Slobodan,
You are rather ill-informed for an electric engineer.
It is true that the device shown in your reference multiplies U and I. But it goes that microsecond for microsecond, not using an average or RMS value.
You could say that your method is scalar multiplication while the method used in kWh meters is vector multiplication. As we all know, you need to include the angle between the units to arrive at a correct answer when vectors are multiplied.
The angle, in this case, is the phase angle, phi, between U and I. And it enters the multiplication as cos(phi).
As you also should know, PF = cos(phi). We are limiting this discussion to sine waves and linear loads. Distorted waveforms define PF in another way.
So, dpc (the guy that first answered the OP) gave a complete and correct answer. No need to confuse things like you have done. Please do not ruin this great forum by adding misconceptions, downright mistakes and "feelings" about technical facts.
Gunnar Englund
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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...