• https://www.pscad.com/webhelp/Master_Library_Models/HVDC_and_FACTS/Space_Vector_Modulation/SVM_Theory.htm
• Space Vector Modulation is a modulation technique that calculates duty cycles of switches to synthesize a desired output voltage on average, without the use of a carrier waveform.
• The Space Vector Modulation component utilizes a two level converter shown in Figure 1. With this converter, there are eight possible states. The states are shown in Table 1 along with the Park’s transformation of these states.
• 
  Figure 1 — Two-Level Converter
• 
  Table 1 — State Table
• By specifying a reference voltage (magnitude and phase), a voltage vector can be reconstructed on the average by using the 8 possible states of the converter. The reconstruction is done by sampling the reference voltage at a given period Ts and computing periods of time to be in certain states so that on the average, the reference voltage is attained. This process is illustrated in Figure 2.
• 
  Figure 2 — Space Vector Modulation in Linear Operating Region
• During any given sampling interval, the reference voltage is reconstructed using equation 1.
• (1)
• Where T1 and T2 are the time shares of the two active states and T0 and T7 are the time shares of the zero states. A1 and A2 are the active vectors and are determined based on the phase of the reference voltage. The time shares are computed using the following expressions. These expressions are only valid in the linear operating region.
• (2)
• (3)
• (4)
• Where m in known as the modulation index and is given by:
• (5)
• The sequence of states used to reconstruct the reference voltage is up to the user; however the SVM block in PSCAD uses a scheme to minimize the number of switching actions per sampling period. The space vector modulation scheme will be operating in a linear mode for a value of the modulation index between 0 and 2/√3. For a modulation index greater than 2/√3, the converter is in a mode known as over-modulation. When in this mode, if the reference voltage crosses the hexagon boundary, the linear equations no longer apply and the time shares for the zero states will disappear. This situation is illustrated in Figure 3.
• 
  Figure 3 — Space Vector Modulation in Over-Modulation Operating Region [See Reference 21]
• When the reference exceeds the hexagon boundary the time shares of the active vectors are found using the following equations:
• (6)
• (7)
• This mode of operation is valid until a modulation index of 4/3. Once the modulation surpasses 4/3, the reference voltage is outside the hexagon boundary at all times. At this point the switching scheme just cycles between non-zero vectors in sequence, which is known as square wave operation.

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