Measuring and testing – Dynamometers – Responsive to torque
Reexamination Certificate
1999-07-08
2001-11-27
Fuller, Benjamin R. (Department: 2855)
Measuring and testing
Dynamometers
Responsive to torque
Reexamination Certificate
active
06321606
ABSTRACT:
BACKGROUND OF THE INVENTION AND RELATED ART STATEMENT
The present invention relates to an apparatus for calculating torque generated by an induction motor (hereinafter referred to as an “induction machine”) driven by a PWM inverter.
According to the prior art, torque generated by an induction machine is obtained for controlling the induction machine from the vector product of the primary magnetic flux vector and the primary current vector of the induction machine as described in “Torque Limited Control for General Purpose Inverter” (1990 NATIONAL CONVENTION RECORD I.E.E. JAPAN, No. 579).
According to this method, however, since the method does not consider an iron loss of the induction machine, a large error may occur in the calculated result in the boosting state in that a reference voltage larger than usual is set with respect to a reference angular frequency, i.e. V/F setting exceeding the rated excitation.
As explained above, torque that an induction motor generates is obtained from the vector product of the primary magnetic flux vector and the primary current vector of the induction machine as described by the following equation (1). Also, the primary magnetic flux vector is calculated based on the primary voltage vector, primary current vector and primary resistance value, as shown by the equation (2).
&tgr;={right arrow over (&phgr;)}
1
×{right arrow over (i)}
1
(1)
{right arrow over (&phgr;)}
1
=∫(
{right arrow over (v)}
1
−r
1
·{right arrow over (i)}
1
)·
dt
(2)
The quantities in equations (1) and (2) are as follows.
{right arrow over (i)}
1
: primary current vector
{right arrow over (&phgr;)}
1
: primary magnetic flux vector
{right arrow over (v)}
1
: primary voltage vector
r
1
: primary resistance value
The following equation (3) is obtained by solving equations (1) and (2) on the rotating coordinate system (d-q axes coordinate system), rotating with the rotor of the induction machine, in the steady state.
τ
=
ϕ
1
d
·
i
1
q
-
ϕ
1
q
·
i
1
d
=
{
(
v
1
q
·
i
1
q
+
v
1
d
·
i
1
d
)
-
r
1
(
i
1
q
2
+
i
1
d
2
)
}
/
ω
1
(
3
)
In equation (3), &ohgr;
1
represents a primary angular frequency. The following equations (4a) and (4b) are obtained from equation (3).
&phgr;
1d
=(
v
1q
−r
1
·i
1q
)/&ohgr;
1
(4a)
&phgr;
1q
=(
r
1
·i
1d
−v
1d
)/&ohgr;
1
(4b)
The numerator on the right side of equation (3) is a formula for obtaining electric power by subtracting the copper loss from electric power inputted to the induction machine. Therefore, this formula does not include so-called iron loss, that is the loss caused by the stator core.
In other words, since equation (3) does not consider the iron loss, a large error may occur in the calculated result in the boosting state in that a reference voltage larger than usual is set with respect to a reference angular frequency, i.e. V/F setting exceeding the rated excitation.
In view of the foregoing, it is an object of the invention to provide a calculating apparatus that facilitates calculating the torque generated by an induction motor in considering the iron loss.
SUMMARY OF THE INVENTION
The right side of equation (3) calculates torque &tgr; by dividing the result (secondary input) of subtracting the primary copper loss {r
1
(i
1q
2
+i
1d
2
)} from the inputted electric power (v
1q
·i
1q
+v
1d
·i
1d
) by the primary angular frequency &ohgr;
1
.
Equation (3) may be rewritten to the following equation (5), in that P
o
represents the secondary input (synchronous watt).
&tgr;=
P
o
/&ohgr;
1
(5)
The following equation (6) shows the relation of the inputted electric power P, secondary input P
o
, copper loss W
c
and iron loss W
i
. Equation (6) neglects the mechanical loss.
P=P
o
+W
c
+W
i
(6)
From equations (5) and (6), the torque that the induction machine generates is expressed by the following equation (7).
τ
=
(
P
-
W
c
-
W
i
)
/
ω
1
=
{
(
V
1
q
·
i
1
q
+
v
1
d
·
i
1
d
)
-
r
1
·
(
i
1
q
2
+
i
1
d
2
)
-
W
i
)
/
ω
1
=
ϕ
1
d
·
i
1
q
-
ϕ
1
q
·
i
1
d
-
W
i
/
ω
1
(
7
)
The iron loss W
i
is expressed by the following equation (8). Hysteresis loss W
h
and eddy current loss W
e
in equation (8) are expressed by the following equations (9) and (10), respectively.
W
i
=W
h
+W
e
(8)
W
h
=&sgr;
h
·f·B
m
2
(9)
W
e
=&sgr;
e
·d
2
·f
2
·B
m
2
(10)
The quantities in equations (9) and (10) are as follows.
f: primary frequency
B
m
: maximum value of magnetic flux density
&sgr;
h
: constant determined by a core material
&sgr;
e
: constant determined by resistivity of a core
d: thickness of the core
Thus, the torque generated by an induction machine is calculated by using equation (7) that considers the iron loss of the induction machine.
The present invention is based on that the torque &tgr; generated by the induction machine is obtained by dividing the secondary input P
o
by the primary angular frequency &ohgr;
1
. The secondary input P
o
is calculated by subtracting the copper loss W
c
and the iron loss W
i
from the inputted electric power P. By dividing the secondary input P
o
by the primary angular frequency &ohgr;
1
, the torque generated by the induction machine is precisely calculated while considering the iron loss.
In other words, the generated torque is calculated by subtracting the result of the division that divides the iron loss W
i
by the primary angular frequency &ohgr;
1
from the calculated torque using the foregoing equation (3), that does not consider the iron loss.
According to an aspect of the invention, there is provided an apparatus for calculating torque that an induction motor generates, based on a reference voltage value fed to an inverter that drives the induction motor, a q-axis current component and a d-axis current component resolved from the detected current of the induction motor on the rotating coordinate system, a primary resistance of the induction motor and a primary angular frequency. The apparatus includes an iron loss calculator that calculates an iron loss of the induction motor based on hysteresis characteristics of a stator core of the induction motor; a divider that divides the calculated iron loss by the primary angular frequency; and an adder that calculates the generated torque by subtracting the result of the division from the torque calculated without considering the iron loss.
According to another aspect of the invention, there is provided an apparatus for calculating torque that an induction motor generates, based on a q-axis voltage component and a d-axis voltage component resolved from an output voltage of an inverter driving the induction motor on the rotating coordinate system, a q-axis current component and a d-axis current component resolved from the detected current of the induction motor on the rotating coordinate system, a primary resistance of the induction motor and a primary angular frequency. The apparatus includes an iron loss calculator that calculates an iron loss of the induction motor based on hysteresis characteristics of the stator core of the induction motor; a divider that divides the calculated iron loss by the primary angular frequency; and an adder that calculates the generated torque by subtracting the result of the division from the torque calculated without considering the iron loss.
The rotating coordinate system used herein is a d-q axes rotating coordinate system using as a reference axis a reference vector position obtained by integrating a primary angular frequency.
Advantageously, the iron loss calculator further calculates an eddy current loss based on characteristics of an eddy current flowing through the stator core of the induction motor and c
Ishii Shin'ichi
Tajima Hirokazu
Fuji Electric & Co., Ltd.
Fuller Benjamin R.
Kanesaka & Takeuchi
Thompson Jewel V.
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