Recent Italian regulation rewards Local Energy Communities (LECs) through two distinct channels: an incentive for virtual shared energy and market access for distributed batteries that provide up-regulation. These incentives often conflict

as charging batteries to maximize the shared energy limits the capacity to provide ancillary services

and vice versa. Currently

quantitative tools for effectively balancing these objectives are lacking respecting the electrical constraints of the low-voltage grid. To fill this gap

a multi-objective optimization is proposed that co-maximizes the revenue from up-regulation and the virtual shared energy reward

under the constraint that the daily energy bill does not exceed a predefined baseline. The implemented mathematical programming formulation utilizes multi-objective second-order cone programming (SOCP) with linear constraints to incorporate the network's physical constraints. Linearization and decomposition techniques are employed to simplify the problem. By adjusting the physical constraints of the network

the impact of energy communities on the distribution network can also be evaluated with different objectives. The model allows the representation of real peer-to-peer trading

quantifying its effects on both revenue streams and voltage profiles as well as power losses. Trade-off analyses performed on an 84-bus radial distribution network

under both constant and variable prices

show that the framework adapts smoothly to market volatility

highlighting when it is advantageous to prioritize up-regulation and when it becomes preferable to maximize the virtual shared energy incentive.