 14 GW of solar). Alternative cases had 33% of annual demand supplied by wind and solar, split evenly, and high wind/low solar and high solar/low wind combinations. The resulting curves had similar shapes, which further confirmed that the various reliability metrics are capturing the same phenomena. The results for two subregions of the Western Interconnection based on a single‐year analysis with an LOLE of 0.1 day/year are shown in Figure 22.4. In several cases, the lines representing alternative reliability metrics are hard to distinguish; this is because the capacity values from the metrics in these cases are so close that they do not have any meaningful differences. The results of this work indicate that the capacity value of wind and solar is relatively robust against the underlying reliability metric if LOLE, LOLH, or EUE are used. Note that this LOLE of 0.1 days/year is a common use of the 1‐day/10‐year standard, but these are not necessarily equivalent as an average annual reliability performance does not capture interannual variability among individual years. We discuss more on these multiyear considerations in the Multiple‐Year Data Sets section.

Role of Transmission Interconnections

Interconnecting two or more systems together will have an impact on resource adequacy. As pointed out in early LOLE work by Calabrese^{[22, 38]}, interconnecting two nonidentical systems will increase reliability (decrease LOLP) in both systems. This is because of the principle of diversity – demand in different areas is only partially correlated. However, the degree of this benefit for a given area depends on its location in the system, the system load level, and the transmission limitations^[39]. Numerous studies have demonstrated this interconnection benefit through multiarea generation reliability analyses, which consider tie line and/or transmission line constraints and inter‐regional cooperation in addition to the regular reliability considerations. Proposed methods for calculating the multiarea reliability include the “system failure mode” approach that accounts for each failure mode probability and expected capacity^[40], Monte Carlo simulations to account for uncertainty^[41], modifications to the capacity outage probability table to account for uncertainties and capacity limitations of both the generators and transmission lines^[42], and more advanced algorithms that explicitly consider individual components in the network (e.g. minimal cuts method in Ref.^[43]). This multiarea issue is widely known, and in NERC^[4], one of the key recommendations for adequacy studies is to clarify the assumptions regarding transmission interconnections to the neighboring system.

Ibanez and Milligan^{[24, 44]} undertook an analysis in the Western Interconnection in the United States to analyze the upper‐bound role that transmission could play in resource adequacy assessments. They used the WWSIS‐2 scenarios to compare the ELCC of the full transmission system at three different aggregations that represent alternative levels of interconnectedness^[1]: business as usual, in which each balancing authority area operator is constrained by transmission to the neighboring system^[2]; regional transmission is a copper sheet, but each region is isolated from the remaining system; and^[3] perfect transmission exists throughout the interconnection (full copper sheet). The objective of the study was to determine how much effective installed capacity could be replaced by transmission using LOLE analysis. Key results are presented in Figure 22.5. The graph shows the reduction in required ELCC made possible by perfect transmission within each subregion and by perfect transmission across the interconnection – with Balkanized system planning, the total required ELCC needed to achieve 1 day/10 years LOLE is 244 GW, whereas with copper‐sheet planning, the levels of ELCC needed for 1 day/10 years is 184 GW. Although copper sheet transmission is unlikely to ever be built, the example does show the trade‐off between transmission and generation and the impact that transmission can potentially have on the need for new resource additions.

Simplified Methods for Calculating Capacity Value of Wind Power

While reliability‐based methods are widely accepted and provide accurate measures of wind and solar capacity values, they require detailed system data and can be computationally expensive to evaluate. Many attempts have been made to develop simplified methods that can provide a good estimate of wind/solar capacity value without requiring a reliability model. Many of these simplified methods estimate the ELCC by approximating the relationship between capacity additions and LOLP or LOLE. These include Garver's method^[45], Garver's method extended to multistate generators^[46], and the Z‐method^[47].

Other approximation approaches calculate the capacity factor of wind and solar over some subset of hours when the system may have the greatest risk of not meeting the load. One of the first applications of this was in PJM in the United States^{[6, 48]}, which uses three years of wind production data, for hours ending 3:00–7:00 p.m. The wind power plant capacity factor is calculated for this time period using a standard assumption if there are fewer than three years of operating data. The accuracy of these capacity factor methods, however, is very sensitive to both the number of hours used and the methods used to select those hours^[49]. The accuracy is also often system‐ and technology‐specific. For instance, considering too many of the peak‐load hours for photovoltaic (PV)^[8] or too few of the peak‐load hours for wind^[49] can underestimate the respective capacity value. Capacity factor approximation methods that use peak‐load hours have also been shown to have decreasing accuracy with higher penetrations of PV as the highest LOLP hours shift from afternoon (without PV) peak load to early evening (with PV) peak “net load” hours^{[50, 51]}. Munoz and Mills^[51] found that the capacity factor approximations based on peak load hours can provide a relatively accurate estimation of the capacity contribution of PV for penetration levels less than 5%.

In practice, various reliability‐based and approximation methods, such as those listed here, as well as ad‐hoc rules of thumb are used for calculating wind and solar capacity values^[48]. For instance, the WECC uses several “standard” values for the capacity credit of wind. Ibanez and Milligan^[36] compared the WECC rules of thumb to results from a full reliability model and found significant differences in several subregions of the interconnection. The key results are shown in Figure 22.6.

As shown in the graph, the rule of thumb sometimes overestimates and sometimes underestimates the wind capacity value that is calculated from a full LOLE model.

The same study found a significant difference in ELCC for solar based on geography. Figure 22.7 shows the capacity value by zone compared to the WECC simplified rule, which uses 60% capacity value for all solar resources in the interconnection.

From the results, it is clear that the capacity value for solar energy is overestimated by the rule of thumb because the actual ELCC values are less than the assumed 60% of rated capacity.

Chronological Data Pairing

The IEEE Wind Capacity Value Task Force paper recommends that hourly demand and wind data should be paired chronologically^[2]. This is because the underlying weather drives the behavior of wind (and solar) and, to some extent, demand. Although correlations may be nonlinear and complex, calculating wind capacity value with a hot sunny still day of demand data paired with a cool windy day of wind production data appears to be inconsistent and problematic. For systems with significant hydropower, it is also important to ensure that the underlying weather – and thus its combined influence on demand, wind power, and hydropower – is preserved. This may be especially important if the system is energy restricted more than capacity restricted.

The chronological pairing of data is motivated by the concern that there is an underlying weather driver that influences both demand and wind (and solar) energy. In Sweden, the annual energy consumption does not vary significantly from year to year, but peak demand does. Figure 22.8 shows the variation in peak demand for a 20‐year period.

Limitations of a Single‐Year Data Set

Many capacity value studies have used a single year of data; however, in recent years, there has been more interest in long‐term contributions to adequacy and multiyear data sets. This is because there is considerable interannual variation in many of the inputs for capacity value evaluation. This section discusses how to deal with variations in forced outage rates, peak load, and energy demand.

When conventional resource data are input into LOLP models, one of the relevant variables is the unit's forced outage rate. This is typically determined by size and type of unit and take into account many years of data. In some cases, forced outage rates are adjusted to take into account particular unit characteristics. The determination of a plant's capacity value is a subset of solving the resource adequacy assessment, which is determining the level of installed generation needed for a time period that may cover many years in the future. Thus, a long‐term average is appropriate because the power supply must be robust against a large number of potential forced outages and still deliver power and energy consistent with the resource adequacy target.

This raises the question of how many years of wind production data are necessary to produce a reasonable long‐term result that is consistent with what is already performed for conventional generators. Because the primary influence on wind production is wind speed, and because wind turbine forced outage rates are very low (approximately 1–2%) and statistically independent of each other, the question of interannual variability requires the use of multiple years of wind data. For example, Zachary et al.^[52] claim that the 25 years of data they analyzed for Great Britain is not enough, and they present an analysis of prevalent weather patterns during high‐demand situations to demonstrate the statistical difficulties. The question of how many years of wind data are necessary for stable capacity value has begun to be explored.

When using multiple years of synchronized time series, it should be taken into account that electricity demand does not stay constant throughout the years. For capacity value evaluation, it is important to capture only the weather‐driven changes in electricity demand that are possibly correlated with wind (and solar). Historical time‐series data for demand contains the impact of economic activity, changes in energy efficiency, and other drivers of demand for electricity – for example, increased use of air‐source heat pumps for heating instead of direct electric heating. If these changes are not removed, the LOLP is not comparable throughout the years and the capacity value calculation may be mainly based on those years that have had the highest nonweather‐induced consumption.

To distinguish the economic or technical changes, it is necessary to have a proxy for their impact. This can be some measure of economic activity, like gross domestic product (GDP), industrial output for energy‐intensive sectors, or number of installed new devices. The data can then be used to perform a statistical operation such as regression analysis to estimate how different factors influence consumption, along with unchanging signals such as time of day, day of week, temperature, and possibly wind and solar irradiation^{[53, 54]}. The correlation coefficients can then be used to normalize the changes that should not influence the capacity value evaluation. Finally, expected future changes in electricity demand and wind power can be overlaid on the processed historical data when analyzing future years.

Hasche et al.^[27] analyzed the question of how many years of data should be used for capacity value in the Ireland power system. Using a 10‐year data set of demand and wind power production data, they calculated the ELCC for various subsets of the data and then compared them to the 10‐year ELCC. The objective was to estimate the number of consecutive years of data needed to approximate the long‐term average. Therefore, each single year of data was run separately with 1000 MW of installed wind capacity, and the capacity value (in MW) is calculated and plotted in the first column of Figure 22.9. Next, all possible consecutive 2‐year sequences were used to calculate the 2‐year capacity values, which are plotted in the same graph in Column 2. This process was repeated for 3, 4, …, 10 years. The results show that increasing the number of consecutive years of data improves the results, which tend to converge to the long‐term value. Using eight years of data, the range of capacity value is within approximately 2% of the 10‐year value, whereas using a single year has a wide spread of results and can under‐or overestimate the result by 10–20%.

Kiviluoma and Helistö^[54] calculated wind power capacity value for Finland using nine years of measured wind power production data. The same data set was employed for this chapter to replicate and extend the work by Hasche et al.^[27]. Similar to the results shown in Figure 22.9 by Hasche et al., Figure 22.10 shows how the capacity value of wind power evolves with an increasing number of years. However, the figure also includes another data set from the same nine‐year period based on NASA (National Aeronautics and Space Administration) MERRA (Modern‐Era Retrospective Analysis for Research and Applications) ReAnalysis data, which was also used to train electricity demand and wind power generation time series for 35 years (see Ref.^[54] for more details). Using ReAnalysis wind data for wind power has significant shortcomings even when the data are scaled to match average historical wind power generation. Consequently, the resulting capacity values are not reliable. However, ReAnalysis data should still give a relevant demonstration for using multiple years in the capacity value calculation. The spread in the ReAnalysis‐based capacity value is somewhat higher than it is in the real data, but it shows a similar decrease as more years are added.

Figure 22.11 shows how the capacity value behaves with 35 years of ReAnalysis data. The capacity value spread for the one‐year cases (leftmost) is not significantly different from the nine‐year analysis, although there is an outlier close to 40% (400 MW) capacity value. The last (rightmost) set has only two temporally independent 17‐year periods (left blue lines). They are still approximately 1.2% from each other. Therefore, even with 17 years of data, there is still considerable uncertainty surrounding the capacity value of wind power. This gives only a lower bound because using more decades of data could show more variation.