Many electricity market participants have a requirement to calculate the probabilistic risk measures, such as earnings at risk (EaR) and value at risk (VaR), for compliance reporting purposes. This requirement is currently hindered by the lack of analytical representations for forecasts of demand (load) and price curves; this motivates numerical simulation and models that need extensive calibration. In this paper, we derive an analytical representation of a state demand forecast which is the aggregated usage of all electricity consumers in a particular region (such as New South Wales or Victoria). We have used two probabilistic benchmarks from the Australian energy market operator as input, which are expressed as forecasted probability of exceedance.

Due to a number of considerations, including asymmetry of these quantiles with respect to the median, we have selected a series of truncated lognormal distributions with two parameters. The procedure of finding these parameters has been reduced to solving (for every half-hour) a single nonlinear equation. As a result, the two-year half-hourly forecast (expected curve) and demand volatility are found by explicit integration with the set of derived distributions. We have also tested an alternative method based on simplifying assumptions; using a nontruncated lognormal distribution, we found that under the test conditions this method produces an identical forward load and volatility curve.