How inputs become prices

The question

If I use one more kWh in this slot, what does it cost my site?

A scheduler for a flexible load asks this for every slot of the next two days and runs the load where the answer is low. The answer is rarely the import price:

• On a sunny afternoon with a full battery, one more kWh is PV that would have been exported, so it costs the export you give up.
• On the evening after, the battery serves the house with the day's solar. A kWh from it costs the export that solar gave up, plus the round trip's loss and the battery's wear: about 0.10 in the worked day, against an evening peak of 0.45.
• After a night of charging from the grid, the battery holds energy bought at the night rate, and a kWh from it costs about that, plus the losses: 0.22 for energy bought at 0.18.
• A battery filled from the grid, with a sunny day ahead, costs about the export price. Kept full, it would leave no room for the day's sun; drawn down, the sun refills it.

The library works out which, slot by slot.

The steps

flowchart TD
    A["Read each input as it stood at the moment<br/>(forecasts received by then, values in force then)"] --> B["Align onto 10-minute slots<br/>over a 48-hour horizon"]
    B --> C{"Every input usable?"}
    C -- "no" --> F["Fallback: every slot at the import price,<br/>causes named"]
    C -- "yes" --> D["Cut PV scenarios<br/>from the forecast's quantiles"]
    D --> E["Project the plant once per scenario:<br/>where every kWh goes, slot by slot"]
    E --> G["Price one more kWh in each slot:<br/>its source now; a battery kWh at<br/>what its energy cost"]
    G --> H["Expected price, pessimistic price,<br/>certainties, regime, surplus, values by source"]

1. Read the inputs as they stood. Each forecast as received by the moment, each measured value in force then. Nothing received later is read, so a replay of the past cannot look ahead (Series and forecasts).
2. Align them onto slots: 10 minutes each, 48 hours ahead by default.
3. Check every input can be used. If one cannot, the valuation falls back to the import price and names why (Missing and stale inputs).
4. Cut PV scenarios. The forecast's quantiles (Solcast's p10, p50 and p90: powers the PV falls short of one time in ten, half the time and nine times in ten; or any other levels with the median) become ten equally likely PV days (PV scenarios and certainty).
5. Project the plant. For each scenario, the plant model says where every kWh goes: to the house, the battery, the grid.
6. Price one more kWh in each slot by what serves it. PV spilling now costs the export it gives up; an import, the import price. A kWh from the battery's cycle costs what the energy in the battery cost, run forward along the projection, plus the discharge's loss and wear (What a stored kWh is worth).
7. Look ahead for a fill. Where the sun will refill the battery before it needs the grid, a kWh drawn costs no more than that sun: a full battery must not be kept full at the cost of the day's PV (The make-up rule).
8. Average over the scenarios, and say how sure the average is.

The pages

Page	The question it answers
The marginal price	Why price one more kWh, and not the average one?
What a stored kWh is worth	What a battery kWh costs, and why it is what its energy cost
The make-up rule	What makes up a kWh taken from the battery, and when that sets the price
PV scenarios and certainty	How an uncertain forecast becomes one price
Regimes and surplus	How a slot's regime and surplus are read from the projection
The battery's lots	Where the energy in the battery came from, and what it cost
The live value	The price now, from the meters, between valuations
Missing and stale inputs	Why a missing input moves the price toward the import price
Scope	What a client brings, and what the library can't model
Requirements	What the library holds itself to (R-1 to R-9)