Home Energy Management Optimization: A Worked Example

The Ravndal household is a hypothetical example we made up to make this concrete — not a real Solvicus customer, and the numbers below are illustrative, not measured data.

The Ravndal household has rooftop solar, a home battery, a heat pump, and an EV — four assets from four different manufacturers, each with its own app and its own simple threshold logic: charge the battery when it's cheap, run the heat pump on a schedule. None of them talk to each other, and none of them are actually minimizing anything.

Why this needs real optimization, not thresholds

A threshold rule (“charge the battery below €0.15/kWh”) reacts to the moment; it has no way to know that tomorrow's prices are cheaper still, or that the EV doesn't need to hit full charge until 7 AM and could shift its load to the overnight solar-adjacent window. Getting the genuinely cheapest 24 hours out of these four assets together means jointly scheduling continuous dispatch decisions — how much to charge or discharge the battery, run the heat pump, or draw for the EV, at every 15-minute interval — against a forecast, not a fixed threshold.

Framing it as an optimization problem

Take a concrete night: the EV must reach 80% state of charge by 7:00 AM, the home battery starts at 30% state of charge, and the heat pump is managing a building with a thermal dissipation rate of 0.5°C/hour, with an indoor comfort band of 20–22°C. Unlike crop rotation or staff scheduling, most of the decision variables here are continuous — how many kWh to charge, not whether to charge — so this leans closer to a linear program than a mixed-integer one; see LP vs. MILP for that distinction. The objective minimizes total electricity cost against tomorrow's dynamic hourly grid pricing and the local solar forecast, while every comfort and charge-deadline constraint holds throughout the night.

What comes back

The result is a full 24-hour dispatch schedule at 15-minute resolution: exactly when to charge or discharge the battery, when to run the heat pump and at what intensity, and when to draw power for the EV — coordinated across all four assets to hit the lowest possible cost while never leaving the EV short of its morning deadline or the house outside its comfort band.

Try it yourself

Home energy management is one of the illustrative use cases we build dedicated solvers for — see the full requirements and an example agent prompt on the Home Energy Management solver page. If you run a similar multi-asset dispatch problem, tell us about it — this is exactly the kind of problem we build custom solvers for.