20
i DC
10
0
580
570
[V]
560
v DC
550
5400
0.005
0.01
0.015
0.02
time [s]
Fig. 9. DC-link voltage and current under unbalanced voltage supply with reduced DC-link
capacitance without compensation.
Fig. 10. Phase voltages and currents under unbalanced voltage supply with reduced DC-link
capacitance with compensation.
40
30
[A]
20
i DC
10
0
580
570
[V]
560
v DC
550
5400
0.005
0.01
0.015
0.02
time [s]
Fig. 11. DC-link voltage and current under unbalanced voltage supply with reduced DC-
link capacitance with compensation.
The change of the input inductance from 10 mH to 5 mH leads to an adequate increase in
the input phase currents as well as in the DC-link current, Figures 12 to 15. The relative
amount of pulsations remain at about the same levels.
Operation of Active Front-End Rectifier in Electric Drive under Unbalanced Voltage Supply
203
Fig. 12. Phase voltages and currents under unbalanced voltage supply with reduced input
inductance without compensation.
40
30
[A]
20
i DC
10
0
580
570
[V]
560
v DC
550
5400
0.005
0.01
0.015
0.02
time [s]
Fig. 13. DC-link voltage and current under unbalanced voltage supply with reduced input
inductance without compensation.
Fig. 14. Phase voltages and currents under unbalanced voltage supply with reduced input
inductance with compensation.
204
Electric Machines and Drives
40
30
[A]
20
i DC
10
0
580
570
[V]
560
v DC
550
5400
0.005
0.01
0.015
0.02
time [s]
Fig. 15. DC-link voltage and current under unbalanced voltage supply with reduced input
inductance with compensation.
Finally, the unbalance caused by shifting the voltage phasor of phase A by 10° was
investigated. Corresponding results due to the changes in circuit parameters are illustrated
in Figures 16 to 27. It can be noted that the effects are similar to the previous case of
unbalance.
Fig. 16. Phase voltages and currents under unbalanced voltage supply without
compensation.
40
30
[A]
20
i DC
10
0
580
570
[V]
560
v DC
550
5400
0.005
0.01
0.015
0.02
time [s]
Fig. 17. DC-link voltage and current under unbalanced voltage supply without
compensation.
Operation of Active Front-End Rectifier in Electric Drive under Unbalanced Voltage Supply
205
Fig. 18. Phase voltages and currents under unbalanced voltage supply with compensation.
40
30
[A]
20
i DC
10
0
580
570
[V]
560
v DC
550
5400
0.005
0.01
0.015
0.02
time [s]
Fig. 19. DC-link voltage and current under unbalanced voltage supply with compensation.
The effect of reduction of the DC-link capacitor from 1000 µF to 500 µF is shown in Figures
20 through 23.
Fig. 20. Phase voltages and currents under unbalanced voltage supply with reduced DC-link
capacitance without compensation.
206
Electric Machines and Drives
40
30
[A]
20
i DC
10
0
580
570
[V]
560
v DC
550
5400
0.005
0.01
0.015
0.02
time [s]
Fig. 21. DC-link voltage and current under unbalanced voltage supply with reduced DC-
link capacitance without compensation.
Fig. 22. Phase voltages and currents under unbalanced voltage supply with reduced DC-link
capacitance with compensation.
40
30
[A]
20
i DC
10
0
580
570
[V]
560
v DC
550
5400
0.005
0.01
0.015
0.02
time [s]
Fig. 23. DC-link voltage and current under unbalanced voltage supply with reduced DC-
link capacitance with compensation.
The corresponding situation for reduced input inductance from 10 mH to 5 mH is illustrated
in Figures 24 to 27.
Operation of Active Front-End Rectifier in Electric Drive under Unbalanced Voltage Supply
207
Fig. 24. Phase voltages and currents under unbalanced voltage supply with reduced input
inductance without compensation.
40
30
[A]
20
i DC
10
0
580
570
[V]
560
v DC
550
5400
0.005
0.01
0.015
0.02
time [s]
Fig. 25. DC-link voltage and current under unbalanced voltage supply with reduced input
inductance without compensation.
Fig. 26. Phase voltages and currents under unbalanced voltage supply with reduced input
inductance with compensation.
208
Electric Machines and Drives
40
30
[A]
20
i DC
10
0
580
570
[V]
560
v DC
550
5400
0.005
0.01
0.015
0.02
time [s]
Fig. 27. DC-link voltage and current under unbalanced voltage supply with reduced input
inductance with compensation.
3.2 Limitation of control range due to unbalanced voltage supply
The necessity to generate the negative sequence component of the switching functions in
order to eliminate the effect of the supply-voltage unbalance on the DC-link voltage
pulsations reduces the control range for the positive sequence component of the switching
functions (Chomat et al., 2009). This is due to the fact that in individual phases the
maximum of the switching function can only reach one at most at any given time. Another
constraint results from the current rating of the converter. The resulting constraints depend
on the value and type of the unbalance.
Analysis of the limitation corresponding to various types of unbalanced supply voltages has
been carried out. The reference parameters of the input impedance were chosen to be
R = 0.1 Ω and L = 10 mH. The input phase voltages had nominal voltage amplitudes of
230 V, nominal frequency of 50 Hz, and mutual phase shifts of 120° to form a three-phase
voltage system in the case of the symmetrical system. The DC-link voltage was set to 400 V.
The choice of the positive sequence component of the switching functions from the available
control range affects both the magnitude of the DC-link current and the currents in
individual input phases. Figure 28 shows what magnitudes of the DC-link current
correspond to the coordinates from the available control range. The unbalance was formed
Fig. 28. DC-link current under unbalanced voltage supply ( L = 10 mH, R = 0.1 Ω,
Vdc = 400 V).
Operation of Active Front-End Rectifier in Electric Drive under Unbalanced Voltage Supply
209
by setting the magnitude of the voltage in phase A to 0.75 p.u. The corresponding maximal
input phase current magnitude, calculated as the maximum of all the phase currents, is
shown in Figure 29. It can be seen from Figure 28 that the resulting DC-link current
decreases in the vertical direction of the operating region, whereas the maximal input
current in Figure 29 decreases in the horizontal direction. The corresponding measure of the
current unbalance is depicted in Figure 30 and the average power factor of all the three
input phases is depicted in Figure 31.
Fig. 29. Maximal input phase current under unbalanced voltage supply ( L = 10 mH,
R = 0.1 Ω, Vdc = 400 V).
Fig. 30. Input current unbalance under unbalanced voltage supply ( L = 10 mH, R = 0.1 Ω,
Vdc = 400 V).
Fig. 31. Power factor under unbalanced voltage supply ( L = 10 mH, R = 0.1 Ω, Vdc = 400 V).
210
Electric Machines and Drives
If we change the value of the input inductance from 10 mH to 1 mH, the constraints caused
by the switching functions remain the same as can be seen from Figures 32 through 35.
However, both the DC-link current and the input current increased nearly ten times as the
input reactance represents the main limiting factor for the currents entering the rectifier. The
excessive values of the currents would, in a case of a real rectifier, impose additional
restrictions to the operating regions resulting from current stress of electronic components
in the bridge. This can also be considered in the shape of new borders of operating regions.
Fig. 32. DC-link current under unbalanced voltage supply ( L = 1 mH, R = 0.1 Ω,
Vdc = 400 V).
Fig. 33. Maximal input phase current under unbalanced voltage supply ( L = 1 mH, R = 0.1 Ω, Vdc = 400 V).
Fig. 34. Input current unbalance under unbalanced voltage supply ( L = 1 mH, R = 0.1 Ω,
Vdc = 400 V).
Operation of Active Front-End Rectifier in Electric Drive under Unbalanced Voltage Supply
211
Fig. 35. Power factor under unbalanced voltage supply ( L = 1 mH, R = 0.1 Ω, Vdc = 400 V).
A different situation arises when the input resistance is increased ten times to 1 Ω. The
corresponding electrical quantities are shown in Figures 36 through 39. The increase in the
DC-link and input phase currents is not as dramatic as the resistance plays less significant
role in limiting the currents than the inductance. The values of the currents are similar to the
ones in the first case.
Fig. 36. DC-link current under unbalanced voltage supply ( L = 1 mH, R = 1 Ω, Vdc = 400 V).
Fig. 37. Maximal input phase current under unbalanced voltage supply ( L = 1 mH, R = 1 Ω,
Vdc = 400 V).
212
Electric Machines and Drives
Fig. 38. Input current unbalance under unbalanced voltage supply ( L = 1 mH, R = 1 Ω,
Vdc = 400 V).
Fig. 39. Power factor under unbalanced voltage supply ( L = 1 mH, R = 1 Ω, Vdc = 400 V).
A change in the DC-link voltage introduces, on the other hand, a noticeable change in the
shape of constraints caused by the limitation of the switching functions. Figures 40 through
43 show the situation for the decrease in the DC-link voltage from 400 V to 200 V and
Figures 45 through 47 show the situation for the increase to 600 V. In the latter case, a rise of
an isolated restricted area in the right hand side of the figure completely surrounded by
available control space can be noticed.
Fig. 40. DC-link current under unbalanced voltage supply ( L = 10 mH, R = 0.1 Ω,
Vdc = 200 V).
Operation of Active Front-End Rectifier in Electric Drive under Unbalanced Voltage Supply
213
Fig. 41. Maximal input phase current under unbalanced voltage supply ( L = 10 mH,
R = 0.1 Ω, Vdc = 200 V).
Fig. 42. Input current unbalance under unbalanced voltage supply ( L = 10 mH, R = 0.1 Ω,
Vdc = 200 V).
Fig. 43. Power factor under unbalanced voltage supply ( L = 10 mH, R = 0.1 Ω,
Vdc = 200 V).