Monte Carlo simulation

Each uncertain input gets a probability distribution instead of a single value. Annual irradiance might be normal, with a mean and a standard deviation. Capital cost might be triangular, with a low, a likely and a high value. The model draws one value for each input, runs, and records the outputs, such as energy, IRR or minimum DSCR. It repeats this thousands of times. Sorting the results gives their distribution. The median run is the P50, and the value exceeded in 90% of runs is the P90.

Material relationships between inputs should be preserved when sampling. Low wind can come with high prices, partly offsetting lost generation revenue; a construction delay can come with higher cost, compounding the downside. Ignoring these relationships can overstate or understate risk. The sampling error of a percentile falls with the square root of the number of runs N, so going from 2,500 runs to 10,000 halves it. The results can be no better than the input ranges. A simulation built on guessed ranges gives precise-looking numbers with little behind them.

Projects face many uncertainties at once, and the worst outcomes come when several go wrong together. Monte Carlo shows how likely those combinations are. Lenders use the low percentiles to size debt and set reserve accounts. Developers use the spread to price risk into a bid or to decide how much revenue to hedge. For a merchant plant or a battery, whose revenue depends on the path prices take, it is often the only practical way to see the downside.