A VRF Surrogate Model and the 'Errors Cancel' Argument
A 90,000 ft², six-story mixed-use building - apartments over ground-floor retail - is modeled with a VRF heat-recovery system and a dedicated outdoor air system. The tool has no native VRF model, so each apartment terminal was represented as a two-pipe fan coil served by a virtual boiler/chiller plant tuned to mimic VRF efficiencies, and the DOAS as a separate constant-volume AHU. The Appendix G baseline is System 2 (PTHP). The proposed model shows only 6% site savings against a 30% design target. The design engineer says heat recovery between simultaneously heating and cooling zones is not represented and fan energy is overstated. A colleague argues that because the same simplification appears in both baseline and proposed, the error cancels.
1. Evaluate the 'the error cancels' argument.
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The argument fails here, on two grounds.
1. The simplification is not the same on both sides. The baseline is a packaged terminal heat pump; the proposed is a virtual plant feeding two-pipe fan coils. Those are different approximations with different bias directions. Cancellation requires the same error applied identically to both models - that is not what was built.
2. Even with an identical approximation, cancellation depends on the measure. Error cancellation is only valid if the approximation responds identically to the design difference being evaluated. Here the difference is the thing being suppressed: inter-zone heat recovery, inverter modulation at part load, and variable-speed fan energy are precisely the mechanisms the surrogate cannot represent. An approximation that removes the benefit cannot be used to estimate the benefit.
Put concretely: the virtual fan coils carry constant fan power proportional to design airflow, so they consume design wattage whenever running. A real VRF terminal at 15% load draws a small fraction of that. The surrogate penalizes the proposed design far more heavily than the baseline, because the baseline PTHP's fan assumption is closer to reality for a constant-speed unit. The bias is not symmetric; it is directionally hostile to the proposed case.
What to concede: the colleague is right that surrogate models are legitimate and often unavoidable. The error is not in using one - it is in reporting its output as a savings estimate without quantifying the bias.
2. Identify the three largest modeling errors and describe how you would correct each.
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1. No inter-zone heat recovery. The surrogate plant cannot let one zone's rejected heat serve another's heating load. Fix by modeling the condenser water loop so simultaneous heating and cooling is permitted - a shared loop with heat-recovery chillers, or a native VRF module if one exists for the tool. Then verify the model actually produces simultaneous heating and cooling calls in the same hour in the residential zones (a north-facing apartment cooling on a sunny winter afternoon while a west-facing unit heats is the case that generates the savings). If the model never produces simultaneous demand, heat recovery cannot show up regardless of plant representation.
2. Fan energy overstated. Constant-volume fans at design wattage are wrong for inverter-driven terminals. Replace with a variable-speed fan curve - at minimum, fan power scaled with the cube of part-load flow ratio plus a static-pressure reset, and a realistic design static pressure rather than a default. Fan energy in a VRF/DOAS design is a large fraction of HVAC energy; this alone can account for several points of the missing savings.
3. Part-load and cold-climate compressor performance. A single tuned efficiency number ignores that VRF capacity and COP fall steeply at low ambient, that defrost cycles penalize cold-hour operation, and that resistance backup may be engaging. Use an ambient-derated performance curve with part-load modulation, and make sure backup heat is represented explicitly rather than hidden in the virtual plant.
Also check the baseline side. Confirm the System 2 baseline carries the prescribed efficiency and fan power for the edition in force. If the baseline is also mis-modeled, the two errors compound and you cannot interpret the 6% at all - fix and document both sides before analysing.
3. How do you report this result to the owner and the design team?
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Report it as not decision-grade, with the direction of the likely bias stated next to the number - not buried in an appendix.
1. Label the result. 'The 6% figure is produced by a surrogate representation that cannot model inter-zone heat recovery or variable-speed fan energy, both of which favour the design. It should be read as a lower bound, not an estimate of expected savings.' A number and its caveat belong in the same paragraph.
2. Bound it. Run sensitivities: fan power at half and at design, VRF efficiency ±25%, heat recovery on and off (using a proxy such as a reduced simultaneous heating/cooling penalty), and backup heat included or excluded. Present a range. If the range straddles the 30% target, say plainly that the model cannot support the claim and that no amount of re-running it will.
3. Document the workaround. In the assumptions log: what the surrogate represents, what it does not, why the tool required it, and which direction the residual bias runs. This is the record that protects the firm when the project underperforms and someone asks what the model said.
4. Recommend a path to a defensible number. Either a tool with a native VRF/heat-recovery model, or a calibrated benchmark from a submetered comparable building. Given capital commitment timelines, the benchmark is often faster and more persuasive to an owner than another simulation.
5. Do not let the 6% circulate alone. Once a number is in a slide deck it outlives its caveats. If the design team wants to keep pushing the design, the honest framing is that the current model cannot rank VRF against alternatives - not that VRF saves 6%.