11.2 kW/ton, BHP/ton, and KPI Dashboards

11.2 kW/ton, BHP/ton, and KPI Dashboards

Chapter 9 defined BHP/ton as a thermodynamic efficiency KPI. This section is the operator dashboard version: take the electrical fields off a CIRO screen, turn them into input kilowatts, divide by real tons, and watch that ratio over time. Monitoring System Performance is 20 outline items. A large slice of that block is whether you can tell a cheap ton from an expensive ton while the plant still looks "running."

Formulas you will type on the simple calculator

Input kW = √3 × V × I × PF / 1000

Use line-to-line volts, a representative line current (average the three if they are close; chase unbalance if they are not), and power factor as a decimal. √3 ≈ 1.732. Displayed kW on a power meter should match this within metering tolerance. If the screen shows kW but not PF, you can back-calculate PF = kW × 1000 / (√3 × V × I) as a sanity check.

Shaft HP ≈ input kW × efficiency / 0.746

Efficiency is the motor efficiency on the screen or nameplate, as a decimal (93% → 0.93). 0.746 kW = 1 HP. This is brake (shaft) horsepower, not nameplate class.

kW/ton = input kW / tons

BHP/ton = shaft HP / tons

Tons must be actual refrigerating effect from a production screen, a heat balance, or a trusted evaporator load — never "the compressor is a 300 HP machine so it must be making design tons." Lower kW/ton and lower BHP/ton are better. Input kW/ton is always higher than shaft kW/ton because the motor is not 100% efficient.

Shaft kW/ton = BHP/ton × 0.746. Input kW/ton = (BHP/ton × 0.746) / η_motor. If you mix input kW into a shaft COP you will compliment yourself on the electric bill you did not reduce.

Worked screen — high-stage screw HS-1 (original values)

HS-1 is a high-stage ammonia screw on an engine-room screen. It is not the West screw from 11.1, and it is not a copy of a RETA stem.

Input kW = 1.732 × 480 × 265 × 0.85 / 1000. 831.36 × 265 = 220,310; × 0.85 = 187,264; ÷ 1000 = 187.3 kW.

kW/ton = 187.3 / 198 = 0.95 kW/ton

Shaft HP = 187.3 × 0.92 / 0.746 = 172.3 / 0.746 = 231 HP.

BHP/ton = 231 / 198 = 1.17 BHP/ton

Nameplate theater: 300 / 198 = 1.52 BHP/ton. That number describes a motor that is not on this machine. If someone uses 300 HP in a COP, the COP is fiction.

Trap: amps per ton. 265 / 198 = 1.34 A/ton. That is not kW/ton. Without V and PF it cannot be power.

Same kW, fewer tons — the KPI that amps will not show

Ice on the low-temperature coils, a starved DX battery, or a recirculator that lost a pump can drop evaporator effect while the high-stage screw still sees roughly the same suction and still draws 187.3 kW. Production falls to 155 tons.

kW/ton = 187.3 / 155 = 1.21 kW/ton

The ammeter did not have to look like a wreck. Tons fell. That is why the dashboard includes both power and capacity. A CIRO abnormal screen that holds amps steady and drops the tonnage field is still abnormal.

Part load: slide valve down, kW/ton often up

HS-1 unloads to 55% slide. Current 198 A, PF 0.78 (light-load PF usually sags), evaporator screen 118 tons.

Input kW = 1.732 × 480 × 198 × 0.78 / 1000. 831.36 × 198 = 164,609; × 0.78 = 128,395; ÷ 1000 = 128.4 kW.

kW/ton = 128.4 / 118 = 1.09 kW/ton

Power fell from 187.3 kW to 128.4 kW. The KPI worsened from 0.95 to 1.09 kW/ton. Slide-valve unloading is not a linear "55% slide means 55% kW and 55% tons." Internal leakage and part-load losses spend extra kW per remaining ton. Sequencing another machine at a better load point can beat parking one screw at 55% — Chapter 13 is the sequencing chapter; here you only need to compute the worse kW/ton so you do not celebrate the lower ammeter.

What belongs on the KPI dashboard

Trend at least these, on a dated sheet or historian, at a defined operating mode (for example "HS-1 at 100% slide, rooms at setpoint"):

Add oil supply temperature if the package is thermosiphon-cooled. Add slide-valve percent and VFD Hz so you do not compare a 40% slide day to a 100% baseline and call it a condenser miracle.

A dashboard without dates is a CIRO screen: NORMAL or ABNORMAL with no elapsed time. Mechanical integrity under OSHA PSM and inspection/testing/maintenance under current IIAR 6 expect recorded readings, not a remembered vibe. The log is how you prove the 28°F approach started in July, not this morning. It is also how you prove a PRV, oil filter, or condenser wash was due from data, not from a fight with production.

Building a weekly trend (original log)

HS-1, 100% slide, similar wet bulb, rooms at setpoint:

Discharge climbed while suction sagged and evaporator TD opened — coils are icing and the condenser is drifting. kW/ton rose from 0.95 to 1.21. Oil-filter ΔP moved, but not enough to explain 30 psi of extra head. The dashboard's job is to show which KPIs moved together so you wash the condenser and defrost, instead of changing oil filters as a personality trait.

If 23 Aug had been the only screen you were handed on CIRO, you would still compute kW/ton and approach. You would not know it took four weeks. That is the whole teaching point of timestamp-free troubleshooting screens: the exam tests whether you can name the abnormal state. The plant tests whether you documented the path.

Sanity checks before you trust a kW/ton

1. Voltage is line-to-line and the motor is actually at that voltage (a 460 V nameplate on a 480 V bus is normal; 430 V on one phase is not).
2. PF is included. Forgetting PF inflates kW by 1/PF (about 18% at 0.85).
3. Tons are live. A frozen "design 200 tons" in a spreadsheet produces a fake KPI.
4. Compare like modes. 55% slide versus 100% slide is not a condenser scorecard.
5. Oil ΔP label. Filter versus lubrication. Logging the wrong one trains the wrong work order.

Exam traps

• Nameplate HP / design tons as BHP/ton.
• Amps/ton or PF itself as if it were kW/ton.
• Celebrating lower kW at part load while kW/ton got worse.
• A dashboard with no dates, then claiming mechanical integrity.
• Mixing input kW/ton with shaft COP without saying which work you used.