Moving beyond Exceedance Probabilities for Assessing Solar and Wind Energy Production Risks

Renewable energy investment decision makers generally rely on exceedance probabilities (e.g. P90: the value that will be exceeded 90% of the time) of projected annual power generation to evaluate future financial risks. These point estimates of probability distributions are generally derived from limited historical weather data and unadjusted for climate change. As a result, exceedance probabilities are (1) hampered by small sample sizes and climate biases, (2) often misinterpreted and incompatible with a theoretically sound probabilistic decision making framework, and (3) unable to properly estimate distributions of extreme events. In this paper, we use a real-world solar production example to demonstrate successive improvements to the standard industry practice via stochastic simulations, Conditional Value at Risk (CVaR), and Extreme Value Analysis (EVA).

Taking a representative set of 100 utility-scale solar sites in the continental US, we consider the problem of estimating the lower tail of annual mean power generation–in other words, the production risk from especially cloudy years. Unfortunately, satellite-based localized historical irradiance data is only available since 1998, causing the results of standard exceedance probability estimation to necessarily be noisy interpolations of order statistics from small and sequentially correlated data sets.

Turning to problem (1) above, we note that these estimates do not account for climate trends–and that no amount of interpolation can make a reliable P99 estimate from 25 data samples. We therefore use our historical weather data across the 100 sites (incorporating site-to-site weather correlations to ameliorate single-site weather data paucity issues) to create localized stochastic weather simulations which both explicitly account for trends in climate and can generate an arbitrary number of independent simulated years of weather data. We verify that our simulation data is realistic and then generate 1000 simulation runs at each location, allowing us to calculate robust and climate-aware exceedance probabilities.

While exceedance probabilities are often thought of as expected power predictions given an extreme event, they actually represent the less relevant (and unrealistically optimistic) maximum production in an extreme event (problem (2)). The more useful expectation is given by the probability weighted integral of production across the tail of the annual production distribution–and is known as the Conditional Value at Risk (CVaR). CVaR takes expectations and uncertainty into account, arriving at an actionable metric appropriate for risk assessment and investment decisions. Notably, CVaR diverges significantly from its exceedance probability counterparts, with the CVaR estimate of annual production in our experiment given a 10th percentile event on average 38% lower than the corresponding P90 exceedance value.

Rare events, however, still require significant interpolation (Problem 3). With 1000 simulation runs, one has only 50 examples of 5% events and 10 examples of 1% events in expectation, making CVaR on these events still a somewhat noisy and sample-dependent metric. Instead of naïvely increasing our experiment size to a technically infeasible and data-inefficient number of simulation runs, we use Extreme Value Analysis (EVA) to fit distributions to the extremes of our weather data. We compare results from bloc-maxima and peaks-over-threshold estimates of tail distributions and calculate CVaR, estimate extreme quantiles, and investigate worst-case scenarios for potential renewable energy investments.

Finally, we compare results from our final architecture of EVA and CVaR on stochastic simulations with the traditional approach of exceedance probabilities on raw historical time series. We find the final architecture to be better for actionable risk assessment, more theoretically sound, and more able to account for the effects of climate trends.