The marginal price¶
The library prices one more kWh: what a flexible load's kWh in a slot costs the site, by the source that would serve it. PV that would have spilled costs the export given up; an import costs the import price; a kWh from the battery costs what the energy in the battery cost.
A flexible load needs the next kWh's cost¶
A load that can run at 13:00 or at 20:00 does not care what the house's energy cost on average. It cares what its kWh will cost in each slot. That is a marginal question: which source gives the kWh, and what does that source's energy cost?
Two things make the answer differ from the price on the tariff:
- A kWh of PV is not free. If the plant would have exported it, using it costs the export you gave up. If it would have been curtailed, it costs nothing.
- A battery moves energy in time. A kWh used at 20:00 may come out of the battery, which holds the afternoon's solar, or the night's grid energy, or both. The kWh costs what that energy cost, through the battery's losses and wear.
So the library projects the plant forward to see which source serves each slot, and what the battery will hold then.
Why not the average cost?¶
An average says what the energy that served the house cost, slot by slot, all sources blended. It fails in two ways.
At night it has no answer. The house runs on the battery. No source is producing in the slot, so the average cost of the slot's sources is 0/0. The battery needs a price of its own: what the energy it holds cost.
It flattens the signal a load needs. Take a day with a 20 kWh house load and a battery, an import price of 0.30 all day, export at 0.07, and losses ignored:
| Day | What happens | The price of a kWh | Imports billed | PV used, at the export it gave up |
|---|---|---|---|---|
| Sunny | the battery fills by 14:00 and spills; it carries the house through the night | 0.07 in every slot: the sun, or the battery's solar | 0 | 20 × 0.07 = 1.40 |
| Short | 12 kWh of PV, none spilled; the plant buys 8 kWh at 0.30 | 0.07 where the sun or the battery's solar serves it, 0.30 where the grid does | 8 × 0.30 = 2.40 | 12 × 0.07 = 0.84 |
On the short day the average cost is (2.40 + 0.84) / 20 = 0.162 in every slot, morning and evening alike. It hides the fact that matters: some hours run on the sun's energy and some on the grid's, and a load that runs in the first costs the site 0.07 a kWh, in the second 0.30.
The battery's price is an average too, but of one thing: the energy in the battery, the source the next kWh would come from. Which lot of that energy a kWh is "drawn" from is bookkeeping, so the library takes the battery's running average (why).
Does the money add up?¶
Charge every kWh the house used at its price, and compare with what the site actually paid: the imports billed, plus the PV used at the export it gave up.
| Day | Load at its price | Imports + PV used | Difference, R |
|---|---|---|---|
| Sunny | 20 × 0.07 = 1.40 | 0 + 1.40 | 0 |
| Short | 12 × 0.07 + 8 × 0.30 = 3.24 | 2.40 + 0.84 | 0 |
Losses ignored, the books balance exactly: each kWh pays what its own energy cost. With losses they still balance: a battery kWh's price includes the loss of the round trip, and the site paid for that loss in the extra solar or grid energy it stored. What is left is small and named:
- the discharge's wear, which the load pays and no bill shows: the battery's own account, for its life;
- the fill's bound, where the sun will refill the battery and a kWh is priced below what its energy cost (the opportunity cost): the load pays less than the energy cost, and the site keeps a kWh of the sun it would otherwise have spilled;
- the forecast's errors: the projection said the battery would hold one thing, and it held another.
The make-up alternative prices the battery's kWh by what replaces it instead. On the short day it says every kWh costs 0.30, because any kWh is made up by an import: the load pays 6.00 against 3.24, and R = 2.76 is the battery's arbitrage, the solar it stored at 0.07 serving the house in place of imports at 0.30.
Each slot is priced as an unannounced kWh¶
Each slot's price assumes the plant runs as forecast up to that slot, and asks what one more kWh there costs. A load that is already planned is in the load forecast. Two loads that both read a slot's price and both run there will each have assumed the other was absent; the supply stack says how much power each price holds for, so a scheduler can see when a load is too big for the margin.
The general rule¶
The marginal price of a slot is what one more kWh used in it costs the site: the export given up for PV that would have spilled, the import price for the grid, and for the battery what the energy it holds cost, through its losses and wear, but no more than the sun that will refill it. All of it under the plant's own dispatch, given the prices, the PV and load forecasts and the battery's state and lots now.
"Under the plant's own dispatch" matters: which source serves a slot, and what the battery will hold then, depend on what the plant will actually do with the battery, not on what an optimal controller could do with it (The plant model).