Voltage modelling of LV feeders with dispersed generation: Probabilistic analytical approach using Beta PDF

- Probabilistic analytical transform of load currents calculates voltage profile on LV feeders with loads and DG.
- Applicable to feeders with balanced or unbalanced connection of single phase loads or DG.
- Fast calculation gives consistent, repeatable results.
- Risk or confidence levels selectable by the user.
- Complete calculation algorithm available.

The published probabilistic analytical modelling of voltages on a low voltage (400/230 V) feeder with passive loads is extended and modified to calculate the variation with dispersed generation (DG). The existing method was based on representing residential loads as Beta distributed currents at any interval of demand, usually the maximum demand or the interval with maximum voltage drop. Now, in addition to probabilistic loads modelled as positive currents out of a feeder, DG is included by modelling the injection as negative current variables described by their Beta PDFs. The statistical elements are manipulated by keeping the load and generation notionally separate at each node so that superposition can be applied to assess separately their effects. This analytical approach calculates the probable voltage drop or rise on the feeder for a selected level of probabilistic confidence. The proposed approach is compared with Monte Carlo simulations. All steps required to perform the calculations are linear and fast because they require no iterations.

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