Can primary energy stand in for the other indicators? A grey relational analysis of reporting proxies in an anonymised renovation sequence

Building energy reports headline primary energy demand, yet clients and funding bodies also look at final energy, emissions, operating costs and plant losses. Whether a single headline indicator adequately represents the others is rarely tested. This paper applies grey relational analysis (GRA), a method designed for short and incomplete data series, to six cumulative model states of an anonymised nonresidential energy consultancy report. Primary energy is the reference series; final energy, useful energy, system losses, CO2, SO2, NOx and fuel costs are the comparison series. With the customary distinguishing coefficient of 0.5, the grey relational grades are 0.997 for SO2, 0.975 for CO2, 0.937 for final energy, 0.929 for fuel costs, 0.847 for useful energy, 0.713 for NOx and 0.688 for system losses. The order is unchanged for distinguishing coefficients between 0.1 and 1.0; with min–max normalisation, only the two weakest indicators swap places. The divergent indicators separate when mechanical ventilation adds electricity demand: primary energy continues to fall, while system losses rise by 17% and NOx by 15% relative to the baseline. A simple factor test explains the pattern. An indicator tracks primary energy when its emission factor is proportional to the primary-energy factor across energy carriers. This holds closely for SO2 (ratio 0.98), approximately for CO2 (0.86) and not for NOx (6.1). Primary energy is therefore a reasonable proxy for carbon and sulphur emissions in this case, but not for nitrogen oxides or plant losses. The results are descriptive and model-based.