Student Laboratory Exercise: Cold-Climate Heat Pump Thermal Balance Point & Inverter Dynamics

1. Pedagogical Learning Objectives

Upon successful completion of this laboratory module, students and engineering trainees will be able to:

• Quantify the linear building heating load slope ($Q_{load}$) as a function of outdoor ambient temperature ($T_o$), indoor design setpoint ($T_i$), and building overall thermal transmission envelope coefficient ($UA$).
• Evaluate the thermal balance point ($T_{BP}$) where heat pump capacity exactly matches total building heat loss, delineating the compressor-only heating regime from the auxiliary/supplemental resistance heating regime.
• Contrast the seasonal performance, coefficient of performance ($\text{COP}$), and auxiliary resistance energy penalties between single-stage baseline heat pumps and inverter-driven variable-speed cold-climate heat pumps (ccASHP).
• Benchmark the economic balance point ($T_{EBP}$) against utility rate structures (electricity $/kWh vs. natural gas $/therm) using deterministic thermodynamic simulations.

2. Theoretical Background & Governing Mathematical Physics

A building envelope exhibits a steady-state heat loss rate proportional to the temperature differential between the indoor heated space and the ambient outdoor environment:

Where:

• $Q_{load}(T_o)$ = Total building heat loss rate at outdoor temperature $T_o$ ($\text{BTU/h}$ or $\text{W}$)
• $Q_{design}$ = Peak 99% ASHRAE winter design heat load ($\text{BTU/h}$)
• $T_{inside}$ = Indoor heating setpoint (typically $70^\circ\text{F}$ / $21.1^\circ\text{C}$)
• $T_{design}$ = 99% ASHRAE winter design dry-bulb temperature ($\text{^\circ F}$)

Conversely, heat pump heating capacity $Q_{hp}(T_o)$ decreases as outdoor temperature drops due to diminishing suction vapor density and lower evaporator saturation pressures. Under AHRI 210/240 testing standard guidelines, capacity is rated at $47^\circ\text{F}$ ($Q_{47}$) and $17^\circ\text{F}$ ($Q_{17}$):

The Thermal Balance Point ($T_{BP}$) is solved where building demand equals heat pump output:

When $T_o < T_{BP}$, the heat pump operates at maximum capacity and supplemental auxiliary heating ($Q_{aux}$) must engage to maintain indoor comfort:

3. Laboratory Apparatus & Interactive Simulation Workbench

Students will conduct computational measurements using the validated deterministic simulation engine:

This web-based workbench executes instant client-side boundary solves, graphing the intersection of building load lines against multi-stage and variable-speed compressor capacity curves, defrost derating penalties, and auxiliary element staging.

4. Step-by-Step Experimental Procedure

1. Setup Baseline Parameters: Set Indoor Design Temperature to $70^\circ\text{F}$, Outdoor Winter Design Temperature to $5^\circ\text{F}$, and Total Design Heat Loss to $48{,}000\text{ BTU/h}$.
2. Scenario A — Standard Single-Stage Equipment: Input rated $47^\circ\text{F}$ capacity of $36{,}000\text{ BTU/h}$ (3 Tons) and $17^\circ\text{F}$ capacity of $22{,}000\text{ BTU/h}$. Record the Thermal Balance Point ($T_{BP}$), auxiliary deficit at $5^\circ\text{F}$, and total electric strip power requirement.
3. Scenario B — Cold-Climate Variable-Speed Heat Pump (ccASHP): Input high-turndown inverter equipment with $47^\circ\text{F}$ capacity of $42{,}000\text{ BTU/h}$, $17^\circ\text{F}$ capacity of $38{,}000\text{ BTU/h}$, and rated $5^\circ\text{F}$ capacity of $34{,}000\text{ BTU/h}$. Record the shifted balance point and reduced auxiliary requirements.
4. Scenario C — Economic Optimization: Input local utility electricity rate of $0.18/\text{kWh}$ and fossil backup gas rate of $1.45/\text{therm}$. Determine the Economic Balance Point ($T_{EBP}$) switchover temperature.

5. Student Data Collection Matrix

6. Post-Lab Analytical Assessment

1. Thermodynamic Lift vs. Suction Density: Explain why the heating capacity of an air-source heat pump degrades rapidly as outdoor temperature declines, focusing on refrigerant specific volume at compressor suction.
2. Defrost Cycle Penalties: When operating between $30^\circ\text{F}$ and $40^\circ\text{F}$ with high relative humidity, frost accumulation on the outdoor evaporator coil requires periodic reverse-cycle defrost. How does this impact net seasonal COP compared to steady-state laboratory ratings?
3. Electrification Grid Impact: Compare the peak electric demand (in kW) at $5^\circ\text{F}$ between Scenario A (relying on 9.2 kW of electric strip heat) versus Scenario B. Discuss the implications for residential electric service sizing (100A vs. 200A panels).

7. Instructor Notes & Pedagogical Solutions Guide