System and method for an inverter for self-excitation of an induction machine
A voltage difference is determined between the observed voltage and a reference direct current bus voltage. A quadrature-axis (q-axis) voltage command is outputted based on a current difference derived from the voltage difference. A commanded direct-axis (d-axis) voltage is determined based on a measured d-axis current and a determined d-axis reference current derived from a mathematical relationship between d-axis residual voltage, the observed voltage and the commanded q-axis voltage, where residual voltage is proportional to a function of the observed voltage and the commanded q-axis voltage. An inverse Parks transformation module or a data processor provides one or more phase voltage command based on inverse Parks transform of the commanded voltages.
1. A method of controlling an inverter coupled to a generator, the method comprising:
measuring an observed voltage across direct current voltage terminals;
determining a voltage difference between the observed voltage and a reference DC bus voltage;
outputting a quadrature-axis (q-axis) voltage command based on a current difference derived from the voltage difference;
determining a commanded direct-axis (d-axis) voltage based on a measured d-axis current and a determined d-axis reference current derived from a mathematical relationship between d-axis residual voltage, the observed voltage and the commanded q-axis voltage in which the d-axis residual voltage is proportional to a function of the observed voltage and the commanded q-axis voltage; and
providing phase voltage command based on inverse Parks transform of the commanded voltages.
2. The method according to claim 1 wherein outputting the q-axis voltage command further comprises:
generating a reference q-axis current command (I q ref ) based on the voltage difference difference between the observed voltage and the reference DC bus voltage;
measuring a q-axis current (I q measured ); and
determining the current difference between the measured q-axis command current and the reference q-axis current command (I q ref ).
3. The method according to claim 1 wherein the determining the commanded d-axis voltage (V d ) further comprises:
determining a d-axis residual voltage (V d residual ) in accordance with a following equation as the relationship:
V
d
residual
=
(
m
V
D
C
measured
)
2
3
-
V
q
2
where:
m is a modulation index which is between zero and approximately 1,
V DC measured is the measured voltage of or between the direct current terminals, and
V q is the quadrature-axis voltage command; and
determining the dxzd-axis reference current (I q ref ) for the corresponding residual d-axis voltage (V d residual ) based on a magnetizing curve or K-factor lookup table stored in a data storage device.
4. The method according to claim 1 wherein the relationship adheres to a following equation:
V
d
residual
=
(
m
V
D
C
measured
)
2
3
-
V
q
2
where:
m is a modulation index which is between zero and approximately 1,
V DC measured is the measured voltage of or between the direct current terminals, and
Vq is the quadrature-axis voltage command.
5. The method according to claim 2 wherein the providing the phase voltage commands further comprises determining the parks transformation in accordance with a following equation of the rotor field orientation:
θ e =θ rotor +∫ω slip dt,
where θ e is an electrical angular position of the rotor;
where θ rotor is a mechanical angular position of the rotor;
and ω slip is an angular slip velocity of the rotor.
6. A method of controlling an inverter coupled to a generator, the method comprising:
measuring an observed voltage across direct current voltage terminals;
determining a voltage difference between the observed voltage and a reference DC bus voltage;
generating, by a controller, a reference q-axis current command (I q ref ) based on the voltage difference;
measuring a q-axis current (I q measured );
determining a current difference between the measured q-axis command current and the reference q-axis current command (I q ref );
outputting, by a current regulator, a q-axis voltage command (V q ) based on input of the current difference;
determining a d-axis residual voltage (V d residual ) in accordance with a following equation:
V
d
residual
=
(
m
V
D
C
measured
)
2
3
-
V
q
2
,
where:
m is a modulation index,
V DC measured is the measured voltage of or between the direct current terminals, and
V q is the quadrature-axis voltage command;
determining d-axis reference current (I d ref ) for the corresponding residual d-axis voltage (V d residual ) based on a magnetizing curve or K-factor lookup table stored in a data storage device;
determining, by a current regulator, the commanded d-axis voltage (V d ) based on a measured d-axis current (I d measured ) and the determined d-axis reference current (I d ref ); and
providing phase voltage commands (V a ,V b ,V c ) based on inverse parks transform of the commanded voltages (V d and V q ).
7. The method according to claim 6 wherein the providing the phase voltage commands further comprises determining the parks transformation in accordance with the following equation of the rotor field orientation:
θ e =θ rotor +∫ω slip dt,
where θ e is an electrical angular position of the rotor;
where θ rotor is a mechanical angular position of the rotor;
and ω slip is an angular slip velocity of the rotor.
8. A system of controlling an inverter coupled to a generator, the system comprising:
a voltage sensor for measuring an observed voltage across direct current voltage terminals;
a voltage difference module for determining a voltage difference between the observed voltage and a reference DC bus voltage;
a first current regulator outputting a q-axis voltage command (V q ) based on a current difference derived from the voltage difference;
a second current regulator for determining a commanded d-axis voltage (V d ) based on a measured d-axis current (I d measured ) and a determined d-axis reference current (I d ref ) derived from a mathematical relationship between d-axis residual voltage (V d residual ), the observed voltage (V DC measured ) and the commanded q-axis voltage (V q ) in which the d-axis residual voltage is proportional to a function of the observed voltage (V DC measured ) and the commanded q-axis voltage (V q ); and
an inverse Parks transformation module for providing phase voltage commands (V a ,V b ,V c ) based on inverse Parks transform of the commanded voltages (V d and V q ).
9. The system according to claim 8 further comprising:
a proportional integral controller for generating a reference q-axis current command (I q ref ) based on the voltage difference;
a current sensor for measuring a q-axis current (I q measured ); and
a current difference module determining the current difference between the measured q-axis current and the reference q-axis current command (I q ref ).
10. The system according to claim 8 further comprising:
an inverter;
a pulse-width modulator coupled to the output of the inverse Parks transformation module and coupled to the inverter;
a residual voltage calculator for determining the d-axis residual voltage (V d residual ) in accordance with a following equation (to fully use of the DC bus and makes the self-excitation robust) as the relationship:
V
d
residual
=
(
m
V
D
C
measured
)
2
3
-
V
q
2
V
d
residual
is the residual direct-axis voltage;
m is the modulation index,
V DC measured is the measured voltage of or between the direct current terminals, and
V q is the quadrature-axis voltage command, and
a data processor to determine the d-axis reference current (I d ref ) for a corresponding residual d-axis voltage (V d residual ) based on a magnetizing curve or K-factor lookup table stored in a data storage device, the magnetizing curve or K-factor lookup table corresponding to a particular electric machine that the inverter controls.
11. The system according to claim 8 wherein the relationship adheres substantially to a following equation:
V
d
residual
=
(
m
V
D
C
measured
)
2
3
-
V
q
2
,
where:
m is a modulation index,
V DC measured is the measured voltage of or between the direct current terminals, and
V q is the quadrature-axis voltage command.
12. The system according to claim 8 wherein the Parks transformation module uses a following equation of the rotor field orientation to provide phase voltage commands (V a ,V b ,V c ):
θ e =θ rotor +∫ω slip dt,
where θ e is an electrical angular position of the rotor;
where θ rotor is a mechanical angular position of the rotor;
and ω slip an angular slip velocity of the rotor.
13. A system of controlling an inverter coupled to a generator, the system comprising:
a voltage sensor for measuring an observed voltage across direct current voltage terminals;
a voltage difference module for determining a voltage difference between the observed voltage and a reference DC bus voltage;
a controller for generating a reference q-axis current command (I q ref ) based on the voltage difference;
a current sensor for measuring a q-axis current (I q measured );
a current difference module for determining a current difference between measured q-axis current and the reference q-axis current command (I q ref );
a first current regulator for outputting a q-axis voltage command (V q ) based on input of the current difference;
a data processor for determining a d-axis residual voltage (V d residual ) in accordance with a following equation (to fully use of the DC bus and makes the self-excitation robust):
V
d
residual
=
(
m
V
D
C
measured
)
2
3
-
V
q
2
,
where:
V d residual is the residual d-axis current,
m is the modulation index,
V DC measured is the measured voltage of or between the direct current terminals, and
V q is the quadrature-axis voltage command;
the data processor determining d-axis reference current (I d ref ) for a corresponding residual d-axis voltage (V d residual ) based on a magnetizing curve or K-factor lookup table stored in a data storage device;
a second current regulator for determining the commanded d-axis voltage (V d ) based on the measured d-axis current (I d measured ) and the determined d-axis reference current (I d ref ); and
an inverse Parks transformation module for providing phase voltage commands (V a ,V b ,V c ) based on inverse parks transform of the commanded voltages (V d and V q ).
14. The system according to claim 13 wherein the Parks transformation is adapted to determine the phase voltage commands in accordance with a following equation of the rotor field orientation:
θ e =θ rotor +∫ω slip dt,
where θ e is an electrical angular position of the rotor;
where θ rotor is a mechanical angular position of the rotor;
and ω slip is an angular slip velocity of the rotor.