Pulse Width Modulation Technique for Multilevel Operation of Five-Phase Dual Voltage Source Inverters

Space vector pulse width modulation (SVPWM) is a technique used to determine the pulse-width 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 split-phase 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 two-level VSI fed open-end 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 open-end 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 common-mode 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.

A power circuit diagram of a five-phase two-level dual VSI is shown in Figure 1 for three-level 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 short-circuiting of the input DC source. The inverters' inputs are supplied with equal/unequal values from isolated dc-link sources and the outputs are connected to the open-end winding.

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Figure 1. Circuit diagram of five phase two-level dual voltage source inverter

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Figure 2. (a) Phase voltage space vector d-q plane; (b) Phase voltage space vectors in x-y plane

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Figure 3. Voltage vector plane and voltage selection for dual inverter

Using the SVPWM scheme, each inverter in a five-phase system has thirty-two switching vectors with thirty active vectors and two zero vectors [5]. The five-phase input voltage and space vector equation are given using power invariant matrix:

$\begin{align}  & {{\text{v}}_{\text{a}}}\text{=}\sqrt{\text{2}}\text{Vcos( }\!\!\omega\!\!\text{ t)} \\  & {{\text{v}}_{\text{b}}}\text{=}\sqrt{\text{2}}\text{Vcos( }\!\!\omega\!\!\text{ t-2 }\!\!\pi\!\!\text{ /5)} \\  & {{\text{v}}_{\text{c}}}\text{=}\sqrt{\text{2}}\text{Vcos( }\!\!\omega\!\!\text{ t-4 }\!\!\pi\!\!\text{ /5)} \\  & {{\text{v}}_{\text{d}}}\text{=}\sqrt{\text{2}}\text{Vcos( }\!\!\omega\!\!\text{ t+4 }\!\!\pi\!\!\text{ /5)} \\  & {{\text{v}}_{\text{e}}}\text{=}\sqrt{\text{2}}\text{Vcos( }\!\!\omega\!\!\text{ t+2 }\!\!\pi\!\!\text{ /5)} \\ \end{align}$                (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), a² = 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 d-q plane using (2a) are shown in Figure 2 and since it is a five-phase system, transformation is further done to obtain space vectors in x-y 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 five-phase 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)

${{\text{T}}_{2}}\text{=}\frac{\left| {{\underline{\text{v}}}_{\text{ref}}} \right|\text{sin}\left( \text{ }\!\!\alpha\!\!\text{ -}\left( \text{k-1} \right)\text{ }\!\!\pi\!\!\text{ /5} \right)}{\left| {{\underline{\text{v}}}_{\text{l}}} \right|\text{sin}\left( \text{ }\!\!\pi\!\!\text{ /5} \right)}{{\text{T}}_{\text{s}}}$           (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 & V₁.

Table 1. Switching sequence for the multi-level operation

During sampling time, two reference voltages generated by both the inverters are used to generate the average voltage vector. Using the proposed method, dual two-level five-phase VSI inverter performance is similar to multilevel operation as in a multi-level 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(V₁ to V₁₀) and ten active vectors for INV 2 (V_1' to V_10') and two null vectors (V₀&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 V₀, V₁, V₂, V₀', V_8', and V₉' and line voltages are presented in black color during the sampling period.

4.2 Using large and medium voltage vectors

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(a)

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(b)

Figure 4. (a). Switching waveforms for five phase two-level dual VSI for multilevel operation using large vectors only; (b). Switching waveforms for five phase two-level dual VSI for multilevel operation using large and medium vectors

Table 2. Switching sequence for the multilevel operation using large and medium vector

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 five-phase 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.

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

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Figure 14. Bar chart of both SVPWM scheme