Heat Pump Performance Metrics

Heat pump performance metrics quantify the thermodynamic efficiency of converting electrical energy into heating or cooling capacity. Understanding these metrics is critical for equipment selection, energy modeling, and regulatory compliance.

Coefficient of Performance (COP)

COP represents the instantaneous thermodynamic efficiency of a heat pump, defined as the ratio of useful heating or cooling output to electrical energy input:

$$\text{COP}{\text{heating}} = \frac{Q{\text{heating}}}{W_{\text{electrical}}} = \frac{Q_{\text{heating}}}{Q_{\text{heating}} - Q_{\text{cooling}}}$$

$$\text{COP}{\text{cooling}} = \frac{Q{\text{cooling}}}{W_{\text{electrical}}} = \frac{Q_{\text{cooling}}}{Q_{\text{heating}} - Q_{\text{cooling}}}$$

Where $Q_{\text{heating}}$ is condenser heat rejection, $Q_{\text{cooling}}$ is evaporator heat absorption, and $W_{\text{electrical}}$ is compressor power plus auxiliary loads.

Theoretical Carnot COP

The theoretical maximum COP for a reversible heat pump operating between two thermal reservoirs is:

$$\text{COP}{\text{Carnot,heating}} = \frac{T{\text{condenser}}}{T_{\text{condenser}} - T_{\text{evaporator}}}$$

$$\text{COP}{\text{Carnot,cooling}} = \frac{T{\text{evaporator}}}{T_{\text{condenser}} - T_{\text{evaporator}}}$$

Where temperatures are absolute (Kelvin). Real heat pumps achieve 30-60% of Carnot efficiency due to irreversibilities: compressor inefficiency, pressure drops, heat exchanger temperature differentials, and superheat/subcooling requirements.

Standard Rating Points

AHRI Standard 210/240 specifies COP rating conditions:

At 47°F outdoor temperature, efficient heat pumps achieve COP values of 3.0-4.5, meaning they deliver 3-4.5 units of heat for every unit of electricity consumed. At 17°F, COP typically degrades to 2.0-3.0 due to increased temperature lift and reduced refrigerant mass flow.

Seasonal Performance Metrics

Seasonal metrics account for part-load operation, cycling losses, defrost cycles, and variable outdoor temperatures throughout the heating or cooling season.

Heating Seasonal Performance Factor (HSPF)

HSPF represents the total heating output during a typical heating season divided by total electrical energy consumed, expressed in Btu/Wh:

$$\text{HSPF} = \frac{\sum Q_{\text{heating,seasonal}}}{\sum W_{\text{electrical,seasonal}}}$$

AHRI Standard 210/240 defines HSPF calculation using a bin method that weights performance at different outdoor temperatures by hours of occurrence in six climatic regions (I through VI, representing varying heating severity).

HSPF2 Rating (DOE 2023 Standard):

The updated HSPF2 metric uses more representative test conditions:

• Lower indoor temperature set point (68°F vs 70°F)
• Additional low-temperature test point (5°F)
• Updated geographic bin data
• Includes distribution system losses

HSPF2 values are typically 15-20% lower numerically than legacy HSPF, though they represent the same equipment. Minimum federal efficiency standards (effective January 2023):

• Split systems: HSPF2 ≥ 7.5 (equivalent to HSPF ≈ 8.8)
• Package systems: HSPF2 ≥ 6.7 (equivalent to HSPF ≈ 8.0)

Regional HSPF Variations

Heat pump seasonal performance varies by climate region:

The same heat pump rated at HSPF2 = 8.5 in Region IV may deliver effective seasonal performance of HSPF2 = 7.0 in Region VI due to extended low-temperature operation where COP degrades.

Seasonal Energy Efficiency Ratio (SEER)

SEER quantifies cooling-mode seasonal efficiency using the same bin methodology:

$$\text{SEER} = \frac{\sum Q_{\text{cooling,seasonal}}}{\sum W_{\text{electrical,seasonal}}}$$

SEER2 Rating (DOE 2023 Standard):

The updated SEER2 metric incorporates:

• Higher external static pressure (0.5 in. w.c. vs 0.1 in. w.c.)
• Lower indoor air flow (280-360 CFM/ton vs 300-450 CFM/ton)
• Updated test procedures

Minimum federal efficiency (effective January 2023):

• Northern states: SEER2 ≥ 13.4
• Southern states: SEER2 ≥ 14.3

High-efficiency equipment achieves SEER2 = 18-22 through variable-speed compressors, enhanced heat exchangers, and optimized refrigerant charge.

Energy Efficiency Ratio (EER)

EER measures steady-state cooling efficiency at peak load conditions (95°F outdoor, 80°F/67°F indoor):

$$\text{EER} = \frac{Q_{\text{cooling,95F}}}{W_{\text{electrical,95F}}}$$

EER correlates with peak demand reduction and is critical for grid reliability. High-efficiency systems maintain EER ≥ 11-13 at design conditions.

Integrated Part-Load Value (IPLV)

IPLV characterizes commercial heat pump efficiency across four load points weighted by typical operating hours:

$$\text{IPLV} = 0.01A + 0.42B + 0.45C + 0.12D$$

Where:

• A = EER at 100% load
• B = EER at 75% load
• C = EER at 50% load
• D = EER at 25% load

IPLV typically exceeds full-load EER by 15-30% for variable-capacity equipment, demonstrating superior part-load efficiency.

Performance Degradation Mechanisms

graph TD
    A[Heat Pump Operating Conditions] --> B[Temperature Lift Increase]
    A --> C[Defrost Cycle Frequency]
    A --> D[Part-Load Cycling]
    A --> E[Distribution Losses]

    B --> F[Reduced COP]
    C --> F
    D --> F
    E --> F

    F --> G[Lower Seasonal Efficiency]

    B --> H[Higher Condensing Temp<br/>Lower Evaporating Temp]
    C --> I[Reverse Operation<br/>Resistance Heat]
    D --> J[On-Off Cycling Losses<br/>Crankcase Heat]
    E --> K[Duct Leakage<br/>Uninsulated Runs]

    style F fill:#ff6b6b
    style G fill:#ff6b6b

Temperature Lift Impact

Heat pump capacity and efficiency degrade with increasing temperature differential between source and sink. For air-source heat pumps, a 1°F increase in temperature lift typically reduces COP by 1-2%:

$$\frac{d(\text{COP})}{d(\Delta T)} \approx -0.01 \text{ to } -0.02 \text{ per °F}$$

This relationship explains why heat pumps excel in moderate climates but require supplemental heat in extreme cold.

Defrost Penalty

Frost accumulation on outdoor coils when operating below 40°F with high humidity requires periodic defrost cycles. During defrost:

1. Reversing valve switches to cooling mode
2. Hot refrigerant melts frost (2-10 minutes)
3. Supplemental resistance heat maintains indoor comfort
4. Energy penalty: 5-15% of heating season energy

Demand defrost controls minimize this penalty by initiating defrost only when necessary based on coil temperature differential, reducing energy waste compared to time-based defrost.

Efficiency Comparison

Conversion Relationships

Approximate conversions between metrics (equipment-dependent):

$$\text{SEER} \approx 3.41 \times \text{Average COP}_{\text{cooling}}$$

$$\text{HSPF} \approx 3.41 \times \text{Average COP}_{\text{heating}}$$

$$\text{EER} = 3.41 \times \text{COP}_{\text{95F}}$$

The factor 3.41 converts COP (dimensionless) to Btu/Wh units. These conversions are approximations because seasonal metrics incorporate cycling, defrost, and distribution losses not captured in steady-state COP.

Regulatory Standards

AHRI Standard 210/240-2023 establishes test procedures and minimum efficiency requirements for unitary air conditioners and heat pumps. DOE 10 CFR Part 430 mandates federal minimum efficiency standards, updated in 2023 to improve national energy savings by approximately 3 quadrillion Btu over 30 years.

Equipment selection should consider both minimum regulatory compliance and life-cycle cost optimization, where higher initial efficiency investment yields long-term energy savings that offset premium first costs.

Components

• Heating Seasonal Performance Factor
• Hspf Calculation Regions
• Region Iv Hspf
• Region V Hspf
• Coefficient Of Performance Heating
• Cop At 47f
• Cop At 17f
• Energy Efficiency Ratio Cooling
• Seasonal Energy Efficiency Ratio
• Integrated Part Load Value