Probabilistic Inversion Techniques in Quantitative Risk Assessment for Power System Load Forecasting

Expert judgment is frequently used to assess parameter values in quantitative risk assessment. Experts can however only be expected to assess observable quantities, not abstract model parameters. This means that we need a method for translating expert assessed uncertainties on model outputs into uncertainties on model parameter values. So we use Probabilistic Inversion (PI) method. The probability distribution on model parameters obtained in this way can be used in a variety of ways, but in particular in an uncertainty analysis or as a Bayes prior. In this paper probabilistic inversion problems are first defined, existing algorithms for solving such problems are also discussed and the algorithms based on iterative algorithms are introduced. Those computational algorithms have proven successful in various projects. Such techniques are indicated when we wish to quantify a model which is new and perhaps unfamiliar to the expert community. There are no measurements for estimating model parameters, and experts are typically unable to give a considered judgment. In such cases, experts are asked to quantify their uncertainty regarding variables which can be predicted by the model. Applications to power system load forecasting in NingXia province of China is discussed. This study illustrates two such techniques, Iterative Proportional Fitting (IPF) and PARmeter Fitting for Uncertain Models (PARFUM) which provide useful tools for the practicing quantities risk assessment. In addition, we also illustrate how expert judgment on predicted observable quantities in combination with probabilistic inversion may be used for model validation.