Probabilistic modelling of parameter variability for analysing grid-connected LV feeders with DG

There is mounting pressure on utilities worldwide to incorporate renewable energy sources in their distribution of electricity. The inclusion of distributed generation (DG) on feeders connected to the grid presents significant problems when feeder performance must be assessed. Two issues arising from the inclusion of DG are voltage regulation and reverse power feed. There is variability in the generation of power from solar panels or from wind turbines due to daily solar cycles and seasonal (weather related) changes. And then there is the daily and seasonal variability due to the stochastic behaviour of domestic loads. Together these present formidable challenges to the analyst. Frequently the problem presents itself when an existing feeder is required to host randomly located elements of embedded generation. This is different from a design analysis that includes both feeder and optimal location of DG. Clearly with so much variability, the conventional approach of using deterministic methods with `average values´ for the input parameters (loads and DG), is less than adequate. For a more realistic approach time-dependent statistical models are required to describe the variability of these kinds of load and generation. Whether the statistical approach of analysing the behaviour of a feeder uses Monte Carlo simulations or a direct probabilistic method, load and generation variability require time-based modelling. This paper presents an approach for modelling both loads and DG as probability Beta probability density functions (PDFs).