5

Impedance Source Inverters

Impedance source inverter (ZSI) is a new approach to DC/AC conversion technology. It was published by Peng in 2003 [1,2,3]. The ZSI circuit diagram shown in Figure 5.1 consists of an x-shaped impedance network formed by two capacitors and two inductors, and it provides unique buck–boost characteristics. Moreover, unlike VSI, the need for dead time would not arise with this topology. Due to these attractive features, it has found numerous industrial applications including variable speed drives and distributed generation (DG). However, it has not been widely researched as a DG topology. Moreover, all these industrial applications require proper closed loop controlling to adjust their operating conditions subject to changes in both input and output conditions. On the other hand, the presence of the x-shaped impedance network and the need for short-circuiting the inverter arm to boost the voltage would complicate the controlling of ZSI.

5.1    Comparison with VSI and CSI

ZSI is a new inverter different from traditional voltage source inverter (VSI) and current source inverter (CSI) devices. In order to understand ZSI’s advantages, it is necessary to compare it with VSI and CSI [3,4]. The VSI has the following conceptual and theoretical barriers and limitations:

1.  The AC output voltage cannot exceed the DC-link voltage. Therefore, the VSI is a buck (step-down) inverter for DC/AC power conversion. For applications where overdrive is desirable and the available DC voltage is limited, an additional DC/DC boost converter is needed to obtain a desired AC output. The additional power converter stage increases system cost and lowers efficiency.

2.  The upper and lower devices of each phase leg cannot be gated on simultaneously either by purpose or by EMI noise. Otherwise, a shoot-through would occur and destroy the devices. The shoot-through problem due to electromagnetic interference (EMI) noise misgating on is a major killer to the converter’s reliability. Dead time to block both upper and lower devices has to be provided in the VSI, which causes waveform distortion, etc.

FIGURE 5.1
Impedance source inverter (ZSI).

3.  An output L-C filter is needed to provide a sinusoidal voltage compared with the current source inverter, which causes additional power loss and control complexity.

The CSI has the following conceptual and theoretical barriers and limitations:

1.  The AC output voltage has to be greater than the original DC voltage that feeds the DC inductor, or the DC voltage produced will always be always smaller than the AC input voltage. Therefore, the CSI is a boost inverter for DC/AC power conversion. For applications where a wide voltage range is desirable, an additional DC–DC buck (or boost) converter is needed. The additional power conversion stage increases system cost and lowers efficiency.

2.  At least one of the upper devices and one of the lower devices must be gated on and maintained on at any time. Otherwise, an open circuit of the DC inductor would occur and destroy the devices. The open circuit problem by EMI noise misgating off is a major concern from the view of the converter’s reliability. Overlap time for safe current commutation is needed in the I-source converter, which also causes waveform distortion, etc.

3.  The main switches of the I-source converter have to block reverse voltage that requires a series diode to be used in combination with high-speed and high-performance transistors such as insulated gate bipolar transistors (IGBTs). This avoids the direct use of low-cost and high-performance performance IGBT modules and intelligent power modules (IPMs).

FIGURE 5.2
Z-source inverter for fuel cell applications.

In addition, both the VSI and the CSI have the following common problems:

1.  They work as either a boost or a buck converter and cannot work as a buck-and-boost converter. That is, their obtainable output voltage range must be either greater or smaller than the input voltage.

2.  Their main circuits cannot be used interchangeably. In other words, the VSI main circuit cannot be used for the CSI, and vice versa.

3.  They are vulnerable to EMI noise that affects reliability.

To overcome the above problems of the traditional VSI and CSI, ZSI was designed as shown in Figure 5.2. It employs a unique impedance network to couple the converter main circuit to the power source. The ZSI overcomes the above-mentioned conceptual and theoretical barriers and limitations of the traditional VSI and CSI, and provides a novel power conversion concept.

In Figure 5.2, a two-port network that consists of split inductors L₁ and L₂ and capacitors C₁ and C₂ connected in an x shape is employed to provide an impedance source (Z-source) coupling the converter (or inverter) to the DC source. Switches used in ZSI can be a combination of switching devices and diodes. Actually, if the two inductors have zero inductance, the ZSI becomes a VSI and if the two capacitors have zero capacitance, the ZSI becomes a CSI. The advantages of the ZSI are listed as follows:

1.  The AC output voltage is not fixed lower or higher than the DC-link (or DC source) voltage. Therefore, the ZSI is a buck–boost inverter for DC/AC power conversion. For applications where overdrive is desirable and the available DC voltage is not limited, there is no need for an additional DC/DC boost converter to obtain a desired AC output. Therefore, the system cost is low and efficiency is high.

2.  The Z-circuit consist of two inductors and two capacitors and can restrict the overvoltage and overcurrent. Therefore, the legs in the main bridge can operate in short circuit and open circuit in a short time. There is no restriction for the main bridge such as dead time for VSI and overlap time for CSI.

3.  ZSI has an anti-noise function. The shoot-through problem by electromagnetic interference (EMI) noise misgating on will not damage the device or the converter’s reliability.

5.2    Equivalent Circuit and Operation

A three-phase ZSI used for fuel cell application is shown in Figure 5.3. It has 9 permissible switching states (vectors): 6 active vectors as a traditional VSI has plus 3 zero vectors when the load terminals are shorted through both the upper and lower devices of any one-phase leg (i.e., both devices are gated on), any two-phase legs, or all three-phase legs. This shoot-through zero state (or vector) is undesirable in the traditional VSI, because it would cause a shoot-through. We call this third zero state (vector) the shoot-through zero state (or vector), which can be generated seven different ways: shoot-through via any one-phase leg, combinations of any two-phase legs, and all three-phase legs. The Z-source network makes the shoot-through zero state possible. This shoot-through zero state provides the unique buck–boost feature to the inverter.

Figure 5.3 shows the equivalent circuit of the ZSI shown in Figure 5.2 when viewed from the DC link. The inverter bridge is equivalent to a short circuit when the inverter bridge is in the shoot-through zero state, as shown in Figure 5.4, whereas the inverter bridge becomes an equivalent current source as shown in Figure 5.5 when in one of the six active states. Note that the inverter bridge can be also represented by a current source with zero value (i.e., an open circuit) when it is in one of the two traditional zero states. Therefore, Figure 5.5 shows the equivalent circuit of the Z-source inverter viewed from the DC link when the inverter bridge is in one of the eight non-shoot-through switching states.

FIGURE 5.3
Equivalent circuit of the Z-source inverter viewed from the DC link.

FIGURE 5.4
Equivalent circuit of the Z-source inverter viewed from the DC link when the inverter bridge is in the shoot-through zero state.

All the traditional pulse width modulation (PWM) schemes can be used to control the Z-source inverter, and their theoretical input–output relationships still hold. Figure 5.6 shows the traditional PWM switching sequence based on the triangular carrier method. In every switching cycle, the two non-shoot-through zero states are used along with two adjacent active states to generate the desired voltage. When the DC voltage is high enough to generate the desired AC voltage, the traditional PWM of Figure 5.6 is used. While the DC voltage is not enough to directly generate a desired output voltage, a modified PWM with shoot-through zero states will be used as shown in Figure 5.7 to boost voltage. It should be noted that each phase leg still switches on and off once per switching cycle. Without changing the total zero-state time interval, shoot-through zero states are evenly allocated into each phase. That is, the active states are unchanged. However, the equivalent DC-link voltage to the inverter is boosted because of the shoot-through states. The detailed relationship will be analyzed in the next section. It is noticeable here that the equivalent switching frequency viewed from the Z-source network is six times the switching frequency of the main inverter, which greatly reduces the required inductance of the Z-source network.

FIGURE 5.5
Equivalent circuit of the Z-source inverter viewed from the DC link when the inverter bridge is in one of the eight non-shoot-through switching states.

FIGURE 5.6
Traditional carrier-based PWM control without shoot-through zero states, where the traditional zero states (vectors) V111 and V000 are generated every switching cycle and determined by the references.

FIGURE 5.7
Modified carrier-based PWM control with shoot-through zero states that are evenly distributed among the three phase legs, while the equivalent active vectors are unchanged.

5.3    Circuit Analysis and Calculations

Assuming that the inductors L₁ and L₂ and capacitors C₁ and C₂ have the same inductance L and capacitance C, respectively, the Z-source network becomes symmetrical. From the symmetry and the equivalent circuits, we have

$V_{\text{C}1}=V_{\text{C}2}=V_{\text{C}}{\upsilon }_{L1}={\upsilon }_{L2}={\upsilon }_L$

(5.1)

Assume that the inverter bridge is in the shoot-through zero state for an interval of T₀ during a switching cycle T. From the equivalent circuit in Figure 5.4, one has

${\upsilon }_L=V_C{\upsilon }_d=2V_C{\upsilon }_i=0$

(5.2)

Now consider that the inverter bridge is in one of the eight non-shoot-through states for an interval of T₁ during the switching cycle T. From the equivalent circuit in Figure 5.4, one has

${\upsilon }_L=V_0-V_C{\upsilon }_d=V_0{\upsilon }_i=V_C-{\upsilon }_L=2V_C-V_0$

(5.3)

where V₀ is the DC source voltage and T = T₀ + T₁. The switching duty cycle k = T₁/T.

The average voltage of the inductors over one switching period should be zero in the steady state, from Equations (5.2) and (5.3); thus, we have

$V_L={\overline{\upsilon }}_L=\frac{T_0{V}_C+T_1(V_0-V_C)}{T}=0$

(5.4)

or

$\frac{V_C}{V_0}=\frac{T_1}{T_1-T_0}$

(5.5)

Similarly, the average DC-link voltage across the inverter bridge can be found as follows:

$V_i={\overline{\upsilon }}_i=\frac{T_0\times 0+T_1(2V_C-V_0)}{T}=\frac{T_1}{T_1-T_0}{V}_0=V_C$

(5.6)

The peak DC-link voltage across the inverter bridge is expressed in Equation (5.3) and can be rewritten as

${\widehat{\upsilon }}_i=V_C-{\upsilon }_L=2V_C-V_0=\frac{T_1}{T_1-T_0}{V}_0=B\cdot V_0$

(5.7)

where

$B=\frac{T}{T_1-T_0}=\frac{1}{1-2\frac{T_0}{T}}\ge 1$

(5.8)

B is the boost factor resulting from the shoot-through zero state. Usually, T₁ is greater than T₀, that is, T₀ < T/2. The peak DC-link voltage ${\widehat{\upsilon }}_i$ is the equivalent DC-link voltage of the inverter. On the other side, the output peak phase voltage from the inverter can be expressed as

${\widehat{\upsilon }}_{ac}=M\cdot \frac{{\widehat{\upsilon }}_i}{2}$

(5.9)

where M is the modulation index. Using Equation (5.7), Equation (5.9) can be further expressed as

${\widehat{\upsilon }}_{ac}=M\cdot B\cdot \frac{V_0}{2}$

(5.10)

For the traditional VSI, we have the well-known relationship: ${\widehat{\upsilon }}_{ac}=M\cdot \frac{V_0}{2}$. Equation (5.10) shows that the output voltage can be stepped up and down by choosing an appropriate buck–boost factor MB.

$MB=\frac{T}{T_1-T_0}M$

(5.11)

MB is changeable from 0 to ∞. From Equations (5.1), (5.5), and (5.8), the capacitor voltage can be expressed as

$V_C=\frac{1-\frac{T_1}{T}}{1-2\frac{T_0}{T}}{V}_0$

(5.12)

The buck–boost factor MB is determined by the modulation index M and boost factor B. The boost factor B as expressed in Equation (5.8) can be controlled by the duty cycle (i.e., interval ratio) of the shoot-through zero state over the non-shoot-through states of the inverter PWM.

Note that the shoot-through zero state does not affect the PWM control of the inverter, because it equivalently produces the same zero voltage to the load terminal. The available shoot-through period is limited by the zero-state period that is determined by the modulation index.

5.4    Simulation and Experimental Results

Simulations have been performed to confirm the above analysis. Figure 5.8 shows the circuit configuration, and Figure 5.9 shows simulation waveforms when the fuel cell stack voltage is V₀ = 150 V and the Z-source network parameters are L₁ = L₂ = L = 160 μH and C₁ = C₂ = C = 1000 μF.

The purpose of the system is to produce a three-phase, 208 V rms power from the fuel cell stack whose voltage changes from 150 to 340 V DC depending on load current. From the simulation waveforms of Figure 5.9, it is clear that the capacitor voltage was boosted to V_C2 = 335 V and the output line-to-line was 208 V rms or 294 V peak. In this case, the modulation index was set to M = 0.642, and the shoot-through duty cycle was set to T₀/T = 0.358, and switching frequency was 10 kHz. The shoot-through zero state was populated evenly among the three phase legs, achieving an equivalent switching frequency of 60 kHz viewed from the Z-source network. Therefore, the required DC inductance is minimized. From the above analysis, we have the following theoretical calculations:

FIGURE 5.8
Simulation and prototype system configuration.

FIGURE 5.9
Simulation waveforms when the fuel cell voltage V = 150 V, inverter modulation index M = 0.642, and shoot-through duty cycle T₀/T = 0.358.

$B=\frac{1}{1-2\frac{T_0}{T}}=\frac{1}{1-0.716}=3.55$

(5.13)

$V_{C1}=V_{C1}=V_C\frac{1-\frac{T_0}{T}}{1-2\frac{T_0}{T}}{V}_0=\frac{1-0.358}{1-0.716}150=339V$

(5.14)

${\widehat{V}}_{ac}=MB\frac{V_0}{2}=0.642\times 0.358\frac{150}{2}=169.5V$

(5.15)

Equation (5.15) is the phase peak voltage, which implies that the line-to-line voltage is 208 V rms or 294 V peak. The above theoretical values are quite consistent with the simulation results. The simulation proved the ZSI concept.

A prototype as shown in Figure 5.8 has been constructed. The same parameters as the simulation were used. Figures 5.10 and 5.11 show experimental results. When the fuel cell voltage is low, as shown in Figure 5.10, the shoot-through state was used to boost the voltage in order to maintain the desired output voltage. The waveforms are consistent with the simulation results. When the fuel-cell voltage is high enough to produce the desired output voltage, the shoot-through state was not used, as shown in Figure 5.11, where the traditional PWM control without shoot-through was used. By controlling the shoot-through state duty cycle or the boost factor, the desired output voltage can be obtained regardless of the fuel cell voltage.

FIGURE 5.10
Experimental waveforms when the fuel cell voltage is low, inverter modulation index M = 0.642, and shoot-through period ratio T₀/T = 0.358 (V₀ and V_C2: 200V/div, V_Lab: 2*200V/div, i_La: 50 A/div, and time: 4 ms/div).

FIGURE 5.11
Experimental waveforms when the fuel cell voltage is high. Inverter modulation index M = 1.0 without using the shoot-through state or shoot-through period ratio T₀/T = 0.

References

1.  Peng, F. Z. 2003. Z-source inverter. IEEE Trans. Ind. Applicat., pp. 504–510.

2.  Trzynadlowski, A. M. 1998. Introduction to Modern Power Electronics. New York: John Wiley & Sons.

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. 2010. Power Electronics: Advanced Conversion Technologies. Boca Raton, FL: Taylor & Francis.