Lighting and un-vented appliances convert their electricity use to heat at a rate of 100% and this heat is added to the conditioned space. This extra heat reduces HVAC load during the heating season and increases it during the cooling season. The extent to which this impacts savings potential depends on the relative length of the heating and cooling seasons and the efficiency of the HVAC systems.
Consider a house with electric baseboard heat and central AC in a heating dominated climate. Let’s say that hours of the year are split between 50% heating, 15% cooling, 35% neither. An upgraded refrigerator saves 300 kWh annually in plug load. During heating hours the electricity cost of replacing the lost heat from the refrigerator is identical to the savings in electricity consumed by the refrigerator. Thus you only save money during parts of the year when that heat is not helping to maintain the house temperature. So that cuts down the potential savings to 150 kWh. The there is an offsetting effect during the cooling season, but the cooling season is much shorter and the AC is much more efficient at removing that extra heat. Let’s say that the AC is 10 SEER, which is about 300% efficiency. So the refrigerator upgrade reduces annual cooling load by 15% * 300kWh = 45kwh. Since the AC efficiency is 300%, this saves an additional 15kWh of cooling electricity use, giving us 165 kWh total savings on the year: 300 kWh saved plug load – 150 kWh added heating + 15 kwh savd cooling.