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Created April 8, 2026 13:09
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TODO with open-fdd
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energy_equations.md

open-fdd default equations for energy penalty

It is structured by equipment type, starting from the zone level and moving up to the central plant. Within each category, the rules are ordered by difficulty to implement: starting with the "low-hanging fruit" (simple boolean logic, schedules, and basic setpoint math) down to the more complex FDD rules (requiring thermodynamic models, enthalpy, or network-level data rollups).

Easy FDD Energy Penalty Equations (open-fdd TODO)

1. General & Override Faults (Easiest to Implement)

These rules apply across multiple equipment types and rely on simple binary states, schedules, or BAS overrides, making them the easiest FDD rules to deploy.

1. Out-of-Schedule Operation (The "Lights Left On" Rule)

  • FDD Trigger: equipOn == true while unocc schedule is active.
  • The Math: Sum the power consumption (or a proxy based on VFD/FLA) over the duration. $$E_{waste} = \sum (P_{equip} \cdot \Delta t)$$

2. Manual Override / Hand-Off-Auto (HOA) in "Hand"

  • FDD Trigger: A fan, pump, or equipment is overridden to 100% via the BAS or at the drive, ignoring its PID loop.
  • The Math: Calculate the difference between the full-load power being drawn and the optimal power that the PID loop would be commanding if it were in Auto. $$kW_{waste} = kW_{max} - \left( kW_{max} \cdot \left( \frac{\text{Speed}{auto_calc}}{\text{Speed}{max}} \right)^3 \right)$$

2. Terminal Unit & Zone Level Faults (VAVs/FCUs)

Starting at the zone level. These dictate the load for the rest of the building.

3. Zone Temperature Deadband Too Tight (Hunting/Cycling)

  • FDD Trigger: The heating setpoint (e.g., 70°F) and cooling setpoint (e.g., 71°F) are too close. The VAV rapidly cycles between opening the cooling damper and striking the reheat valve.
  • The Math: This creates an artificial simultaneous heating and cooling penalty over a rolling window. Calculate the sum of the opposing energy streams during the hunting period. $$E_{waste_total} = \int (Q_{cooling_delivered} + Q_{heating_delivered}) , dt$$

4. VAV Minimum Airflow Setpoint Too High (Over-ventilation & Reheat)

  • FDD Trigger: The zone is unoccupied or satisfied, but the VAV damper is maintaining a minimum flow that exceeds the design minimum or ASHRAE 62.1 requirements.
  • The Math: The penalty is twofold: wasted fan energy pushing the extra air, and wasted boiler energy reheating that air to prevent subcooling the space. $$Q_{reheat_waste} = 1.08 \cdot (\text{CFM}{actual} - \text{CFM}{design_min}) \cdot (T_{zone} - T_{supply})$$

3. Air-Side Faults & AHU Setpoint Failures

Air Handling Units and Rooftop Units.

5. AHU Supply Air Temperature (SAT) Not Resetting (GL36 Failure)

  • Reverse GL36 Trigger: The totalRequests for cooling = 0, but the AHU SAT_Setpoint is stuck at SPmin (e.g., 55°F) instead of trimming up to SPmax (e.g., 65°F).
  • The Math: Calculate the sensible cooling energy wasted by supplying air colder than necessary. $$Q_{waste} = 1.08 \cdot \text{CFM}{ahu} \cdot (SAT{opt} - SAT_{actual})$$

6. Static Pressure Setpoint Not Resetting (GL36 Failure)

  • Reverse GL36 Trigger: VAV totalRequests = 0, but AHU duct static pressure is at SPmax.
  • The Math: Use fan affinity laws (power varies roughly by exponent 1.5 relative to pressure). $$kW_{waste} = kW_{actual} - \left( kW_{actual} \cdot \left( \frac{P_{opt}}{P_{actual}} \right)^{1.5} \right)$$

7. Simultaneous Heating & Cooling: Leaking AHU Valve

  • FDD Trigger: AHU is in cooling (coolCmd > 0), but the hot water valve is leaking (evidenced by a temperature rise across the HW coil).
  • The Math: Calculate wasted BTUs based on the $\Delta T$ across the closed coil, then convert to wasted compressor kW and boiler gas. $$Q_{waste} = 1.08 \cdot \text{CFM} \cdot \Delta T_{coil}$$ $$kW_{waste} = \frac{Q_{waste}}{3412 \cdot COP_{chiller}}$$

8. Dirty Filter / Fouled Coil (Excessive Fan Static Pressure)

  • FDD Trigger: The pressure drop ($\Delta P$) across the filter or coil exceeds the clean-state baseline by a significant margin (e.g., > 0.5 inWC), forcing the VFD to ramp up.
  • The Math: Use standard fan shaft power equations to isolate the specific electrical penalty of the blockage. $$kW_{waste} = \frac{\text{CFM} \cdot \Delta P_{excess}}{6356 \cdot \eta_{fan} \cdot \eta_{motor}} \cdot 0.746$$

9. Missed Free Cooling (Air-Side Economizer)

  • FDD Trigger: OAT is 55°F (favorable for free cooling), building needs cooling, but Outside Air Damper is stuck at minimum.
  • The Math: Calculate the difference between actual mixed air and ideal mixed air, converting the missed "free" BTUs into mechanical compressor kW. $$Q_{missed} = 1.08 \cdot \text{CFM} \cdot (T_{return} - T_{outside})$$

10. Energy Recovery Wheel / DOAS Failure

  • FDD Trigger: The outside air is extreme (e.g., 95°F or 20°F), the Dedicated Outside Air System (DOAS) is running, but the enthalpy wheel is disabled, broken, or bypassed.
  • The Math: The mechanical cooling/heating coil now has to pick up the load the wheel should have handled. Calculate the total enthalpy difference. $$Q_{waste} = 4.5 \cdot \text{CFM}{oa} \cdot (\Delta h{wheel_design} - \Delta h_{wheel_actual})$$ Divide $Q_{waste}$ by the chiller/boiler efficiency to get the dollar penalty.

11. Simultaneous Heating & Cooling: Overcooling & Downstream VAV Reheat (Hardest AHU rule because it requires VAV-to-AHU data mapping)

  • FDD Trigger: AHU SAT is satisfying the setpoint (e.g., 55°F), but multiple downstream VAVs are simultaneously running max reheat to prevent freezing the space.
  • The Math: The penalty is double. You pay the chiller to overcool the air, and you pay the boiler to heat it back up. Calculate the sensible heat from the overcooled SAT to the ideal neutral SAT (e.g., 65°F). $$Q_{reheat_waste} = 1.08 \cdot \text{CFM}{vav} \cdot (T{ideal_SAT} - T_{actual_SAT})$$

4. Central Plant & Waterside Faults

Chillers, Boilers, Cooling Towers, and Pumps. These are high-impact but often require more complex data points.

12. Chiller Running During Low Load / Missed Free Cooling

  • FDD Trigger: Chiller is ON, but OAT is < 50°F (should be using waterside economizer/free cooling) OR all AHU CHW valves are < 10% (no building load).
  • The Math: Sum the baseline minimum power of the chiller, condenser pump, and cooling tower fans running unnecessarily. $$E_{waste} = \sum (kW_{chiller_min} + kW_{pumps}) \cdot \Delta t$$

13. Boiler Running in Deadband or No Load

  • FDD Trigger: HW Plant is ON, but OAT is in the deadband (e.g., 55°F - 65°F) OR totalHwResetReq = 0.
  • The Math: Calculate the wasted standby gas and hot water pump electrical energy. $$E_{waste} = \sum (kW_{hw_pump} \cdot \Delta t) + \sum (\text{Boiler_Min_BTU} \cdot \Delta t)$$

14. Equipment Short Cycling (Wear and Tear + Efficiency Drop)

  • FDD Trigger: Chiller or Boiler cycles ON / OFF more than manufacturer recommendations (e.g., > 6 times per hour).
  • The Math: Apply a flat financial penalty for wear-and-tear based on estimated equipment life reduction, plus an inefficiency penalty multiplier for the hour (since start-up sequences are highly inefficient). $$\text{Penalty ($)} = (\text{Start Count} - \text{Allowed Starts}) \cdot \text{Cost}{wear} + (E{consumed} \cdot 0.10)$$

15. Chilled Water Supply Temp (CHWST) Not Resetting

  • Reverse GL36 Trigger: Chiller has been running for > 1 hour, OAT is < 70°F or CHW valves are mostly closed, but CHWST is stuck at design (e.g., 42°F) instead of resetting to 55°F.
  • The Math: Use the FDD engineering rule of thumb: Chiller efficiency drops ~1.5% to 2% for every 1°F the CHWST is colder than necessary. $$kW_{waste} = kW_{actual} \cdot 0.015 \cdot (CHWST_{opt} - CHWST_{actual})$$

16. Pump Differential Pressure (DP) Not Resetting

  • Reverse GL36 Trigger: Plant loop totalRequests = 0, but CHW/HW pump DP setpoint is stuck at chwDpMax.
  • The Math: Pump affinity laws apply here just like fans. Power varies by the cube of speed, but roughly 1.5 to 2.0 relative to differential pressure. $$kW_{waste} = kW_{actual} - \left( kW_{actual} \cdot \left( \frac{DP_{opt}}{DP_{actual}} \right)^{1.5} \right)$$

17. Cooling Tower Wet Bulb Approach Failure (Wasted Fan Energy)

  • FDD Trigger: Cooling tower fans are ramping up to 100%, but the Condenser Water Supply (CWS) temperature is already satisfying the setpoint, OR the setpoint is physically impossible (e.g., setpoint is below current Wet Bulb + Tower Approach).
  • The Math: If the fans are hunting an impossible setpoint, calculate the difference between the actual fan kW and the optimal fan kW (derived from affinity laws based on the required heat rejection). $$kW_{waste} = kW_{fan_actual} - \left( kW_{fan_design} \cdot \left( \frac{\text{Speed}{opt}}{\text{Speed}{max}} \right)^3 \right)$$

18. Degraded Chiller / DX Unit Capacity (Fouled Condenser / Low Refrigerant) (Hardest plant rule)

  • FDD Trigger: The chiller is drawing near-maximum power, but the $\Delta T$ on the chilled water loop is much smaller than design, indicating the Coefficient of Performance ($COP$) has tanked.
  • The Math: Calculate the actual tonnage being produced versus the power being consumed. Compare this $COP_{actual}$ against the manufacturer's $COP_{design}$ at the current lift conditions. $$kW_{waste} = Q_{load} \cdot \left( \frac{1}{3.412 \cdot COP_{actual}} - \frac{1}{3.412 \cdot COP_{design}} \right)$$
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