Monte Carlo Sampling Techniques for the Efficient Estimation of Risk Metrics of a Stochastic Distribution Grid Power Demand Model

Abstract

The Distribution System Operator (DSO) Alliander has the ambition to explore possibilities of improving its predictive demand modelling applications. This research aims to contribute to one of these, the Advanced Net DEcision Support (ANDES) model, which provides detailed predictions for long-term capacity planning. This thesis pursues two main objectives: Firstly, the creation of a probabilistic power demand model which reflects the volatile nature of real customer demand in an adequate manner. Secondly, the development and evaluation of methods to estimate certain model output quantities of interest in a computationally efficient manner. To this end, variance reduction techniques have been investigated. Self-tuning Importance Sampling (IS) methods giving different weight to time steps and/or customer load profiles have been developed. In order to make the optimisation stage superfluous, additionally an approach to find a generalised asset distribution has been investigated. The essential finding from evaluating all considered methods was that their performance in terms of efficiency and accuracy depends mainly on two variables – the order of magnitude of the estimated quantity and the number of customers connected to an asset in question. For small assets and an estimated overload probability of the order 1e-5 or smaller, all profile IS methods and especially the generalised bin probability IS showed the strongest performance with average speed-ups of 5-30 times with respect to the reference method of sampling full annual traces. For assets with more than 80 customers and small overload probabilities, the profile IS methods were found to frequently produce estimates of a significantly too small order of magnitude. Conventional Monte Carlo (MC) sampling and time step IS, in turn, produced reliable estimates regardless of the number of customers. For assets of all sizes with an estimated overload probability of the order 1e-4 and larger, conventional MC sampling showed the best performance with speed-ups above 5 times. Overall, conventional MC sampling performed robustly in all circumstances, while IS demonstrated its potential to significantly increase the estimation efficiency of rare event probabilities in certain cases. To determine which magnitudes demand maxima and minima can potentially reach, Extreme Value Theory (EVT) has been applied. The computationally more efficient methods and extreme value inference were considered not compatible, sampling full annual traces appears to be required for a reliable estimation of maximum and minimum demand return levels. Based on the findings of this thesis, a flexible algorithm could be investigated in future research which employs IS for rare event probabilities and conventional MC sampling otherwise. For an integrated evaluation of all risk metrics, the algorithm could initially sample 200 entire annual traces to be used for extreme value inference.