Inverter vector driving system and method for estimating capacitance using the same
The present invention relates to an inverter vector driving system and a method for estimating capacitance using the same. The present invention provides a method for estimating capacitance in an inverter vector driving system including a capacitor to which a rectified DC voltage of a three-phase power supply is charged, and a PWM inverter configured to transform the DC voltage into a three-phase AC voltage to be applied to a motor of an induction motor, including: operating the motor of the IM in a regeneration mode; generating a d-axis voltage command and a q-axis voltage command for the motor; adjusting a pulse of the PWM inverter by using the d-axis voltage command and the q-axis voltage command; and estimating capacitance of the capacitor by using a DC-link voltage and a DC-link current that are generated at the capacitor due to the inclusion of the AC component.
1. A method for estimating capacitance in an inverter vector driving system including a capacitor to which a rectified DC voltage of a three-phase power supply is charged and a PWM inverter configured to transform the DC voltage into a three-phase AC voltage to be applied to an induction motor (IM), comprising:
operating the motor in a regeneration mode;
generating a d-axis voltage command using a d-axis current command of a d-q coordinate system for the motor and a d-axis DC current obtained from the motor, and generating a q-axis voltage command using a q-axis current command, a q-axis DC current obtained from the motor, a q-axis current command including a predetermined AC component, and a q-axis AC current obtained from the motor;
adjusting a pulse of the PWM inverter by using the d-axis voltage command and the q-axis voltage command; and
estimating capacitance of the capacitor by using a DC-link voltage and a DC-link current that are generated at the capacitor due to the inclusion of the AC component.
2. The method of claim 1 , wherein
the q-axis AC current and the q-axis DC current are obtained by allowing the q-axis current of the motor on the d-q coordinate system obtained during an operation of the motor to respectively pass through a band pass filter (BPF) and a band stop filter (BSF).
3. The method of claim 1 , wherein
the generating of the d-axis voltage command and the q-axis voltage command includes:
generating the d-axis voltage command by performing proportional integral control of a value obtained by subtracting the d-axis DC current from the d-axis current command; and
generating the q-axis voltage command by summing a result of performing proportional integral control of a value obtained by subtracting the q-axis DC current from the q-axis current command, and a result of performing proportional resonant control of a value obtained by subtracting the q-axis AC current from a q-axis current command including the AC component.
4. The method of claim 1 , wherein
the DC-link current (i dc,cal ) is calculated by the following Equation:
i
d
c
,
ca
l
=
T
sa
i
a
+
T
sb
i
b
+
T
s
c
i
c
T
s
wherein, T sa , T sb , and T sc respectively represent gating times for three upper switches included in the PWM inverter, i a , i b , and i c represent phase currents measured at three-phases of the motor, and the T s represents a sampling time.
5. The method of claim 4 , wherein
the estimating of capacitance of the capacitor includes
estimating capacitance of the capacitor by using the recursive least square algorithm (RLS algorithm) such that an error cost function has a minimum value:
e 2 ( n )=└BPF[ i dc ( n )]− Ĉ ( n )BPF[ v′ dc ( n )]┘ 2
wherein, e 2 (n) is an error cost function, BPF[·]is an output value passed through the band pass filter (BPF), i dc is the DC-link current, v dc is the DC-link voltage, and Ĉ(n) is estimated capacitance of the capacitor.
6. The method of claim 5 , wherein
the estimated capacitance of the capacitor is updated by the following equation:
C
^
(
n
+
1
)
=
C
^
(
n
)
+
μ
(
n
)
BPF
[
v
d
c
′
(
n
)
]
×
{
BPF
[
i
d
c
(
n
)
]
-
C
^
(
n
)
BPF
[
v
d
c
′
(
n
)
]
}
wherein, μ(n) is a gain correction value.
7. An inverter vector driving system for estimating capacitance comprising:
a capacitor to which a rectified DC voltage of a three-phase power supply is charged;
a PWM inverter configured to transform the DC voltage into a three-phase AC voltage to be applied to a motor of an IM;
a calculating unit configured, while the motor is operated in a regeneration mode, to generate a d-axis voltage command using a d-axis current command of a d-q coordinate system for the motor and a d-axis DC current obtained from the motor, and to generate a q-axis voltage command using a q-axis current command, a q-axis DC current obtained from the motor, a q-axis current command including a predetermined AC component, and a q-axis AC current obtained from the motor;
a pulse adjusting unit configured to adjust a pulse of the PWM inverter by using the d-axis voltage command and the q-axis voltage command; and
an estimating unit configured to estimate capacitance of the capacitor by using a DC-link voltage and a DC-link current which are generated at the capacitor by the inclusion of the AC component.
8. The system of claim 7 , wherein
the q-axis AC current and the q-axis DC current are obtained by
allowing the q-axis current of the motor on the d-q coordinate system obtained during an operation of the motor to respectively pass through a band pass filter (BPF) and a band stop filter (BSF).
9. The system of claim 7 , wherein
the calculating unit is configured to
generate the d-axis voltage command by performing proportional integral control of a value obtained by subtracting the d-axis DC current from the d-axis current command, and
to generate the q-axis voltage command by summing a result of performing proportional integral control of a value obtained by subtracting the q-axis DC current from the q-axis current command and a result of performing proportional resonant control of a value obtained by subtracting the q-axis AC current from a q-axis current command including the AC component.
10. The system of claim 7 , wherein
the DC-link current (i dc,cal ) is calculated by the following equation:
i
d
c
,
ca
l
=
T
sa
i
a
+
T
s
b
i
b
+
T
s
c
i
c
T
s
wherein, T sa , T sb , and T sc respectively represent gating times for three upper switches included in the PWM inverter, i a , i b , and i c represent phase currents measured at three-phases of the motor, and the T s represents a sampling time.
11. The system of claim 10 , wherein
the estimating unit is configured to estimate
capacitance of the capacitor by using the recursive least square algorithm (RLS algorithm) such that an error cost function has a minimum value:
e 2 ( n )=└BPF[ i dc ( n )]− Ĉ ( n )BPF[ v′ dc ( n )]┘ 2
wherein, e 2 (n) is an error cost function, BPF[·]is an output value passed through the band pass filter (BPF), i dc is the DC-link current, v dc is the DC-link voltage, and Ĉ(n) is estimated capacitance of the capacitor.
12. The system of claim 11 , wherein
the estimated capacitance of the capacitor is updated by the following equation:
C
^
(
n
+
1
)
=
C
^
(
n
)
+
μ
(
n
)
BPF
[
v
d
c
′
(
n
)
]
×
{
BPF
[
i
d
c
(
n
)
]
-
C
^
(
n
)
BPF
[
v
d
c
′
(
n
)
]
}
wherein, μ(n) is a gain correction value.
13. The method of claim 2 , wherein
the generating of the d-axis voltage command and the q-axis voltage command includes:
generating the d-axis voltage command by performing proportional integral control of a value obtained by subtracting the d-axis DC current from the d-axis current command; and
generating the q-axis voltage command by summing a result of performing proportional integral control of a value obtained by subtracting the q-axis DC current from the q-axis current command, and a result of performing proportional resonant control of a value obtained by subtracting the q-axis AC current from a q-axis current command including the AC component.
14. The system of claim 8 , wherein
the calculating unit is configured to
generate the d-axis voltage command by performing proportional integral control of a value obtained by subtracting the d-axis DC current from the d-axis current command, and
to generate the q-axis voltage command by summing a result of performing proportional integral control of a value obtained by subtracting the q-axis DC current from the q-axis current command and a result of performing proportional resonant control of a value obtained by subtracting the q-axis AC current from a q-axis current command including the AC component.