Insights

May 2026

A novel method for direct calculation of marginal ELCCs from optimization-based resource adequacy models

Sylvan Energy Analytics

If you are paying attention to resource adequacy, you’ve probably at some point had to sit through a talk or read a paper or participate in a debate about effective load carrying capabilities. ELCC – the key to fairly crediting resources for their contribution to system reliability – is one of the most crucial and frustrating topics in our industry today. Every RA program and capacity market has a different approach to calculating ELCCs. After years of debate, the industry seems to be converging around marginal ELCCs (versus average or some combination) for resource accreditation in RA programs and capacity markets. This is good news for those concerned with traditional market principles and for those seeking simplicity, but even calculating marginal ELCCs can be complicated.

Today’s marginal ELCC calculations are either hard or wrong

E3 put out a paper last year on critical hour reliability frameworks, which described three common approaches to calculating marginal ELCCs around the country (E3 2025). Two of the approaches (“Repeated LOLE runs” and “Marginal Reliability Improvement”) are essentially in-and-out approaches, in which you run a full LOLE study without new resources first and then additional LOLE studies with a little bit of each resource. If you want to calculate ELCCs for ten resources, you have to conduct eleven runs.

These approaches are theoretically accurate. They ensure that ELCCs reflect energy adequacy as well as capacity adequacy, can evaluate resources with very different operational capabilities and constraints, and can account for interactions between resources (such as renewables and storage). The downside of these approaches is that they typically involve a lot of computation. They usually require conducting multiple LOLE runs, which limits how many resource types can be examined and makes updating ELCCs as conditions change both time-consuming and challenging.

The third approach that E3 describes (DLOL) avoids all this computation by examining resource availability during critical hours. This is a more pragmatic approach, but it can be much less accurate, especially when a system relies on resources with energy-related constraints, such as hydropower and storage. For these systems, resource availability during hours with unserved energy in an LOLE simulation is not a good proxy for resource contribution to adequacy. Consider a system with a lot of solar and storage. Solar may not be available during the most critical hours, but the ability to dispatch storage in those hours may depend on the availability of solar earlier in the day. This is exactly the type of problem the CPUC’s Slice of Day requirements were designed to address.

An alternative, optimization-based solution

In the interest of improving both the accuracy and ease of marginal ELCC calculations, we’d like to propose an alternative approach, a variation of which we first developed for a paper with GridLab a couple of years ago (Sylvan 2024).

Crucial to our approach is the use of optimization to simulate dispatch decisions within RA models. Not all RA models use optimization. Some instead rely on heuristics, or mathematical dispatch rules that approximate, but do not optimize, dispatch decisions. This can be faster than optimization, which is helpful when the model must test millions of potential conditions to identify periods with loss of load risk, but it can also miss important dynamics on the system, including resource co-optimization, part of the core value proposition of day-ahead markets. Optimization models may be slower, but they capture these dynamics with more accuracy.

The other advantage of using optimization models – and key to the mathematical trick we use here – is that they can calculate shadow prices. When an optimization model minimizes costs, shadow prices represent the marginal cost associated with each binding constraint. For example, the shadow price on the hourly load balance constraint represents the reduction in total cost achieved by relaxing demand by one unit in that hour, a marginal value commonly known as the market price (i.e., the marginal cost for serving the last unit of load). Linear optimization models, as part of their algorithms, automatically calculate these shadow prices for every constraint. We don’t need to run the model twice to calculate the price of the last megawatt of load – we simply ask the model to print it out along with the optimal solution.

So how do we leverage shadow prices to get marginal ELCCs? Our approach involves four steps:

1) Objective Function Formulation: We set the objective function for the dispatch simulation to minimize the maximum unserved energy experienced across an operational window, for example a day or a week. This is equivalent to telling the optimization model to minimize the “perfect capacity” need across each operational window.

2) Installed Capacity Variables and Constraints: We add a capacity variable and a corresponding capacity constraint for each resource type for which we would like a marginal ELCC value. We constrain the variable to be less than or equal to the resource’s installed capacity. The optimization will set the capacity variables of all resources to their maximum values to avoid unserved load – or, more precisely, to minimize the “perfect capacity” needed to avoid load shed. This means that the capacity constraints will bind during operational windows with unserved energy (and the resource capacities will equal the installed capacities in the portfolio).

3) Shadow Price ELCCs: We tell the optimization to print the shadow prices of the installed capacity constraints. These shadow prices, by definition, represent the perfect capacity need that could be avoided with an additional marginal amount of each resource type. This approach fully accounts for all the operational dynamics across the operational window, including hydro dispatch and renewable and storage co-optimization. These values exactly reflect the marginal capacity contributions of the resource types across the operational window, expressed as a percent of the marginal contribution of perfect capacity. And the model can do this for as many resource types as we would like, all within a single run.

4) Combining Results: Finally, we must decide how to combine these operational window-specific capacity contributions into ELCCs that reflect all the operational windows in which there is loss of load risk. For the sake of simplicity and stability, one option is to calculate a weighted average of the operational window-specific capacity contributions, where the weights are the perfect capacity needs in the operational windows. This places more importance on resource contributions during windows with greater capacity needs. For sufficiently tractable systems and problems, all operational windows could be combined into a single optimization.

This approach is fully operational within GridPath, Sylvan’s open-source power system planning model, leveraging the platform’s ability to add investment variables to resource adequacy runs (part of the platform’s broader capability to combine capacity expansion, production cost, and RA models into a single formulation). And theoretically it can be implemented in any optimization-based dispatch model for use in RA studies. That’s why we’re sharing it here!

Opportunities for further innovation

Calculating marginal ELCCs for transmission. This approach can also be used to calculate marginal ELCCs for transmission investments that expand any transmission-constrained paths included in the dispatch optimization. You simply add investment variables to expand those paths and constrain them based on current path limits in Step 2. The shadow prices and resulting marginal ELCCs will represent the marginal perfect capacity needs avoided by adding 1 MW of additional transfer capability over each constrained path.

Adapting to EUE-based standards. Variations on this approach can also be used to calculate the contribution to lowering expected unserved energy (EUE). This is essentially what we did in our GridLab paper in 2024 and is equivalent to the Marginal Reliability Improvement concept. Some recent academic papers have been submitted exploring this same concept (Zhang et. al. 2026(a) and Zhang et. al. 2026(b)).

Toward more accurate, efficient, and transparent near-term RA analysis

Using optimization-based models for RA analysis and marginal ELCC calculations offers improved accuracy over heuristic approaches and repeated in-and-out runs of complex and opaque RA models. While elegant, the drawback of this approach is of course that optimization models can be slow relative to heuristic dispatch models. This can be mitigated if simplifications are made to the dispatch formulation and the ability to calculate many ELCCs in a single run, rather than many runs, can help make up for longer runtimes.

Our proposed approach to calculating ELCCs is also not mutually exclusive with the use of heuristic-based RA models. Either heuristic-based or optimization-based models can be used to identify the critical operational windows that have loss of load risk – for near-term studies, there will be a handful of these events, rather than the millions of conditions evaluated in the full RA simulation. Focusing on a narrower set of circumstances mitigates computational concerns with using optimization-based models in this application. It also provides decision makers with concrete examples of the types of highly constrained circumstances that an RA program or capacity market needs to address and a more rigorous examination of resource capabilities and operational constraints during these events. More transparency into these events would go a long way toward building trust around RA methodologies and frameworks.

Optimization models can also incorporate operational details that are too complicated for heuristic models, and relevant constraints – for example transmission constraints – can be layered in as needed. When combined with the shadow price-based methodology for calculating marginal ELCCs, an optimization-based approach to examining critical operational windows offers a rare opportunity to improve the accuracy, efficiency, and transparency of near-term RA analysis.

References:

E3 2025. Energy & Environmental Economics, Inc. “Resource Adequacy for the Energy Transition: A Critical Periods Reliability Framework and its Applications in Planning and Markets,” August 2025, https://www.ethree.com/wp-content/uploads/2025/08/E3_Critical-Periods-Reliability-Framework_White-Paper.pdf

Sylvan 2024. Hart, E., “Iterative portfolio optimization: an essential tool for reliable and clean electricity planning,” GridLab and Sylvan Energy Analytics, Dec 2024, https://gridlab.org/wp-content/uploads/2024/12/GridLab-Sylvan_Iterative-Portfolio-Optimization.pdf.

Zhang et. al. 2026(a). See Qian Zhang, Feng Zhao, Gord Stephen, Chanan Singh, Le Xie, “A Gradient-Based Capacity Accreditation Framework in Resource Adequacy: Formulation, Computation, and Practical Implications,” https://arxiv.org/abs/2601.22087

Zhang et. al. 2026(b). Qian Zhang, Feng Zhao, Tongxin Zheng, Le Xie, “Reformulating Energy Storage Capacity Accreditation Problem with Marginal Reliability Impact,” https://arxiv.org/abs/2601.22096.