Integrating the voltage across the primary looks like a rather touchy business to me. The problem is that all circuits have offset, and all circuits also have a drift in that offset. Any offset in the integrator will drive the power circuit such that a permanent, constant net DC component appears in the voltage over the primary. That will cause a DC current in the primary, depending on that voltage and the winding resistance. To get this DC current low enough, the integrator's worst-case offset needs to be low enough, and that might be hard to achieve. In my transformer the ratio of winding resistance to saturation current is such that only about 1mV of total DC voltage component is acceptable across the primary. The integrator and all related circuitry would need to be better than that, in terms of offset.
I will think it all over.
It may seem 'touchy' but it has been done and it works.
Back in the 1980's we had a customer that complained about the noise from the 10kwatt converter we supplied. The workers in the same room with the converter could not stand the noise as the flux walked first one way then the other way. We designed and tested this integrating type circuit and it solved the flux problem which solved the audible noise problem.
That was a pretty big converter too, about the size of a human coffin standing on one end. It was used as a backup for the computers. They put it right in the computer room which may have been a mistake, but they probably could not put it anywhere else.
If i remember right the customer was GE, one of their buildings either in PA or NJ in the early to mid 1980's.
About the possible 'offset' issue...
We know how to deal with offset by now and these days we can get op amps that have such little offset that we may not even be able to measure it with a gain of 100. We did it back then with regular op amps. We may have used an actual inductor to do the integration though i cant remember that well now. I know at least the first version used an inductor we had wound ourselves in the winding department.
The circuit does not have to be particularly fast, we were working with 50Hz, 60Hz, and 400Hz max.
Before that, back in the 1970's, the company i worked for made precision electronic weight scales used by pharmaceutical companies for animal drug testing research. We used op amps with adjustable offset to solve the offset issues.
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