Space vector modulation

Space vector modulation (SVM) is an algorithm for the control of pulse-width modulation (PWM), invented by Gerhard Pfaff, Alois Weschta, and Albert Wick in 1982. ^{[1] [2]} It is used for the creation of alternating current (AC) waveforms; most commonly to drive 3 phase AC powered motors at varying speeds from DC using multiple class-D amplifiers. There are variations of SVM that result in different quality and computational requirements. One active area of development is in the reduction of total harmonic distortion (THD) created by the rapid switching inherent to these algorithms.

Principle

Topology of a basic three-phase inverter

A three-phase inverter as shown to the right converts a DC supply, via a series of switches, to three output legs which could be connected to a three-phase motor.

The switches must be controlled so that at no time are both switches in the same leg turned on or else the DC supply would be shorted. This requirement may be met by the complementary operation of the switches within a leg. i.e. if A⁺ is on then A⁻ is off and vice versa. This leads to eight possible switching vectors for the inverter, V₀ through V₇ with six active switching vectors and two zero vectors.

Vector	A+	B+	C+	A−	B−	C−	VAB	VBC	VCA
V0 = {000}	OFF	OFF	OFF	ON	ON	ON	0	0	0	zero vector
V1 = {100}	ON	OFF	OFF	OFF	ON	ON	+Vdc	0	−Vdc	active vector
V2 = {110}	ON	ON	OFF	OFF	OFF	ON	0	+Vdc	−Vdc	active vector
V3 = {010}	OFF	ON	OFF	ON	OFF	ON	−Vdc	+Vdc	0	active vector
V4 = {011}	OFF	ON	ON	ON	OFF	OFF	−Vdc	0	+Vdc	active vector
V5 = {001}	OFF	OFF	ON	ON	ON	OFF	0	−Vdc	+Vdc	active vector
V6 = {101}	ON	OFF	ON	OFF	ON	OFF	+Vdc	−Vdc	0	active vector
V7 = {111}	ON	ON	ON	OFF	OFF	OFF	0	0	0	zero vector

Note that looking down the columns for the active switching vectors V_1-6, the output voltages vary as a pulsed sinusoid, with each leg offset by 120 degrees of phase angle.

To implement space vector modulation, a reference signal V_ref is sampled with a frequency f_s (T_s = 1/f_s). The reference signal may be generated from three separate phase references using the ${\displaystyle \alpha \beta \gamma }$ transform. The reference vector is then synthesized using a combination of the two adjacent active switching vectors and one or both of the zero vectors. Various strategies of selecting the order of the vectors and which zero vector(s) to use exist. Strategy selection will affect the harmonic content and the switching losses  [ de ].

All eight possible switching vectors for a three-leg inverter using space vector modulation. An example V_ref is shown in the first sector. V_{ref_MAX} is the maximum amplitude of V_ref before non-linear overmodulation is reached.

More complicated SVM strategies for the unbalanced operation of four-leg three-phase inverters do exist. In these strategies the switching vectors define a 3D shape (a hexagonal prism in ${\displaystyle \alpha \beta \gamma }$ coordinates ^[3] or a dodecahedron in abc coordinates ^[4] ) rather than a 2D hexagon. General SVM techniques are also available for converters with any number of legs and levels. ^[5]

See also

• αβγ transform
• Inverter (electrical)
• pulse-width modulation

References

1. M.P. Kazmierkowski; R. Krishnan & F. Blaabjerg (2002). Control in Power Electronics: Selected Problems. San Diego: Academic Press. ISBN   978-0-12-402772-5.
2. Bimal K. Bose (2014). "Engineering and Technology History Wiki: Power electronics" . Retrieved 29 Dec 2023.
3. R. Zhang, V. Himamshu Prasad, D. Boroyevich and F.C. Lee, "Three-Dimensional Space Vector Modulation for Four-Leg Voltage-Source Converters," IEEE Power Electronics Letters, vol. 17, no. 3, May 2002
4. M.A. Perales, M.M. Prats, R.Portillo, J.L. Mora, J.I. León, and L.G. Franquelo, "Three-Dimensional Space Vector Modulation in abc Coordinates for Four-Leg Voltage Source Converters," IEEE Power Electronics Letters, vol. 1, no. 4, December 2003
5. Ó. Lopez, J. Alvarez, J. Doval-Gandoy and F. D. Freijedo, "Multilevel Multiphase Space Vector PWM Algorithm," in IEEE Transactions on Industrial Electronics, vol. 55, no. 5, pp. 1933-1942, May 2008.