ELECTRIC DRIVES

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ELECTRIC DRIVES
Ion Boldea S.A.Nasar 1998
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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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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 GTOs symbol a.) and
its ideal characteristic b.)
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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 GTOs symbol a.) and
its ideal characteristic b.)
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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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a.) b.) Figure 3.6. IGBTs 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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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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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 t1T 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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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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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 3.10. Vd versus LsId
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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 3.11. 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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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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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)
(3.15)
or the form factor (F.F.)
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 1500. 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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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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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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3.4. CURRENT COMMUTATION WITH Id ct AND LS?0
For the constant d.c. current Id ct (figure
3.12),
a.)
Figure 3.12. Current commutation in single sided
rectifier with Id ct. a.) equivalent circuit
b.) source current c.) rectified voltage
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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 lt 0 D3D4 conduct while after
commutation (wt gt 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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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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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 3.13. Three phase diode rectifier
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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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The corresponding waveforms for Ls 0 are shown
in figure 3.14 and for Ls?0 in figure 3.15.
Figure 3.14. Three phase ideal waveforms for Ls
0
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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 3.15. Three phase current commutation with
Ls ?0
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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 3.16. Three phase rectifier with finite Ls
and infinite Cd (Vd ct.) - the source current
and voltage
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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 22.7270
The ideal no load voltage Vd0 (3.25) is
(3.29)
(3.30)
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For the three phase diode rectifier (3.27) u is
(3.31)
u 12.220
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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3.6. PHASE - CONTROLLED RECTIFIERS (A.C. - D.C.
CONVERTERS)
Table 3.1. Phase controlled rectifier circuits
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3.7. D.C. - D.C. CONVERTERS (CHOPPERS)
Table 3.2. Single phase chopper configurations
for d.c. brush motors
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Figure 3.17. 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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3.8. D.C. - A.C. CONVERTERS (INVERTERS)
Figure 3.18. Voltage source PWM inverter a. basic
configuration b. output waveforms
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Figure 3.19. Current source inverter a. basic
configuration b. ideal output waveforms
a.)
b.)
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Figure 3.20. 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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Figure 3.21. 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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3.9. DIRECT A.C. - A.C. CONVERTERS
Figure 3.22. Six - pulse cycloconvertor for a.c.
motor drives