Battery power and energy
The key idea
Battery energy capacity sets how long storage can help. Its power limit sets how much demand it can supply at one time. Both constraints must pass.
Read both ratings
A 60 kWh battery and a 10 kW converter do not form an unlimited 60 kW source. The converter limits instantaneous output to 10 kW. Stored energy then limits how long that output can continue.
Not all nominal energy is available. The permitted state-of-charge range may leave a reserve at the bottom and headroom at the top. Conversion losses also reduce energy delivered to the AC bus.
Try the two limiting cases
The example begins at 90% state of charge and supplies a constant 10 kW demand. First, increase the energy capacity while leaving the power limit at 10 kW. Next, reduce the power limit to 5 kW. Even a full large battery now leaves half of the demand unmet.
- Usable stored energy
- 48 kWh
- Delivered energy
- 45.6 kWh
- Unmet demand
- 74.4 kWh
- Battery output
- Demand
Read the exact values
| Time / step | Battery output | Demand |
|---|---|---|
| 00:00 | 10.00 | 10.00 |
| 01:00 | 10.00 | 10.00 |
| 02:00 | 10.00 | 10.00 |
| 03:00 | 10.00 | 10.00 |
| 04:00 | 5.60 | 10.00 |
| 05:00 | 0.00 | 10.00 |
| 06:00 | 0.00 | 10.00 |
| 07:00 | 0.00 | 10.00 |
| 08:00 | 0.00 | 10.00 |
| 09:00 | 0.00 | 10.00 |
| 10:00 | 0.00 | 10.00 |
| 11:00 | 0.00 | 10.00 |
- Stored energy
Read the exact values
| Time / step | Stored energy |
|---|---|
| 0 h | 54.00 |
| 1 h | 43.47 |
| 2 h | 32.95 |
| 3 h | 22.42 |
| 4 h | 11.89 |
| 5 h | 6.00 |
| 6 h | 6.00 |
| 7 h | 6.00 |
| 8 h | 6.00 |
| 9 h | 6.00 |
| 10 h | 6.00 |
| 11 h | 6.00 |
| 12 h | 6.00 |
Model note · 12-hour discharge test at a fixed 10 kW demand. Initial SoC 90%, minimum SoC 10%, one-way efficiency 95%. No charging, degradation or temperature limits. Values are hourly means.
The stored-energy curve shows the battery state. The output curve shows power delivered at the AC terminal. The final partial hour is represented by its mean output; the model does not claim that the battery can sustain that average for the entire hour before reaching its limit.
State the operating boundary
State of charge, or SoC, is the fraction of nominal stored energy remaining in this simple model. Usable stored energy depends on the allowed SoC range. The energy reaching the load also depends on discharge efficiency.
A battery can be full and still fail a high power peak. It can also meet the peak briefly and then reach its minimum SoC. These are different design findings and need different changes.
The math, if you want itOptional — the page reads completely without it
For nominal capacity C and an allowed state-of-charge window:
usable stored energy
Eusable = C · ( SoCmax − SoCmin )
The 60 kWh example has 60 × (0.9 − 0.1) = 48 kWh usable. At 95% discharge efficiency that is 45.6 kWh at the AC terminal, before any other constraint.
stored energy, step by step
Enext = E + η · Pcharge · Δt − Pdischarge · Δtη
Each step is limited by the power rating and the SoC bounds; charging and discharging do not occur in the same step here.
round trip from two one-way efficiencies
ηround trip = ηcharge · ηdischarge = 0.95 × 0.95 ≈ 0.90
Do not use 90.25% for both one-way terms; that counts the losses twice. Real performance also depends on technology, rate, temperature and ageing, which this example omits.
See it in Phasor
Enter storage energy, converter power and operating limits. Inspect the simulated SoC alongside unmet demand so a shortage can be traced to energy, power or dispatch behaviour.
Continue the design path
Bring storage into the hybrid plant energy balance, then compare generator dispatch strategies.