6. Quasi-Impedance Source Inverters

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In recent years, many researchers have worked in many directions to develop impedance source inverters (ZSIs) to achieve different objectives [1,2,3,4,5,6,7,8]. Some have worked on developing different kinds of topological variations, whereas others have worked on developing ZSI into different applications where controller design, modeling and analyzing its operating modes, and developing modulation methods are addressed. Theoretically, ZSI can produce infinite gain like many other DC/DC boosting topologies; however, it is well known that this cannot be achieved due to effects of parasitic components where the gain tends to drop drastically [1]. Conversely, high boost could increase power losses and instability. On the other hand, shoot-through interval, the variable that is responsible for increasing the gain and is interdependent with the other variable modulation index that controls the output of the ZSI, also imposes limitations on variability and thereby the boosting of output voltage. That is, an increase in boosting factor would compromise the modulation index and result in lower modulation index [2]. Also, the voltage stress on the switches would be high due to the pulsating nature of the output voltage.

Unlike the DC/DC converters, so far researchers of ZSIs have not concentrated on improving the gain of the converter. This opens a significant research gap in the field of ZSI development, especially in some applications such as solar and fuel cells where generated power is integrated into the grid and may require high voltage gain to match the voltage difference and also to compensate for the voltage variations. Its effect is significant when such sources are connected to 415 V three-phase systems. In the case of fuel and solar cells, although it is possible to increase the number of cells to increase the voltage, there are other influencing factors that need to be taken into account. Sometimes, the available number of cells is limited, or environmental factors could come into play due to shading of light for some cells, which could result in poor overall energy catchment. Some manufacturers produce fuel cells with lower voltage to achieve a faster response. Such factors could demand power converters with a larger boosting ratio. This cannot be realized with a single ZSI. Hence, this chapter focuses on developing a new family of ZSIs that would realize extended boosting capability.

6.1 Introduction to ZSI and Basic Topologies

The basic topology of ZSI was originally proposed by Peng. This is a single-stage buck–boost topology due to the presence of the x-shaped impedance network as shown in Figure 6.1a, which allows the safe shoot-through of inverter arms, avoiding the dead time that was needed in traditional VSI. However, unlike the VSI, the original ZSI does not share the ground point of the DC source with the converter, and also the current drawn from the source will be discontinuous; these would be disadvantages in some applications, and it may be required to have a decoupling capacitor bank at the front end to avoid current discontinuity. Subsequently, the ZSI was modified as shown in Figure 6.1b and 6.1c, where now an impedance network is placed at the bottom or top arm of the inverter. The advantage of this topology is that in one topology ground point can be shared, and in both cases the voltage stress on the component is much lower compared to that of the traditional ZSI. However, the current discontinuity was still present, and so an alternative continuous current quasi-ZSI (qZSI) is proposed, but this continuous current circuit is not considered in developing new converters. In terms of topology, the qZSI has no disadvantage over the traditional topology. In this chapter, a discontinuous current qZSI inverter is used to extend the boosting capability. In summary, the proposed qZSIs operate similarly to the original ZSI, and the same modulation schemes can be applied.

6.2 Extended Boost qZSI Topologies

In this chapter, four new converter topologies are proposed. Mainly these topologies can be categorized into diode-assisted boost or capacitor-assisted boost, and then they can be further divided into continuous current and discontinuous current topologies. Their operation is extensively described in the coming sections. All these topologies can be modulated using the modulation methods proposed for the original ZSI. In this context, the modulation method proposed is used. The other advantage of the proposed new topologies is their expandability. This was not possible with the original ZSI; that is, if one needs additional boosting, another stage can be cascaded at the front end. The new topology would operate with the same number of active switches. The only addition would be one inductor, one capacitor, and two diodes for the diode-assisted case and one inductor, two capacitors, and one diode for the capacitor-assisted case for each added new stage. By defining the shoot-through duty ratio (D_S), then, for each added new stage, the boosting factor can be increased with a factor of 1/(1-D_S) in the case of the diode-assisted topology. Then the capacitor-assisted topology would have a boosting factor of 1/(1–3D_S) compared to 1/(1–2D_S) in the traditional topology. However, similar to the other boosting topologies, it is not advisable to operate with very high or very low shoot-through values. Also, careful consideration is needed in selecting the boosting factor modulation index for the suitable topology to achieve the high efficiency. These aspects need further research, and they will be addressed in a future paper.

FIGURE 6.1
Various ZSIs.

6.2.1 Diode-Assisted Extended Boost qZSI Topologies

In this category, two new families of topologies are proposed, namely, the continuous current and the discontinuous current type topology. Figure 6.2 shows the continuous current type topology, and it can be extended to have very high boost by cascading more stages as shown in Figure 6.3. This new topology comprises an additional inductor, a capacitor, and two diodes. The operating principle of this additional impedance networks is similar to that found in cascaded boost and Luo converters [4,5,6,7]. The added impedance network provides the boosting function without disturbing the operation inverter.

FIGURE 6.2
Diode-assisted extended boost continuous current qZSI.

FIGURE 6.3
Diode-assisted extended boost discontinuous current qZSI.

First, considering the continuous current topology and its steady-stage operation, we know that this converter has three operating states similar to those of the traditional ZSI topology. For simplicity, it can be classified into shoot-through and non-shoot-through states. Then the inverter’s action is replaced by a current source plus a single switch. First, consider the non-shoot-through state, which is represented with an open switch. Also, diodes D₁ and D₂ are conducting, and D₃ is in blocking state; therefore, the inductors discharge, and the capacitors are charged. Figure 6.4b shows the equivalent circuit diagram for the non-shoot-through state.

By applying KVL, the following steady-state relationships can be observed: V_DC + v_L3 = V_c3, v_L1 = V_c1, V_L2 = V_c2, and V_S = V_c3+V_c2 + V_L1. Figure 6.4c shows the equivalent circuit diagram for the shoot-through state, where it is represented with the closed switch and D₃ is conducting, and D₁ and D₂ diodes are in blocking state where all the inductors get charged. Energy is transferred from the source to the inductor or the capacitor to the inductor, while capacitors are discharged. Similar relationships can be derived as V_DC + v_L3 = 0, V_c3 + V_L2 + V_c1 = 0, V_c3 + V_c2 + V_L1 = 0, and V_S = 0, V_c3 + V_c2 = V_L1. Since the average voltage across the inductors is zero and, by defining the shoot-through duty ratio as D_S and non-shoot-through duty ratio as D_A where D_A + D_S = 1, the following relations can be derived:

FIGURE 6.4
Simplified diagram of diode-assisted extended boost continuous current qZSI: (a) continuous current, (b) discontinuous current, (c) high-extended continuous current.

$V_{C 3} = \frac{1}{1 - D_{5}} V_{D C} a n d V_{C 1} = V_{C 2} = \frac{D_{S}}{1 - 2 D_{S}} V_{C 3} = \frac{D_{S}}{(1 - 2 D_{S}) (1 - D_{S})} V_{D C}$ $V_{C 3} = \frac{1}{1 - D_{5}} V_{D C} a n d V_{C 1} = V_{C 2} = \frac{D_{S}}{1 - 2 D_{S}} V_{C 3} = \frac{D_{S}}{(1 - 2 D_{S}) (1 - D_{S})} V_{D C}$

(6.1)

From the above equations, the peak voltage across the inverter ${\hat{υ}}_{S}$ ${\hat{υ}}_{S}$ and the peak AC output voltage ${\hat{υ}}_{x}$ ${\hat{υ}}_{x}$ can be obtained as follows:

${\hat{υ}}_{S} = \frac{1}{(1 - 2 D_{S}) (1 - D_{S})} V_{D C} a n d {\hat{υ}}_{x} = M \frac{{\hat{υ}}_{S}}{2}$ ${\hat{υ}}_{S} = \frac{1}{(1 - 2 D_{S}) (1 - D_{S})} V_{D C} a n d {\hat{υ}}_{x} = M \frac{{\hat{υ}}_{S}}{2}$

(6.2)

Define $B = \frac{1}{(1 - 2 D_{S}) (1 - D_{S})}$ $B = \frac{1}{(1 - 2 D_{S}) (1 - D_{S})}$ , the boost factor in the DC side, then the peak AC side can be written as:

${\hat{υ}}_{x} = B (M \frac{V_{D C}}{2})$ ${\hat{υ}}_{x} = B (M \frac{V_{D C}}{2})$

(6.3)

Now the boosting factor has increased by a factor of 1/(1-D_S) compared to that of the original ZSI. Similarly, the steady-state equations can be derived for the diode-assisted extended boost discontinuous current qZSI. Then it is possible to prove that this converter also has the same boosting factor as that of the continuous current topology. Also, the voltage stress on the capacitors are similar, except the voltage across capacitor 3 can be shown to be V_c3 = D_S/(1 - D_S)*V_DC. By studying these two topologies, it can be noted that with the discontinuous current topology, the capacitors are subjected to a small voltage stress, and if there is no boosting, then the voltage across them is zero. Also, it is possible to derive the boost factor for topologies shown in Figures 6.2b and 6.3b as $B = \frac{1}{(1 - 2 D_{S}) (1 - D_{S})}$ $B = \frac{1}{(1 - 2 D_{S}) (1 - D_{S})}$

6.2.2 Capacitor-Assisted Extended Boost qZSI Topologies

Similar to the previous family of extended boost qZSIs, this section is proposing another family of converters. The difference is now that a much higher boost is achieved with only a simple structural change to the previous topology. Now D₃ is replaced with a capacitor as shown in Figure 6.4. In this context also, two topological variations are derived as continuous current or discontinuous current forms as shown in Figure 6.5.

In the previous scenario, the steady-state relations are derived using the continuous current topology; therefore, in this context the discontinuous current topology is considered. In this case also, the converter’s three operating states are simplified into shoot-through and non-shoot-through states.

The simplified circuit diagram is shown in Figure 6.6a. First, consider the non-shoot-through state shown in Figure 6.6b, which is represented with an open switch. As diodes D₁ and D₂ are conducting, the inductors discharge and capacitors get charged. Then by applying KVL, the following steady-state relationships can be observed. V_DC + V_c3 + V_c2 + V_c1 = V_S and V_DC + V_c3 + V_c4 + V_c1 = V_S, V_c1 = v_L1, V_c2 = v_L2, V_c3 = v_L3, V_DC + V_c3 = V_d, V_c2 = V_c4. Figure 6.6c shows the equivalent circuit diagram for the shoot-through state where it is represented with the closed switch. Both diodes D₁ and D₂ are in blocking state where all the inductors are charged and energy is transferred from the source to inductors or the capacitor to inductors, while capacitors are discharged. Similar relationships can be derived as V_DC + v_L3 + V_c4 + V_c1 = 0, V_DC + V_c3 = V_d, V_d + V_L1 + V_c2 = 0, V_d + V_L2 + V_c1 = 0, and V_S = 0. Considering the fact that the average voltage across the inductors is zero, the following relations can be derived:

FIGURE 6.5
Capacitor-assisted extended boost qZSIs.

$V_{d} = \frac{1 - 2 D_{S}}{1 - 3 D_{S}} V_{D C} and V_{C 1} = V_{C 2} = V_{C 3} = V_{C 4} = \frac{D_{S}}{1 - 2 D_{S}} V_{d} = \frac{D_{S}}{1 - 3 D_{S}} V_{D C}$ $V_{d} = \frac{1 - 2 D_{S}}{1 - 3 D_{S}} V_{D C} and V_{C 1} = V_{C 2} = V_{C 3} = V_{C 4} = \frac{D_{S}}{1 - 2 D_{S}} V_{d} = \frac{D_{S}}{1 - 3 D_{S}} V_{D C}$

(6.4)

Then, from the above equations, the peak voltage across the inverter ${\hat{υ}}_{S}$ ${\hat{υ}}_{S}$ be obtained as follows:

${\hat{υ}}_{S} = \frac{1}{1 - 3 D_{S}} V_{D C}$ ${\hat{υ}}_{S} = \frac{1}{1 - 3 D_{S}} V_{D C}$

(6.5)

Similar equations can be derived for the continuous current topology. Now the difference would be the continuity of source current and the difference in voltage across the. The voltage across the C₃ can be obtained as V_C3 = V_d. Now the voltage across the capacitor is much larger than with discontinuous current topology. Similarly, it is possible to derive the boost factor for topologies shown in Figure 6.5c and 6.5d as $B = \frac{1}{1 - 4 D_{S}}$ $B = \frac{1}{1 - 4 D_{S}}$ .

6.2.3 Simulation Results

Extensive simulation studies are performed on the open-loop configuration of all proposed topologies in Matlab/Simulink® using the modulation method proposed [1]. However, due to space limitations, only a few results are presented. This would validate the operation of diode-assisted and capacitor-assisted topologies as well as continuous current and discontinuous current topologies. Here, three cases are simulated. In all three cases, the input voltage is kept constant at 240 V and a three-phase load of 9.7 Ω resistor bank is used. All DC side capacitors are 1000 μF, and inductors are 3.5 mH. The AC side second-order filter is used with a 10 μF capacitor and a 7 mH inductor. In all three cases, the converter is operated with zero boosting in the beginning and, at t = 250 ms, the shoot-through is increased to 0.25 while the modulation index kept constant at 0.7. Figures 6.7,6.8,6.9 show the simulation results corresponding to topologies shown in Figures 6.2a, 6.3a, and 6.5b. From these figures, it is possible to note that in the first two cases equal boosting is achieved and the difference is the voltage across VC3. This agrees with the theoretical finding. From Figure 6.9, it can be noted that with the capacitor-assisted topology a much higher boosting can be achieved with the same shoot-through value; also voltages across all four capacitors are equal and agree with the equations derived in the previous section. A comprehensive set of simulation results will be presented in the full paper based on this chapter.

FIGURE 6.6
Simplified diagram of capacitor-assisted extended boost continuous current qZSI.

FIGURE 6.7
Simulation results for diode-assisted extended boost continuous current qZSI.

FIGURE 6.8
Simulation results for diode-assisted extended boost discontinuous current qZSI.

FIGURE 6.9
Simulation results for capacitor-assisted extended boost discontinuous current qZSI.

References

1. Gajanayake, C. J. and Luo, F. L. 2009. Extended boost Z-source inverters. Proc. IEEE ECCE’2009, pp. 368–373.

2. Gajanayake, C. J., Vilathgamuwa, D. M. and Loh, P. C., 2007. Development of a comprehensive model and a multiloop controller for Z-source inverter DG systems. IEEE Trans. Ind. Electron., pp.2352–2359.

3. Anderson, J. and Peng, F. Z. 2008. Four quasi-Z-Source inverters. Proc. IEEE PESC’2008, pp. 2743–2749.

4. Luo, F. L. and Ye, H. 2005. Advanced DC/DC Converters. Boca Raton, FL: CRC Press.

5. Luo, F. L. and Ye, H. 2005. Essential DC/DC Converters, Boca Raton, FL: Taylor & Francis.

6. Luo, F. L. 1999. Positive output Luo-converters: Voltage lift technique. IEE Proc. Electric Power Applicat., pp. 415–432.

7. Luo, F. L. 1999. Positive output Luo-converters: Voltage lift technique. IEE Proc. Electric Power Applicat., pp. 208–224.

8. Ortiz-Lopez, M. G., Leyva-Ramos, J. E., Carbajal-Gutierrez, E., and Morales-Saldana, J. A. 2008. Modelling and analysis of switch-mode cascade converters with a single active switch. Power Electronics, IET, pp. 478–487.

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