The Voltage-Squared CVR Saving
Ada re-derives why a small voltage cut yields a squared energy cut
ADA · CALCULATION AUDIT
Foundations · optional physics
The Voltage-Squared CVR Saving
A utility serving 500,000 customers and 15 TWh a year trims distribution voltage from 120 V to 116 V — a mere 3.33% cut. Because a resistive load’s power scales with voltage squared, the chapter claims that small trim becomes a 6.56% energy cut worth $39.3M a year against a $0.5–2M investment. This audit squares the ratio line by line and asks whether that exponent really turns a modest tap-change into a 20–80× first-year payback — provided the loads truly are resistive.
Companion to the chapter Smart Grid and Energy IoT — every number here comes from that chapter.
Ada's Calculation Audit: the voltage-squared CVR saving — why a 3.3% voltage cut yields a 6.56% energy cut, ~4 minutes
Conservation Voltage Reduction leans on one physics fact: a resistive load's power scales with voltage squared. Squaring the ratio is where the saving actually comes from.
The working
1. Square the voltage ratio. 116 V ÷ 120 V = 0.9667, a 3.33% trim. For a resistive load P = V²/R, so the power ratio is the square:
Squaring nearly doubles the 3.33% voltage trim into a 6.56% energy cut on resistive load.
2. Apply it to the resistive share. 15 TWh/yr × 0.40 resistive = 6.0 TWh, so savings = 6.0 × 0.0656 = 0.393 TWh/yr.
3. Turn energy into money and ROI. 0.393 TWh = 393 million kWh × $0.10 = $39.3M/yr. Against a $0.5–2M VVO investment that is $39.3M ÷ $0.5M = 79× down to $39.3M ÷ $2M = 20× first-year ROI.
| Step | Arithmetic | Result |
|---|---|---|
| Voltage ratio | 116 ÷ 120 | 0.9667 (−3.33%) |
| Power ratio (V²) | 0.9667² | 0.9344 |
| Energy cut | 1 − 0.9344 | 6.56% |
| Resistive energy | 15 × 0.40 | 6.0 TWh/yr |
| Savings | 6.0 × 0.0656 | 0.393 TWh/yr |
| Value | 0.393e9 kWh × $0.10 | $39.3M/yr |
| ROI | $39.3M ÷ $0.5–2M | 20–80× |
What the audit buys you: the whole business case rides on the exponent — a 3.3% voltage trim would be trivial if power were linear in voltage, but the V² law doubles it to 6.56%, turning a modest tap-change into a $39M-a-year, 20–80× payback, provided the loads really are resistive.
Every number above is taken from the chapter's own CVR voltage-saving example and re-derived step by step.