  This paper proposes a zone-based privacy-preserving billing protocol for
local energy markets that takes into account energy volume deviations of market
participants from their bids. Our protocol incorporates participants' locations
on the grid for splitting the deviations cost. The proposed billing model
employs multiparty computation so that the accurate calculation of individual
bills is performed in a decentralised and privacy-preserving manner. We also
present a security analysis as well as performance evaluations for different
security settings. The results show superiority of the honest-majority model to
the dishonest majority in terms of computational efficiency. They also show
that the billing can be executed for 5000 users in less than nine seconds in
the online phase for all security settings, demonstrating its feasibility to be
deployed in real local energy markets.
