@HUGHG Not a problem to write out a long message as I don’t mind sharing my thoughts on this sort of thing.
Average humidity in the UK can vary quite a bit according to this site: Average Humidity in the United Kingdom - Current Results
If it’s a foggy day, you have to assume it’ll have a very high humidity and on a hot summers day with no rain in weeks, fairly low. It’ll vary quite a bit all over the country. Given the defrost cycle is going to have a negative impact compared to milder days and generally speaking kW output of most heat pumps declines as you fall in ambient temperature towards 0C ambient temp, I would look at the kW output graphs vs ambient temperature to aid sizing rather than worry too much about the effects of humidity.
As for compressor control algorithms, each manufacturer has its own ways they employ when it comes to inverter control and protecting the compressor. Many compressors have a minimum run time that they must run for to prevent undue wear on bearings etc. Running a compressor at a fixed RPM for a set time on startup helps the system to stabilise within a likely safe operating zone inside the compressor envelope. It will also help ensure the oil is returned to where it needs to be. After a time has elapsed, it’s likely a PID algorithm takes over to monitor kW output, looking at flow and return temperatures and the rate of change of temperature.
See note from Copeland on this topic: Determining minimum run time for ZP*KB compressors
and this Recommended minimum run time from startup to shutdown for scroll compressors
and if you want an example of some generic application notes Copeland provide as an example for OEM system builders have a look at this: https://climate.emerson.com/documents/copeland-scroll-variable-speed-compressors-xhv0181p-to-xhv0382p-application-guidelines-en-gb-5260810.pdf
Interesting @MyForest mentions wind speed. I’ve watched an electronic expansion valve play hunt the suction superheat setpoint value game before where there is a varying, yet very strong wind present. Wind conditions can have a noticable impact on performance.
On the fixed speed systems I work with, there is a 6 or 7 minute minimum run time to ensure compressor longevity. After that time has elapsed, the heat pump controller then looks at the return set temperature to see if the target has been met, and if so, switch off the compressor. If return set point + hysteresis is met before the minimum time has elapsed, tough, compressor will keep going until its minimum run time has finished. Protection of compressor comes before niceties of exact hit set points.
If set point has not been met after x elapsed time, then it will increase in power stage by bringing on another compressor (on multi compressor systems) and monitor that for x mins before deciding if another compressor is needed or not and repeat.
The only things that can stop a system I work on before “minimum run time” has completed are safety events such as a high pressure event, hot gas stat triggered, soft starter error, low pressure event, loss of control of electronic expansion valve, sensor fault etc. All those are safety critical events which take higher priority than minimum compressor runtime.
There is also a rule that the electricity Distribution Network Operators like heat pumps to obey and that is not to perform more than 3 compressor starts per hour. It is likely this rule is programmed into most heat pumps sold in the UK, but it’s worth bearing in mind if you have a no-name Chinese built thing off ebay churning away in the back garden as a DIY affair.
One thing that might be worth looking at in oversized heat pump installs is an inline buffer tank on the heating circuit (but check with the manufacturer first!) Increasing heating circuit system volume will increase run times, decrease starts per hour / starts per day and with inverter controlled setups, might allow longer running at a lower RPM state where the CoP figures may well be higher. It also gives greater thermal energy to assist with reverse cycle defrosts. It can also give a potential mounting point to backup immersion elements for the heating circuit if no backup or flow boiler is in situ.