View source for Space vector modulation

{{Modulation techniques}}
'''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.<ref name=control>
{{cite book
 |author1=M.P. Kazmierkowski |author2=R. Krishnan |author3=F. Blaabjerg  |name-list-style=amp | title = Control in Power Electronics: Selected Problems
 | publisher = San Diego: Academic Press
 | year = 2002
 | isbn = 978-0-12-402772-5
 | url = https://books.google.com/books?id=6_dmMHEyvrkC&dq=%22space+vector+modulation%22+intitle:%22Control+in+Power+Electronics%22&pg=PA373
 }}</ref><ref name=invention>
{{cite web |url=https://ethw.org/Power_electronics |title=Engineering and Technology History Wiki: Power electronics |author1=Bimal K. Bose |date=2014 |access-date=29 Dec 2023}}</ref> It is used for the creation of [[alternating current]] (AC) [[waveform]]s; most commonly to drive [[3 phase]] AC powered motors at varying speeds from DC using multiple [[Switching amplifier|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==
[[File:Three leg inverter.gif|240px|thumb|right|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<sup>+</sup> is on then A<sup>−</sup> is off and vice versa. This leads to eight possible switching vectors for the inverter, V<sub>0</sub> through V<sub>7</sub> with six active switching vectors and two zero vectors.

{| class="wikitable" border="1" style="margin: 1em auto;"
|-
! Vector
! A<sup>+</sup>
! B<sup>+</sup>
! C<sup>+</sup>
! A<sup>−</sup>
! B<sup>−</sup>
! C<sup>−</sup>
! V<sub>AB</sub>
! V<sub>BC</sub>
! V<sub>CA</sub>
! 
|-
| V<sub>0</sub> = {000}
| align="center"| OFF
| align="center"| OFF
| align="center"| OFF
| align="center"| ON
| align="center"| ON
| align="center"| ON
| align="center"| 0
| align="center"| 0
| align="center"| 0
| zero vector
|-
| V<sub>1</sub> = {100}
| align="center"| ON
| align="center"| OFF
| align="center"| OFF
| align="center"| OFF
| align="center"| ON
| align="center"| ON
| align="center"| +V<sub>dc</sub>
| align="center"| 0
| align="center"| −V<sub>dc</sub>
| active vector
|-
| V<sub>2</sub> = {110}
| align="center"| ON
| align="center"| ON
| align="center"| OFF
| align="center"| OFF
| align="center"| OFF
| align="center"| ON
| align="center"| 0
| align="center"| +V<sub>dc</sub>
| align="center"| −V<sub>dc</sub>
| active vector
|-
| V<sub>3</sub> = {010}
| align="center"| OFF
| align="center"| ON
| align="center"| OFF
| align="center"| ON
| align="center"| OFF
| align="center"| ON
| align="center"| −V<sub>dc</sub>
| align="center"| +V<sub>dc</sub>
| align="center"| 0
| active vector
|-
| V<sub>4</sub> = {011}
| align="center"| OFF
| align="center"| ON
| align="center"| ON
| align="center"| ON
| align="center"| OFF
| align="center"| OFF
| align="center"| −V<sub>dc</sub>
| align="center"| 0
| align="center"| +V<sub>dc</sub>
| active vector
|-
| V<sub>5</sub> = {001}
| align="center"| OFF
| align="center"| OFF
| align="center"| ON
| align="center"| ON
| align="center"| ON
| align="center"| OFF
| align="center"| 0
| align="center"| −V<sub>dc</sub>
| align="center"| +V<sub>dc</sub>
| active vector
|-
| V<sub>6</sub> = {101}
| align="center"| ON
| align="center"| OFF
| align="center"| ON
| align="center"| OFF
| align="center"| ON
| align="center"| OFF
| align="center"| +V<sub>dc</sub>
| align="center"| −V<sub>dc</sub>
| align="center"| 0
| active vector
|-
| V<sub>7</sub> = {111}
| align="center"| ON
| align="center"| ON
| align="center"| ON
| align="center"| OFF
| align="center"| OFF
| align="center"| OFF
| align="center"| 0
| align="center"| 0
| align="center"| 0
| zero vector
|}

Note that looking down the columns for the active switching vectors V<sub>1-6</sub>, the output voltages vary as a pulsed sinusoid, with each leg offset by 120 degrees of [[Phasor (electronics)|phase angle]].

To implement space vector modulation, a reference signal V<sub>ref</sub> is sampled with a frequency f<sub>s</sub> (T<sub>s</sub> = 1/f<sub>s</sub>). The reference signal may be generated from three separate phase references using the [[Alpha beta gamma transform|<math>\alpha\beta\gamma</math> 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 {{ill|switching loss|lt=switching losses|de|Schaltverluste}}.

[[File:Space Vector Modulation.gif|center|thumb|400px|All eight possible switching vectors for a three-leg inverter using space vector modulation. An example V<sub>ref</sub> is shown in the first sector. V<sub>ref_MAX</sub> is the maximum amplitude of V<sub>ref</sub> 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 (geometry)|prism]] in <math>\alpha\beta\gamma</math> coordinates<ref>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</ref> or a [[dodecahedron]] in abc coordinates<ref>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</ref>) rather than a 2D [[hexagon]]. General SVM techniques are also available for converters with any number of legs and levels.<ref>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.</ref>

==See also==
* [[Alpha–beta transformation|αβγ transform]]
* [[Inverter (electrical)]]
* [[pulse-width modulation]]

==References==
{{reflist}}

{{DEFAULTSORT:Space Vector Modulation}}
[[Category:Electrical engineering]]
[[Category:Control theory]]