An improved Z-source inverter with high voltage boost ability

An improved high voltage boost Z-source inverter topology is proposed to improve voltage boost ability. Compared to the conventional Z-source inverter, it can produce very high voltage boost with a short shoot-through duty ratio, the voltage stress on Z-source capacitors and inverter-bridge is greatly reduced, and has inherent limitation to inrush current at startup. The addition of a input capacitor and an active switch allows the current in the Z source network to flow in the reverse direction, which adapts to a wide range of the load change. Theoretical analysis, the operation principle of the proposed topology and comparison with the conventional topology are explicitly described. Simulation and experimental results are presented to demonstrate the new features.


Introduction
A Z-source inverter (ZSI) is proposed as the single-stage inverter topology to demonstrate both buck and boost power conversion ability in [1] as shown in Fig. 1. Z-source inverter has found widespread applications, and attracted the interest of researchers in recent years. Some scholars have carried out in ZSI applications such as photovoltaic power generation [2,3], motor drive [4] and electric vehicle [5,6]. There are also some scholars who have studied ZSI modeling analysis, modulation methods and topology improvements [7][8][9][10][11][12][13].
Despite the above advantages, the conventional ZSI also shows the some drawbacks, such as the voltage and current surge caused by starting, the limited boost capability and intermittent input current. In order to overcome the voltage stress across capacitors and inrush current at starting, a improved ZSI is proposed in [14]. In [15], a quasi-ZSI is recommended to solve the elements voltage stresses. However, as the conventional ZSI, the quasi-ZSI has no high voltage gain. High gain ZSI is introduced in [16,17]. A high voltage boost ZSI (HVB ZSI) in [17] is shown in Fig. 2, however the high number of passive elements increases the volume and loss of the inverter.
To reduce the high volume and weight, a switched-inductor ZSI has been presented to obtain high-voltage gains in [18], but it bears higher capacitor voltage stress than the conventional ZSI and quasi-ZSI. In [19][20][21], new switchedinductor inverters were proposed to enhance characteristics of the presented SBI in [18]. In [22,23], the topologies for half-bridge SBI have been presented. The inverters use more active elements rather than capacitors and inductors. By using more active elements, switching loss can effectively reduce.
In this paper, an improved ZSI with high voltage boost ability (HVB-ZSI) is proposed. It employs a input capacitor and an active switch to make the current in the Z-source network to flow in the reverse direction, which makes inverter not only has high boost capacity but also has the ability to adapt to a wide range of load changes. In the following sections, different operating states of the improved HVB-ZSI are investigated. It has the advantages of low Z-source capacitor voltage stress and current surge limitation at startup. Theoretical analysis for the proposed topology is investigated and comparison with other topologies is also provided. The improved performance is validated by both simulated and experimental results.

Structure of proposed Z-source inverter
The circuit of the improved HVB-ZSI is shown in Fig. 3. The circuit components are almost the same as the HVB-ZSI shown in Fig. 2. The difference is that the position of the inverter bridge and Z-source network is exchanged and their connection direction is reversed. It can suppress the start-up inrush current [9], and the damage of the inverter caused by the start-up inrush current is avoided. The second difference is that the active switch SW 7 and its control mode are added to the improved HVB-ZSI, the current in the improved Z source network can flow in the reverse direction. The diode D 13 ensures the current flowing in one direction of the supply, and input capacitor C in is added to the input side to provide a path for the reverse current, therefore the quality of the output voltage is improved.
I n F i g . 3 , a s s u m i n g t h a t C 1 = C 2 , L 1 = L 2 = L 3 = L 4 = L 5 = L 6 , the network becomes symmetrical. From the symmetry circuits, the voltages across capacitors and inductors are shown in Eq. 1

Operating state of proposed Z-source inverter
There are 9 switching states of the proposed HVB-ZSI, including a shoot-through zero vector state, two traditional zero-vector states and 6 effective vector states. According to the current direction, there are 8 operating states of the proposed HVB-ZSI, as shown in Fig. 4. In addition, the inverter side can be simplified by an equivalent current source when the inverter is in the effective vector state.
(1) State 1: The inverter is in the shoot-through zero vector state and the active switch SW7 is off, as shown in Fig. 4a. Although the inverter is in the shoot-through zero state, the inductor current cannot change suddenly. The freewheeling diodes of the inverter arm are on, the dc-link voltage V i is clamped to zero by freewheeling diodes, and three inductors of the Z-source network are connected in parallel. The inductor currents flow in reverse and decrease. The voltage across inductors can be expressed as where V dc is the input dc voltage. (2) State 2: The inverter is still in the shoot-through zero vector state and the active switch SW7 is also off, as shown in Fig. 4b. At this time, because the switch tube of the inverter bridge arm is turned on, the Z source network capacitors and the input capacitor charge (4) State 4: The inverter runs in a valid vector state, as shown in Fig. 4d. The inductors current i L and the freewheeling diode current i D of the active switch SW7 satisfy the following inequality (4).
In this state, the power supply directly delivers power to the load, and the Z-source network inductors charge to the capacitors.
(5) State 5: The inverter is in the valid vector state, as shown in Fig. 4e. In this state, as the inductors current i L continue to decrease, the capacitors of the Z-source network supply power to the load. In this case, the inductors current i L satisfies the inequality (5).
(6) State 6: The inverter is still in the valid vector state, as shown in Fig. 4f. The inductors' current satisfy the inequality (6).
At the end of state 5, the active switch SW7 starts to conduct, the input current is less than zero and flows in reverse. According to the analysis of the above 8 states, we can see that the dc link voltage V i of the proposed ZSI is equal to (V dc + 2V C ) in the valid vector state and the traditional zero-vector state. In this way, the dc link voltage will not be distorted in the all operating states, which eliminates the three special abnormal operating states when the conventional Z-source inverter is under the light load or small inductance.

Control strategy of switch SW7
According to the 8 operating states of the above circuit, the active switch SW7 can provide a reversely flowing path for the reverse current, and the output current meets the requirement of load current. The switch SW7 is off in state 1 and state 2 of the shoot-through state, the current flows through the freewheeling diode of SW7 in mode 3, 4 and 5 of the non shoot-through state, and the switch SW7 is on in state 6, 7 and 8. So, the driving signal of the switch SW7 is opposite to the shoot-through signal.

Analysis of proposed Z-source network
The 8 operating states in Fig. 4 can be simplified. If the voltage relationship of the circuit is only considered, the operating states can be simplified into two operating states, that is, the shoot-through state and the non shoot-through state. Figure 5 shows the equivalent circuit of the proposed topology shown in Fig. 3 when viewed from the inverter side. The inverter bridge is equivalent to a short circuit when the inverter bridge is in the shoot-through zero state, as shown in Fig. 5a. From Fig. 5a, we have The inverter bridge becomes an equivalent current source as shown in Fig. 5b when in the non-shoot-through state. The following equations can be derived in this state: The average value of the inductor voltage over one switching period should be zero in the steady state, the shoot-through duty cycle is D, from (7) and (8), we can get The peak dc-link voltage across the inverter bridge is expressed as where B is the boost factor. The boost factors of the conventional Z-source inverter [1] and HVB-ZSI [13] are expressed as follows The comparison of B in the three topologies is shown in Fig. 6 obtained from (11) and (12). From Fig. 6, it is obvious that the boost ability of the proposed HVB-ZSI is higher than the conventional ZSI when the shoot-through duty cycle D is same. The proposed HVB-ZSI has the same boost factor as the HVB-ZSI.

Voltage gain
The voltage gain G of the ZSI is the product of the voltage boost factor B and the modulation index M and it is determined by the modulation index and boost factor. The boost factors as expressed in (11) and (12) can be controlled by duty cycle of the shoot-through zero state over the non-shoot-through The voltage gains of the conventional ZSI [1] and the HVB-ZSI [14] and can be expressed as follows Figure 7 shows the maximum voltage gain G versus D of the proposed HVB-ZSI, HVB-ZSI and the conventional ZSI obtained from Eqs. 13 and 14. According to Fig. 7, we can see that the maximum voltage gain G of the proposed HVB-VSI is the same as that of HVB-VSI and is much higher than that of the conventional ZSI under the same shoot-through duty ratio D. It means that a smaller D is used in the proposed HVB-VSI to output the same ac voltage.

Capacitor voltage
Based on the above analysis, it can be seen that the Z-source capacitor voltage stress of the proposed HVB-ZSI is shown in Eq. (9). The capacitor voltages of the conventional ZSI and the HVB-ZSI are expressed as Figure 8 shows the comparison of V c /V dc in the three topologies. As shown in Fig. 8, when D increases, so do the capacitor voltages V c of the three topologies. However, it can be seen that the capacitor voltage stress of the proposed HVB-ZSI is significantly lower than HVB-ZSI under the same shoot-through duty ratio D. If the voltage gains of the three inverter topologies are same, the D of the proposed HVB-ZSI can be expressed as Substituting (16) into (9), the Z-source capacitor voltage stress of the proposed HVB-ZSI is expressed as The capacitor voltage stress of the conventional ZSI and HVB-ZSI can be expressed as The comparison of V c /V dc in the three topologies is shown in Fig. 9. From Fig. 9, it is obvious that the Z-source capacitor voltage stress of the proposed HVB-ZSI is much lower than that of the conventional ZSI and the HVB-ZSI under the same voltage gain G.

Z-source inductor current ripple
The average Z-source inductor current equals the average input current. Therefore, for the proposed topology during the non-shoot-through state, the Z-source inductor current decreases and the current ripple can be expressed as  (9) into (19), the current ripple is expressed as follows For the conventional ZSI and HVB-ZSI, however, during the non-shoot-through state, the current ripple can be expressed as From (20) and (22), we can see that the current ripple of the proposed HVB-ZSI is the same that of HVB-ZSI.
If the input voltages are same, at a given voltage gain G, the inductor current ripple of the proposed HVB-ZSI and HVB-ZSI under simple boost control can be expressed as (23), and the inductor current ripple of the conventional ZSI can be expressed as (24).
where k 1 and k 2 are the inductor current ripple coefficient, Fig. 10 shows the comparison of the inductor current ripple coefficient k of three topologies. Fig. 10, we can know that the inductor current ripple coefficient of the proposed HVB-ZSI and HVB-ZSI is significantly lesser than the conventional ZSI under the same voltage gain G.

Power tube voltage stress
The voltage stress on the power tubes of the proposed HVB-ZSI is the peak dc-link voltage. Under the simple boost control, the power tube voltage stress V S of the proposed HVB-ZSI can be expressed as The power tube voltages of the conventional ZSI and HVB-ZSI can be expressed as The comparison of V s in the three topologies is shown in Fig. 11. As shown in Fig. 11, the power tube voltage stress on the inverter-bridge of the proposed HVB-ZSI and the HVB-ZSI is much smaller than that of the conventional ZSI under the same voltage gain G. Table 1 compares different features of the proposed HVB ZSI with other topologies. As shown in Table 1, the proposed HVB ZSI and HVB ZSI have the most passive components. Moreover, the proposed HVB ZSI has the moderate switches and totally the most components in Table 1. In the proposed HVB ZSI, when the shoot-through duty cycle is moderate, the voltage stresses of the switches, diodes and capacitors are lower than HVB ZSI. Compared with other topologies, the proposed HVB ZSI and HVB ZSI have the highest boost factor. Among the topologies of Table 1, proposed HVB ZSI and HVB ZSI have highest inductor current stresses. Due to the highest voltage gain, the inverter outputs the largest power.

Comparison with other topologies
Voltage stress of the components based on the voltage gain is shown in Table 2. It can be seen from Table 2 that the voltage stress of the components is related to the voltage gain and the input voltage. In order to better compare the voltage stress of different topologies, the corresponding results are shown in Table 3 when G = 2 and V dc = 100 V. It can be seen from Table 3 that the proposed HVB ZSI has the lowest diode voltage and capacitor voltage stress.  Table 1 Comparison of different three-phase topologies Table 2 voltage stress of the components based on the voltage gain 1 3

Simulation results
The above analysis was confirmed by simulation. The simulation results were given to confirm the above advantages of the proposed HVB-ZSI. Simple boost control is used in simulation. Two straight lines to control the shoot-through states are used, as shown in Fig. 12. When the triangular waveform is greater than the upper envelope, V p , or lower than the bottom envelope, V n , the circuit turns into shoot-through state. Otherwise it operates just as traditional carrier-based PWM.
The simulation parameters are: (1) Z-source network: L 1 = L 2 = L 3 = L 4 = L 5 = L 6 = 500 µH, C 1 = C 2 = 1200 µF; (2) Output filter: L = 1500 µH, C f = 50 µF; (3) Switching frequency: 10 kHz; (4) Three-phase resistance load R = 15Ω/phase; Case 1: V dc = 100 V, the shoot-through duty ratio D = 0.1925, the modulation ratio M = 0.8075. In this case, according to the above analysis, we can get B = 6, G = 4.863, The simulation results of the proposed HVB-ZSI are shown in Fig. 13a. From Fig. 13a, we can see that in the proposed HVB-ZSI, V C is boosted to 250 V in steady state, V i is boosted to 600 V, and the inrush current is much smaller than the conventional one. Figure 13b shows the simulation results of the HVB-ZSI. From Fig. 13b, it is obvious that V C is boosted to 380 V, V i is boosted to 600 V, and there's a huge inrush current at start. V C is quickly charged to 540 V. Then, the impulse voltage and impulse current may damage the inverter.
From the Fig. 13, we can see that the voltage boost capability of the two HVB-ZSI topologies is the same under the same D and M, the capacitor voltage of the proposed HVB-ZSI is less than that of the HVB-ZSI and inrush current at start-up is also significantly reduced.
The input diode D 13 current, capacitor voltage, switch SW7 current and voltage of the proposed HVB-ZSI are shown in Fig. 14. It can be seen from these results, D 13 current, capacitor voltage V C , and switch SW7 current and voltage are about 350 A, 252 V, 90 A and 600 V, respectively, in the steady-state condition. The simulation results are consistent with the theoretical analysis. Figure 15 shows the input diode D in current and capacitor voltage of HVB-ZSI. It can be seen that the current and capacitor voltage are about 140A and 373 V in the steady state condition, which are larger than the proposed HVB-ZSI.
The DC link voltage and the inductor current simulation waveforms of the proposed HVB-ZSI and the HVB-ZSI at Table 3 Voltage stress values when G = 2 and V dc = 100 V Proposed HVB ZSI (V) HVB ZSI (V) [17] Improved ZSI (V) [14] SBI (V) [18] Embedded-Type qSBI (V) [20] HB-SBI (V) [7] Conventional ZSI (V) [  In the case of the HVB-ZSI, in order to output the same ac voltage, the shoot-through duty ratio is 0.1461 and the modulation ratio M is 0.8539. The simulation results for the HVB-ZSI are shown in the Fig. 17b. From Fig. 17b, we can see that V C is boosted to 205 V and V i is boosted to 311 V. The capacitor voltage stress is greatly increased and huge inrush current occurs at startup.
To study dynamic response of the proposed HVB ZSI, assuming that the input voltage of the proposed HVB ZSI suddenly drops from 200 to 150 V at 0.5 s, the capacitor voltage begins to drop from the original 160 V, and the DC link voltage drops from 550 V. At the same time, due to the adjustment of the voltage and current double loops, the shoot-through duty cycle D begins to rise, which make capacitor voltage rapid rise to compensate for the input voltage drop. After 0.2 s adjustment, D was increased from 0.11 to 0.18, and the capacitor voltage and output voltage remain unchanged after a short period of adjustment. The whole process is shown in Fig. 18.

Study on efficiency and power loss
The efficiency and power loss of proposed HVB ZSI and HVB ZSI are further studied. The power loss calculation method of component in [23] is used. The power loss of the proposed HVB-ZSI and HVB-ZSI are calculated according to the parameters summarized in Table 4 for V dc = 100 V and B = 6.
The input power and output power of the proposed HVB ZSI are about 450 W and 370 W and the efficiency is 82.24%, but output power of HVB ZSI are only 344 W and the efficiency is only 76.44%. Figure 19 shows the power losses simulation results. The power loss of both inverters is calculated as [24]. It can be seen from Fig. 19 that the total power loss of the proposed HVB-ZSI is about 80 W and the total power loss of the HVB-ZSI is about 106 W.
The efficiency curve of the proposed HVB ZSI and HVB ZSI under different output power values is shown in Fig. 20 according to parameters shown in Table 4 when V dc = 100 V and the output voltage is 220 V. The value of output power is changed by changing the output load (R), and the efficiency values of different output powers are obtained. The efficiency calculation is based on the power loss equations in [24]. From Fig. 20, it can be seen that the efficiency of the proposed HVB ZSI is higher than that of HVB ZSI.

Experiment results
A hardware circuit, as shown in Fig. 21, was built. The main component parameters are shown in Table 4. Figures 22 and 23 show the comparison of main components size and weight between two inverters. The main component parameters are shown in the Table 4. Size and weight of each component can be obtained from the datasheet. It can be seen from Figs.22 and 23 that volumes and weights of the proposed HVB ZSI have decreased by 17.2% and 24.8% respectively compared with those of the HVB ZSI. From the aforementioned power loss, the HVB ZSI has higher power loss than the proposed HVB ZSI. So for heat dissipation, volume and weight of the heat sink of HVB ZSI is larger than those of the proposed HVB ZSI. Figures 24 and 25 show experimental results. Figure 24 shows the experimental results in case 1. V C is about   Figure 25 shows the experimental results in case 2. V C is 105 V, V i is boosted to 415 V, and the output line voltage is 220 V.

Conclusion
This paper has presented a new Z-source inverter topology with high voltage boost ability. Compared to the previous Z-source inverter with high voltage boost ability, the new topology has following unique features and advantages: (1) The Z-source capacitor voltage stress is reduced greatly under the same boost ability; (2) The ability to adapt to a wide range of load increases the quality of the output voltage; (3) The inrush current can be suppressed with a proper start control strategy. The improved performance of the proposed ZSI is confirmed by simulation and experimental results.