The coordination between the systems is achieved by telling the electrical heater it is a hot day when it is supposed to be off
The solution I selected is similar to the expensive systems that can be bought. I replaced the control system for the heat pump with a design of my own, which both controls the heat pump, and knows about the electrical heater, and forces it to cooperate with the heat pump.
I knew I could easily fix the cooperation, since I could not figure any time I would like the heat pump to be off when the electrical heater was on. Thus, what is needed is to force the electrical heater to be off until it is allowed, and when the electrical heater is allowed, force the heat pump to be on as well (except when it reaches the minus 10 degree Celsius temperature when the heat pump should not be used at all). The logic above sounded to me like a simple relay logic.
In Sweden where I live, it is not allowed for me to make any changes to any part using 220 Volt. Thus, placing a relay on the power input to the electrical heater was out of the question. Considering the high currents used during cold winter nights, it would be an expensive relay as well. But there was an easier solution. The outside temperature is measured by the electrical heater through a temperature sensitive resistanse. So what I have done is to connect a relay on the cable to that electrical resistanse. Whenever I want the electrical heater to stay off, I use the relay to tell it that it is 30 degrees Celsius outside. At so high temperatures, it will not want to have more than 10 degrees on the radiator water. Which means it never goes on as long as it believes the outside temperature is that high.
The control for the heat pump itself was a little harder to decide how to do it. It had to keep the good thing of the old system, trying to avoid switching the heat pump on and off to frequently. It also had to assure that the temperature swings inside became lower than today. Thus, simply changing the temperature sensor to something with say 0.2 degree Celsius gap instead of a 0.6 degree gap would not be a good idea (the heat pump would be likely to go on and off more frequently).
The solution came from deciding not to base the on and off logic on a difference in temperature, but to base it on accumulation of temperature difference from a threshold multiplied by minutes (temperature minutes). A temperature difference of a whole degree during a minute is one temperature minute. So is a temperature difference of a tenth of a degree during ten minutes.
Temperature minutes are calculated with sign, so if a falling temperature is changed to a slowly increasing temperature (for example by the sun rising), the ongoing countdown will when the temperature has risen to above the threshold start adding temperature minutes instead of subtracting them, and the total temperature minutes will be accumulated until back at the original starting point.
Using this concept, I aimed originally at a countdown of 40 temperature minutes before making a switch. Thus, a temperature difference of a tenth of a degree is not a reason to make a change until after a quite long time (400 minutes, or more than 6 hours). But a temperature difference of 0.6 degrees will only be allowed a little more than an hour. And to reach a temperature difference of 0.6 degrees, we most probably would first pass 0.5, 0.4, ... all of these differences accumulating temperature minutes, in reality meaning that a difference of 0.6 degrees is very unlikely to get to occur, unless the temperature is falling very fast. After a few years, I have learned that in normal operations, the heat varies within 0.4 degrees from highest to lowest, with the exception of when the temperature is close to the limit for the heat pump, then the variations reaches 0.7 degree from max to min.
When the two above logics where decided upon, I constructed the logic unit. It is based on a relay, plus a microchip that controls the relay, and a temeperature sensor, and a display, and three buttons. I built it like this, with digital devices rather than analogue devices, since my belief was that the logic of the control and display system would be the complicated parts, and thus an analogie design would quickly become either inadequate, or too expensive and complicated. The control device has been in the house for four years now, and works like a charm.