The research paper published by IJSER journal is about PID compensated, Stability improved Impedance Source Inverter (ZSI)

ISSN 2229-5518

151

PID compensated, Stability improved Impedance

Source Inverter (ZSI)

G. Shiva, K. Hrishikes, R. Issan Raj

Abstract— This paper presents the design of Closed loop voltage mode control for impedance-source inverter using Proportional Integral Derivative (PID) controller. The control action is performed by regulating the DC-link voltage at the input side. Mathematical model of the inverter is developed and the control parameters are designed using Bode plot. MATLAB – Simulink model has been developed for simulation. From the results, it was shown that the proposed controller is very well capable to regulate the AC output voltage.

Index Terms— Inverters, Impedance-source inverter, PID controller, PID Compensation, Shoot-through state, Stability analysis, Voltage mode control.

1 INTRODUCTION

—————————— ——————————
HE Conventional Voltage Source Inverter (VSI) is a common circuit topology used in converting DC power to AC power. However, it can only produce output AC
voltage lower than the input. This is the main drawback for the VSI.

As compared to VSI, impedance-source inverter (ZSI) is a relatively new topology. The main feature of ZSI is that it can boost up its output voltage higher than the input in one stage DC-AC power conversion. Hence, a compact and high efficiency power converter is obtained. In addition, the reliability is improved due to the insertion of shoot-through interval [1]. The structure of the ZSI is depicted in Fig. 1.

Fig. 1. Z-Source Inverter structure

Numerous control techniques have been proposed for controlling ZSI. In [2], [3], [4] the DC-link voltage is indirectly controlled by the capacitor voltage (Vc) of the impedance network. The capacitor voltage can be kept constant at a desired value through the selection of proper shoot-through duty ratio [2] and Kp and Ki parameters [3], [4] by the controllers. However,

measurement of the input voltage (Vin) and Vc. Two types of controller, voltage mode and current programmed mode, are designed based on the above method. In [7], the design procedure proposed in [6] is utilized to design voltage mode and current mode control for a high-performance z-source inverter.

This paper presents the design of voltage mode control for a conventional z-source inverter using PID controller. The controller regulates the AC output by controlling the DC-link voltage at the input side. The PWM pulses needed for triggering the inverter’s switches are generated using modulation method presented in [2].

2 Z-SOURCE INVERTER OPERATION

In the operation of ZSI, the third state called shoot-through state exists together with the null states and the active states. Shoot-through state is a condition where both switches of an inverter leg in PWM inverter conduct simultaneously, which is prohibited in traditional VSI’s since they may cause a short circuit condition that could destroy the inverter.
Thus, there are two conditions in the operation of ZSI, the
shoot-through state and the non shoot-through state. With symmetric z-source network, i.e. L1 = L2 = L and C1 = C2 = C, the inverter side of z-source network can treated by an equivalent current source with a finite current during non shoot through state and a zero current during shoot through state. The equivalent circuit of the two conditions can be seen in Fig. 2(a) and (b) respectively [1], [8].
From Fig. 2, the voltage across z-source capacitor is

𝑇𝑠ℎ

when the inverter experiences a step change of input voltage, the

𝑇𝑛𝑠

1−� 𝑇

1−𝐷0

DC-link voltage changes though Vc keeps constant and tends to

𝑉𝐶 = �𝑇

−𝑇

� 𝑉𝑖𝑛 = �

𝑇𝑠ℎ � 𝑉𝑖𝑛 = 1−2𝐷

𝑉𝑖𝑛 (1)

become uncontrollable. This will result in distortion in the

𝑛𝑠

𝑠ℎ

1−2� 𝑇 0

inverter’s output voltage. The other work proposed in [5] used a PID controller to maintain the peak DC-link voltage directly through direct measurement. It requires additional circuitry for peak detection of the DC-link voltage. Hence the control becomes more complex. In [6], a method for controlling the output voltage of Z-Source Converter (ZSC) is proposed. The output voltage, which is the DC-link voltage, is estimated by the

Peak DC-link voltage across the inverter bridge is given by

𝑉�𝑑𝑐 = 2𝑉𝐶 − 𝑉𝑖𝑛 = 𝐵𝑉𝑖𝑛 (2)

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The research paper published by IJSER journal is about PID compensated, Stability improved Impedance Source Inverter (ZSI)

ISSN 2229-5518


The output peak phase voltage is defined as

TABLE 1

SIMULATION PARAMETERS

152

𝑚𝑉�𝑑𝑐

𝑚(𝐵𝑉𝑖𝑛)

𝑚𝑉𝑖𝑛

𝑣�𝑎𝑐 =


= = 𝐵 �

2 2

(3)

2

𝑇𝑠ℎ : shoot-through period
𝑇𝑛𝑠 : non-shoot-through period
𝑇 : switching period
𝑚 : modulation index
𝐷0 : shoot-through duty ratio
𝑉𝑖𝑛 : inverter’s DC input voltage

Units: V = volts, micro H = micro henry, mF = milli farad, mH = milli henry. D0 represents duty ratio

Using parameters listed in Table 1, the transfer function (4) can be rewritten as

𝐺𝑣𝑑 (𝑠) =

2.06×10−7 𝑠 2+216𝑠 +32920

5.4×10−8 𝑠 3+8.23×10−6𝑠 2 +0.0948𝑠 +14.34

(5)

Fig. 2. Equivalent circuit of z-source inverter (a) Non-shoot- through state (b) Shoot-through state

The magnitude and phase asymptotes of the ZSI’s loop gain without compensator is sketched in Fig. 8. The phase margin is

0.003280. It is inadequately too small for power converter application which usually needs 250 – 600 phase margin. A

controller is needed to increase the phase margin.

A PID controller is then designed. The final PID transfer function is obtained and given by

3 CONTROLLER DESIGN

𝐺𝐶 (𝑠) = 6.107

(𝑠+1000)(𝑠+1000)

𝑠(𝑠+30200)

(6)

The complete system configuration for ZSI connected to a three phase load is shown in Fig. 3. The average output voltage of ZSI depends on the DC-link voltage and the modulation index. The control strategy is to control the ZSI from the DC side only. The modulation index is adjusted
using the relationship m + 𝐷0 = 1.
The DC-link voltage, Vdc, is taken as the control target and
the control algorithm is shown in Fig. 7. The control (duty
ratio) to peak DC-link voltage transfer function can be expressed as (4) [7].

The magnitude and phase asymptote of the system compensated

by this PID controller is depicted in Fig. 9. It is observed from

Fig. 9 that using PID controller, the phase margin increases to

250 at crossover frequency 471 Hz, somewhat adequate to ensure stable operation under disturbances.

So, a PID controller is designed to improve phase margin. This PID controller is used to provide switching pulses. The modulation method is modified from conventional modulation method.

Equation (4) is given by,

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The research paper published by IJSER journal is about PID compensated, Stability improved Impedance Source Inverter (ZSI)

ISSN 2229-5518

153

(−2𝐼𝐿 + 𝐼𝑙 )𝐿𝑙 𝐿𝑠 2 + [(−2𝐼𝐿 + 𝐼𝑙 )𝑅𝑙 𝐿 + (1 − 𝐷0 )(2𝑉𝐶 − 𝑉𝑖𝑛 )𝐿 + (1 − 2𝐷0 )(2𝑉𝑐 − 𝑉𝑖𝑛 )𝐿𝑙 ]𝑠 + (1 − 2𝐷0 )(2𝑉𝑐 − 𝑉𝑖𝑛 )𝑅𝑙

𝐺𝑣𝑑 (𝑠) =

𝐿 𝐿𝐿𝑠 3 + 𝑅 𝐿𝐿𝑠 2 + [2𝐿(1 − 𝐷 )2 + 𝐿 (2𝐷

− 1)2]𝑠 + 𝑅 (2𝐷

− 1)2

𝑙 𝑙

0 𝑙 0

𝑙 0


The switching method which produces shoot-through state is shown in the following figure which can be easily understood.

Fig. 3. Voltage mode control of z-source inverter using PID

controller

The modified pulse width modulation is employed here to achieve shoot through state. It can be understood as using the following figures

Fig. 5. Modified carrier-based PW M control with shoot through zero states that are evenly distributed among the three phase legs, where the equivalent active vectors are unchanged

Fig. 4. Traditional carrier-based PW M control without shoot- through zero states, where the traditional zero states (vectors) V111 and V000 are generated every switching cycle and

4 MODIFIED MODULATION METHOD

Fig. 6 shows the modulation strategy for creating the shoot through duty cycle d0 to control the dc-link boost voltage. In order to obtain the transfer function of d0 /v m to design the controller, we have to modify the traditional modulation method. All the boost control methods (simple boost control, maximum boost control, and constant maximum boost control, etc.,) can modify with this method. The shoot through duty cycle d0 can be expressed as

determined by the references

𝐷0 = 2 �1 −

𝑇𝑛𝑠 � = 2 �1 −

𝑇

𝑉𝑡𝑟𝑖 −𝑉 ′ 𝑚 � =

𝑉𝑡𝑟𝑖

2𝑉′𝑚

𝑉𝑡𝑟𝑖

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The research paper published by IJSER journal is about PID compensated, Stability improved Impedance Source Inverter (ZSI)


ISSN 2229-5518

154

Fig. 6. Modulation method; (a)Simple control method; (b)Modified modulation

Fig. 8. Bode plot of open loop or uncompensated ZSI

Fig. 7. Control algorithm of z-source peak DC-link voltage

5 SIMULATION RESULTS AND DISCUSSIONS

The above discussed method of designing a PID Compensated ZSI is simulated in Matlab/Simulink software. The stability analysis of open loop or uncompensated ZSI along with closed loop or PID compensated ZSI is compared using Bode plot. From the improved phase margin of closed loop system it is shown that PID compensated system is more stable the uncompensated system.
The voltage mode control of ZSI is alone taken into
consideration. This control strategy can be extended for
current mode control also.

Fig. 9. Bode plot of PID compensated ZSI

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The research paper published by IJSER journal is about PID compensated, Stability improved Impedance Source Inverter (ZSI)

ISSN 2229-5518

155

no. 2, pp. 680-686, March/April 2010.

[7] O. Ellabban, J. V. Mierlo, and P. Lataire, “Voltage mode and current mode control for a 30 kW high-performance z-source inverter”, in Proc. IEEE EPEC, 2009, pp. 1-6.

[8] C. S. Thelukuntla and M. Veerachary, “ Resonant controller based single-phase z-source inverter with LCL-filter”, in Proc. Joint Conference on Power Electronics, Drives, and Energy System and Power India, 2010, pp. 1-6.

[9] B.Y. Husodo and S.M. Ayob, “Design of Proportional Integral

Derivative (PID) Controller for Impedance-Source Inverter”, in Proc. IEEE ICCAIE, 2011, pp. 121-125.

AUTHORS

G.Shiva received his Bachelor of Engineering degree in Electronics and Instrumentation Engineering from Anna University in 2008. He is currently pursuing Master of Engineering in Control and Instrumentation in the same university. His areas of interests are power electronics and

control systems. shivageie@gmail.com

Fig. 10. Output voltage of ZSI for an input of 210V

6 CONCLUSION

Since the usage of solar energy for domestic appliances is upcoming, the conversion of variable DC voltage to constant AC voltage becomes area of interest for scholars and researchers. The one of the best method for the above mentioned power conversion is using Impedance Source Inverter (ZSI). The proposed control strategy for voltage mode control is effective and capable of regulating output AC voltage very well with improved stability. The control strategy can be extended for current mode control also.

REFERENCES

[1] F. Z. Peng, "Z-source inverter", IEEE Transactions on Industry

Applications, vol. 39, pp. 504-510, Mar-Apr 2003.

[2] X. Ding, Z. Qian, S. Yang, B. Chu, and F. Z. Peng, “A PID control strategy for DC-link boost voltage in z-source inverter”, in Proc. IEEE APEC, 2007, pp. 1145-1148.

[3] X. Ding, Z. Qian, S. Yang, B. Chu, and F. Z. Peng, “A dircet peak DC- link boost voltage control strategy in z-source inverter”, in Proc. IEEE APEC, 2007, pp. 405-411.

[4] M. J. Rastegar Fatemi, S. Mirzakuchaki, S. M. J. Rastegar Fatemi, “Wide-range control of output voltage in z-source inverter by neural network”, in Proc. IEEE ICEMS, 2008, pp. 1653-1658.

[5] X. Ding, Z. Qian, S. Yang, B. Chu, and F. Z. Peng, “A dircet DC-link boost voltage PID-like fuzzy control strategy in z-source inverter”, in Proc. IEEE PESC, 2008, pp. 405-411.

[6] G. Sen and M. E. Buluk, “Voltage and current-programmed modes in

control of the z-source converter”, IEEE Trans. on Ind. Appl., vol. 46,

K.Hrishikes M.E. completed B.E. in Instrumentation and Control Engineering from Madurai Kamaraj University in the year 1993 and M.E in Electronics and Control Engineering from Sathyabama University in the year 2005. Now he is working as Assistant Professor (Sel. Grade) in SRM Valliammai engineering College, Chennai and has an experience of

15 years in teaching. He handles classes for both UG and PG projects. He bagged best teacher award during the year 2009 in Valliammai Engineering College. He has presented many papers in national conferences and international conferences. His areas of interests are process control and control system. hrishikes.ks@gmail.com

R.Issan Raj M.E. received his Bachelor of Engineering degree in

Electronics and Communication Engineering from Anna University in

2006. He received his Master of Engineering in Control and Instrumentation in the same university in 2011. He has 3 years of teaching experience and is now currently working as Assistant Professor in Valliammai Engineering College. His areas of interests are controller design and embedded system. issanraj@gmail.com

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