What is the objective that mathematically defines "grid stability" for a collectively owned local energy market?

Minimize, over time, the gap between total local supply and total local demand — and add a penalty for every unit imported from the external grid.

The market is treated as collectively owned with one primary objective: dynamic supply-demand balancing. Formally it minimises, summed over each time period, the absolute imbalance between everything supplied locally (DER generation, battery discharge, EV exchange, plus any external import) and everything demanded (load plus transmission loss). Two design choices matter:

• Absolute value. Both surplus and shortage are penalised — the target is a match, not a maximum output.
• Penalty on external import. A weighting term punishes reliance on power imported from the external grid, pushing the market to balance itself internally; importing is even constrained to happen only when local generation falls short of demand.

Transmission loss grows with the square of total power moved, so moving less power (staying balanced locally) is doubly rewarded.