Specific Consumption Rose 5% - Is the Plant Really Degraded?
A food-processing plant supplies 24 months of monthly electricity and production data. Year over year, output fell from 1,340 t to 1,205 t per month while electricity fell from 705,000 kWh to 668,000 kWh, so specific consumption rose from 526 to 554 kWh/t (+5.3%). The energy manager calls this 'plant degradation' and asks for approval of a $200,000 refrigeration and HVAC re-commissioning project. Meanwhile the July bill shows a new peak demand of 640 kW (previous maximum 560 kW) and a power-factor charge that has never appeared before. A regression of all 24 months gives monthly kWh = 212,000 + 379 × tonnes, with R² = 0.94.
1. Is the 5.3% rise in kWh/t evidence of degraded plant performance? Support your answer with the regression.
Read the worked answer
No - the rise is almost entirely a denominator effect.
The model separates a fixed term from a throughput term:
- Base load = 212,000 kWh/month, i.e. 31.7% of the current 668,000 kWh.
- Slope = 379 kWh/t, unchanged by definition within the single model.
Rewrite the ratio metric: kWh/t = 212,000/t + 379.
- At 1,340 t: 212,000/1,340 + 379 = 158 + 379 = 537 kWh/t (model)
- At 1,205 t: 212,000/1,205 + 379 = 176 + 379 = 555 kWh/t (model)
The +18 kWh/t in the model is exactly the drop in throughput diluting a fixed base. The plant did not become less efficient; the fixed load stayed while tonnes fell.
Test against the model: predicted for 1,205 t = 212,000 + 379 × 1,205 = 668,700 kWh; actual 668,000 kWh - 0.1% below prediction, i.e. no residual to explain.
The valid question is whether the intercept moved. Run a rolling regression or a structural-break test on the 24 months. If the intercept rose at a specific month, that month's change (a new freezer, extended 24/7 operation, a stuck valve) is the target - not a plant-wide re-commissioning.
2. What does the new 640 kW peak and the first-ever power-factor charge tell you, and what do you investigate next?
Read the worked answer
These are billing-structure signals, not efficiency signals.
- Peak demand 640 kW vs 560 kW: with a typical 11- or 12-month ratchet, this single July event could set the billed demand for up to a year. Check the tariff. The cost is immediate and larger than the 5% kWh/t story: 80 kW × $14/kW-month × 12 ≈ $13,400/yr of pure ratchet cost, recurring until the peak is reset.
- New power-factor charge: something changed the reactive load. Candidates: a new chiller or VSD bank with a failed/failing capacitor bank, oversized lightly-loaded motors, a UPS installation, or harmonic distortion from new drives defeating the correction capacitors. This is the same evidence trail as a structural break in the regression.
Investigation sequence
- Pull 15-minute interval data for July - what time of day, which day, was it a production event or a simultaneous-start event?
- Check the change log: commissioning, capital additions, control changes in that month.
- Confirm with a weekend shutdown test: kill everything and see the residual, then bring loads on one at a time.
- Review the PF penalty calculation and metering; a failed capacitor bank is cheap to fix and often recovers the whole charge.
Prioritise the demand and PF issues ahead of the $200,000 project - they are the same month, likely the same cause, and cost far less to resolve.
3. Suppose you confirm that base load rose by 40 kW at a point in the 24 months. Quantify the annual cost and describe the measurement that confirms it.
Read the worked answer
Cost
- Energy: 40 kW × 8,760 h = 350,400 kWh/yr ≈ $42,000/yr at $0.12/kWh
- Demand: 40 kW × $14/kW-month × 12 ≈ $6,700/yr
- Combined ≈ $49,000/yr - a payback under 4 years on a $200,000 project, but only if the fix is aimed at the 40 kW, not spread plant-wide.
Confirmation measurement
- Night-time baseline: with production off, log the main incomer for two weeks. Compare the current night floor to the same period before the break.
- Load survey at the break date: loggers on the candidate boards (refrigeration, HVAC, compressed air) - whichever circuit steps up at the same date is the cause.
- Weekend shutdown test: isolate each plant area in turn and watch the night floor fall. This is the only reliable way to attribute base load when there is no sub-metering.
- Normalise and verify: re-run the regression with the post-break months separated; the intercept should step, the slope should not.
The regression gave you the diagnosis; only sub-metering gives you the attribution that justifies the capital spend.