Why can voltage error be converted to current using a PI controller in dq-frame?

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As shown in: Voltage Control Block

How could a PI controller convert the voltage error to current (in voltage control block)? or How could a PI controller convert the current error to voltage (in current control block)? attached link for figure Take the voltage control of inverter as an example, where current control and voltage control are used. The voltage error, which comes from the load side (ABC to dq-frame), can be converted to a current reference using a PI controller. The current reference is used for the current control. kindly, help me that how could a PI controller convert the current error to voltage (or voltage reference)? or explain that particular scenario. Thanks in Advance

I'm working on controlling techniques of voltage of three-phase inverter, and I'm created the simulation. But for calculation purposes I can't find equations in d-q frame for current control block and voltage control block cause it helps me to generate PWM for inverter switching. If you can help me to share equations or a paper that can help me then I'll be really thankful to you, kindly help me in this problem as I have to calculate the parameters to check out the results. Thanks, once again!

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