A U-shape vulnerability of ΔT-based defrost control in subarctic heat pumps: Evidence from a 26-unit parallel field test and a paired DEB–FEB metric framework

Building heating decarbonization in cold climates depends on air-source heat pumps (ASHPs) delivering their nameplate seasonal performance, yet field audits keep recording a rated-vs-realized COP gap that is largest at the cold extreme. The gap is operational rather than material: hardware is sized correctly, but the control strategy is suboptimal. Commercial defrost control has been diagnosed almost exclusively through single-sided indicators of over-defrost — defrost frequency or the defrost-phase energy fraction — which are silent on the converse failure: a controller that fails to dispatch needed defrosts and runs with a frost-blocked coil. Using a 26-unit parallel field test of mass-produced enhanced vapor injection ASHPs in Mohe, China (ambient down to −42 °C), we expose a U-shape control-failure geometry that the single-sided view masks. We introduce a paired metric framework: Defrost Energy Burden (DEB), the fraction of electrical input consumed by the defrost phase, captures over-defrost; Frost Energy Burden (FEB), the shortfall of observed COP relative to each unit's frost-free laboratory baseline at the same ambient, captures under-defrost. The 124 Brand×T-RH bins partition into four quadrants (cutoffs 19.17% DEB/7.80% FEB), with median combined waste rising 9.8%→44.5%. The 28 frost-blocked bins span 11 brands and hide a median 12.8% COP shortfall invisible to DEB-only diagnostics. Five brands swing between branches across temperature zones in the same factory-new unit — most consistent with control-coupled rather than hardware drivers. The findings motivate a U-shape Strategy Robustness Test in extreme-cold certification protocols (e.g., GB/T 25127, EN 14511) probing both branches.