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Small HVAC Control Demonstrations in Larger Buildings Often Overestimate Savings

Arash J. Khabbazi, Kevin J. Kircher

Abstract

How much energy, money, and emissions can advanced control of heating and cooling equipment save in real buildings? To address this question, researchers sometimes control a small number of thermal zones within a larger multi-zone building, then report savings for the controlled zones only. That approach can overestimate savings by neglecting heat transfer between controlled zones and adjacent zones. This paper mathematically characterizes the overestimation error when the dynamics are linear and the objectives are linear in the thermal load, as usually holds when optimizing energy efficiency, energy costs, or emissions. Overestimation errors can be large even in seemingly innocuous situations. For example, when controlling only interior zones that have no direct thermal contact with the outdoors, all perceived savings are fictitious. This paper provides an alternative estimation method based on the controlled and adjacent zones' temperature measurements. The new method does not require estimating how much energy the building would have used under baseline operations, so it removes the additional measurement and verification challenge of accurate baseline estimation.

Small HVAC Control Demonstrations in Larger Buildings Often Overestimate Savings

Abstract

How much energy, money, and emissions can advanced control of heating and cooling equipment save in real buildings? To address this question, researchers sometimes control a small number of thermal zones within a larger multi-zone building, then report savings for the controlled zones only. That approach can overestimate savings by neglecting heat transfer between controlled zones and adjacent zones. This paper mathematically characterizes the overestimation error when the dynamics are linear and the objectives are linear in the thermal load, as usually holds when optimizing energy efficiency, energy costs, or emissions. Overestimation errors can be large even in seemingly innocuous situations. For example, when controlling only interior zones that have no direct thermal contact with the outdoors, all perceived savings are fictitious. This paper provides an alternative estimation method based on the controlled and adjacent zones' temperature measurements. The new method does not require estimating how much energy the building would have used under baseline operations, so it removes the additional measurement and verification challenge of accurate baseline estimation.
Paper Structure (9 sections, 1 theorem, 26 equations, 5 figures, 1 table)

This paper contains 9 sections, 1 theorem, 26 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Main Theoretical Results
  3. Assumptions and Model
  4. Theorem and Remarks
  5. Numerical Example
  6. Setting, Building, and Input Data
  7. Simulation Results
  8. Limitations and Future Work
  9. Conclusion

Key Result

Theorem 1

If the assumptions and model in § model hold, then reporting only the observed cost savings for the controlled zones 1, …, $m$ overestimates the whole-building cost savings by To correct this overestimation error, researchers can report either or which are two equivalent and exact expressions for the whole-building cost savings.

Figures (5)

  • Figure 1: Zone $i$ in a thermal circuit representing an arbitrary $n$-zone building.
  • Figure 2: Savings overestimation errors for a square zone with adiabatic floor and ceiling. Errors are larger for controlled zones with less exterior surface area, more exterior insulation, or less interior insulation.
  • Figure 3: Advanced control system operates only Zone 1 within the two-zone building. Exterior walls have better insulation than interior walls.
  • Figure 4: Simulation input data represent five cold days in West Lafayette, Indiana, from December of 2022.
  • Figure 5: Zone temperatures (top row), heat pump power output (middle), and electricity cost (bottom) for Zone 1 under advanced control (left column) and for Zone 2 under default control (right column). While advanced control decreases energy costs in Zone 1, it also increases energy costs in Zone 2.

Theorems & Definitions (1)

  • Theorem 1