For each load-capex scenario, we optimize the solar-array and battery sizing that minimizes total capex per unit of utilization for a 1 MW off-grid load, using NREL 5-minute solar production data. Hover over the chart to see the optimal system at each load capex.
| Load capex ($/kW-load) | Power capex ($/kW-load) | Utilization | Total capex ($/kW-load) | Total capex / utilization ($/kW-load) |
|---|---|---|---|---|
| $10 | $125 | 32.3% | $135 | $417 |
| $16 | $128 | 33.1% | $145 | $436 |
| $26 | $133 | 34.1% | $159 | $467 |
| $43 | $137 | 35.0% | $180 | $514 |
| $70 | $142 | 36.0% | $212 | $589 |
| $113 | $148 | 36.8% | $261 | $708 |
| $183 | $154 | 37.6% | $338 | $897 |
| $298 | $162 | 38.4% | $460 | $1.2k |
| $400 | $171 | 39.1% | $571 | $1.5k |
| $483 | $179 | 39.6% | $663 | $1.7k |
| $785 | $230 | 42.0% | $1.0k | $2.4k |
| $1.3k | $1.5k | 86.9% | $2.8k | $3.2k |
| $2.1k | $1.6k | 90.5% | $3.7k | $4.1k |
| $3.4k | $1.8k | 93.7% | $5.1k | $5.5k |
| $5.5k | $2.0k | 96.5% | $7.4k | $7.7k |
| $8.9k | $2.1k | 97.7% | $10.9k | $11.2k |
| $14.4k | $2.2k | 98.4% | $16.6k | $16.8k |
| $23.4k | $2.2k | 98.8% | $25.6k | $25.9k |
| $37.9k | $2.4k | 99.1% | $40.3k | $40.6k |
| $61.6k | $2.5k | 99.4% | $64.0k | $64.5k |
| $100.0k | $2.6k | 99.5% | $102.6k | $103.1k |
Look at two points on the curve. A $400/kW load runs 39% of the time and costs $1.5k/kW of utilization. A $1.3k/kW load runs 86% of the time and costs $3.2k/kW. The cheap plant that sits idle most of the year is twice as efficient with capital as the expensive one that almost never stops.
This is the opposite of what everyone assumes. If uptime were what you were really buying, the 86% number would be the cheaper one. It isn't. The batteries you need to keep a plant running at night cost more than the plant does.
So the answer is not a bigger battery. It's a cheaper load—one you can afford to leave off when the sun goes down. Build it that way and every dollar of capex buys you more output than it would have if you had insisted on running all the time.
Assumptions: solar $100/kW, battery $100/kWh. Power system capex is the optimal solar + battery capex; utilization is the fraction of time the load can run.