There are two types of solar water heating system for us to choose. One is with a gas auxiliary tank system and the other one is with a electric auxiliary tan system. Whether one of these two system is more efficient and appropriate depends on the individual household’s own condition. We need to choose carefully before making a decision of which system should be installed because “This will help you determine the energy savings and payback period of investing in a more energy-efficient system, which will probably have a higher purchase price” (*Estimating the cost and energy efficiency of solar water heating system*). To compare the two systems, we need to know the way to calculate their annual operating cost to determine whether one system is more efficient in the long run.

* different system has different solar energy factor (SEF).

**For the solar water heating system with gas auxiliary tank system:**

According to the DOE test procedure for hot water heaters, the average energy usage os a three person households is about 0.4105 therm per day.

365 × 0.4105 ÷ SEF × Fuel Cost (therm) = estimated annual operating cost

The SEF of the gas auxiliary system is about 1.1 and the gas cost is about $1.10/therm

So we have: 365 × 0.4105 ÷ 1.1 × $1.10 = **$149.83**

**For the solar water heating system with electric auxiliary tank system:**

The average usage of electric energy of a household of three people per day is about 12.03 kWh

365 × 12.03 kWh/day ÷ SEF × Electricity Cost (kWh)= estimated annual operating cost

The SEF of the electric auxiliary system is about 2.0 and the cost on electricity is about $0.08/kWh

So we have: 365 X 12.03 ÷ 2.0 X $0.08 = **$175.64**

Of course, for different households the situation will be different as well, and so is the cost. The calculation above just shows one possible situation. They serves for telling us how to calculate the annual operating cost of different solar water heating system.

**Estimating the Cost and Energy Efficiency of a Solar Water Heaterhttp://energy.gov/energysaver/articles/estimating-cost-and-energy-efficiency-solar-water-heater**

John RoeCan you explain what is the definition of “solar energy factor”? How is this quantity measured or estimated? Is it a constant of the system design, or is it likely to change as the volumes of hot water drawn vary?

A therm is a unit of energy. The phrase “the average energy usage os a three person households is about 0.4105 therm” is not dimensionally correct – it needs a time unit (like “therms per hour” or “therms per week”).

The numbers here duplicate those in the source referenced. You should carry out your own calculations.