Climate warming and increasing variability challenges the electricity supply in warm seasons. A good quantitative representation of the relationship between warm-season electricity consumption and weather condition provides necessary information for long-term electricity planning and short-term electricity management. In this study, an extended version of cooling degree days (ECDD) is proposed for better characterisation of this relationship. The ECDD includes temperature, residual temperature and specific humidity effects. The residual temperature is introduced for the first time to reflect the building thermal inertia effect on electricity consumption. The study is based on the electricity consumption data of four multiple-street city blocks and three office buildings. It is found that the residual temperature effect is about 20% of the current-day temperature effect at the block scale, and increases with a large variation at the building scale. Investigation of this residual temperature effect provides insight to the influence of building designs and structures on electricity consumption. The specific humidity effect appears to be more important at the building scale than at the block scale. A building with high energy performance does not necessarily have low specific humidity dependence. The new ECDD better reflects the weather dependence of electricity consumption than the conventional CDD method.