SIAM News Blog

Renewables Reliability in an Era of Force Majeure

By René Aïd, Mike Ludkovski, and Ronnie Sircar

Following the global lockdown in March 2020, the SIAM Activity Group on Financial Mathematics and Engineering launched a virtual seminar series to maintain a sense of connectivity within the worldwide financial mathematics community. In addition to individual talks, the series included an inaugural panel discussion about energy markets that focused on the COVID-19 pandemic’s effect on energy production, novel negative oil prices, and research opportunities from renewable sources’ increased impact on electricity production. The panel, which was moderated by Ronnie Sircar (Princeton University), consisted of René Aïd (Paris Dauphine University), Glen Swindle (Scoville Risk Partners), Zef Lokhandwalla (Bloomberg L.P.), and Mike Ludkovski (University of California, Santa Barbara).

The horrific power outages (and ensuing consequences) in Texas during February 2021 served as a prime example of the ramifications of electric grids that are run as essentially deterministic systems; they are unprepared for extreme weather events, despite the introduction of more weather-dependent production sources. A decade ago, experts were concerned with electricity price spikes in Texas due to summer heat waves [7]. Now the southern U.S. states must determine whether recent events will inspire them to winterize their generation units — and if so, to what degree and at what cost.

Figure 1. Temperature-adjusted electricity consumption in Texas by customer class for April/May 2020 versus the same period in 2019. Figure courtesy of Steve Cicala [6].
Aside from upending our daily lives, COVID-19 has dramatically impacted the energy industry. Lockdowns both significantly lowered overall energy consumption and changed the nature of this consumption. For example, the shift to a work-from-home lifestyle and erosion of the typical 9 a.m. to 5 p.m. pattern placed strains on electricity grid operators, who had to simultaneously adjust to daily time shifts and spatial changes in energy consumption (from commercial cores to residential neighborhoods). The resulting change in the shape of electricity demand will likely be long lasting (see Figure 1).

As another COVID-19-driven effect, April 2020 saw one of the most spectacular examples of a price collapse. Crude oil prices dropped into negative territory, touching a low of -$40.32 on April 20, 2020 [4]. While financial prices tend to be positive, the need to actually take delivery and then store all that crude—a physical commodity—created giant market distortions. When every available storage facility filled up (due to decreased demand) and significant bottlenecks arose, financial traders were forced to pay to get rid of their crude futures and respective obligations to receive physical barrels. The result was a several-day trading extravaganza, with reports of lost and gained fortunes and even some auxiliary systems shutting down, as they were not programmed to expect negative prices.

In a related development, the pandemic triggered the little-known force majeure clause of electricity futures contracts in France. Electricity suppliers invoked the clause to suspend their obligation to buy electricity from the national Electricité de France (EDF). EDF operates the French nuclear plants and is regulated to sell between 100 and 150 terawatt hours of nuclear energy via a forward contract at the fixed 42 euro/megawatt hour price. Retailers bought all of this power forward in October 2019; but by March 2020, when they should have taken delivery, the spot electricity price had crashed — along with the demand. To avoid large financial losses, the buyers claimed force majeure. The case was initially settled in their favor but is currently under appeal.

In contrast to crude oil, negative electricity prices have become commonplace all over the world. The culprit is the sun; power demand remains steady during midday, but solar production is now enormous — for example, it supplies more than 50 percent of total demand in California. As a result, there is really too much solar energy in some places at certain times. To keep the lights on in the evening, operators regularly curtail solar (and often wind) energy generation so that fossil-fueled plants with slow ramping times can remain active and economically viable (see Figure 2). At the same time, renewable generation is highly noisy and can experience forecast errors of up to 10 percent, even on a day-ahead time scale; large deviations cause price spikes.

Figure 2. California Independent System Operator (ISO) monthly curtailment of renewable generators. Curtailment records were established in 2020. Figure courtesy of [5] and licensed with permission from the California ISO. Any statements, conclusions, summaries or other commentaries expressed herein do not reflect the opinions or endorsement of the California ISO.

Tackling this challenge requires collaboration between applied mathematicians, power system engineers, and policymakers. It starts with quantification of the uncertainties in daily grid operation and eventually will necessitate a redesign of the electricity markets that remain geared towards firm energy suppliers. Decentralization, improved forecasting, faster optimization of distribution and dispatch, and risk allocation are all imperative for a smooth transition to a renewables-based grid. Recently, the Advanced Research Project Agency–Energy (ARPA-E) within the U.S. Department of Energy ran the Performance-based Energy Resource Feedback, Optimization, and Risk Management (PERFORM) solicitation [1] to address this challenge; it is now funding 13 multidisciplinary projects. Application of the mathematical toolbox to manage renewables uncertainty is an emerging theme. The new paradigm requires researchers to embrace the unavoidable fluctuation of wind and solar energy availability, and re-engineer our energy systems accordingly. SIAM News readers can contribute to this enterprise by engaging with climate scientists to enhance numerical weather forecasting systems for probabilistic location-specific solar and wind predictions, or working with power engineers to build faster solvers for the highly non-convex unit commitment problems that are necessary for hour-by-hour balancing.

Thanks to ever more cost-effective technology, demand for renewables grew unabatedly even as overall energy consumption decreased during lockdown. 2020 therefore shattered many records; renewable energy even surpassed coal production in the Electric Reliability Council of Texas grid. One component of this shift is the decentralization of energy production that is exemplified by the growing use of rooftop solar panels. Such behind-the-meter resources—which are managed by consumers rather than utility companies—open a new frontier in energy use management and enable novel solutions through customer cooperation. An active research strand is tackling these problems with mean-field stochastic models and principal-agent models that were recently developed by economists and financial mathematicians. A paradigmatic example of modeling distributed local storage via the mean-field game (MFG) framework published last year [3]. The authors of the study employed the MFG approximation to design a price-based signal that aligns consumer behavior with the interests of grid balancing.

Similarly, researchers utilized recent developments in continuous-time optimal contract theory to create an implementable demand response contract that allows the utility to control the responsiveness of a pool of consumers, thus significantly increasing demand response’s reliability when necessary [2]. The potential of demand response was evidenced in California in August 2020, when vigorous social media campaigns for short-term electricity conservation helped the state avoid rolling brownouts that were trigged by record heat waves. When activated ad hoc in an emergency setting, the use of internet-based, decentralized tools to shape electricity demand has the potential to reduce the need for costly batteries or the construction of new fossil fuel plants. A related topic that is highly amenable to optimization and stochastic techniques is the design and implementation of smart charging networks that would adaptively charge electric vehicles overnight to maximally benefit overall grid management.

[1] Advanced Research Projects Agency – Energy. Performance-based energy resource feedback, optimization, and risk management (PERFORM). Retrieved from
[2] Aïd, R., Possamaï, D., & Touzi, N. (2017, June 1). Electricity demand response and optimal contract theory. SIAM News, 50(5), p. 1.
[3] Alasseur, C., Tahar, B., & Matoussi, A. (2020). An extended mean field game for storages in smart grids. J. Optim. Theory Appl., 184, 644-670.
[4] Bloomberg News. (2020, April 25). The 20 minutes that broke the U.S. oil market. Bloomberg. Retrieved from
[5] California Independent System Operator. Managing oversupply. Retrieved from
[6] Cicala, S. (2020). Powering work from home. NBER working paper series. National Bureau of Economic Research. Retrieved from
[7] Coulon, M., Powell, W., & Sircar, R. (2013). A model for hedging load and price risk in the Texas electricity market. Energy Econ., 40, 976-988.

  René Aïd is a professor of economics in the Department of Economics at Paris Dauphine University. 
Mike Ludkovski is a professor in the Department of Statistics and Applied Probability at the University of California, Santa Barbara. 
   Ronnie Sircar is a professor in the Department of Operations Research and Financial Engineering at Princeton University.
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