No COVID19 climate silver lining in the US power sector
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Statistical significance of power sector CO_{2} emissions
Our analysis of U.S. power sector CO_{2} emissions requires three types of data: net generation by fuel, emissions factors by fuel, and heating and CDDs. We obtain net generation by fuel from the U.S. Energy Information Administration (EIA) Form EIA923^{29}, which reports monthly generation and fuel consumption for every power plant. We obtain Form EIA923 data for the period between January 2016 and December 2020. Monthly plantlevel emissions are computed by multiplying fuel consumption for each plant by fuel codespecific emissions factors published by the EIA and U.S. Environmental Protection Agency (EPA)^{30,31,32}. Total CO_{2} emissions for the contiguous U.S. are evaluated by aggregating plantlevel emissions. We obtain populationweighted heating degree day (HDD) and cooling degree day (CDD) data from the EIA^{33}.
We employ a Gaussian process (GP) regression model to forecast CO_{2} emissions in the contiguous United States. GP regression models are a class of Bayesian nonparametric models. They assume that every finite collection of random variables has a multivariate normal distribution. GP regressions can be used, as in our case, to forecast the likely ranges of variables corresponding to future periods based on observed historical data. GP regressions are appropriate for testing the statistical significance and estimating the uncertainty of outcomes impacted by seasons and other periodic variables^{34,35}. GP regressions have been used to forecast electricity demand and prices, wind and solar power generation, CO_{2} emissions, battery stateofcharge, and optimal grid management strategies, among other related applications^{36,37,38,39,40,41,42,43,44}.
We develop a GP regression that represents a counterfactual scenario in which the COVID19 pandemic had not occurred. It is developed using the Python GPy library^{35}. The GP regression is fit on vector time series data that describes CO_{2} emissions, HDDs, and CDDs in the contiguous U.S. To forecast CO_{2} emissions, we fit a constant term (bias kernel), a trend term (linear kernel), and a combination of sinusoidal terms (a standard periodic kernel) to historical CO_{2} emissions data. The constant and trend terms capture average yearoveryear trends while the periodic term, which is constrained to model oneyear periods, describes repeating seasonal patterns in the time series. Bias and linear kernels are used to model the impacts of populationweighted HDDs and CDDs on CO_{2} emissions. The GP model is fit using a SciPy implementation of the LBFGSB algorithm with five random restarts^{45}. The LBFGSB algorithm is a standard optimization technique^{46,47}; LBFGSB and multiple random restarts are commonly used to fit GPs. Our optimization settings yield model runs that are highly stable and reproducible. The GP model explicitly captures weather, mediumterm CO_{2} emissions trends, and seasonality. We attribute the remaining Gaussian noise to factors that are not modeled explicitly, such as shortterm macroeconomic changes, discrete or nonlinear changes to the powersystem, and outlier events.
The GP regression is fit to historical emissions data for the period January 2016 through February 2020, the last month before COVID19related shelterinplace orders took effect. This historical period is long enough to obtain a strong model fit but not so long as to necessitate additional nonlinear approximations or more complicated multiyear regression methods. The regression model is used to forecast emissions from March through December 2020. Such a forecast is a probabilistic representation of what emissions would have been in a counterfactual scenario in which COVID19 had not occurred.
We compare observed to forecasted data and evaluate deviations between the two. The GP methodology allows us to estimate the statistical significance of these deviations. The model generates Gaussian distributions of values in each forecasted month in the counterfactual scenario. Given these Gaussian distributions, statistical hypothesis testing amounts to determinations of 95% CI levels and a simple decision rule: if the observed CO_{2} emissions level is outside of the 95% CI, we reject the null hypothesis that the observation could have occurred with reasonable probability in the absence of COVID19. In other words, if the observed CO_{2} emissions level is outside of the 95% CI, we infer statistically significant impacts of COVID19 on CO_{2} emissions. If the observed value is within the 95% CI, we accept or fail to reject the null hypothesis and conclude that deviations are not statistically significant under our decision rule.
Impacts of electricity generation (E) and carbon intensity of electricity supply (C/E) on COVID19related CO_{2} emissions
We apply the same steps and use the same data sources to derive time seriesâ€™ for electricity generation (E) and carbon intensity of electricity supply (C/E) that we do to derive a time series for CO_{2} emissions.
We assess counterfactual and observed values of E and C/E. The counterfactual scenario assumes the continuation of historical power sector CO_{2} emissions in the absence of COVID19. The same probabilistic modeling framework that is described in the previous subsection is used to estimate counterfactual values for E and C/E.
As in our counterfactual analysis of CO_{2} emissions, we include a linear kernel, a bias kernel, and a constrained standard periodic kernel in the GP regressions to capture both shortterm and mediumterm trends in E and C/E over a period from January 2016 to February 2020. Linear and bias kernels are also used for HDD and CDD data. The GP regressiondefined counterfactual data is compared to observed data from March to December 2020.
E and C/E are modeled independently and the joint relationships between those terms are not modeled. As such, the product of the E and C/E values in a given month is not necessarily equal to C, the CO_{2} emissions that are computed in that month.
Impact of COVID19 on U.S. coal plant retirements
Estimates of coalfired power plant profitability rely on data related to electricity market prices and capacity auction clearing prices. We also rely on data related to the locations, installed generating capacities, variable costs, and fixed costs of coalfired electricity generation units.
Historical hourly zonal electricity market prices are obtained from S&P Global Market Intelligence (S&P)^{48}. We obtain hourly historical price data for 57 electricity market zones for the period between January 1, 2018 and December 31, 2020.
Forecasts of monthly average regional electricity market prices are obtained from the U.S. Energy Information Administration (EIA)^{49,50}. The EIA publishes monthly average wholesale electricity market prices in a single zone in each electricity market region. Two market price forecasts published by the EIA are obtained: a forecast published in January 2020 prior to COVID19related shelterinplace orders, and another forecast published in January 2021, after shelterinplace orders took effect.
Two electricity market price scenarios are constructed, hourly for each zone, from the monthly EIA forecasts. A counterfactual hourly price scenario reflects the electricity market price forecasts from March 2020 through December 2022 published by the EIA in January 2020. The other hourly scenario reflects our current expectations of electricity market prices. The current expectations scenario reflects actual historical market prices from March through December 2020 and electricity market price forecasts from January 2021 through December 2022. Figure 5 shows the capacityweighted monthly average electricity prices in our counterfactual and current expectations scenarios.
Capacity auction clearing prices are obtained from S&P for the four electricity market regions that administer forward capacity auctions: Midcontinent Independent System Operator (MISO), New England, New York, and Pennsylvaniaâˆ’New Jerseyâˆ’Maryland (PJM) interconnection^{51}. In these four regions, generators submit offers to electricity system operators to provide generation capacity in a future capacity commitment period, in exchange for payment from electricity system operators. MISO, New England, and PJM run annual capacity auctions for forward capacity commitment periods beginning June 1 and ending May 31. New York runs biannual capacity auctions that correspond to a winter capacity commitment period between November 1 and April 30, and a summer capacity commitment period between May 1 and October 31. Capacity auction clearing prices are established on a zonal basis.
We obtain actual zonal capacity auction clearing prices through May 31, 2023 for New England. For PJM, price data are available through May 31, 2022. We assume that prices for the subsequent annual commitment period, ending May 31, 2023, are the averages of the prices in the previous five periods. For MISO, price data are available through May 31, 2021. We assume that prices for the subsequent annual commitment periods, ending May 31, 2022 and 2023, are the averages of the prices in the previous four periods. For New York, price data is available through April 30, 2021. We assume that prices for the two subsequent summer commitment periods and the two subsequent winter periods are the averages of the prices in the previous three summer and winter periods, respectively.
The locations, installed generation capacities, and variable costs of each coalfired electricity generation unit in the seven U.S. electricity market regions are obtained from S&P^{52}. Such data is obtained for 2019, the latest year in which data is available. Those data report the regional and zonal locations of each generation unit, the month and year that each unit entered into service, the operating capacity of each unit, and the variable and fixed costs of each unit. Coalfired cogeneration facilities that produce both electricity and heat are excluded. Such facilities typically supply electricity directly to industrial and commercial facilities. It is difficult to estimate the profitability of such units because they do not earn electricity market revenues for the electricity they supply directly to those facilities.
Finally, an estimate of the weighted average cost of capital (WACC) of coalfired electricity generation units is obtained from the U.S. National Renewable Energy Laboratory (NREL) Annual Technology Baseline 2019^{53}. We adopt an annual WACC of 4.61%.
The profitability of coalfired power plant units is estimated. The profitability (P) for a given month (m) and generation unit (u) is calculated as that unitâ€™s electricity and capacity market revenues (E_{m,u} and C_{m,u}, respectively) net of variable operating costs and fixed operating and maintenance (O&M) costs (V_{m,u} and F_{m,u} respectively):
$${P}_{m,u}=({E}_{m,u}+{C}_{m,u})({V}_{m,u}+{F}_{m,u})$$
(1)
We describe below the methods we use to estimate expected zonal hourly electricity market prices, monthly electricity market revenues and variable costs, monthly capacity market revenues, and overall profitability for the period between March 1, 2020 and December 31, 2022.
Zonal hourly electricity market prices
Profitability is estimated across two sets of electricity market prices: one set based on an electricity market price forecast published by the EIA in January 2020, prior to COVID19related shelterinplace orders, and another set based on actual historical prices between March and December 2020 and an electricity market price forecast published by the EIA in January 2021.
Each of the seven electricity market regions has multiple electricity market zones. The EIA publishes average monthly market price forecasts for each of the seven electricity market regions. Those monthly regional market price forecasts are converted to hourly zonal market price forecasts. Such a step is necessary to accurately model expected electricity market revenues, variable costs, and capacity market revenues, which are allocated on a zonal basis. The following procedure is performed to determine the forecasted hourly prices in a given month and electricity market zone:

1.
For a given month and electricity market zone and region (e.g., June, American Electric Power zone, PJM region), average prices in that month (e.g., June) are determined for each of the three years prior to 2021 for which we obtain historical data, 2018, 2019, and 2020.

2.
We compute the differences of those historical average prices with the corresponding monthly price forecast in the appropriate electricity market region (e.g., June 2020, PJM region) published by the EIA.

3.
The hourly prices from the historical month associated with the smallest difference that we compute in Step 2 are adopted as our hourly zonal forecast price profile.

4.
We shift the hourly zonal forecast price profile up or down by a constant value such that the average monthly zonal price (e.g., June 2020, American Electric Power zone) is equal to the average monthly regional price (e.g., June 2020, PJM region) published by the EIA.
That series of steps are applied to each forecast month and each zone in each electricity market region. Two sets of hourly price forecasts are developed for each zone: one set based on monthly price forecasts published by the EIA in January 2020, prior to COVID19related shelterinplace orders, and another set based on actual historical prices between March and December 2020, and monthly price forecasts published by the EIA in January 2021.
Monthly electricity market profits and variable costs
The electricity market revenue and variable operating costs for a given generation unit are estimated by determining the number of hours in a month in which that unit is online. We assume a generation unit is online for the hours in which the electricity market price is greater than or equal to the unitâ€™s variable cost of operation. For each month, we generate a price duration curve (PDC) in which we order hourly electricity prices from highest to lowest. The PDC is used to estimate total variable operating costs and electricity market revenues.
The use of PDCs is illustrated in Fig. 6. In Fig. 6, we show two PDCs that correspond to hourly electricity prices in June 2020 in the American Electric Power (AEP) zone in the PJM region. The prices in Fig. 6a reflect an electricity price forecast published by the EIA in January 2020, prior to shelterinplace orders, and the prices in Fig. 6b reflect actual prices in June 2020. The horizontal dashed lines reflect the variable operating cost ($/MWh) of a coal unit in the AEP zone, “Rockport ST1.â€ Monthly electricity market profits are shown in blue and monthly total variable operating costs ($) in yellow. The vertical gray lines indicate the numbers of hours in which it is profitable for Rockport ST1 to operate in each of the two scenarios.
Electricity market profits and variable operating costs are calculated for each of the 845 coalfired generation units in the seven electricity market regions in the U.S.
Monthly capacity market revenues
Four of the seven electricity market regions, MISO, New England, New York, and PJM, run annual or biannual generation capacity auctions in which those regional operators solicit bids from generation units to be available to provide capacity in a future capacity commitment period^{51}.
We assume that a generation unit bids into a capacity auction such that the unit can expect to be profitable if its bid clears in a given capacity commitment period. For a generation unit (u) that does not otherwise expect to be profitable in a given capacity commitment period (cp), that unit submits a capacity bid such that the present value of cash flows associated with its bid (B_{cp,u}) would cover the present value of the sum of its variable costs and fixed O&M costs (V_{cp,u} and F_{cp,u} respectively) net of the present value of electricity market revenues (E_{cp,u}). For a generation unit that does expect to be profitable in a given capacity commitment period, that unit bids zero dollars into the capacity auction for that period. Equation (2) shows the bidding behavior for generation units that do not expect to be profitable in electricity markets alone, in a given capacity commitment period.
$${B}_{{{{{mathrm{cp}}}}},u}={V}_{{{{{mathrm{cp}}}}},u}+{F}_{{{{{mathrm{cp}}}}},u}{E}_{{{{{mathrm{cp}}}}},u}$$
(2)
Capacity auction clearing prices are obtained or estimated for each capacity commitment period through 2022 for each of the four regions that run forward capacity auctions. Those clearing prices are established on a zonal basis. A generation unit that submits a bid that is equal to or lower than the auction clearing price receives capacity market revenues. A generation unit (u) that clears in a given commitment period (cp) in a given zone (z) receives capacity market revenue (C) in a given month (m) equal to the zonal auction clearing price (G_{cp,z}), in units of $/MWday, multiplied by the operating capacity of the unit (O_{u}) and the number of days in the month (n):
$${C}_{m,u}={G}_{{{{{mathrm{cp}}}}},z}times {O}_{u}times n$$
(3)
Capacity market revenues are calculated for every coalfired electricity generation unit in New England, New York, MISO, and PJM, and for every month in the period from March 1, 2020 to December 31, 2022.
Overall profitability for the period between March 1, 2020 and December 31, 2022
The overall profitability of each coalfired generation unit is estimated for the period between March 1, 2020 and December 31, 2022. The overall profitability (P) for each unit (u) is estimated as the sum of discounted cash flows in each month, where m ranges from 1 to 34, the number of months in the period. L_{m} is the monthly nominal net cash flow, and r is the WACC (Eq. (4)). We apply a monthly WACC of 0.38% that we derive from an annual WACC of 4.61%, consistent with the NREL Annual Technology Baseline 2019.
$${P}_{u}=mathop{sum}limits^{m}frac{{L}_{m}}{{(1+r)}^{m}}$$
(4)
The monthly nominal net cash flow (L_{m}) is the sum of monthly nominal electricity and capacity market revenues net of the sum of monthly nominal variable costs and fixed O&M costs. The profitability of every coal generation unit is calculated in two scenarios: a counterfactual scenario that relies on an electricity market price forecast published by the EIA in January 2020 prior to shelterinplace orders, and a scenario that reflects our current expectations and is based on actual prices in March through December, and a price forecast published by the EIA in January 2021.
Reporting summary
Further information on research design is available in the Nature Research Reporting Summary linked to this article.
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