Electric power conversion systems – Current conversion – With means to introduce or eliminate frequency components
Reexamination Certificate
1999-09-28
2001-03-27
Berhane, Adolf Deneke (Department: 2838)
Electric power conversion systems
Current conversion
With means to introduce or eliminate frequency components
C363S041000
Reexamination Certificate
active
06208537
ABSTRACT:
CROSS-REFERENCE TO RELATED APPLICATIONS
Not applicable.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
Not applicable.
BACKGROUND OF THE INVENTION
Often a need arises to provide variable-frequency/amplitude voltage to a load. One commonly used method to provide a variable frequency/amplitude voltage is with a Pulse Width Modulated (PWM) Voltage Source Inverter (VSI). Positive and negative DC bus voltages are provided to a VSI and, in a three phases system, three voltage supply cables link VSI outputs to a load. Exemplary VSIs include switches which are controlled to alternately link the supply cables to the positive and negative DC buses thereby producing high frequency voltage pulses on the cables. The changing average voltages of the pulses on each cable over a period defines a fundamental low frequency alternating voltage on the cable having an amplitude and a frequency.
Amplitude of the cable voltage is controlled by adjusting the ratio of positive to negative phase portions of each high-frequency pulse. Frequency of the cable voltage is controlled by altering the period over which the average high-frequency pulses alternate from positive phase to negative phase.
A controller is linked to each of the VSI switches and provides separate control signals to the switches to control the pulses. To determine when to turn switches on and off the controller receives three modulating signals Vm and a carrier signal Vc. An exemplary carrier signal Vc and a small portion of an exemplary modulating signal Vm are illustrated in FIG.
2
. Carrier signal Vc includes a saw tooth signal having a relatively high carrier frequency f
c
and a peak carrier amplitude {circumflex over (V)}
c
and is generally kept constant throughout control operation. Modulating signals Vm typically include sinusoidal signals (only a portion shown in
FIG. 2
) having relatively lower frequencies f
m
and a peak amplitude {circumflex over (V)}
m
. The controller compares the reference and carrier signals and, based on relative magnitudes, turns switches on and off in a manner well known in the controls industry. Because the reference signals are sinusoidal the resulting fundamental voltage on each cable is also, ideally, essentially sinusoidal.
In the controls art an amplitude modulation index is defined as:
m
a
=
V
^
m
V
^
c
Eq
.
1
while a frequency modulation index is defined as:
m
f
=
f
c
f
m
Eq
.
2
As well known in the controls industry, high frequency PWM AC voltage pulses at the VSI outputs cause PWM harmonics which are often not tolerable when provided to a passive loads. Similarly, under certain conditions, high frequency PWM AC voltage pulses will cause a dynamic load such as a three phase Y-connected motor to overheat. This is because high iron core losses and high winding resistance copper losses are associated with high-frequency PWM harmonics applied to motor terminals.
The PWM VSI line-to-neutral output voltage harmonic spectrum is determined by conventional Fourier analysis of the high frequency pulsed voltage waveforms which are provided on voltage supply cables. Line-to-neutral voltage is defined as from a line or cable to a “zero voltage” reference node between the positive and negative DC rails. The mathematics of Fourier analysis defines an equivalent voltage source representation for a pulsed waveform which is a series sum of a sinewave fundamental voltage and sinewave harmonic voltages. Thus, a PWM VSI line-to-neutral output voltage source may be viewed as a sum of a sinewave fundamental voltage at the fundamental output frequency f
1
in series with all the sinewave harmonic voltages V
h
at associated harmonic frequencies f
h
which comprise the waveform as determined from the Fourier analysis.
{circumflex over (V)}
p
is the peak amplitude of the line-to-neutral sinewave fundamental frequency voltage component referenced to the zero reference node, and is defined as:
V
^
p
=
m
a
·
V
d
c
2
Eq
.
3
The rms fundamental line-to-line voltage (V
∥
)
1
is therefore:
(
V
II
)
1
=
3
2
(
V
^
p
)
=
3
2
m
a
·
V
d
c
2
=
0.612
m
a
·
V
d
c
Eq
.
4
Theoretically, the harmonic voltage frequencies f
h
are also equally well defined for those skilled in the art and are:
f
h
=(h)f
1
=(jm
f
±k)f
1
jf
c
±kf
1
Eq. 5
where j is an integer and k is an integer representing a particular sideband. Thus, the harmonic voltages f
h
in the inverter output voltage waveform appear as sidebands centered around the carrier switching frequency f
c
and its multiples (e.g., 2f
c
, 3f
c
, 4f
c
, etc.) This general pattern holds true for all values of m
a
in the range between 0 and 1.
Rms harmonic components of the inverter line-to-line output voltage (V
11
)
h
can be calculated from a normalized harmonic table as well known in the art. The harmonic amplitudes are tabulated in Table 1 as a function of amplitude modulation ratio ma and assuming an odd frequency modulation index m
f
which is greater than 9. Only those harmonics with significant amplitudes up to j=4 (see Eq. 5) are included in Table 1.
As an example of how to calculate the values in Table 1, assume a 480 V 60 Hz sinewave system voltage is applied to a variable speed drive input having a 6 pulse diode bridge front end and a VSI output which powers a 460 V 60 Hz motor @ 52 Hz. The VSI V
dc
bus voltage is 1.35*480 V or 650 V
dc
, using conventional bridge rectifier AC/DC conversion formulas. At 52 Hz the motor requires a fundamental rms voltage component of (52 Hz/60 Hz)*460 V or 399 Vrms. The normalized fundamental component ratio is thus [(V
11
)
1
/V
dc
] or [399/650 =0.612]. From Table 1, this corresponds to a modulation index ratio of m
a
=1. Examination of the m
a
=1.0 column shows that the harmonic voltages centered at the carrier frequency f
c
and twice the carrier frequency 2f
c
are the two highest harmonic voltage magnitudes which contribute to a non-sinusoidal output voltage. Specifically, from Equation 5, these particular line-to-line harmonic rms voltages exist with 126.75 Vrms @ f
c
+/−104 Hz and 72.5 Vrms @ 2f
c
+/−52 Hz.
In general Table 1 shows that f
c
harmonics only become dominant in the 30 Hz to 60 Hz range while the 2f
c
harmonics are dominant throughout the 0 to 60 Hz range.
TABLE 1
Generalized harmonics of V
11
for a large and odd mf > 9
[(V
11
)
h
/V
dc
] Tabulated as Function of m
a
, where (V
11
)h is rms Value
of the Harmonic Voltages
Modulation Index (m
a
)
0.2
0.4
0.6
0.8
1.0
Fundamental Component
0.122
0.245
0.367
0.490
0.612
(h = 1)
[(V
II
)
1
/V
dc
]
Typical output frequency (Hz)
10
20
31
42
52
[for 460 V, 60 Hz load]
[(V
II
)
h
/V
dc
]
m
f
± 2
0.010
0.037
0.080
0.135
0.195
m
f
± 4
0.005
0.011
2 m
f
± 1
0.116
0.200
0.227
0.192
0.111
2 m
f
± 5
0.008
0.020
3 m
f
± 2
0.027
0.085
0.124
0.108
0.038
3 m
f
± 4
0.007
0.029
0.064
0.096
4 m
f
± 1
0.100
0.096
0.005
0.064
0.042
4 m
f
± 5
0.021
0.051
0.073
4 m
f
± 7
0.010
0.030
In the linear PWM modulation mode, the peak amplitude of the sinewave fundamental frequency voltage increases proportionately with an increase in m
a
from 0 to 1. In the PWM over-modulation mode, the peak of the sinusoidal modulating signal exceeds the peak of the carrier signal. Thus, as a result, the quantity of PWM pulses begins to decrease and inverter output voltage increases. Unlike in the linear region, the sinewave fundamental frequency rms voltage component increases non-linearly with an increase in m
a
>1 in the PWM over-modulation mode.
In the over-modulation region more significant sideband harmonics appear centered around the harmonic frequency f
c
and its multiples (e.g. 2f
c
, 3f
c
). However, the amplitudes of the dominant harmonics are not as large as in the m
a
<1 region. Fo
Buchholz Brian R.
Skibinski Gary L.
Berhane Adolf Deneke
Horn John J.
Jaskolski Michael A.
Rockwell Technologies LLC
Walbrun William R.
LandOfFree
Series resonant sinewave output filter and design methodology does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Series resonant sinewave output filter and design methodology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Series resonant sinewave output filter and design methodology will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-2488779