On the Correlation between Prosumers in Probabilistic Analysis of Low Voltage Distribution Systems

Abstract

In LV systems, Probabilistic Load Flow techniques have been developed in order to accurately assess the uncertainty associated to fluctuating PV generation and are based on the use of pseudo-sequential Monte Carlo simulations. Those probabilistic tools are practically developed on the direct basis of the data provided by smart meters or on irradiance measurements. Based on this information, the statistical behavior of each PV generation unit (prosumer) is defined for each quarter of an hour of a “typical day” (per month or, even, per year) and a sampling on the exchanged power with the grid is made for each simulated quarter of an hour. Currently, when sampling PV generation in the Monte Carlo framework, no particular attention is paid on the correlation existing between PV units. Practically, this correlation could change with time and will influence the behavior of the LV network. In that way, in this contribution, a fast incremental algorithm is implemented and repeated for each quarter of an hour of each defined “typical day”. Thanks to this non-iterative approach, clusters of PV generation are defined for each quarter of an hour and are based on a pre-defined geographical correlation threshold. It is shown that the correlation between PV units connected to the same LV system stays high for each useful 15min interval of the day and that, practically, all PV generation units can be grouped in a single cluster and considered as entirely correlated. The same process is conducted for the load and the correlation between load and PV generation for each customer is also taken into account. Finally, in order to demonstrate the interest of the proposed study, a new sampling process based on the defined PV/load clusters is implemented and the collected indices (probability of overvoltage…) are compared with the ones computed when only considering complete independency between all the connected LV customers.
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