Method and apparatus for rejecting the second harmonic current in an active converter with an unbalanced AC line voltage source

• US 20060034104A1
• Filed: 08/13/2004
• Published: 02/16/2006
• Est. Priority Date: 08/13/2004
• Status: Active Grant

• Current Assignee: Rockwell Automation Technologies Incorporated (Rockwell Automation, Inc.)
• Original Assignee: Rockwell Automation Technologies Incorporated (Rockwell Automation, Inc.)
• Inventors: Royak, Semyon, Breitzmann, Robert John
• Granted Patent: US 7,355,865 B2
• Time in Patent Office: Days
• US Class Current: 363/39
• CPC Class Codes: H02M 1/12 Arrangements for reducing harmonics from ac input or output
• CPC Class Codes: H02M 1/4233 using a bridge converter comprising active switches
• CPC Class Codes: Y02B 70/10 Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes

Abstract

A method and apparatus for altering converter control as a function of the degree of unbalance in supply line voltages to substantially eliminate second harmonics on the supply lines caused by active control of the converter including identifying supply line peak amplitude values and using the peak values to identify potential second harmonics and then altering command values as a function of the potential second harmonic components.

Claims

1. A method for use with a controller and a converter where the controller actively controls the converter to convert three phase voltages on three supply lines to a DC voltage across positive and negative DC buses, the method comprising the steps of:

identifying the peak amplitudes of the three phase supply line voltages;

using the peak amplitudes to identify a second harmonic component that would be generated on the supply lines by the converter during normal operation due to unbalance in the peak amplitudes; and

altering control of the converter as a function of the identified second harmonic.

2. The method of claim 1 wherein the controller generates command voltages to control the converter, the step of altering control of the converter including modifying the command voltages as a function of the identified second harmonic.

3. The method of claim 2 wherein the step of identifying the peak amplitudes includes sensing the RMS line-to-line voltages and using the RMS line-to-line voltages to identify the peak amplitudes.

4. The method of claim 3 wherein the step of identifying the peak amplitudes includes the step of solving the following equations:

$a=\sqrt{\frac{2}{3}}·<br><br>V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}^2-V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}^2\right)}{V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}}$ $b=\sqrt{\frac{2}{3}}·<br><br>V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}^2-V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}^2\right)}{V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}}$ $c=\sqrt{\frac{2}{3}}·<br><br>V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}^2-V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}^2\right)}{V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}},$

where a, b and c are the peak amplitudes and where V<sub>ab—

RMS</sub>, V<sub>bc—

RMS</sub> and V<sub>ca—

RMS</sub> are the first, second and third RMS line-to-line voltages that occur between the first and second, second and third and third and first lines, respectively.

5. The method of claim 2 wherein the controller receives a DC reference voltage and controls the converter to cause the DC voltage across the DC buses to track the reference voltage, the method further including the step of using the reference voltage to identify d and q-axis voltage difference values, the step of identifying the second harmonic components including the step of identifying d and q-axis components of the second harmonic, the step of modifying the command voltages including mathematically combining the difference values and the second harmonic components to identify two phase d and q-axis command voltages.

6. The method of claim 5 wherein the step of mathematically combining includes adding the d and q-axis second harmonic components to the d and q-axis difference values.

7. The method of claim 6 further including the step of using the peak amplitudes to identify a DC offset and wherein the step of modifying the command voltages further includes adding the DC offset to the q-axis difference value along with the q-axis second harmonic component.

8. The method of claim 5 wherein the peak amplitudes of the three supply line voltages are a, b and c and wherein the step of identifying the d and q axis second harmonic components includes using the peak amplitudes to identify a two phase amplitude A_min by solving the following equation:

$A_{\min }=\frac{A_{\mathrm{\alpha <br><br>}}·<br><br>\mathrm{Sin}<br><br>\left({\mathrm{\phi <br><br>}}_{\mathrm{\alpha <br><br>}}\right)+A_{\mathrm{\beta <br><br>}}·<br><br>\mathrm{Cos}<br><br>\left({\mathrm{\phi <br><br>}}_{\mathrm{\beta <br><br>}}\right)}{2}$ $\mathrm{where}<br><br>\text{;<br><br>}$ $A_{\mathrm{\alpha <br><br>}}=\frac{e_0^{*}}{3}·<br><br>\sqrt{{\left(a^{*}+b^{*}\right)}^2+{\left(a^{*}+c^{*}\right)}^2+2<br><br>{\left(a^{*}\right)}^2-b^{*}·<br><br>c^{*}}$ $A_{\mathrm{\beta <br><br>}}=\frac{e_0^{*}}{\sqrt{3}}·<br><br>\sqrt{{\left(b^{*}+c^{*}\right)}^2-b^{*}·<br><br>c^{*}}$ $\underset{\mathrm{\alpha <br><br>}}{\mathrm{\phi <br><br>}}=\mathrm{arc}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{tg}<br><br>\left[\frac{\sqrt{3}·<br><br>\left(b^{*}-c^{*}\right)}{4<br><br>a^{*}+b^{*}+c^{*}}\right]$ ${\mathrm{\phi <br><br>}}_{\mathrm{\beta <br><br>}}=\mathrm{arc}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{tg}<br><br>\left[\frac{\sqrt{3}·<br><br>\left(b^{*}+c^{*}\right)}{b^{*}-c^{*}}\right]$ $\mathrm{where}<br><br>\text{;<br><br>}$ $e_0^{*}=\frac{a+b+c}{3};<br><br>\mathrm{and}$ $a^{*}=\frac{a}{e_0^{*}};<br><br>b^{*}=\frac{b}{e_0^{*}};<br><br>c^{*}=\frac{c}{e_0^{*}}.$

9. The method of claim 8 further including the step of identifying the frequency of the second harmonic of the supply line voltages and using the frequency to identify a two phase supply voltage angle, the step of identifying the second harmonic components including identifying the q-axis second harmonic component by multiplying value A_min by the sine of the voltage angle and identifying the d-axis second harmonic component by multiplying value A_min by the cosine of the voltage angle.

10. The method of claim 5 wherein the step of using the reference voltage to identify d and q-axis voltage difference values includes using the reference voltage to identifying d and q-axis command currents, obtaining d and q-axis feedback currents, subtracting the d and q-axis feedback currents from the d and q-axis command currents, respectively, and using the d and q-axis command currents to identify the voltage difference values.

11. The method of claim 2 wherein the controller receives a DC reference voltage and controls the converter to cause the DC voltage across the DC buses to track the reference voltage, the method further including the step of using the reference voltage to identify first, second and third phase voltage difference values, the step of identifying the second harmonic components including the step of identifying first, second and third phase components of the second harmonic corresponding to the first, second and third supply lines, respectively, the step of modifying the command voltages including mathematically combining the difference values and the second harmonic components to identify first, second and third command voltages.

12. The method of claim 11 wherein the step of mathematically combining includes adding the first, second and third phase second harmonic components to the first, second and third phase difference values.

13. The method of claim 11 wherein the step of identifying the peak amplitudes includes the step of solving the following equations:

$a=\sqrt{\frac{2}{3}}·<br><br>V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}^2-V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}^2\right)}{V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}}$ $b=\sqrt{\frac{2}{3}}·<br><br>V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}^2-V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}^2\right)}{V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}}$ $c=\sqrt{\frac{2}{3}}·<br><br>V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}^2-V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}^2\right)}{V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}},$

where a, b and c are the peak amplitudes and where V<sub>ab—

RMS</sub>, V<sub>bc—

RMS</sub> and V<sub>ca—

RMS</sub> are the first, second and third RMS line-to-line voltages that occur between the first and second, second and third and third and first lines, respectively.

14. The method of claim 11 further including the step of identifying the frequency of the supply line voltages and using the frequency to identify a supply voltage angle, the step of identifying the second harmonic components including identifying the q-axis second harmonic component by multiplying peak values a, b and c by the sine of the supply voltage angle, the sine of the supply voltage angle less 120 degrees and the sine of the supply voltage angle plus 120 degrees, respectively.

15. The method of claim 11 wherein the step of using the reference voltage to identify voltage difference values includes using the reference voltage to identifying first, second and third phase reference currents, obtaining first, second and third phase feedback currents, subtracting the first, second and third phase feedback currents from the first, second and third reference currents to identify first, second and third command currents, respectively, and using the first, second and third phase command currents to identify the voltage difference values.

33. The method of claim 14 also for identifying a second harmonic component that would be generated on the supply lines by the converter during normal operation due to unbalance in the peak amplitudes and using the identified second harmonic component to alter control of a converter linked to the supply lines to convert the AC voltage on the supply lines to a DC bus voltage across positive and negative DC buses.

16. An apparatus for use with a converter where the converter is actively controlled to convert three phase voltages on three supply lines to a DC voltage across positive and negative DC buses, the apparatus comprising:

a processor programmed to perform the steps of;

identifying the peak amplitudes of the three phase supply line voltages;

using the peak amplitudes to identify a second harmonic component that would be generated on the supply lines by the converter during normal operation due to unbalance in the peak amplitudes; and

altering control of the converter as a function of the identified second harmonic.

17. The apparatus of claim 16 wherein the processor is further programmed to generate command voltages to control the converter, the processor performing the step of altering control of the converter by modifying the command voltages as a function of the identified second harmonic.

18. The apparatus of claim 17 wherein the processor performs the step of identifying the peak amplitudes by sensing the RMS line-to-line voltages and using the RMS line-to-line voltages to identify the peak amplitudes.

19. The apparatus of claim 18 wherein the processor performs the step of identifying the peak amplitudes by solving the following equations:

$a=\sqrt{\frac{2}{3}}·<br><br>V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}^2-V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}^2\right)}{V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}}$ $b=\sqrt{\frac{2}{3}}·<br><br>V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}^2-V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}^2\right)}{V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}}$ $c=\sqrt{\frac{2}{3}}·<br><br>V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}^2-V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}^2\right)}{V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}},$

where a, b and c are the peak amplitudes and where V<sub>ab—

RMS</sub>, V<sub>bc—

RMS</sub> and V<sub>ca—

RMS</sub> are the first, second and third RMS line-to-line voltages that occur between the first and second, second and third and third and first lines, respectively.

20. The apparatus of claim 17 wherein the processor receives a DC reference voltage and controls the converter to cause the DC voltage across the DC buses to track the reference voltage, the processor further programmed to perform the step of using the reference voltage to identify d and q-axis voltage difference values, the processor performing the step of identifying the second harmonic components by identifying d and q-axis components of the second harmonic, the processor by mathematically combining the difference values and the second harmonic components to identify two phase d and q-axis command voltages.

21. The apparatus of claim 20 wherein the processor is programmed to perform the step of mathematically combining by adding the d and q-axis second harmonic components to the d and q-axis difference values.

22. The apparatus of claim 20 wherein the processor is further programmed to perform the step of using the peak amplitudes to identify a DC offset and wherein the processor is programmed to modify the command voltages by adding the DC offset to the q-axis difference value along with the q-axis second harmonic component.

23. The apparatus of claim 21 wherein the peak amplitudes of the three supply line voltages are a, b and c and wherein the processor performs the step of identifying the d and q axis second harmonic components by using the peak amplitudes to identify a two phase amplitude A_min by solving the following equation:

$a=\sqrt{\frac{2}{3}}·<br><br>V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}^2-V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}^2\right)}{V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}}$ $b=\sqrt{\frac{2}{3}}·<br><br>V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}^2-V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}^2\right)}{V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}}$ $c=\sqrt{\frac{2}{3}}·<br><br>V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}^2-V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}^2\right)}{V_{{\mathrm{ab}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{bc}}_{-}<br><br>\mathrm{RMS}}+V_{{\mathrm{ca}}_{-}<br><br>\mathrm{RMS}}},$

24. The apparatus of claim 23 wherein the processor is further programmed to perform the steps of identifying the frequency of the second harmonic of the supply line voltages and using the frequency to identify a two phase supply voltage, the processor performing the step of identifying the second harmonic components including identifying the q-axis second harmonic component by multiplying value A_min by the sine of the voltage angle and identifying the d-axis second harmonic component by multiplying value A_min by the cosine of the voltage angle.

25. The apparatus of claim 23 wherein the processor performs the step of using the reference voltage to identify d and q-axis voltage difference values using the reference voltage to identifying d and q-axis command currents, obtaining d and q-axis feedback currents, subtracting the d and q-axis feedback currents from the d and q-axis command currents, respectively, and using the d and q-axis command currents to identify the voltage difference values.

26. The apparatus of claim 17 wherein the processor receives a DC reference voltage and controls the converter to cause the DC voltage across the DC buses to track the reference voltage, the processor further programmed to perform the step of using the reference voltage to identify first, second and third phase voltage difference values, the processor performing the step of identifying the second harmonic components by identifying first, second and third phase components of the second harmonic corresponding to the first, second and third supply lines, respectively, the processor programmed to perform the step of modifying the command voltages by mathematically combining the difference values and the second harmonic components to identify first, second and third command voltages.

27. The apparatus of claim 26 wherein the processor is programmed to perform the step of mathematically combining by adding the first, second and third phase second harmonic components to the first, second and third phase difference values.

28. The apparatus of claim 26 wherein the processor is programmed to identifying the peak amplitudes by solving the following equations:

$\begin{array}{c}a=\sqrt{\frac{2}{3}}·<br><br>V_{\mathrm{ab\_RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{\mathrm{ca\_RMS}}^2-V_{\mathrm{bc\_RMS}}^2\right)}{V_{\mathrm{ab\_RMS}}+V_{\mathrm{bc\_RMS}}+V_{\mathrm{ca\_RMS}}}\\ b=\sqrt{\frac{2}{3}}·<br><br>V_{\mathrm{bc\_RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{\mathrm{ab\_RMS}}^2-V_{\mathrm{ca\_RMS}}^2\right)}{V_{\mathrm{ab\_RMS}}+V_{\mathrm{bc\_RMS}}+V_{\mathrm{ca\_RMS}}}\\ c=\sqrt{\frac{2}{3}}·<br><br>V_{\mathrm{ca\_RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{\mathrm{bc\_RMS}}^2-V_{\mathrm{ab\_RMS}}^2\right)}{V_{\mathrm{ab\_RMS}}+V_{\mathrm{bc\_RMS}}+V_{\mathrm{ca\_RMS}}},\end{array}$

where a, b and c are the peak amplitudes and where V<sub>ab—

RMS</sub>, V<sub>bc—

RMS</sub> and V<sub>ca—

RMS</sub> are the first, second and third RMS line-to-line voltages that occur between the first and second, second and third and third and first lines, respectively.

29. The apparatus of claim 26 wherein the processor is further programmed to perform the steps of identifying the frequency of the supply line voltages and using the frequency to identify a supply voltage angle, the processor performing the step of identifying the second harmonic components by identifying the q-axis second harmonic component by multiplying peak values a, b and c by the sine of the supply voltage angle, the sine of the supply voltage angle less 120 degrees and the sine of the supply voltage angle plus 120 degrees, respectively.

30. The apparatus of claim 26 wherein the processor is programmed to perform the step of using the reference voltage to identify voltage difference values by using the reference voltage to identifying first, second and third phase reference currents, obtaining first, second and third phase feedback currents, subtracting the first, second and third phase feedback currents from the first, second and third reference currents to identify first, second and third command currents, respectively, and using the first, second and third phase command currents to identify the voltage difference values.

31. A method for use with a controller and a converter wherein the controller receives a reference voltage and generates first, second and third phase control voltages as a function of the reference voltage, the converter receiving the first, second and third phase control voltages and first, second and third phase line voltages and converting the line voltages to a DC voltage across positive and negative DC buses as a function of the control voltages where the line voltages may be unbalanced, the method for substantially reducing the second harmonics in the first, second and third phase line currents caused by drawing current from the lines when the line voltages are unbalanced, the method comprising the steps of:

identifying first, second and third RMS line-to-line voltages;

using the RMS line-to-line voltages to identify peak line voltage values;

mathematically combining the peak line voltage values and at least a derivative of the reference voltage to generate the first, second and third phase command voltages; and

using the first, second and third phase command voltages to control the converter.

32. A method for use with first, second and third voltage supply lines that feed a converter, the method for identifying the peak amplitudes of the line voltages, the method comprising the steps of:

obtaining RMS line-to-line voltages from the supply lines; and

solving the following equations to identify the peak amplitudes a, b and c of the voltages on the first, second and third supply lines, respectively;

$\begin{array}{c}a=\sqrt{\frac{2}{3}}·<br><br>V_{\mathrm{ab\_RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{\mathrm{ca\_RMS}}^2-V_{\mathrm{bc\_RMS}}^2\right)}{V_{\mathrm{ab\_RMS}}+V_{\mathrm{bc\_RMS}}+V_{\mathrm{ca\_RMS}}}\\ b=\sqrt{\frac{2}{3}}·<br><br>V_{\mathrm{bc\_RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{\mathrm{ab\_RMS}}^2-V_{\mathrm{ca\_RMS}}^2\right)}{V_{\mathrm{ab\_RMS}}+V_{\mathrm{bc\_RMS}}+V_{\mathrm{ca\_RMS}}}\\ c=\sqrt{\frac{2}{3}}·<br><br>V_{\mathrm{ca\_RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{\mathrm{bc\_RMS}}^2-V_{\mathrm{ab\_RMS}}^2\right)}{V_{\mathrm{ab\_RMS}}+V_{\mathrm{bc\_RMS}}+V_{\mathrm{ca\_RMS}}}\end{array}$

where V<sub>ab—

RMS</sub>, V<sub>bc—

RMS</sub> and V<sub>ca—

RMS</sub> are the first, second and third RMS line-to-line voltages that occur between the first and second, second and third and third and first lines, respectively.

34. A method for use with a controller and a converter wherein the controller receives a reference voltage and generates first, second and third phase control voltages as a function of the reference voltage, the converter receiving the first, second and third phase control voltages and first, second and third phase line voltages and converting the line voltages to a DC voltage across positive and negative DC buses as a function of the control voltages where the line voltages may be unbalanced, the method for substantially reducing second harmonics in the first, second and third phase line currents caused by drawing current from the lines when the line voltages are unbalanced, the method comprising the steps of:

obtaining first, second and third RMS line-to-line voltages;

identifying the first, second and third peak amplitudes a, b and c, of the first, second and third supply line voltages, respectively, by solving the following equations;

$\begin{array}{c}a=\sqrt{\frac{2}{3}}·<br><br>V_{\mathrm{ab\_RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{\mathrm{ca\_RMS}}^2-V_{\mathrm{bc\_RMS}}^2\right)}{V_{\mathrm{ab\_RMS}}+V_{\mathrm{bc\_RMS}}+V_{\mathrm{ca\_RMS}}}\\ b=\sqrt{\frac{2}{3}}·<br><br>V_{\mathrm{bc\_RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{\mathrm{ab\_RMS}}^2-V_{\mathrm{ca\_RMS}}^2\right)}{V_{\mathrm{ab\_RMS}}+V_{\mathrm{bc\_RMS}}+V_{\mathrm{ca\_RMS}}}\\ c=\sqrt{\frac{2}{3}}·<br><br>V_{\mathrm{ca\_RMS}}+\sqrt{\frac{3}{2}}·<br><br>\frac{\left(V_{\mathrm{bc\_RMS}}^2-V_{\mathrm{ab\_RMS}}^2\right)}{V_{\mathrm{ab\_RMS}}+V_{\mathrm{bc\_RMS}}+V_{\mathrm{ca\_RMS}}},\end{array}$

respectively, where V<sub>ab—

RMS</sub>, V<sub>bc—

RMS</sub> and V<sub>ca—

RMS</sub> are the first, second and third RMS line-to-line voltages that occur between the first and second, second and third and third and first lines, respectively;

using the peak amplitudes to identify feed forward voltages;

mathematically combining the feed forward voltages and at least a derivative of the reference voltage to generate the first, second and third phase command voltages; and

using the first, second and third phase command voltages to control the converter.

35. A method for use with a controller and a converter where the controller actively controls the converter to convert three phase voltages on three supply lines to a DC voltage across positive and negative DC buses, the method comprising the steps of:

identifying the peak amplitudes a, b and c of the three phase supply line voltages;

identifying a two phase amplitude value A_min by solving the following equation;

$\begin{array}{c}{A}_{\min }=\frac{A_{\mathrm{\alpha <br><br>}}·<br><br>\mathrm{Sin}<br><br>\left({\mathrm{\phi <br><br>}}_{\mathrm{\alpha <br><br>}}\right)+A_{\mathrm{\beta <br><br>}}·<br><br>\mathrm{Cos}<br><br>\left({\mathrm{\phi <br><br>}}_{\mathrm{\beta <br><br>}}\right)}{2}\\ \mathrm{where}<br><br>\text{;<br><br>}\\ A_{\mathrm{\alpha <br><br>}}=\frac{e_0^{*}}{3}<br><br>\sqrt{{\left(a^{*}+b^{*}\right)}^2+{\left(a^{*}+c^{*}\right)}^2+2<br><br>{\left(a^{*}\right)}^2-b^{*}·<br><br>c^{*}}\\ A_{\mathrm{\beta <br><br>}}=\frac{e_0^{*}}{\sqrt{3}}·<br><br>\sqrt{{\left(b^{*}+c^{*}\right)}^2-b^{*}·<br><br>c^{*}}\\ {\mathrm{\phi <br><br>}}_{\mathrm{\alpha <br><br>}}=\mathrm{arc}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{tg}\left[\frac{\sqrt{3}·<br><br>\left(b^{*}-c^{*}\right)}{4<br><br>a^{*}+b^{*}+c^{*}}\right]\\ {\mathrm{\phi <br><br>}}_{\mathrm{\beta <br><br>}}=\mathrm{arc}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{tg}\left[\frac{\sqrt{3}·<br><br>\left(b^{*}+c^{*}\right)}{b^{*}-c^{*}}\right]\\ \mathrm{where}<br><br>\text{;<br><br>}\\ e_0^{*}=\frac{a+b+c}{3};<br><br>\mathrm{and}\\ \begin{array}{ccc}{a}^{*}=\frac{a}{e_0^{*}};<br><br>& b^{*}=\frac{b}{e_0^{*}};<br><br>& c^{*}=\frac{c}{e_0^{*}}\end{array}\end{array}$

using value Amin to identify d and q-axis second harmonic components that would be generated on the supply lines by the converter during normal operation due to unbalance in the peak amplitudes;

using the d and q-axis second harmonic components to alter control of the converter thereby substantially minimizing the second harmonic components on the three phase supply lines.

36. A method for use with a controller and a converter where the controller actively controls the converter to convert three phase voltages on three supply lines to a DC voltage across positive and negative DC buses, the method comprising the steps of:

identifying unbalance in the peak amplitudes of the three phase supply line voltages; and

using the unbalance to alter control of the converter to substantially eliminate generation of second harmonics on the supply lines due to active converter control.