  Battery storage, particularly residential battery storage coupled with
rooftop PV, is emerging as an essential component of the smart grid technology
mix. However, including battery storage and other flexible resources like
electric vehicles and loads with thermal inertia into a probabilistic analysis
based on Monte Carlo (MC) simulation is challenging, because their operational
profiles are determined by computationally intensive optimization.
Additionally, MC analysis requires a large pool of statistically-representative
demand profiles to sample from. As a result, the analysis of the network impact
of PV-battery systems has attracted little attention in the existing
literature. To fill these knowledge gaps, this paper proposes a novel
probabilistic framework to study the impact of PV-battery systems on
low-voltage distribution networks. Specifically, the framework incorporates
home energy management(HEM) operational decisions within the MC time series
power flow analysis. First, using available smart meter data, we use a Bayesian
nonparametric model to generate statistically-representative synthetic demand
and PV profiles. Second, a policy function approximation that emulates battery
scheduling decisions is used to make the simulation of optimization-based HEM
feasible within the MC framework. The efficacy of our method is demonstrated on
three representative low-voltage feeders, where the computation time to execute
our MC framework is 5% of that when using explicit optimization methods in each
MC sample. The assessment results show that uncoordinated battery scheduling
has a limited beneficial impact, which is against the conjecture that batteries
will serendipitously mitigate the technical problems induced by PV generation.
