The voltage numbers sound good to me. One of the problems with the 3 is that its systems are different than most vehicles, hence norms are not what one would anticipate. I think that is why your mechanic thinks there is still a problem. Also voltages are temperature dependent - as the temperature drops below freezing, alternator output voltages tend to rise.
Under high load conditions, a normal alternator regulator setup would raise the voltage and the voltage would stay high until the load exceeded the alternator output and then you would see a drop in voltage.
The 3, not so. The regulator receives what is call a PWM signal from the ECM. Depending upon a number of conditions, emission controls being primary, the alternator amps and volts may cut back under increased load demand to reduce the hp required by the engine to operate the alternator. To compensate, the ECU cuts various loads off, say the heated seats, the heated windscreen, the radio amp etc. In other words, you may have turned a system on, but the computer has cycled it or dialled it back but there is rarely any physical indication of that.
There are a number of alternator and regulator related files, (among others), per the link below that attempts to explain the power generation system in greater detail. That is why the more stock you keep your 3, the better it will operate as what may seem like a minor change can have major consequences unless the affected systems are truly understood. I think the LR engineers are still learning; hence no one really knows all the quirks.
That is how a deteriorating brake light switch can affect the operation of the radiator fan - who would have thought? I expect your fan will be OK now except on very cold days when it may fuss a bit.
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