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To supply fivephase variable speed drives, fivephase voltage source inverters are used. Some of the applications of fivephase variable speed drives are traction, electric & hybridelectric vehicles, and ship propulsion. Different control systems are available for the controlled output of the fivephase VSI, but space vector pulse width modulation is popular because of its simpler digital implementation. In this paper, the SVPWM schemes have proposed and analyzed for the multilevel operation of a fivephase dual voltage source inverter. The proposed techniques do not contribute a voltage balancing issues such as in multilevel neutral point clamped (NPC) inverters. The author analyzed the performance of fivephase VSI based on THD and fundamental components. Matlab/Simulink model has provided for results verification.
fivephase voltage source inverter, multilevel inverters, space vector pulse width modulation, total harmonic distortion
In the various industrial applications as traction, electric & hybridelectric vehicles, and ship propulsion, variable speed AC drives are required. Usually, the threephase machine is using to get the controlled output for this purpose but has some limitations in terms of power. To overcome these limitations in terms of more power, researches are going on more than threephase i.e. polyphase machine. Polyphase machines have lots of advantages over threephase like less volume to weight ratio, lower dclink current harmonics, reducing rotor current harmonics, better noise, vibration characteristics, and many more. The detail description of these advantages is mentioned in the Refs. [1, 2]. The first fivephase induction motor i.e. first step in the polyphase machine has investigated in 1969 [3]. One of the main differences between threephase and fivephase machine is that threephase machines have a single stator current component across the dq axis whereas fivephase machines have more than one stator current component as the axis increases [4, 5]. Due to an increase in additional component, generated torque is also increasing. This property makes the fivephase system very different from the threephase system.
A system that can provide a controlled fivephase output supply, i.e. a fivephase inverter, is needed for powering the fivephase induction motor. This inverter input is a dc source, and the output is a controlled voltage and the frequency fivephase AC. Various control schemes are available for controlling the output of fivephase VSI, but the space vector pulse width modulation scheme is very common because of its advantages and easy digital implementation. A detailed overview of the SVPWM for the fivephase system can be found in the literature [59].
Researchers are also focusing on multilevel inverters. The multilevel term defines more than twolevel whose performance is better than the twolevel inverter because of lesser harmonics, electromagnetic interference, and higher dclink voltages. The multilevel inverter is applicable for high voltage applications whereas twolevel inverter has limitations. The benefits and the various topologies utilized in multilevel converters are elaborated in detail in the Refs. [10, 11]. Multilevel converters have many benefits, but they also have some drawbacks e.g., cost and circuit complexity increase as the output level increases.
In this article, the author discusses the fivephase twolevel dual voltage source inverter. The author also proposes two controlling schemes for multilevel operation using space vector pulse width modulation for a fivephase twolevel dual VSI. The author presented the vector diagram, switching table, switching waveform using two neighbouring large space vectors only then by using a combined application of medium and large space vectors. Here the objective is to preset the multilevel operation for five phase using twolevel dual inverter system to minimize the complexity along with the cost of multilevel converters. In last results are verified in Simulink environment.
Space vector pulse width modulation (SVPWM) is a technique used to determine the pulsewidth modulated signals for the inverter switches in order to generate the desired phase voltages to the motor. The realization of SVPWM is based on proper selection of switching states of inverter in stationary reference frame and calculation of appropriate switching time periods [12].
An efficient PWM using a space vector method has been described to control the performance of splitphase induction motor operation using a dual voltage source inverter, which also helps to eliminate fifth and seventh harmonics in the output voltage of the motor [13]. For a dual twolevel VSI fed openend winding, voltage space phasor fluctuations and zero sequence currents elimination have been presented in literature [14]. The least number of switches for each inverter, for the output voltage control has been presented Shivakumar et al. [15] and to reduce the switching for the duration of the changeover of inverters from switching to clamping and vice versa has presented in Mohan et al. [16]. In order to minimize neutral point fluctuations, zero sequence currents, and suppress triple harmonic currents, the openend winding induction motor switching scheme was presented by Somasekhar et al. [17, 18]. A switching scheme has been presented by Kalaiselvi et al. [19] without using sector identification and lookup tables and to eliminate the commonmode voltage, and reduce the current ripple and decrease the total switching in both inverters [20]. A unified SVPWM scheme for dual voltage source inverters has been presented by Chen and Sun [21], and this has become the basis for the proposed schemes in this paper. In the proposed scheme, inverter system having two different dc voltage sources to minimize the total switching frequency and to provide the region identification for each sector.
Analysis and simulation were performed on a fivephase multilevel inverter using a carrierbased PWM with imbalance conditions on the induction machine [22], and the comparative simulation study was given by Jyothi and Rao [23] for a fivephase twolevel and threelevel inverter based on output efficiency. A phase opposition disposition (POD) and in phase disposition (IPD) control system comparison was analyzed for the control of the THD in output voltage and current for threelevel fivephase inverters [24]. A new switch ladder topology has been presented to evaluate the performance level using symmetric and asymmetric sources for fivephase multilevel inverter drive [25, 26]. For threestage ttype neutral point clamped (NPC), threephase inverters using SVPWM [27], and three level NPC fivephase inverters, simulation and experimental analysis have been presented to minimize the typical mode voltage using redundant switching state voltage vectors [28]. The NPC inverter and the cascaded inverter topology were discussed to reduce the bearing current and commonmode voltage in the fivephase multilevel inverter [29]. The complexity of the power circuit and the cost of multilevel converters increase as the output level increases. The switch numbers in the twolevel dual inverter and threelevel single inverter system are the same, but the topology used in the threelevel single inverter system needed additional voltage balancing capacitors and diodes. By using a dual inverter system, which does not need any additional diodes and capacitors, this condition can be resolved, and output ripples are greatly reduced [30]. This technique also simplifies the identification of regions in sectors and reduces the overall switching frequency.
A power circuit diagram of a fivephase twolevel dual VSI is shown in Figure 1 for threelevel operation. Here is a positive end converter (blue inverter) referred to as INV 1 and a negative end converter (green inverter) referred to as INV 2. Five legs are composed in each inverter having two semiconductor switches in each leg i.e. IGBT, totaling ten switches. The operation of both switches on the same leg is complementary, to avoid the shortcircuiting of the input DC source. The inverters' inputs are supplied with equal/unequal values from isolated dclink sources and the outputs are connected to the openend winding.
Figure 1. Circuit diagram of five phase twolevel dual voltage source inverter
Figure 2. (a) Phase voltage space vector dq plane; (b) Phase voltage space vectors in xy plane
Figure 3. Voltage vector plane and voltage selection for dual inverter
Using the SVPWM scheme, each inverter in a fivephase system has thirtytwo switching vectors with thirty active vectors and two zero vectors [5]. The fivephase input voltage and space vector equation are given using power invariant matrix:
$\begin{align} & {{\text{v}}_{\text{a}}}\text{=}\sqrt{\text{2}}\text{Vcos( }\!\!\omega\!\!\text{ t)} \\ & {{\text{v}}_{\text{b}}}\text{=}\sqrt{\text{2}}\text{Vcos( }\!\!\omega\!\!\text{ t2 }\!\!\pi\!\!\text{ /5)} \\ & {{\text{v}}_{\text{c}}}\text{=}\sqrt{\text{2}}\text{Vcos( }\!\!\omega\!\!\text{ t4 }\!\!\pi\!\!\text{ /5)} \\ & {{\text{v}}_{\text{d}}}\text{=}\sqrt{\text{2}}\text{Vcos( }\!\!\omega\!\!\text{ t+4 }\!\!\pi\!\!\text{ /5)} \\ & {{\text{v}}_{\text{e}}}\text{=}\sqrt{\text{2}}\text{Vcos( }\!\!\omega\!\!\text{ t+2 }\!\!\pi\!\!\text{ /5)} \\ \end{align}$ (1)
${{\underline{v}}_{dq}}=\frac{2}{5}({{v}_{a}}+\underline{a}{{v}_{b}}+{{\underline{a}}^{2}}{{v}_{c}}+{{\underline{a}}^{*2}}{{v}_{d}}+{{\underline{a}}^{*}}{{v}_{e}})$ (2a)
${{\underline{v}}_{xy}}=\frac{2}{5}({{v}_{a}}+{{\underline{a}}^{2}}{{v}_{b}}+{{\underline{a}}^{*}}{{v}_{c}}+{{\underline{a}}^{{}}}{{v}_{d}}+{{\underline{a}}^{*2}}{{v}_{e}})$ (2b)
where, a = exp(j2p/5), a^{2} = exp(j4p/5), a* = exp(j2p/5), a*^{2 }= exp(j4p/5) and * stands for a complex conjugate. The phase voltage space vectors thus obtained in dq plane using (2a) are shown in Figure 2 and since it is a fivephase system, transformation is further done to obtain space vectors in xy plane using (2b) and the resulting space vectors are shown in Figure 3.
All the thirty active vectors have divided in three groups according to their magnitude i.e. large vectors, medium vectors and small vectors. The author has proposed two PWM schemes for the fivephase dual VSI (a) using only large vectors (b) using large and medium vectors.
The selection of switching voltage for the dual inverter having two different dc voltage sources is illustrated in Figure 3.
4.1 Using only large voltage vectors
For the generation of reference voltage vector, two neighboring large active voltage vectors, and one null voltage vector is used for every inverter [30]. The duration of time of both the active space voltage vector has presented by
${{\text{T}}_{1}}\text{=}\frac{\left {{\underline{\text{v}}}_{\text{ref}}} \right\text{sin}\left( \text{k }\!\!\pi\!\!\text{ /5 }\!\!\alpha\!\!\text{ } \right)}{\left {{\underline{\text{v}}}_{\text{l}}} \right\text{sin}\left( \text{ }\!\!\pi\!\!\text{ /5} \right)}{{\text{T}}_{\text{s}}}$ (3)
${{\text{T}}_{2}}\text{=}\frac{\left {{\underline{\text{v}}}_{\text{ref}}} \right\text{sin}\left( \text{ }\!\!\alpha\!\!\text{ }\left( \text{k1} \right)\text{ }\!\!\pi\!\!\text{ /5} \right)}{\left {{\underline{\text{v}}}_{\text{l}}} \right\text{sin}\left( \text{ }\!\!\pi\!\!\text{ /5} \right)}{{\text{T}}_{\text{s}}}$ (4)
${{\text{T}}_{\text{0}}}\text{=}{{\text{T}}_{\text{s}}}\text{}{{\text{T}}_{1}}\text{}{{\text{T}}_{2}}$ (5)
Here symbol, $\mathrm{k}=$ sector number $(\mathrm{k}=1$ to 10 for five phase $)$, $\left\underline{v}_{l}\right=\frac{2}{5} V_{d c} 2 \cos (\pi / 5)=$ peak of length of large voltage vector, $\underline{v}_{\mathrm{ref}}=$ reference vector, $\mathrm{l}=$ large space vectors, $\mathrm{T}_{\mathrm{s}}=$ sampling period and θ(0, π/5) = angle between V_{ref} & V_{1}.
Table 1. Switching sequence for the multilevel operation
Sector 
Switching Sequence 

I 
V0 
V2 
V1 
V0 
V1 
V2 
V0 
00000 
11000 
11001 
11111 
11001 
11000 
00000 

II 
V0 
V2 
V3 
V0 
V3 
V2 
V0 
00000 
11000 
11100 
11111 
11100 
11000 
00000 

III 
V0 
V4 
V3 
V0 
V3 
V4 
V0 
00000 
01100 
11100 
11111 
11100 
01100 
00000 

IV 
V0 
V4 
V5 
V0 
V5 
V4 
V0 
00000 
01100 
01110 
11111 
01110 
01100 
00000 

V 
V0 
V6 
V5 
V0 
V5 
V6 
V0 
00000 
00110 
01110 
11111 
01110 
10110 
00000 

VI 
V0 
V6 
V7 
V0 
V7 
V6 
V0 
00000 
00110 
00111 
11111 
00111 
10110 
00000 

VII 
V0 
V8 
V7 
V0 
V7 
V8 
V0 
00000 
00011 
00111 
11111 
00111 
00011 
00000 

VIII 
V0 
V8 
V9 
V0 
V9 
V8 
V0 
00000 
00011 
10011 
11111 
10011 
00011 
00000 

IX 
V0 
V10 
V9 
V0 
V9 
V10 
V0 
00000 
10001 
10011 
11111 
10011 
10001 
00000 

X 
V0 
V10 
V1 
V0 
V1 
V10 
V0 
00000 
10001 
11001 
11111 
11001 
10001 
00000 
During sampling time, two reference voltages generated by both the inverters are used to generate the average voltage vector. Using the proposed method, dual twolevel fivephase VSI inverter performance is similar to multilevel operation as in a multilevel neutral point clamped (NPC) inverter. Another advantage of this scheme is that, along with minimizing switching losses, it minimizes the overall total harmonic distortion, the switching pattern for multilevel operations is shown in Table 1.
During the synthesis process both the reference voltages Vref & Vref' produced by each inverter move in all the ten sectors (I to X) in decagon vector diagram using ten active vectors for INV 1(V_{1} to V_{10}) and ten active vectors for INV 2 (V_{1'} to V_{10'}) and two null vectors (V_{0}&V_{0'}) positioned at origin. It is a key feature to reduce the switching losses, switching, and overall THD for inverter function. The switching waveform for dual VSI for both reference voltages (Vref & Vref’) are in Figure 4(a). For greater comprehension switching pattern is presented in blue for INV 1 and green for INV 2 utilizing space vector V_{0}, V_{1}, V_{2}, V_{0}', V_{8'}, and V_{9}' and line voltages are presented in black color during the sampling period.
4.2 Using large and medium voltage vectors
(a)
(b)
Figure 4. (a). Switching waveforms for five phase twolevel dual VSI for multilevel operation using large vectors only; (b). Switching waveforms for five phase twolevel dual VSI for multilevel operation using large and medium vectors
Table 2. Switching sequence for the multilevel operation using large and medium vector
Sector 
Switching Sequence 

I 
V0 
V1 
V2 
V1 
V2 
V0 
V2 
V1 
V2 
V1 
V0 
00000 
10000 
11000 
11001 
11101 
11111 
11101 
11001 
11000 
10000 
00000 

II 
V0 
V3 
V2 
V3 
V2 
V0 
V2 
V3 
V2 
V3 
V0 
00000 
01000 
11000 
11100 
11101 
11111 
11101 
11100 
11000 
01000 
00000 

III 
V0 
V3 
V4 
V3 
V4 
V0 
V4 
V3 
V4 
V3 
V0 
00000 
01000 
01100 
11100 
11110 
11111 
11110 
11100 
01100 
01000 
00000 

IV 
V0 
V5 
V4 
V5 
V4 
V0 
V4 
V5 
V4 
V5 
V0 
00000 
00100 
01100 
01110 
11110 
11111 
11110 
01110 
01100 
00100 
00000 

V 
V0 
V5 
V6 
V5 
V6 
V0 
V6 
V5 
V6 
V5 
V0 
00000 
00100 
00110 
01110 
01111 
11111 
01111 
01110 
10110 
00100 
00000 

VI 
V0 
V7 
V6 
V7 
V6 
V0 
V6 
V7 
V6 
V7 
V0 
00000 
00010 
00110 
00111 
01111 
11111 
01111 
00111 
10110 
00010 
00000 

VII 
V0 
V7 
V8 
V7 
V8 
V0 
V8 
V7 
V8 
V7 
V0 
00000 
00010 
00011 
00111 
10111 
11111 
10111 
00111 
00011 
00010 
00000 

VIII 
V0 
V9 
V8 
V9 
V8 
V0 
V8 
V9 
V8 
V9 
V0 
00000 
00001 
00011 
10011 
10111 
11111 
10111 
10011 
00011 
00001 
00000 

IX 
V0 
V9 
V10 
V9 
V10 
V0 
V10 
V9 
V10 
V9 
V0 
00000 
00001 
10001 
10011 
11011 
11111 
11011 
10011 
10001 
00001 
00000 

X 
V0 
V1 
V10 
V1 
V10 
V0 
V10 
V1 
V10 
V1 
V0 
00000 
10000 
10001 
11001 
11011 
11111 
11011 
11001 
10001 
10000 
00000 
The harmonic content is present in the output phase voltages using only large voltage vectors. This implies that, as only two active vectors are often used in each sector, we do not get satisfactory results. For a pure sinusoidal voltage waveform, the number of vectors should be one less than the number of phases [30]. This means that four active voltage vectors should be used rather than two to achieve satisfactory sinusoidal outcomes in a fivephase system. For each inverter, two neighboring large and two neighboring medium active voltage vectors are used for the generation of reference voltage vectors along with one null voltage vector. The switching waveform for dual VSI for both reference voltages (Vref & Vref’) using large and medium vectors are in Figure 4(b). The duration of time of both the active space voltage vector has presented by:
${{\text{T}}_{\text{al}}}\text{=}\frac{\left {{\underline{\text{v}}}_{\text{l}}} \right}{\left {{\underline{\text{v}}}_{\text{l}}} \right\text{+}\left {{\underline{\text{v}}}_{\text{m}}} \right}{{\text{T}}_{\text{a}}}$
${{\text{T}}_{\text{bl}}}\text{=}\frac{\left {{\underline{\text{v}}}_{\text{l}}} \right}{\left {{\underline{\text{v}}}_{\text{l}}} \right\text{+}\left {{\underline{\text{v}}}_{\text{m}}} \right}{{\text{T}}_{\text{b}}}$
${{\text{T}}_{\text{am}}}\text{=}\frac{\left {{\underline{\text{v}}}_{\text{m}}} \right}{\left {{\underline{\text{v}}}_{\text{l}}} \right\text{+}\left {{\underline{\text{v}}}_{\text{m}}} \right}{{\text{T}}_{\text{a}}}$
${{\text{T}}_{\text{bm}}}\text{=}\frac{\left {{\underline{\text{v}}}_{\text{m}}} \right}{\left {{\underline{\text{v}}}_{\text{l}}} \right\text{+}\left {{\underline{\text{v}}}_{\text{m}}} \right}{{\text{T}}_{\text{b}}}$
${{\text{T}}_{\text{0}}}\text{=}{{\text{T}}_{\text{s}}}\text{}{{\text{T}}_{\text{al}}}\text{}{{\text{T}}_{\text{am}}}\text{}{{\text{T}}_{\text{bl}}}\text{}{{\text{T}}_{\text{bm}}}$
All the symbols have its usual meaning. Switching pattern for multilevel operation using large and medium vector is displays in Table 2.
Figure 5 shows the Matlab/Simulink model for the dual fivephase voltage source inverter for multilevel output in which the first block shows the generation of reference voltage. Magnitude and angle are the output of this block. This provides the switching signal for different semiconductors of voltage source inverter block devices with the help of Matlab code, repeating sequence signal, and zeroorder hold circuit. The output of this block is stored in fivephase voltages in the voltage acquisition block workspace after passing through the lowpass filter block.
Figures 6(a) and 6(b) are showing the output phase voltages for INV 1 and INV 2 using only large vectors. Figure 7 displays filtered phase voltages of INV1. The output voltages possess sufficient amount of third order harmonic along with small amount of 7th order harmonic. These harmonics are generated due to xy components of space voltage vectors and will present in output whatever the reference voltage value may be when only large vectors are utilized to control the output of inverter. Figure 8 shows the filtered line voltages for INV 2.
PhasetoNeutral value of Voltage Space Vectors for large vector and for medium vector is given by Eq. (6) and (7) respectively.
$\begin{align} & \left {{\underline{\text{v}}}_{1}} \right\text{=}2/5{{V}_{DC}}2\cos (\pi /5)\exp (jk\pi /5)\text{ } \\ & \text{for }k=0,1,\cdots 9 \\ \end{align}$ (6)
$\begin{align} & \left {{\underline{\text{v}}}_{\text{m}}} \right=2/5{{V}_{DC}}\exp (jk\pi /5)\text{ } \\ & \text{for }k=0,1,2\cdots 9 \\\end{align}$ (7)
Adjacent LinetoLine value of Voltage Space Vectors for large vector and for medium vector is given by Eq. (8) and (9) respectively.
$\begin{align} & \left {{{\underset{\scriptscriptstyle}{V}}}_{1}} \right=\sqrt{1.382}* \\ & 2/5{{V}_{DC}}2\cos (\pi /5)\exp (j(2k+1)\pi /10) \\ & \text{for }k=1,2\cdots 9 \\ \end{align}$ (8)
$\begin{align} & \left {{{\underset{\scriptscriptstyle}{V}}}_{m}} \right=\sqrt{0.528}* \\ & 2/5{{V}_{DC}}2\cos (\pi /5)\exp (j(2k+1)\pi /10) \\ & \text{for }k=1,2\cdots 9 \\ \end{align}$ (9)
Figure 5. Matlab/Simulink Model of dual fivephase VSI
(a)
(b)
Figure 6 (a). Phase voltage of INV1; (b). Phase voltage of INV2
The dclink voltage parameter is kept unity whereas switching frequency and fundamental frequency are 2 kHz and 50 Hz for simulation. Figure 9 shows the harmonic output spectrum for the voltage 'a' phase. It only has a fundamental voltage with a magnitude of 0.4218 p.u. r.m.s at a frequency of 50 Hz. The total harmonic distortion (THD) in the output is 23.97% and weighted total harmonic distortion (WTHD) is 12.46% of the fundamental, which shows that the results near the sinusoidal.
Simulation results for threelevel operation using large and medium voltage vectors are in Figure 10 to Figure 12. Figures 10(a) and 10(b) display the phase voltages for INV1 and INV2 and Figure 11 show the filtered phase voltages for INV1. While Figure 12 shows the filtered line voltage for INV 2. All the parameters for simulation are kept the same.
Figure 7. Filtered phase voltage of INV1
Figure 8. Filtered line voltage of INV2
Figure 9. Harmonic spectrum of inverter output phase voltage
(a)
(b)
Figure 10. (a). Phase voltage of INV1; (b). Phase voltage of INV2
Figure 13 exhibits the harmonic spectrum of output for phase ‘a’ voltage. It contains only fundamental voltage having magnitude of 0.3756 p.u. r.m.s at a frequency of 50 Hz. The total harmonic distortion (THD) in the output is 3.30% and weighted total harmonic distortion (WTHD) is 1.81% of the fundamental, which is very less as compared to the previous scheme.
Figure 11. Filtered phase voltage of INV1
Figure 12. Filtered line voltage of INV2
Figure 13. Harmonic spectrum of inverter output phase voltage
In accordance with the fundamental Component, THD, and WTHD, the contribution of both the presented SVPWM scheme has been examined and a comparative analysis has been concluded. The comparison of both SVPWM schemes is shown in Table 3 and Figure 14 is showing the bar chart for quick comprehension. It is clear here that, compared to the first SVPWM scheme, the scheme using large and medium voltage vectors has very low order harmonic content.
The time of application of large and medium vectors is proportionally divided according to their length. The first system offers sinusoidal efficiency, but only up to 85.41% of the total achievable basic output is operational. The second scheme makes it possible to fully utilise the available DC bus voltage. It is known that the highest reference value to be reached is between 85.41% and 100%. The inverter's reference voltage exceeds the maximum output circle because of this. The application time of different voltage vectors is dependent on the voltage and variable amplitude of the reference voltage.
The study shows that using only large vectors to validate the concept, the output contains 23.97% THD and 12.46% WTHD, which indicates that the losses are substantial. It is because the output contains a sufficient amount of 3rd order harmonics i.e. 23.8349% and a small amount of 7th order harmonics i.e. 2.504650%.
When the author uses the large and medium vectors together, the results are much better compared to the previous scheme to reduce THD. The output includes 3.30% THD and 1.81% WTHD only using large and medium vectors. 3rd order harmonics decrease from 23.834% to 3.2474% and 7th order harmonic has reduced to 2.50% to 0.436947%
Table 3. Comparison of both the SVPWM Schemes
Description 
using large vector only 
using large & medium vectors 
Fundamental Component 
42.18% 
37.56% 
Total Harmonic Distortion 
23.97% 
3.30% 
Weighted Total Harmonic Distortion 
12.46% 
1.81% 
3rd order Harmonic 
23.834900% 
3.247490% 
7th order Harmonic 
2.504650% 
0.436947% 
Figure 14. Bar chart of both SVPWM scheme
In this paper, two SVPWM schemes for a twolevel fivephase dual voltage source inverter are presented to achieve multilevel performance. The first scheme is by using large vectors only, which generates the nonsinusoidal output results due to significant loworder harmonics presence. Another approach utilizes both large and medium voltage vectors to obtain sinusoidal output results, which shows that as compared to the first scheme, the second technique has low values of loworder harmonics. These SVPWM techniques are easy and effective to implement. The presented schemes may apply easily in high power medium voltage applications. A similar concept may be extended to a higher phase number inverter system in the future along with a practical realization.
SVPWM 
Space Vector pulse width modulation 
VSI 
Voltage source inverter 
THD 
Total harmonic distortion 
WTHD 
Weighted total harmonic distortion 
NPC 
Neutral point clamped 
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