Sizing the Energy: Why Four Hours and Not Five
Four hours is the industry default. It appears in term sheets, in procurement specifications and in investment papers, usually without a calculation behind it.
There is one, and it produces an uncomfortable result. On the same price shape, the same costs and the same cost of capital, the optimal duration is:
1 cycle per day → 2 hours
1.4 cycles per day → 3 hours
2 cycles per day → 4 hours
Duration and cycling frequency are not two decisions. They are one. You cannot choose how many hours without choosing how hard to run, and four hours is only the right answer for an asset that can and will cycle roughly twice a day.
This post builds the calculation: the marginal hour's revenue, the marginal hour's cost, where they cross, and the physical limit that caps the whole thing.
ℹ️ Note: The price shape is a single representative volatile day used to demonstrate method. Real analysis needs the full 8,760-hour series for the specific node. The structure of the result generalises; the specific crossing point does not.
What Is the Duration Decision?
The choice of how many megawatt-hours to build behind a given megawatt of power. Expressed as hours — a 100 MW battery with 400 MWh is a four-hour battery — and decided by comparing what each additional hour earns against what it costs.
Both sides of that comparison have a specific shape, and the shapes are what make the answer non-obvious.
The Marginal Hour Earns Less Than the One Before It
Because the battery takes the best hours first.
A one-hour battery discharges into the single most valuable hour of the day and charges in the single cheapest. A two-hour battery adds the second best hour and the second cheapest — both worse than the first pair, by construction.
On the representative day, at 88% round-trip efficiency:
| Hour added | Marginal revenue per cycle |
|---|---|
| 1st | $85.91/MW |
| 2nd | $77.77 |
| 3rd | $67.77 |
| 4th | $50.36 |
| 5th | $32.09 |
| 6th | $26.82 |
| 7th | $19.82 |
| 8th | $13.68 |
The decline is not gentle. The eighth hour earns 16% of what the first does. And the shape is a property of the price distribution, not of the battery — a market with a flatter daily profile has a steeper decline, and a market with two distinct peaks has a flatter one.
This is why duration decisions do not transfer between markets. The same asset, the same cost, a different price shape, and a different answer.
The Marginal Hour Costs the Same Every Time
Because an extra hour buys cells and nothing else.
As the next post sets out in detail, battery cost splits into a power component and an energy component:
Total cost ($/kW) = Pack cost ($/kWh) × duration (hours) + BOS cost ($/kW)
The balance of plant — inverters, transformers, controls, civil works, grid connection — is incurred once per megawatt. Adding an hour adds only the pack. So the marginal cost of each hour is constant, at the pack cost:
Pack cost $180/kWh
Per MW, per added hour $180,000
Annualised at 12% over 15 years (÷ 6.8109) = $26,428/MW/yr
A flat line against a declining one. The optimum is where they cross, and everything now depends on how many times a year the marginal hour gets used.
Where They Cross
Revenue per year is the marginal hour's revenue per cycle multiplied by the number of cycles. So the number of cycles moves the entire revenue curve up or down against a fixed cost line.
| Hour | At 365 cycles | At 730 cycles | Annual cost |
|---|---|---|---|
| 1st | $31,357 | $62,714 | $26,428 |
| 2nd | $28,387 | $56,774 | $26,428 |
| 3rd | $24,737 | $49,474 | $26,428 |
| 4th | $18,383 | $36,765 | $26,428 |
| 5th | $11,713 | $23,426 | $26,428 |
| 6th | $9,789 | $19,577 | $26,428 |
Read down each column to the last row that clears the cost.
At one cycle a day, the optimum is two hours. The third hour earns $24,737 against a $26,428 cost and does not pay for itself.
At two cycles a day, the optimum is four hours. The fifth hour earns $23,426 against the same cost and stops.
Same battery, same market, same cost of capital. The only thing that changed was how often it runs.
So "Four Hours" Is a Statement About Cycling
That is the substantive finding, and it reframes the question.
A specification of four hours is implicitly a commitment to cycling roughly twice a day. If the asset ends up cycling once — because the price shape has a single peak, because the warranty limits throughput, or because the dispatch strategy is more conservative than the model assumed — then two of those four hours were capital that will not earn its cost.
Conversely, an asset genuinely able to cycle twice daily and built at two hours has left revenue on the table.
The practical instruction is to derive the duration from the cycling strategy rather than choosing both independently. And the cycling strategy is itself constrained, which brings in the limit that caps everything.
The Physical Ceiling
There are only twenty-four hours in a day, and a cycle uses them twice.
Discharging for D hours requires charging for D / RTE hours, because round-trip efficiency means more energy goes in than comes out. So each cycle commits:
Hours per cycle = D + D / RTE = D × (1 + 1/0.88) = D × 2.136
Run that against the possibilities:
| Cycles/day | Duration | Hours committed of 24 | |
|---|---|---|---|
| 1 | 2 hours | 4.3 | |
| 1 | 4 hours | 8.5 | |
| 1 | 6 hours | 12.8 | |
| 2 | 2 hours | 8.5 | |
| 2 | 4 hours | 17.1 | tight |
| 2 | 6 hours | 25.6 | impossible |
The last row is not a commercial judgement. Twenty-five point six hours do not exist in a day.
Maximum duration at 2 cycles/day = 24 ÷ (2 × 2.136) = 5.62 hours
A two-cycle strategy caps duration at about 5.6 hours, and round-trip efficiency is what makes the cap tighter than the naive arithmetic of twenty-four divided by four events. Below 88% efficiency the ceiling falls further.
That ceiling is the reason the industry converged where it did. Four hours at two cycles commits 17.1 of 24 hours — demanding but feasible, with enough slack for the charge and discharge windows to sit where the prices actually are rather than wherever there is room.
What Would Move the Answer?
Four things, and none of them is the battery.
A wider price shape. Larger spreads lift the whole revenue curve and push the crossing point later. This is the mechanism by which growing renewable penetration lengthens optimal duration — more midday depression and steeper evening ramps mean more valuable hours to fill.
A second daily peak. A market with distinct morning and evening peaks supports two cycles naturally. One with a single evening peak does not, and no amount of willingness to cycle creates a second spread that is not there.
Cheaper cells. The marginal cost line falls, so more hours clear it. This is the dominant long-run driver, and it is why optimal duration has been lengthening.
Capacity accreditation. Where duration buys accreditation in steps — 55% at four hours, 65% at six on the ladder from the Series C post — a step can justify an hour that arbitrage alone would reject. That is a genuine reason to build past the arbitrage optimum, and it should be identified as such rather than folded into a single revenue number.
So Why Not Five?
The title's question, and the honest answer is that in a market with capacity accreditation, five is often right and four is the arbitrage-only answer.
The accreditation ladder from the Series C post steps from 55% at four hours to 65% at six. That is ten percentage points of accreditation spread across two hours:
Accreditation step, 4 → 6 hours (65% − 55%) × $118,625 = $11,862/MW/yr
Per hour of duration ÷ 2 = $5,931/MW/yr
Add that to the arbitrage value of the fifth hour at two cycles a day:
Fifth hour, arbitrage = $23,426
Fifth hour, accreditation contribution = $5,931
--------
Total = $29,357
Marginal cost = $26,428
→ clears
The sixth hour does not: $19,577 plus $5,931 is $25,508 against the same $26,428.
So on these assumptions the answer set is:
| Arbitrage only | With capacity accreditation | |
|---|---|---|
| 1 cycle/day | 2 hours | 2 hours |
| 2 cycles/day | 4 hours | 5 hours |
Four is the right answer in an energy-only market. Five is the right answer where capacity accreditation is available and the asset can cycle twice. The industry's default of four is therefore correct for ERCOT-type markets and conservative by roughly one hour for PJM-type ones — which is a real, computable gap that a standard specification conceals.
The instruction that follows: identify which hour is justified by which revenue. An hour that clears only because of accreditation is an hour exposed to the accreditation ladder being revised, and the Series C post documented that those ratings fall as penetration rises. That is a materially different risk from an hour justified by arbitrage.
Why the Answer Has Been Lengthening
Because the cost line has been falling faster than the revenue curve has been flattening.
Run the same calculation at a pack cost of $120/kWh instead of $180:
Marginal cost at $180/kWh = $26,428/MW/yr
Marginal cost at $120/kWh = $17,619/MW/yr
| Arbitrage only | With accreditation | |
|---|---|---|
| 1 cycle/day | 2 → 4 hours | 2 → 5 hours |
| 2 cycles/day | 4 → 6 hours | 5 → 7 hours |
A one-third reduction in cell cost roughly doubles the optimal duration at one cycle a day. Nothing about the market changed; the marginal hour simply became cheap enough that hours previously rejected now clear.
That is the mechanism behind the industry's drift toward longer durations, and it means a duration standard set at one cell price is wrong at another. A specification of four hours written when cells were expensive is not a technical conclusion — it is a price observation that has since been overtaken.
Two implications worth carrying.
Duration decisions should be dated. A configuration standard adopted three years ago encodes a cost that no longer applies, and re-running the calculation is cheap.
Procurement timing interacts with configuration. A project procuring cells in a falling market should be asking whether its duration specification was set against the price it will actually pay, or against the price when the specification was written.
What If the Offtake Specifies It?
The case where none of the above is a decision.
Under a tolling agreement the toller buys dispatch rights over a defined power and duration, and the configuration is a contractual term rather than an optimisation output. The calculation in this post does not disappear — it becomes a negotiating input instead of a design one.
Three uses for it in that setting.
Pricing the toll. If the toller specifies four hours and the arbitrage-plus-accreditation optimum is five, the owner is building a configuration that leaves value unrealised, and the capacity payment should reflect that.
Testing the throughput limit. The toll's cycle cap and the duration together determine the hours committed per day. A four-hour toll permitting two cycles commits 17.1 hours of every 24 — which is tight, and worth confirming the toller understands before it is agreed rather than after.
Establishing who benefits from cheaper cells. A long toll signed at today's configuration fixes the duration for its term while cell prices continue to fall. Whether the owner may augment to a longer duration, and who captures the resulting value, is a clause worth having.
How Do You Build the Duration Calculation in Excel?
As two curves and a crossing, with the cycling assumption stated as an input rather than buried.
The marginal revenue curve
Sort the day's prices ascending: s = SORT(prices)
For duration d:
Sell(d) = SUM(LARGE(s, 1:d))
Buy(d) = SUM(SMALL(s, 1:d)) / RTE
Margin(d) = Sell(d) − Buy(d)
Marginal_Hour(d) = Margin(d) − Margin(d−1)
The marginal cost line
Marginal_Cost = Pack_$/kWh × 1,000 ÷ Annuity(Cost_of_Capital, Life)
= 180,000 ÷ 6.8109 = $26,428/MW/yr
The optimum
Optimal_Duration = MAX d such that Marginal_Hour(d) × Cycles ≥ Marginal_Cost
The feasibility check that must sit alongside it
Hours_Committed = Duration × Cycles × (1 + 1/RTE)
IF Hours_Committed > 24 THEN infeasible
Max_Duration = 24 ÷ (Cycles × (1 + 1/RTE))
A model that returns six hours at two cycles a day has returned a configuration that cannot be operated, and nothing downstream of it is meaningful.
The output that matters
PF_OptimalDuration (hours)
PF_ImpliedCyclesPerDay the assumption it depends on
PF_MaxFeasibleDuration the physical ceiling
PF_MarginalHourValue at the chosen duration
The second line is the one to publish alongside the first. A duration recommendation without its cycling assumption is half a statement, and the half that is missing is the one that moved the answer from two hours to four.
ℹ️ Note: Run this on the full annual price series, not a representative day. A single day fixes the shape and removes the seasonal variation that determines how many days actually support two cycles — which is the input the whole calculation turns on.
Why the annual series matters more than the method
The representative day above makes the mechanism visible and overstates the precision of the answer, for a specific reason worth naming.
Cycling frequency is not a choice made once. It is a daily outcome of whether that day's price shape contains a spread wide enough to clear the round-trip efficiency loss and the degradation cost. Some days offer two such spreads, many offer one, and a meaningful number offer none worth taking.
So "two cycles a day" is not an operating policy — it is an annual average of a highly variable daily count, and the distribution behind it matters as much as the mean. A year averaging two cycles made up of 150 two-cycle days, 150 one-cycle days and 65 idle days is a different asset from one cycling steadily twice every day, even though both produce 730 cycles.
Two consequences for the duration calculation.
The marginal hour is used less often than the average implies. The fifth hour of a five-hour battery is only used on days with an exceptionally wide spread. Its effective utilisation is therefore well below the headline cycle count, which pushes the optimum shorter than a flat average suggests.
Seasonality concentrates the value. In most markets the widest spreads cluster in a few months. A duration justified by summer economics is carrying capital through a winter that does not use it, and the annual calculation is what reveals whether that trade works.
The practical fix is to compute the marginal hour's utilisation directly from the price series — the count of days on which the battery would actually have reached that depth — rather than multiplying a marginal value by an assumed cycle count. It is more work and it is the difference between a defensible duration and a plausible one.
To build the marginal revenue curve, the cost line, the crossing and the feasibility ceiling, prompt Dezzmond with your price series, pack cost and cost of capital.
What Do Developers and Lenders Actually Check?
- What cycling assumption is the duration based on? It determines the answer.
- Is that cycling rate achievable given the price shape — are there two distinct spreads a day?
- Does the warranty permit it? Throughput limits bind independently of economics.
- Is the configuration time-feasible? Duration × cycles × 2.136 must be under 24.
- What is the marginal hour's value at the chosen duration, and how close is it to the cost line?
- Is any hour justified by accreditation rather than arbitrage? Say which.
- Has the calculation been run on the full year or on a representative day?
Frequently Asked Questions
Why is four hours the industry standard?
Because it is the arbitrage optimum for an asset cycling roughly twice a day, and because it is the first rung of the capacity accreditation ladder in markets that have one. On a single-cycle strategy the same calculation gives two hours.
Why does each additional hour earn less?
Because the battery discharges into the best hours first. The second hour is by construction less valuable than the first, and on the worked day the eighth hour earns 16% of what the first does.
Why is the marginal cost constant?
Because an extra hour of duration buys cells only. The balance of plant — inverters, transformers, civil works, connection — is incurred once per megawatt and does not change with duration.
Is there a physical limit on duration?
Yes. Each cycle commits duration × (1 + 1/RTE) hours, so a two-cycle strategy caps duration at about 5.6 hours at 88% efficiency. Six hours at two cycles a day requires 25.6 hours in a day.
So should it be four hours or five?
Four is the arbitrage-only optimum at two cycles a day. Five clears once capacity accreditation is included, because the step from 55% to 65% between four and six hours is worth about $5,931 per megawatt-year per hour. So four suits an energy-only market and five suits one with a capacity construct.
How much does a cheaper cell change the answer?
A great deal. Dropping the pack cost from $180 to $120/kWh takes the optimum from two hours to four at one cycle a day, and from four to six at two cycles — a one-third cost reduction roughly doubling the answer.
What lengthens optimal duration over time?
Cheaper cells, which lower the marginal cost line; wider price spreads from renewable penetration, which lift the revenue curve; and capacity accreditation steps that reward duration independently of arbitrage.
Closing: State the Cycling Assumption
The answer to "why four hours" is not four hours. It is: because we intend to cycle twice a day, into a price shape that supports two distinct spreads, with a warranty that permits the throughput, at a cell cost of around $180 per kilowatt-hour and a cost of capital of twelve percent.
Change any one of those and the answer changes. Drop to one cycle and it is two hours. Halve the cell cost and it is longer. Move to a market with a single evening peak and the second cycle does not exist to be run.
None of that is difficult to compute. It is two curves, a crossing point and a feasibility check — a morning's work against a real price series, and it produces a number that can be defended rather than inherited.
The conventional four hours will often turn out to be right. The value is not in overturning it; it is in knowing which of the assumptions underneath it is doing the work, so that when one of them moves — and cell costs and price shapes both move constantly — the configuration decision moves with it instead of being carried forward from a specification written three years earlier.
The next post takes the cost side of that crossing properly: why the cost per kilowatt-hour falls as duration rises, and what that does to the comparison.
Sources: Berkeley Lab — Value of Adding Up to 4-Hour Duration Batteries to Solar or Wind · Timera Energy — What Battery Durations Are Investable? · Modo Energy — Battery Dispatch Model · NREL — Utility-Scale Battery Storage, Annual Technology Baseline