Group captivity

Two batteries are each allowed both PV systems, and neither is individually stuck — but together they need every watt the two PV systems make. Deciding feasibility one sink at a time cannot see that; this is the case the max- flow solver exists for.

What this case shows

• Feasibility is a property of groups of sinks, not of single sinks.
• A flexible sink must not take local power a tight group needs.
• When restrictions cannot all be honoured, the sink with the fewest permitted alternatives is served first and the deficit falls on the sinks that had somewhere else to go.

Each snapshot below is one set of readings on this wiring, drawn as a flow chart — how to read it.

Hall tight pair

Group captivity · snapshot 01

bat_c idle. {bat_a, bat_b} exactly exhaust east+west, so the 200 W home load must be served entirely from the grid.

Reading	W	Of gross	Share	Made of
Gross power	400 W	1		grid 200 W · east 100 W · west 100 W
Grid import	200 W	1/2		grid 200 W
Grid export	0 W	0		nothing exported
PV production	200 W	1/2		east 100 W · west 100 W
Charging power	200 W	1/2		bat_a 100 W · bat_b 100 W
Discharging power	0 W	0		no battery discharging
Standby power	0 W	0		no standby draw
Self-consumption	200 W	1/2		grid 200 W
Metering imbalanceok	0 W	0		readings reconcile exactly
Home base load	200 W	1/2		unmetered remainder of consumption

Idle: bat_c · 0 WRibbon widths are watts in every view. Hover, focus or tap a ribbon to see the sensor behind it.

Unsatisfiable overlap

Group captivity · snapshot 02

bat_c now draws 100 W and is captive to east alone. Captive demand (300 W) exceeds local supply (200 W): someone must be deficited.

Reading	W	Of gross	Share	Made of
Gross power	400 W	1		grid 200 W · east 100 W · west 100 W
Grid import	200 W	1/2		grid 200 W
Grid export	0 W	0		nothing exported
PV production	200 W	1/2		east 100 W · west 100 W
Charging power	300 W	3/4		bat_a 100 W · bat_b 100 W · bat_c 100 W
Discharging power	0 W	0		no battery discharging
Standby power	0 W	0		no standby draw
Self-consumption	100 W	1/4		grid 100 W
Metering imbalanceok	0 W	0		readings reconcile exactly
Home base load	100 W	1/4		unmetered remainder of consumption

▲ a restriction is relaxed: the readings cannot be met without it.Ribbon widths are watts in every view. Hover, focus or tap a ribbon to see the sensor behind it.

Why this case exists

This is the case the max-flow solver exists for, and it is worth walking through slowly.

bat_a and bat_b may each charge from either PV system. Neither is individually stuck — either PV system could cover either battery. But together they draw exactly what the two PV systems make, so as a pair they need every local watt. Any allocation that gives local power to somebody else leaves one of them short.

Asking "what must this sink take from this source?" one sink at a time cannot see that. It is Hall's condition, which quantifies over every subset of sinks, and no per-sink patch reproduces it. Watch the home base load in the first snapshot: it is unrestricted and could physically take solar, but it is served entirely from the grid because the pair have first claim.

The second snapshot then overloads the same wiring deliberately, and that is where the model runs out of settled answers.