Facilities Energy Retrofit Decision (Cross-Domain)¶
This example is intentionally non-CBE. It shows how the same reasoning method applies in facilities, mechanical, and electrical contexts.
Decision question¶
Should a campus chilled-water secondary loop remain constant-speed or be retrofitted with VFD control for part-load operation?
Boundary and basis¶
- System: one 45 kW secondary circulation pump, annual operation 3,200 hours.
- Current state: throttling valve used to reduce flow during part-load periods.
- Comparison basis: annual energy use and simple payback.
Belief update¶
I initially believed retrofit savings would be modest because the installed pump operates at high motor efficiency. After applying affinity-law scaling to part-load operation, I now recognize that control strategy can dominate annual energy use more than nameplate efficiency.
Assumption + failure condition¶
Assumption: 65% of annual hours are at 60-80% of design flow. Failure condition: if operating logs show less than 30% part-load hours, retrofit economics weaken substantially.
Math to physical link¶
Using pump affinity, shaft power scales approximately with speed cubed. Reducing speed from 100% to 80% gives an expected power ratio near 0.8^3 = 0.512. That matches the physical mechanism: lower impeller speed sharply reduces hydraulic work and motor load at lower flow demand. This cubic relationship is also why throttling wastes energy: the pump stays near full speed while excess head is dissipated across the valve.
Back-of-the-envelope energy estimate¶
- Baseline constant-speed energy: 45 kW x 3,200 hr = 144 MWh/year.
- Part-load share (assumed 65% of annual hours at about 80% speed):
- 0.65 x 144 x 0.512 = 47.9 MWh/year.
- Remaining full-load share:
- 0.35 x 144 = 50.4 MWh/year.
- Estimated VFD total:
- 47.9 + 50.4 = 98.3 MWh/year.
- Estimated savings:
- 144 - 98.3 = 45.7 MWh/year (about 46 MWh/year).
This estimate gives an order-of-magnitude check and explains why the <20 MWh/year switching condition is decision-relevant.
Tradeoff summary with switching condition¶
- Constant speed + throttling
- Pros: no new capital, minimal commissioning.
- Cons: persistent energy waste at part load, higher valve wear.
- VFD retrofit
- Pros: lower part-load energy, better control authority, lower mechanical stress.
- Cons: upfront cost, commissioning effort, harmonics mitigation check.
Switch to constant-speed preference if: - measured annual savings are <20 MWh/year, or - installed retrofit cost exceeds campus simple-payback policy (typically 3-5 years).
At 46 MWh/year savings, annual value is about $3,700-$5,500 at $0.08-$0.12 per kWh, so a 3-5 year policy implies a rough installed-cost window of about $11k-$28k.
Recommendation¶
The retrofit is likely justified given expected savings on the order of tens of MWh per year. Proceed with VFD retrofit if a one-month trend capture confirms the assumed part-load distribution before procurement.
Reversal conditions¶
Reconsider recommendation if any of the following occur: 1. Measured part-load hours are below 30% of annual runtime. 2. Utility tariff shifts to demand-dominant pricing that erodes energy-savings value. 3. Existing motor or drive compatibility requires major electrical rework.
Evidence to collect before final decision¶
- Pump trend data at 5-15 minute resolution over at least one month.
- Flow versus valve position during part-load operation.
- Motor current versus estimated hydraulic load.
- Hourly load profile showing fraction of time below 80% speed-equivalent demand.
Mindsets demonstrated¶
Rubric annotation (example)¶
- Belief update quality: 4/4 (prior belief + explicit revision trigger)
- Math-to-physical link: 4/4 (equation tied to physical behavior)
- Decision defense: 3/4 (clear recommendation and reversal conditions; full score requires field evidence package completion)