1. ELECTRIC DRIVES
Ion Boldea S.A.Nasar
1998
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2. 3. POWER ELECTRONIC CONVERTERS (P.E.Cs) FOR DRIVES
3.1. POWER ELECTRONIC SWITCHES (P.E.Ss)
a.) b.)
Figure 3.1.The diode symbol a.) and its ideal characteristic b.)
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3. Figure 3.3. The GTO’s symbol a.) and its ideal characteristic b.)
The thyristor is used especially in P.E.Cs having an interface with a.c. power grids, at high power levels and low commutation frequencies (up to 300Hz in general).
a.) b.)
Figure 3.3. The GTO’s symbol a.) and its ideal characteristic b.)
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4. Figure 3.3. The GTO’s symbol a.) and its ideal characteristic b.)
The GTO (gate turn off thyristor) (figure 3.3) is a fully controllable P.E.S.. Its saturation is obtained as for the thyristor but its blocking is accessible when a negative current iG is applied to the command (driver) circuit.
a.) b.)
Figure 3.3. The GTO’s symbol a.) and its ideal characteristic b.)
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5. Figure 3.5. MOS transistor symbol a.) and its ideal characteristic
a.) b.)
Figure 3.4. The bipolar junction transistor symbol a.) and its ideal characteristic b.)
a.) b.)
Figure 3.5. MOS transistor symbol a.) and its ideal characteristic
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6. Figure 3.6. IGBT’s symbol a.) and its ideal characteristic b.)
a.) b.)
Figure 3.6. IGBT’s symbol a.) and its ideal characteristic b.)
The P.E.Cs may be classified in many ways. In what follows we will refer to their input and output voltage / current waveforms and distinguish:
a.c. - d.c. converters (or rectifiers);
d.c. - d.c. converters (or choppers);
a.c. - d.c. - a.c. converters (indirect a.c. - a.c. converters) - 2 stages;
a.c. - a.c. converters (direct a.c. - a.c. converters).
We should notice that a.c. - d.c. - a.c. converters contain an a.c. - d.c. source side converter (rectifier) and a d.c. - a.c. converter called inverter. These converters are mostly used with a.c. motor drives of all power levels.
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7. 3. 2. THE LINE FREQUENCY DIODE RECTIFIER FOR CONSTANT D. C
3.2. THE LINE FREQUENCY DIODE RECTIFIER FOR CONSTANT D.C. OUTPUT VOLTAGE Vd
Figure 3.7. Diode rectifier with output filter capacitor
a. single phase b. three phase
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8. Figure 3.8.Basic rectifier equivalent circuit a.)
Let us consider first a basic rectifier circuit (figure 3.8) with instantaneous commutation and a line source inductance Ls providing constant Vd on no load.
Figure 3.8.Basic rectifier equivalent circuit a.)
and the voltage and current waveforms b.)
The diode starts conducting when at t1. At t2 Vs = Vd but, due to inductance Ls, the current goes on in the diode until it dies out at t3 such that Aon = Aoff. In fact the integral of inductance voltage VL from t1 to t1+T should be zero, that is the average flux in the coil per cycle is zero:
(3.1)
As Vd is close to the maximum value , the current i becomes zero prior to the negative (next) cycle of Vs.
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9. Figure 3.9. Single phase rectifier - the waveforms
Figure 3.8 illustrates only the positive voltage, that is diodes D1 - D2 conducting. For the negative Vs, D3 - D4 are open and a similar current waveform is added (figure 3.9).
Figure 3.9. Single phase rectifier - the waveforms
As long as the current id is non zero:
(3.2)
(3.3)
For qon: (3.4)
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10. Finally the average coil flux linkage LsId is:
For wt = qoff, id(wt) = 0 and from (3.3) we may calculate qoff as a function of qon.
Finally the average coil flux linkage LsId is:
(3.5)
For given values of LsId, iteratively qon, qoff and finally Vd are obtained from (3.3) - (3.5) (figure 3.10).
Figure Vd versus LsId
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11. 3.3. LINE CURRENT HARMONICS
WITH DIODE RECTIFIERS
The line current has the same shape as id in figure 3.9 but with alternate polarities (figure 3.11).
Figure Source current shape
Also the current fundamental is lagging the source voltage by the displacement power factor (DPF) angle j1:
(3.6)
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12. where Vs is the r.m.s. voltage value.
The source current r.m.s. value is Is. Thus the apparent power magnitude S is:
(3.7)
where Vs is the r.m.s. voltage value.
The power factor (3.8)
where (3.9)
So (3.10)
A strong distortion in the line current will reduce the ratio Is1 / Is and thus a small power factor PF is obtained even if DPF is unity.
Now (3.11)
The total harmonic current distortion THD (%) is:
(3.12)
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13. or the form factor (F.F.): (3.15)
where (3.13)
The peak current Ispeak is also important to be defined as a relative value constant called the crest factor (C.F.):
(3.14)
or the form factor (F.F.):
(3.15)
It has been shown that the displacement power factor DPF is above 0.9 but the power factor PF is poor if the source inductance Ls is small.
Example 3.1.
A single phase diode rectifier with constant e.m.f. is fed from an a.c. source with the voltage (Vs = 120V, w = 367rad/s). The discontinuous source current (figure 3.11) initiates at qon = 600 and becomes zero at qoff = The source inductance Ls = 5mH. Calculate the d.c. side voltage Vd and the waveform of the source current id(wt).
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14. According to figure 3.9 from (3.3) we obtain:
(3.16)
(3.17)
From (3.17):
(3.18)
Now from (3.3) again:
(3.19)
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15. Consequently:
(3.20)
Though not convenient to use, (3.19) - (3.20) allow for the computation of Is (rms), peak current Ispeak, fundamental I1, TDH% (3.12), crest factor (3.14), average d.c. output current Id.
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16. a.) equivalent circuit;
3.4. CURRENT COMMUTATION
WITH Id = ct AND LS0
For the constant d.c. current Id = ct (figure 3.12),
a.)
Figure Current commutation in single sided rectifier with Id = ct.
a.) equivalent circuit;
b.) source current;
c.) rectified voltage
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17. Now the average d.c. voltage Vd is:
Ideally (Ls = 0), the source current will change stepwise from -Id to Id at wt = 0 and wt = p (figure 3.12.b). Due to the nonzero Ls, during commutation, all four diodes conduct and thus Vd = 0. For wt < 0 D3D4 conduct while after commutation (wt > u) only D1D2 are on.
As Vd = 0, the source voltage during commutation is dropped solely across inductance Ls:
(3.21)
Through integration for the commutation interval (0,u):
(3.22)
(3.23)
We find:
Now the average d.c. voltage Vd is:
(3.24)
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18. is the ideal (Ls = 0) average d.c. voltage (figure 3.12c).
where (3.25)
is the ideal (Ls = 0) average d.c. voltage (figure 3.12c).
So the source inductance Ls produces a reduction in the d.c. output voltage for constant d.c. output current. The current commutation is not instantaneous and during the overlapping period angle u all four diodes are conducting.
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19. 3.5. THREE PHASE DIODE RECTIFIERS
In industrial applications three phase a.c. sources are available, so three phase rectifiers seem the obvious choice (figure 3.13).
Figure Three phase diode rectifier
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20. with where VLL is the line voltage (rms).
The load resistance RL with a filtering capacitor Cd may be replaced by a constant d.c. current source Id. Using the same rationale as in the previous paragraph we obtain:
(3.26)
with where VLL is the line voltage (rms).
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21. Figure 3.14. Three phase ideal waveforms for Ls = 0
The corresponding waveforms for Ls = 0 are shown in figure 3.14 and for Ls0 in figure 3.15.
Figure Three phase ideal waveforms for Ls = 0
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22. Figure 3.15. Three phase current commutation with Ls 0
For nonzero Ls a reduction of output d.c. voltage (3.26) is accompanied by all three phases conducting during the commutation angle u (figure 3.15).
Figure Three phase current commutation with Ls 0
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23. On the other hand, for constant d. c
On the other hand, for constant d.c. voltage (infinite capacitance Cd), as for the single phase rectifier, the source current waveform is as in figure 3.16.
Figure Three phase rectifier with finite Ls and infinite Cd (Vd = ct.) - the source current and voltage
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24. The ideal no load voltage Vd0 (3.25) is:
Example 3.3. Commutation overlapping angle u.
For a single phase or three phase a.c. system (star connection) with phase voltage , calculate the commutation angles u, ideal no load voltage and load voltage of single or three phase diode rectifier delivering a constant d.c. current Id = 10A for the source inductance Ls = 5mH.
Solution:
For the single - phase diode rectifier, using (3.23):
(3.28)
u =
The ideal no load voltage Vd0 (3.25) is:
(3.29)
(3.30)
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25. For the three phase diode rectifier (3.27) u is:
(3.31)
u =
Vd0 and Vd (from 3.26) are:
(3.32)
(3.33)
Thus the filtering capacitor Cd is notably smaller in three phase than in single phase diode rectifiers.
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26. 3.6. PHASE - CONTROLLED RECTIFIERS (A.C. - D.C. CONVERTERS)
Table 3.1. Phase controlled rectifier circuits
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27. Electric Drives

28. Electric Drives

29. 3.7. D.C. - D.C. CONVERTERS (CHOPPERS)
Table 3.2. Single phase chopper configurations for d.c. brush motors
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30. Electric Drives

31. Figure 3. 17. Multiphase d. c. - d. c
Figure Multiphase d.c. - d.c. converters for switched reluctance motors
If an a.c. source is available a diode rectifier and filter are used in front of all choppers (figure 3.17).
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32. 3.8. D.C. - A.C. CONVERTERS (INVERTERS)
Figure Voltage source PWM inverter
a. basic configuration
b. output waveforms
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33. Figure 3.19. Current source inverter a. basic configuration
b. ideal output waveforms
a.)
b.)
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34. Figure 3. 20. Bi-directional power flow (dual) a. c. - d. c
Figure Bi-directional power flow (dual) a.c. - d.c. converter with unity power factor and sinusoidal inputs - d.c. voltage link
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35. Figure A.c. - d.c. - a.c. converter with bi-directional power flow and unity input power factor - d.c. current link
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36. 3.9. DIRECT A.C. - A.C. CONVERTERS
Figure Six - pulse cycloconvertor for a.c. motor drives
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