Hello ,
Here is the explanation of why the line currents are unbalanced.
If you zoom in at the waveform of voltage across winding (W1) of all the three transformers (“linear transformer”, “linear transformer1” , ”linear transformer2”) , you will see that they are actually not zero, and have a DC shift with respect to each other. From the scope, we can see that they are not balanced and have their values approximately equal to (1v, 0v ,-1v) respectively. The magnitude of these voltages seems very small, but actually the impedence of our system is very low, which eventually results in considerable circulatory current to flow across lines. This is the reason for unbalance line currents.
SOLUTION:
I have worked upon the Simulink model provided by you and made a couple of changes so that it works as per your expectation. I have also attached the modified Simulink model with this answer. The modifications made are as follows:
- Replace the star- connected primary windings (“w2”) of (“linear transformer”, “linear transformer1” , ”linear transformer2”) to a delta connected windings.
- The main reason behind this is, the delta connected winding will allow the flow of zero sequence current, internally across the windings. But, these currents will not be present in the lines (on inverter side).
- Re tuned the PI- controllers (“PID Controller 14” and “PID Controller 15”) of the outer voltage control loop.
- A PI controller is better, as it ensures zero steady state error. I changed the value of “Integral (I)” part to 10. Earlier, it was 0.
Results of simulation:
Below given waveform is of measured “uod1” for reference value = 0.
Below given waveform is of measured “uoq1” for reference value = 0.
Below given waveform is of measured “uod1” for reference value of 10.
Below given waveform is of measured “uoq1” for reference value of -10.
Conclusions: the reference voltages are tracked properly.
Below given waveforms are of source and load currents when reference “uod1” = 0 and reference “uoq1” = 0. We can see that they are balanced.
Below given waveforms are of source and load currents when reference “uod1” = 10 and reference “uoq1” =-10.
We can see that Line currents are balanced under all conditions.
For better dynamic performance, you can retune the PI controllers.
I hope this is as per your expectations !
