Conductor resistance increases with temperature, directly affecting solar cable performance and efficiency. Understanding temperature coefficient impact enables accurate system design and helps prevent performance degradation in high-temperature installations.
Understanding Temperature Coefficient
Definition: Temperature coefficient of resistance describes how electrical resistance changes with temperature. For copper conductors, resistance increases approximately 0.4% per degree Celsius above the reference temperature of 20°C.
This relationship follows a predictable pattern expressed as: R(T) = R(20°C) × [1 + α × (T - 20°C)]
Where α (alpha) represents the temperature coefficient—approximately 0.00393 per °C for copper.
Practical Meaning: A copper conductor with 1.0Ω resistance at 20°C will exhibit approximately 1.28Ω resistance at 90°C—a 28% increase. This substantial change significantly impacts voltage drop calculations and power losses in solar installations.
Temperature Impact on Cable Resistance
Operating Temperature Range: Solar cables operate across wide temperature ranges depending on installation conditions:
Minimum: -40°C in cold climates during winter nights
Maximum: +90°C in hot climates with direct sun exposure and high electrical loading
Resistance at these temperature extremes varies considerably from standard room temperature values.
Cable Heating Sources: Multiple factors contribute to PV cable operating temperature:
Internal heating from resistive losses (I²R heating) as current flows through conductors. This self-heating effect increases with higher current loads and becomes more pronounced in undersized conductors.
Ambient temperature in installation environment. Desert installations routinely experience 45-50°C ambient conditions, while tropical regions combine high temperature with high humidity.
Solar radiation heating cable jackets exposed to direct sunlight. Black cable jackets can reach surface temperatures 20-30°C above ambient when exposed to full sun.
Bundling effects when multiple cables are installed together in conduit or cable trays, limiting heat dissipation and raising temperatures above single-cable operating conditions.
Voltage Drop Calculations with Temperature
Standard vs Operating Temperature: Most voltage drop calculations use resistance values at 75°C, representing typical operating conditions. However, actual operating temperatures vary based on specific installation conditions.
Calculation Example: Consider a 6mm² copper conductor with DC resistance of 3.39 Ω/km at 75°C:
At 20°C: R = 3.39 × [1 + 0.00393 × (20-75)] = 2.66 Ω/km At 90°C: R = 3.39 × [1 + 0.00393 × (90-75)] = 3.59 Ω/km
For a 50-meter cable run carrying 20 amperes:
At 20°C: Voltage drop = 2 × 20A × 2.66 Ω/km × 0.05km = 5.32V
At 90°C: Voltage drop = 2 × 20A × 3.59 Ω/km × 0.05km = 7.18V
The 35% increase in voltage drop at elevated temperature significantly impacts system performance, particularly in lower-voltage systems where percentage voltage drop is more critical.
Power Loss Temperature Dependency
Resistive Power Loss: Power dissipated in conductors follows P = I²R. As temperature increases resistance, power losses increase proportionally.
Using the previous example at 20A current:
At 20°C: Power loss = 20² × 2.66 × 0.05 = 53.2W per 50m
At 90°C: Power loss = 20² × 3.59 × 0.05 = 71.8W per 50m
This 35% increase in power loss at elevated temperature reduces system efficiency and generates additional heat, creating a feedback loop where increased temperature raises losses, which generates more heat.
Design Considerations for Temperature Effects
Conservative Design Approach: Prudent system design accounts for worst-case temperature conditions rather than average or standard conditions.
Conductor Sizing: When sizing solar cables, calculate voltage drop using expected maximum operating temperature rather than standard 75°C reference. This ensures voltage drop remains acceptable even during peak temperature conditions.
For installations in hot climates or with limited ventilation, use resistance values at 90°C or higher for design calculations. This conservative approach prevents unexpected voltage drop issues during actual operation.
Ampacity Derating: Cable ampacity ratings assume specific operating temperatures. When ambient or installation conditions create higher starting temperatures, additional derating beyond standard factors becomes necessary.
Installation Environment Impact
Desert Installations: Ambient temperatures exceeding 45°C combined with direct solar exposure create particularly challenging thermal conditions. Cables installed on roofs or in above-ground conduit may reach 80-90°C during peak production periods.
Design calculations for these installations should use 85-90°C as the operating temperature assumption to ensure adequate performance margins.
Tropical Climates: High humidity combined with elevated temperatures creates different challenges. While peak temperatures may not reach desert levels, sustained high temperatures throughout the year prevent thermal recovery periods.
Conduit and Cable Tray Installations: Enclosed installations with limited air circulation experience higher temperatures than cables in free air. Multiple cables in conduit create bundling effects that further increase temperatures beyond single-cable conditions.
Monitoring and Verification
Thermal Imaging: Infrared cameras identify hot spots indicating excessive resistance from poor connections or undersized conductors. Temperature measurements validate design assumptions and identify potential issues before failures occur.
Performance Monitoring: Comparing actual voltage drop under load with design predictions helps verify that temperature effects are within expected ranges. Unexpectedly high voltage drop may indicate temperature-related resistance increases exceeding design assumptions.
Material Quality Impact
Copper Purity Effects: High-purity oxygen-free copper exhibits slightly lower temperature coefficient than standard copper grades. While the difference is modest, it contributes to reduced temperature-related performance degradation.
KUKA CABLE uses tinned oxygen-free copper conductors, ensuring consistent electrical properties across temperature ranges and minimizing resistance variations that could affect system performance.
Connection Quality: Poor connections exhibit higher resistance and generate excessive heat. Temperature coefficient effects amplify connection problems—a marginal connection at room temperature may fail completely at elevated operating temperatures.
Standards and Testing Requirements
Temperature Rating Standards: IEC 62930 and UL 4703 specify temperature ratings for solar cables, typically 90°C for standard cables and 120°C for enhanced temperature ratings.
These ratings ensure insulation maintains integrity at maximum conductor temperatures. However, designers must still account for temperature coefficient effects on electrical performance within these temperature limits.
Testing Protocols: Cable testing includes high-temperature performance verification, confirming that electrical properties remain within specifications across the rated temperature range. This includes resistance measurements at elevated temperatures and voltage drop verification under thermal loading.
Practical Design Guidelines
Use Appropriate Reference Temperature: Select design calculation temperature based on expected maximum operating conditions rather than standard reference values. This prevents undersizing and ensures adequate performance margins.
Account for All Heating Sources: Consider combined effects of ambient temperature, solar radiation, and I²R heating when estimating operating temperature. Don't rely solely on ambient temperature specifications.
Verify Worst-Case Scenarios: Design for peak thermal stress conditions—midday summer operation in hot climates with maximum electrical loading. Systems adequate for average conditions may experience problems during peak stress periods.
Monitor Actual Performance: Use installed system data to validate design assumptions. Unexpected voltage drop or efficiency losses may indicate temperature effects exceeding design predictions, requiring corrective action.
Conclusion
Temperature coefficient impact on conductor resistance significantly affects solar cable performance, particularly in installations experiencing elevated operating temperatures. Accurate system design requires accounting for resistance increases at actual operating temperatures rather than relying on room temperature or standard reference values.
By understanding and properly accounting for temperature coefficient effects, designers can ensure solar installations maintain adequate voltage regulation and minimize resistive losses throughout their operational lifetime—even during peak thermal stress conditions.
Contact KUKA CABLE technical team for design assistance accounting for temperature coefficient effects in your specific solar installation conditions.
