We press a button or set the timer, and a little later it tells us when the bath is ready. If the bath's empty it's easy. It knows how much water is in the tank, it knows how hot it is, and it knows how much needs to go into the bath. If the bath has some water in it, then it must decide how much water needs adding and how much to heat up the water. Either it can add water from the tank, which will be relatively hot, or it can send water from the bath through the tank, from which it will take heat, in accordance with the second law of thermodynamics. Adding hot water is a lot more effective than circulating the existing water since the exchange has inefficiencies and there are heat losses as the water goes through the pipes between bath and boiler, even though we insulated them and kept them as short as possible. This is where the problems start.
Sometimes, there is not really enough heat in the tank to effectively heat up the bath. The bath brain probably starts off by adding hot water to the bath, then thinks that it's still not hot enough, so it starts circulating the heat to get it warmer. What it doesn't realise is that the heat from the boiler isn't going to get to the bath, or the part of the tank where the pipes from the bath are circulating may not be as hot as the part with the thermometer in. Rather than heat going into the bath, it may start leaving the bath, and dissipating into the larger thermal system following the inevitable fate of entropy. Then the bath's brain thinks "sod it", and gives up, without saying anything.
The bath talks to us, but it doesn't know how to say sorry.
This lukewarm bath situation is most likely to happen after a very cold night, when the heat pump is so inefficient that the energy would have been better spent drilling for oil in the Japan Sea. Obviously, I could just switch the boiler to be on all the time, or to "o-makase" (trust me) mode and let it switch on when it's warmer in the day time, but I don't really trust it.
I would like to change the heating system so that the atmospheric heat source for the boiler is not night-time air, but the air flowing under the solar panels in the daytime.
This is the situation on a couple of clear, cold days in winter, midnight at the beginning of 13th January to midnight at the end of 14th. The black line is the temperature outside. The air temperature drops around 9 below zero on the first night, then up to around 2 degrees in the heat of the next day's sun. Then it plummets to -14 the following night and up to about 2 degrees again the following day. This leaves pretty cold temperatures for the Eco Cute to squeeze heat out of, leading to great inefficiency.
The blue line is the temperature of air flowing through the channel under the solar panels on the roof. At night it gets just as cold as outside temperature. In fact on the night of the 13th, it was over 2 degrees colder because of the effect of the roof radiating heat to the stratosphere on a cloudless night. In the daytime, it gets over 30 degrees. If we could use the air from the channels in the middle of the day, rather than the air outside in the middle of the night, the air temperature could be 40 or 50 degrees higher. At this higher temperature, the heat pump would be much more efficient.
The coldest nights and the warmest days are when it is clear, and of course it's not sunny every day. For example, this is the temperature on the panels the day it snowed. You can see the 14th and 15th January here, and how the temperature below the panels is just above freezing. In this case we have nothing to lose. The following day, with some snow still left on the roof, the temperature still got up above 10 degrees in the day time. You can see the temperatures from 12th January to 17th February below, perhaps averaging 25 or 30 degrees under the panels in the hottest part of the day, compared to minus 3 or 4 degrees outside at night.
The main use of hot water is probably the bath, which we usually run at night time, so another advantage of switching from night time heat pumping to daytime heat pumping would be that the hot water would have less time to cool down, so we would need to use less of it. In terms of economics, this would mean a switch from using bought night time electricity to using our own generated electricity. Since we're buying off-peak electricity at 9 yen, but selling our electricity at 48 yen, the system would have to be 5 times more efficient to be worth changing. However, we only have a 10 year contract for selling our electricity at 48 yen, and no idea what may happen after that.
This graph may give us an idea of how much energy we would save. Heat pumps are rated by COP, coefficient of performance, rather than efficiency. This corresponds to the amount of heat coming out compared to the amount of energy put in. So if you used 1 kW of electricity and got 5 kW of heat, that would be a COP of 5. The COP is affected by the temperatures inside and outside, so if you're trying to heat up luke warm water with hot air, you're going to get a much higher COP than trying to make hot water very hot from cold air. I've seen that Eco Cutes have a COP of 3.8, but this is a meaningless figure, unless you know precisely what operating conditions that was under. In the real world, not the world of advertising and eco-posturing, the COP for a particular heat pump is on a curve, dependent on the temperature of condensation, which happens outside, and the temperature of evaporation, which happens inside. Many heat pump manufacturers do not publish COP charts. From the graph above I estimate that if the temperature outside is 20 degrees higher, the COP will double.
(The COP graph was stolen from Science Direct's website, from a paper which I did not pay $36 to read, by Forrest Meggers and Hansjurg Leibundgut of ETH Zurich, Faculty of Architecture, Institute of Technology in Architecture, Building Systems Group, "The potential of wastewater heat and exergy: Decentralized high-temperature recovery with a heat pump". I hope they don't mind.)
