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This is a hazardous thing to build due to high voltages and parts that can explode if it is not built correctly with suitable parts.
This is what I think from looking at the circuit diagram, might not be competely correct.
It is a big feedback loop.
U1 is a microcontroller running software. The software creates a pulse width modulated output on pin 13. Narrow pulses cause a small amount of energy to be sent to the inverter output. Wide pulses transfer lots of energy to the inverter output.
The PWM signal coming out of U1 is converted into two differential signals by U8A and U6A.
The differential signal is converted into four signals by U7.
The four signals make U5 and U6 drive the IRF840 MOSFETs.
The mosfets are arranged to form an H bridge.
The timing of the signals controlling the MOSFETs has to be correct.
Q1 and Q2 are connected in series across the DC power supply,
if the control signal is wrong so that they are both turned on
at the same time there will be a loud bang and the MOSFETs will explode.
You can read more about PWM control and H bridge circuits to learn more.
The PWM pulses are much shorter than the 50 or 60Hz AC cycles.
When the MOSFETS switch the voltage across the primary of transformer TR2
changes quickly (under 1uS) but the current through the transformer
changes more slowly due to the transformer inductance.
This turns the fast pulses into a slower AC signal.
I guess that this inverter is for 24volt DC input, actually 28volts with
fully charged batteries down to 22volts with exhausted batteries.
Turns ratio of transformer TR2 will be selected so that 24volt pulses on
the primary produce 110VAC out of the secondary.
L2 and C13 are a low pass filter to reduce high frequency noise on the AC output.
It looks like TR1 is a current transformer, the primary is in series with the AC
output. It is used to measure the current the inverter is supplying.
The analog input pins on the microcontrollers handle signals that are between 0
and 5 volts. U3A and U3C are level shifting circuits so that the signal
representing AC current is centered on 2.5volts.
The circuit around U3B turns the 110VAC interter output into a low voltage
signal centered on 2.5VDC that microcontroller U1 can measure with its internal ADC.
I assume that the software running in U1 will change the PWM output to keep
the AC output voltage correct.
U9 microcontroller measures voltages using its internal ADC and shows numbers for
battery voltage, AC output voltage and AC output current on the LCD screen.
The hex files (inside the rar files), are the compiled software for the two microcontrollers.
You can load the files into MPLAB software and see a dissassembly listing.
The compiled hex files do not contain any comments, variable names or function names
so it is hard to understand what they do. You can work out what the software
does with a lot of study.