Implementation of Space Vector Modulation (SVM ) Inveter

Prelude
SVM is a sophisticated digital control algorithm employed in modern Inverters for the generation of a three phase pure sine AC voltage. SVM Inverters are mostly used to power high performance industrial drives such as three phase AC induction motors. Unlike the conventional sinusoidal PWM, this form of modulation utilizes more available DC supply voltage (15% more voltage output), produces a sine wave with less Total Harmonic Distortion (THD) and offers more degree of freedom in the implementation [1].

Lots of papers have been published on this topic, but many are too complicated for comprehension by many average learners, while others have failed to provide in-depth implementation details. This piece provides all the necessary information required to design and implement practical SVM Inverter in a simplified format.

The basic theory of Space Vector Modulation
The principle of space vector modulation is based on the application of space vectors as shown in the space vector hexagon of figure 1.1. The diagram of basic three phase inverter is shown in figure 1.0. As the IGBTs/MOSFETs in fig 1.0 are switched on and off, eight possible switching vectors V0 through V7 are realised. These switching vectors consists of six active switching vectors (V1 to V6 ) and two zero (non-active) vectors (V0 and V7) as shown in figure 1.1.

Referring to figure 1.1, the Vref is the resultant output voltage from the SVM Inveter. Implementing space vector modulation requires the reference voltage Vref to be generated, and this is achieved by sampling two adjacent vectors of the Space Vector hexagon within a given time period Ts = 1/ Fs.











Figure 1.0 (left): 3 phase inverter;  and fig 1.1 (right): Space Vector Hexagon

SVM Design
Space Vector PWM control is realized using the following steps:
Step 1: Determine |Vref| and angle (α)
Step 2: Determine switching timing T1, T2, T0
Step 3: Determine the switching sequence


Figure 1.4 shows the Pictorial analysis of the reference voltage Vref.

Figure 1.4: Pictorial analysis of Vref in sector 1

Step 1: Determination of Vref, and angle (α)

The magnitude of the voltage reference Vref is expressed as,

|Vref| =m * Vdc

Where, m is the modulation index.

The modulation index m of SVM Inverter normally ranges from 0 to 0.866.

NB: Magnitude of Vref is directly proportional to modulation index.

From fig.1.4, the angle α is given as,

If Vref is built up at time t = 2.5ms for 50 Hz fundamental frequency [2], then the angle α is calculated below with Pi = 180 degrees: 

Step 2: Determination of time duration T1, T2, T0

The sampling time Ts is expressed as: 

Several formulas exist in theory for calculating the precise value of T1 and T2 [3] [4]. For this implementation, the Values of T1 and T2 were computed using equation 1 and 2: 

Step 3: Determine the switching sequence

Possible Solutions

Various strategies for selecting the order of vectors, and which zero vectors to use exist. The Strategy adopted will affect the harmonic content and the switching losses. This implementation relies on Symmetric Sequence SVM algorithm due to the low THD associated with it [5].

Symmetric SVM Algorithm

The timing sequence and the resulting switching waveform for Symmetric Sequence SVM in sector 1 is shown in figure 1.2.

Figure 1.2: Typical witching waveform of symmetric SVM in Sector 1


For the Symmetric SVM sequence, the expected waveform of the switching signals for the upper arm transistors in each of the six sectors of the hexagon are shown in figure 1.3.

Figure 1.3: SVM waveforms for the six sectors


Table 1.0 shows the sequence of vectors for the six sectors. 

Design specifications

Calculations
The switching times for T0, T1, and T2 were computed as follows:

T1 = 200us × 2/√3 × 0.6 × sin (60-45) = 36us

T2 = 200us × 2/√3 × 0.6 × sin 45 = 98us

Therefore, T0/7 = Ts − (T1 + T2) = 200us − (36 + 98)us

T0/7 = 200us − 134 = 66us
Therefore, T0 = T7 = 66us/2 = 33us 

Hence, 

T0 = 33us
T1 = 36us
T2 = 98us

Implementation
The implementation involved writing the required code that will actualize the Space Vector Modulation. The flow chart of figure 1.5 was used to develop the SVM code. 

Figure 1.5:  Design flowchart

Table 1.2 shows the hex equivalence of the SVM data required for firmware implementation. The two lower bits (bit 0 and 1) of the data line are filled with zeros. The code that implements the SVM algorithm can be accessed here - SVM Code.

Table 1.2: The hex equivalent of the switching vectors

Vectors	A,B,C,A’,B’,C’	HEX
V0	000111	1Ch
V1	100011	8Ch
V2	110001	C4h
V3	010101	54h
V4	011100	70h
V5	001110	38h
V6	101010	A8h
V7	111000	E0h

The complete schematic for this implementation is shown in figure 1.6. For more description of the schematics, please see the video demo below.

Figure 1.6: SVM Inverter schematic

DEMO Video: SVM INverter 

Simulation Results and Discussions
The resultant SVM waveforms generated from the microcontroller are shown in figure 1.6. The result is in agreement with the theoretical symmetric SVM patterns shown in figure 1.3.

Figure 1.6: SVM signals from MCU


The phase voltages (Va, Vb and Vc) generated from the SVM inverter are shown in figure 1.7. It can be seen that the phase voltages are pure sine wave. Figure 1.8 shows the phase voltages with a phase difference of 120 degrees.

Figure 1.7: The phase voltages from the SVM Inverter

Figure 1.8: result showing the phase difference of 120 degrees

Conclusion
The aim of this work which was to generate a pure sine wave from a DC using Space Vector Modulation was successfully achieved, as demonstrated in the results.

Why not give it a trial, and see how Space Vector Modulation helps you realize a pure sine wave Inverter!