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Operational constraints of zero-sequence current feeding in bearingless PM synchronous machines

Betriebsgrenzen einer Nullstrom-Speisung in lagerlosen PM-Synchronmaschinen

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Abstract

For magnetically levitated drives with a 3-phase stator winding, one degree of freedom in the rotor motion can be controlled through a zero-sequence current. For example, an axial active magnetic bearing or a single-phase motor winding can be fed by this zero-sequence current. The zero-sequence current feeding is advantageous due to the saving of power electronic switches. This way, the 4-quadrant chopper can be replaced by connecting the coil to be fed with the star point of the 3-phase winding. The field of application for this principle is limited by non-linearities at high inverter modulation degrees since the maximum possible voltages of the zero-sequence current system and the 3-phase current system are mutually dependent. Therefore, a pulse width modulation is discussed, which prioritizes the 3-phase voltage system over the zero-sequence voltage system, in contrast to a modulation without prioritization. These two methods are evaluated by the maximum possible voltages and the voltage harmonic content. If only one of the two current systems demands high-voltage values, such as in the combination of a magnetic bearing and a motor winding, the zero-sequence current feeding is well-suited.

Zusammenfassung

Bei magnetgelagerten Antrieben mit 3-phasiger Statorwicklung kann ein Freiheitsgrad der Bewegung des Rotors durch einen Nullstrom geregelt werden. Beispielsweise kann ein axiales, aktives Magnetlager, aber auch eine einphasige Wicklung zur Drehmomentgenerierung mit diesem Nullstrom gespeist werden. Die Nullstromspeisung hat ihren Vorteil in der Einsparung von leistungselektronischen Stellelementen. Der sonst benötigte 4-Quadranten-Steller entfällt, indem die zu bestromende Wicklung mit dem Sternpunkt der 3-phasigen Wicklung verbunden wird. Der Einsatzbereich dieses Prinzips ist vor allem durch die Nichtlinearitäten bei hohen Umrichteraussteuergraden begrenzt, da sich dann die stellbaren Spannungen des Nullstromsystems und des Drehstromsystems gegenseitig bedingen. Deshalb wird ein Verfahren diskutiert, bei dem die Spannungen des Drehstromsystems priorisiert gegenüber dem Nullstromsystem gestellt werden, und eines, bei dem keine Priorisierung vorgenommen wird. Beide Verfahren werden mit der Speisung durch einen 4-Quadranten-Steller verglichen. Wird nur in einem der beiden Stromsysteme eine hohe Spannungsamplitude benötigt, etwa in der Kombination aus Magnetlager und Motorwicklung, ist die Nullstromspeisung sehr gut geeignet.

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Abbreviations

\(\varphi _{\mathrm{Z,A}}\)/\(\varphi _{\mathrm{Z,B}}\) :

Electric potential of star point ZA/ZB

\(\tau _{\mathrm{RL,ax}}\) :

Axial bearing electric time constant

\(f_{\mathrm{sw}}\) :

Switching frequency

\(F_{\mathrm{z,N}}\) :

Rated axial force

\(i_{\mathrm{ax}}\)/\(i_{\mathrm{0}}\) :

Axial bearing / zero-sequence current

\(i_{\mathrm{dq,D}}\)/\(i_{\mathrm{dq,L}}\) :

\(dq\)-component of drive / suspension current

\(k\) :

Time harmonic order

\(k_{\mathrm{F,z}}\) :

Axial force-current coefficient

\(L_{\mathrm{ax}}\) :

Axial bearing inductance

\(m_{\mathrm{a}}\) :

Amplitude modulation degree

\(m_{\mathrm{f}}\) :

Switching frequency as multiple of the synchronous frequency

\(m_{\mathrm{R}}\) :

Rotor mass

\(n_{\mathrm{N}}\)/\(n_{\mathrm{max}}\) :

Rated / maximum speed

\(2p\) :

Pole count

\(P_{\mathrm{N}}\) :

Rated power

\(R_{\mathrm{ax}}\) :

Axial bearing resistance

\(t\) :

Time

\(T_{\mathrm{sw}}\) :

Switching period

\(\underline{u}_{\mathrm{\alpha \beta ,A}}\)/\(\underline{u}_{\mathrm{\alpha \beta ,B}}\) :

Voltage space vector of 3-phase system A/B

\(\underline{u}_{\mathrm{\alpha \beta ,D}}\)/\(\underline{u}_{\mathrm{\alpha \beta ,L}}\) :

Voltage space vector of drive (differential mode)/ suspension (common mode) winding system

\(u_{\mathrm{ax}}\)/\(u_{\mathrm{s}}\) :

Axial bearing / AC phase voltage

\(u_{\mathrm{p}}\) :

Back-EMF

\(U_{\mathrm{DC}}\) :

DC-link voltage

\(\mathit{WTHD}0\) :

Weighted total harmonic distortion with regards to \(U_{\mathrm{DC}}/2\)

\(X_{\mathrm{D}}\)/\(X_{\mathrm{L}}\) :

Drive / levitation winding phase reactance

\(z\) :

Axial position

4Q-CB-PWM:

4-quadrant chopper feeding with carrier-based pulse width modulation

AMB:

Active magnetic bearing

CB-PWM:

Zero-sequence current feeding with carrier-based pulse width modulation

DOF:

Degree of freedom

SV-PWM:

Zero-sequence current feeding with space vector pulse width modulation

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Acknowledgement

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 437667923, BI 701/22-1 (Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) – 437667923, BI 701/22-1). Supported by KEBA Industrial Automation Germany GmbH.

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  1. Institute of Electrical Energy Conversion, TU Darmstadt, Landgraf-Georg-Str. 4, 64283, Darmstadt, Deutschland

    Daniel Dietz

  2. Institute of Electrical Energy Conversion, TU Darmstadt, Darmstadt, Deutschland

    Andreas Binder

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Correspondence to Daniel Dietz.

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Dietz, D., Binder, A. Operational constraints of zero-sequence current feeding in bearingless PM synchronous machines. Elektrotech. Inftech. 138, 383–393 (2021). https://doi.org/10.1007/s00502-021-00902-4

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