Z-Source Inverter Fed**Induction Motor**

**This article presents a simplified analysis of ZSI and the steady state operation of 3-Φ induction motor fed by ZSI. Results of simulation study and experimentation are also included...**

**- Prof. Adarsh J Mehta, **

**Dr. Ashwini A Godbole**

The traditional general-purpose motor drive or Adjustable Speed Drive (ASD) system is based on the Voltage Source Inverter (VSI), which consists of a diode rectifier in the front end with the DC link capacitor, and Inverter Bridge. The VSI is a buck (or step-down) converter that can only produce an AC voltage limited by the DC link voltage that is equal to 1.35 times the line voltage. Because of this nature, the VSI based ASD system suffers from the following limitations and problems:

- The voltage obtained at output is limited which is less than the input line voltage
- The ASD systems are limited by the voltage sags and results in shut down of the system at critical loads. Also, the DC capacitor in an ASD system cannot hold DC voltage above the operational level due to its relatively low energy storage capacity under such voltage sags
- The ride-through capacity is lagging in VSI, which leads to serious problem for sensitive loads driven by ASDs
- The ASD system can be accompanied with fly back converter or boost converter having energy storage capacity or diode rectifier to achieve ride-through; but, these combined circuits suffer with disadvantages of cost, size/weight, and complexity
- Diode rectifier produces inrush and harmonic current, which can further pollute the line. The traditional ASD system also suffers from low power factor
- EMIs majorly responsible for miss-gating, which can cause shoot-through that lowers the performance of the inverter
- The dead time needed to avoid shoot-through creates distortion and unstable operation at low speeds.

**Z-Source Inverter (ZSI)**

The ZSI is shown in Fig. 1. It consists of voltage source from the rectifier supply, impedance network, and three phase inverter with A.C. motor load. AC voltage is rectified to DC voltage by the rectifier. The rectifier unit consist of six diodes, which are connected in bridge way. This rectified output DC voltage fed to the Z-network, which consists of two equal inductors (L1, L2) and two equal capacitors (C1, C2). The network inductors are connected in series arms and capacitors are connected in diagonal arms.

**Fig 1: Z-Source Inverter...**

The impedance network is used to buck or boost the input voltage depends upon the boosting factor. This network also acts as a second order filter. The output voltage from impedance network is fed to the three phase inverter main circuit. The inverter main circuit consists of six switches. Gating signals are generated from the driving circuit and fed to the inverter operates and the output of inverter is fed to the AC load or motor.

**Equivalent Circuit of ZSI**

The three phase impedance source inverter bridge has nine switching states unlike the traditional VSI that has eight switching states. Because of this special structure, the ZSI has an additional switching state, when the load terminals are shorted through both the upper and lower switching devices of any phase leg, which called the Shoot-Through (ST) state besides the eight traditional Non-Shoots Through (NST) states. The ZSI has two operating modes: non-shoot-through mode and shoot-through mode, as shown in Fig. 3 and 4 respectively. During the ST switching state, the input diode is reverse biased; the input DC source is isolated from the load, and the two capacitors discharge energy to the inductors and to the load. During the NST switching states, the input diode turns ON, and the DC input voltage source as well as the inductors transfer energy to the load and charge the capacitors, as a result the DC-link voltage of bridge is boosted.The impedance source inverter bridge has one extra zero state, when the load terminals are shorted through both upper and lower devices of any one phase leg or all three phase legs. This shoot through zero state is forbidden in the VSI, because it would cause a shoot- through. This network makes the shoot through zero state possible. This state provides the unique buck-boost feature to the inverter. The equivalent switching frequency from the impedance source network is six times the switching frequency of the main inverter, which greatly reduces the required inductance of the impedance source network. The equivalent circuit of the ZSI is shown in Fig. 2.

**Fig 2: Equivalent circuit of ZSI...**

**Mathematical Analysis of Z-Source Network**

The impact of the phase leg shoot through on the inverter performance can be analysed using the equivalent circuit shown in Fig. 3 and Fig. 4. Assume the inductors (L1 and L2) and capacitors (C1 and C2) have the same inductance and capacitance values respectively; the Z-source network becomes symmetrical.

**Fig 3: Equivalent circuit when ZSI in shoot through state...**

In shoot through state the inverter side of Z-Source network is shorted during time interval T0 as in Fig. 3. Therefore, L1=L2=L and C1=C2=C.

Vc1 = Vc2 = Vc =VL1 = VL2 = VL

Vd = VL +Vc= Vc + Vc= 2 Vc ..........(1)

Vi = 0

Alternatively, when in non-shoot through active or null state current flows from Z-Source network through the inverter topology to connect AC load during time interval T1. The inverter side of the Z-Source network can nowbe represented by an equivalent circuit as shown in Fig. 4.

**Fig 4: Equivalent circuit when ZSI in non-shoot through state...**

The following equations can be written:

VL = Vdc - VC

Vd = Vdc

Vi = VC – VL

Putting VL = Vdc – VC in above equation

Vi = VC – (Vdc– VC) = VC – Vdc + VC = 2 VC – Vdc ....... (2)

Averaging the voltage across a Z-source inductor over a switching period (0 to T),

VC = T1 / (T1 – To) Vdc .….. (3)

Using equations (2) and (3)

The peak DC-link voltage across the inverter bridge is

Vi = 2 VC – Vdc

= 2 [T1 / (T1 – To) Vdc] – Vdc

= (2 T1 - T1 + T0) / (T1 - T0) Vdc

= (T1 + T0) / (T1 - T0) Vdc = (T1 + T0)/(T1 + T0 - 2T0) Vdc

= (T) / (T - 2T0) Vdc

= 1 / (1 - 2To/T) Vdc….. (4)

Vi = B. Vdc……(5)

Where, B = T/(T1 - To) i.e. ≥ 1 and B is a boost factor, T-Switching period.

The peak AC output phase voltage, For Z- source

Vac = M.Vi/2 = B.M Vdc /2

In the traditional sources, Vac = M. Vdc/2, where M is modulation index. The output voltage can be stepped up and down by choosing an appropriate buck – Boost factor BB = B.M (it varies from 0 to α), where α = firing angle. The Buck – Boost factor BB is determined by the modulation index M and the Boost factor B. The boost factor B can be controlled by duty cycle of the shoot through zero state over the non-shoot through states of the PWM inverter.

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

**Description of ZSI - Hardware**

A ZSI has been fabricated using IGBT switches and associated control circuits and a microcontroller. A switching frequency of 10kHz is used. The parameters of Z-network are L1 = L2 = 1mH; and C1 = C2 = 900μF. The inductors and capacitors were oversized in the prototype for possible regenerative operation during deceleration or inverter trips.

**Fig 5: Hardware configuration...**

An uncontrolled rectifier using diodes whose output voltage is 314 volts DC is fed to the Znetwork. The ZSI is used to control a 3-Φ squirrel cage induction motor whose specifications are given in Table I.

ZSI and loading arrangements are shown in fig. 5. The block diagram of the circuit is also shown in fig. 6.

**Simulation & Experimental Results**

**Simulation Results**

For carrying out simulation a model of ZSI and induction motor is developed in MATLAB-SIMULINK using Power System blockset. This model is shown in fig. 7. The simulation studied out for no load, rated conditions and a step change of load from no-load to half load. The waveforms of line voltages and rotor speed build up are shown in fig. 8 and fig. 9 respectively. The following MATLAB simulation is done for loaded condition i.e., the three phase induction motor used in the simulation circuit is loaded mechanically by providing an input torque of 6.26 N-m.

**Fig 6: Block diagram of proposed circuit...**

**Fig 7: Simulation circuit for Z-Source Inverter fed Induction Motor...**

**i) Inverter Output Line to Line Voltages (VL):**

**Fig 8: Inverter output line to line voltages...**

**ii) Rotor Speed (N):**

**Hardware Results:**

Table II indicates the variables of interest under no-load and rated load conditions with an AC input voltage of 230V (line-line). The rectifier output voltage is seen as 326.3V on no-load operation of the motor as shown in fig. 11. The inverter voltage could not be pushed up to rated value and the load test has to be carried out at value of 215 V to limit the current to safe values.

**Load Test:** A load test was carried out on the Z-Source unit to measure the full load current that the inverter would supply three phase induction motor.

From Table III it is seen that the full load current the proposed inverter circuit can supply is 1.85 Amperes.The line voltage Vab and rectified voltages are shown in fig.11 and 12 respectively.

**Fig 10: THD analysis of ZSI...**

**Fig 11: Rectifier output voltage (No load)...**

**Fig 12: Inverter line to line voltage Vab...**

**Conclusion**

This article has presented a simplified analysis of ZSI and the steady state operation of 3-Φ induction motor fed by ZSI. Results of simulation study and experimentation are also included and there is a fairly close agreement between the simulation and experimental results.

**Prof. Adarsh J Mehta is Assistant Professor, Nagesh Karajagi Orchid College of Engineering & Technology, Solapur. Dr. Ashwini A Godbole is Professor, All India Shri Shivaji Memorial Society’s College of Engineering, Pune.**

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