The house we are building here in lovely Massachusetts, USA… almost a Passive House, but not quite certifiable… well, we can heat it with a hair dryer (1500 W of heat). And two on a very cold day (6F design temperature). Does this mean our heating bills will be low? Pretty low, I imagine, yes. But not zero.
Let’s do some math… And first let’s simplify things… the HDD (heating degree days) for Stow, MA is somewhere around 7200 (base 68F) meaning that if you multiply the days of the year we need heat times the temperature differential between the inside and outside temperature on these days, you’ll get 7200. It’s a little more exact than this (think “area under the curve” from calculus — using hour by hour measurements), but that’s the basic idea.
So let’s simplify it even more. Let’s call every winter day exactly 32F outside vs 68F inside and assume our 1500 W can keep up with that (which from my back-of-the-envelope calculations seems about right…) So that’s a delta of 36F. Now how many days is that? 7200 F*days / 36 F = 200 days = 6.66 months. Let’s go crazy and call it 7 months.
OK, so let’s say one really did run a hair dryer for 7 months, 24 hours a day. What would that cost to run 1500 W (1.5kW) that whole time? Well, we pay $0.20/KWh. So using the factor-label method to keep track of our units… making sure numerators and denominators cancel out, that’s:
7 months * 30 days/month * 24 h / day * 1.5 KW * $0.20 / KWh = $1,512.00 per year
In other words, kinda a lot!!!!
But that’s why people don’t typically use electric heat, it’s expensive. (It’s also not a great idea because fossil-fuel power plants are roughly 33% efficient in converting the fuel to electricity… I imagine that’s exactly why it’s expensive! So… it’s better to use it in direct form at your house…) That’s where the heat pump comes in. If we factor in the 2.7 COP (coefficient of performance) of our Mitsubishi “Mr Slim” air-source heat pumps that’s:
$ 1512 / 2.7 = $560
OK, now we’re talking! This also happens to be almost exactly the number you would get if you calculated the cost of delivering 1500W of heat via propane or natural gas. That would be fine and dandy too. So the 2.7 COP mainly serves to green up the electricity use, getting back to parity with using propane directly. 2.7 * 0.33 = 0.8991 (probably about the efficiency of a Rinnai propane direct-vent heater)
Now, the reality is that I hope most of this heat comes from active solar heating. But more on that later!