Industry: Environmental Product: ModelRisk Application: Evaluating Uncertainty in Renewable Energy Projects
A renewable-energy developer brought a 150 MWac solar PV project to its investment committee on a single deterministic line: a long-run yield of about 274 GWh in year one, a power-purchase price, a capex number, and an internal rate of return that cleared the 8% hurdle. The committee approved it. Then the lenders' technical advisor asked the question that sinks single-point business cases: what is the P90 energy? Project finance is not sized on the expected generation -- it is sized on the 90%-exceedance level, the low-resource year the debt must still service. A point estimate has no P90. It cannot be financed.
The team rebuilt the asset in ModelRisk as a probabilistic yield-and-economics model: monthly plane-of-array resource with a persistent annual anomaly, performance ratio, availability, degradation over a 25-year life, and uncertain PPA price and capex feeding NPV and project IRR. The first output banks ask for is the generation distribution and its P50/P90 split.
The median year-one generation is P50 = 274 GWh, matching the deterministic line. But the financeable number sits lower: P90 (the 90%-exceedance level) = 257 GWh, while the upside P10 = 292 GWh. The P90 is 93.5% of the P50 -- an 18 GWh-per-year haircut the single line never carried, and the level the debt-sizing model actually uses.
Solar yield is the product of several uncertain factors, and a deterministic model multiplies their central values and stops. The resource varies year to year; the performance ratio depends on soiling, temperature and inverter clipping; availability is never 100%; and the panels degrade. Treat each at its mean and you get a confident 274 GWh that describes no actual year. The subtle trap is the resource itself: irradiance varies month to month, but the dominant driver of annual energy is a whole-year anomaly -- a sunny or cloudy year shared across all twelve months. Model the months as independent and they average away, collapsing the annual spread the bank cares about. The model imposes a persistent annual resource anomaly, and the check confirms it bites: the year-one anomaly correlates +0.90 with year-one energy. Because the anomaly is shared within each year rather than i.i.d. across months, the spread survives -- which is exactly why the P90 sits a real 18 GWh below the P50 instead of a fraction of that.
Energy is only half the bankability test. Feeding the generation distribution, an uncertain PPA price (Triangular $52-78/MWh) and uncertain capex (Triangular $0.78-1.08/Wac) through 25 years of cash flow produces a full IRR distribution against the 8% hurdle.
The P50 IRR is 9.7%, comfortably above the 8% hurdle, and the probability the project clears the hurdle is 85% with a 96% probability of positive NPV (mean NPV $33.5M, P10 $8.3M). That is a fundable project -- but the 85% is the honest headline, not the 9.7%. The P10 IRR of 7.7% sits just below the hurdle: in roughly one resource-and-price scenario in seven, the project under-clears, which is precisely the tail a minimum-revenue floor or a tighter PPA is there to cover.
The P90 is a year-one figure, but the asset has to perform for 25 years against steady degradation. The fan chart shows the generation cone narrowing-and-sliding over the life.
Median generation falls from 274 GWh in year one to 240 GWh by year 25 -- degradation alone erodes about 12% of median energy over the life -- while resource variability keeps each year's P10-P90 band open. A debt-service profile sized on year-one P90 with no degradation glide-path would be progressively short; the fan is what lets the structuring team match the repayment schedule to the declining floor.
The tornado ranks the one-at-a-time P10-to-P90 swing of each input on project NPV.
The PPA price moves NPV by $44M across its range -- the dominant driver -- ahead of capex at $25M and the resource anomaly at $23M; the performance ratio, degradation and opex matter far less. The ranking redirects effort: locking the PPA price and tightening the capex contract de-risk the return far more than refining the engineering loss factors the technical team naturally gravitates to.
For a renewable project, the number that gets financed is not the expected yield -- it is the P90, and the 18 GWh between the P50 and the P90 is the difference between a deterministic line that looks bankable and a distribution that actually is.