Controller Design for Improved Switched Inductor (SL)

INTERNATIONAL JOURNAL OF ADVANCED RENEWABLE ENERGY RESEARCH M.A.Ismeil et al., Vol. 1, Issue. 6, pp. 345-353, 2012

Controller Design for Improved Switched Inductor (SL) Z-Source Inverter for Photovoltiac Applications M.A.Ismeil*, Ayman Francees , Ralph Kennel Department of Electrical Drive systems and power electronics Technical University of Munich Munich ,Germany *Corresponding Author E-mail’s Address: [email protected]

Abstract— this paper presents an improved SL Z-source inverter topology for photovoltaic. Because of the limitation of the classical Z-source inverter, the SL Z-source inverter has been proposed to increase the voltage gain. With improved SL Z-source inverter topology, the capacitor voltage stress can be reduced. A PI controller is designed to control the AC-side and the DC-side of the SL Z-source inverter in order to get the required output voltage. The system is digitally simulated using the Matlab/Simulink/SimPower Software Environment and fully validated for efficient conversion system. Index Terms— Switched inductor, Z-source, boost ability, PWM, PI controller, grid-connected photovoltaic.

phases or three phases, this case is not allowed in the control strategy of the traditional inverter. On the other side, this alternative topology gives more flexibility and allows boosting the voltage across the DC- Link bus. The boost factor B can be expressed as follows [4]: B=

1 1 = 2T 1 − o 1 − 2D T

(1)

Where: T0 is the interval of the shoot-through zero state during a switching cycle T. D is the duty ratio of the shoot through for each cycle and equals to T0/T.

I. INTRODUCTION Actually there is a very significant interest in grid connected systems of renewable energy sources, especially PV sources, these system are basically power electronics converters, where the main target in these applications research is to minimize the cost and to improve their efficiency. Contrary to the classical structures, the use of one stage instead of two stages and removing the transformer from AC side if it is used will decrease drastically the cost of PV system interface for grid connection [1]. Three-phase voltage-source pulse width modulation (PWM) inverters have been widely used for DC/AC power conversion because they can produce a variable voltage and variable frequency power. In the same time a lot of control strategies have been used to fulfill the aforementioned requirements and to improve the quality of the output voltage of the three phase inverter, On the other hand these inverters need dead time to avoid the arm-short and snubber circuits to suppress the switching spikes [2]. In 2002, the topology of the Z-source inverter was proposed to overcome the limitations of traditional inverter such as the boosting mode and the problems of short circuit [3]. The idea of this topology is based on building an impedance network (Z network) which is used to replace the traditional DC link as shown in Figure 1. Therefore; an additional zero state will appear following to the leg shoot- through of one phase, two

Figure. 1 Classical Z-Source Inverter

However, this proposed topology of Z-source has some drawbacks, such as a large voltage stress across the switches and capacitors, huge inrush current and small boost factor. Indeed, different control strategies were used to overcome some of the aforementioned problems, where the voltage stress across the switches and capacitors is reduced and the boost is increased [5-7]. In another hand, there are other techniques such as switched-capacitor (SC), switchedinductor (SL), hybrid SC/SL, voltage multiplier cells and voltage-lift (VL) techniques, have been greatly used for increasing the step-up capacity in transformerless and

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INTERNATIONAL JOURNAL OF ADVANCED RENEWABLE ENERGY RESEARCH M.A.Ismeil et al., Vol. 1, Issue. 6, pp. 345-353, 2012

cascade structures. Therefore, it will be a good solution for improving impedance-type inverters, if a combination between the Z-Source inverter and advanced DC-DC enhancement techniques is designed [8-14]. The work presented in this paper is based on the SL Z-source inverter topology. The concept of the switched inductor (SL) techniques has been integrated into the classical Z-source impedance network [15], consequently a new SL Z-source impedance network topology has been obtained. This topology is shown in Figure 2 and it is called the SL Z-source inverter. It is clear that the new conception is totally different from any other existing Z-source inverters compared to the circuit structures and operation principles. The new obtained boost factor is efficiently increased; it is expressed as follows: B=

1+ D 1 − 3D

(2)

factor beside the limitation of the range of the index modulation. The main scientific contributions of this paper can be summarized as follows: A. This study aims in investigating a new topology with high boost factor. B. In this paper, the voltage stress across the capacitors and switches is reduced. C. In this paper the inrush current problem is removed. D. This paper explores a control strategy to regulate capacitor voltage, and produce desired AC voltage The remainder of the paper was organized as follows: In section II modified topology of SL will be presented, In section III the operation modes of the new topology will be described in details, in section IV the stress will be studied, in section V a simple boost control in PWM switching will be presented, in section VI control methodology will be describes, in section VII simulation results will be presented, Finally, in section VIII, conclusion of the paper will be presented.

Figure 3 Improved Z-source Inverter

Figure. 2. SL Z-source Inverter

On the other hand, the voltage stress across the switches and capacitors remains large and the inrush current is still within huge values. Because of this limitation an improved Zsource inverter was proposed [16, 17]. Indeed, the improved topology has exactly the same components as the previous topology, whereas, the network impedance is moved to be placed after the inverter as shown in Figure 3. It was found that the voltage stress across the capacitors and switches is reduced, whereas there was no improvement for the boost

II. IMPROVED SL Z-SOURCE The topology presented in Figure 2 is improved in the present work, where the main aim is to avoid the problems of the first topology by minimizing the voltage stress across the capacitors and switches, while the boost factor obtained in the previous topology is kept the same. This idea is based on moving the SL Z-source to be placed after the inverter in series Fig 4. As it is shown clearly, this new topology is different from that presented in Figure 3.

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INTERNATIONAL JOURNAL OF ADVANCED RENEWABLE ENERGY RESEARCH M.A.Ismeil et al., Vol. 1, Issue. 6, pp. 345-353, 2012

B. Shoot-Through State The shoot-through actions of the top and bottom arms of the main circuit, and its equivalent circuit are shown in Figure 6(a). When the switch S is on, the different states of the diodes Din , D1 , D2 , D3 , D4 , D5 and D6 are presented in Table. I, it is obvious that when the two diodes D1 and D2 are turned on the inductors L1 and L3 are charged, and the diode D3 is turned off. On the other side when the two diodes D4 and D5 are turned on the inductors L2 and L4 are charged, and the diode D6 is turned off, In this case the diode Din remains turned off. In this mode the relation between the input voltage, capacitor voltage and the inductance voltage can be presented by the following equation:

III. OPERATION PRINCIPLE OF IMPROVED SL Z-SOURCE

C. Non-Shoot-Through State

The equivalent circuit of improved SL Z-source proposed in this paper is shown in Fig 5; this topology will be studied under the following assumptions: A. Assumptions 1) Improved SL Z-source operates in CCM continuous conduction mode. 2) All components are assumed ideal and L1 = L2 = L3 = L4 = L , C1 = C2 = C 3) Because of the Symmetry of the inductors and the capacitors:

(3)

Vin + VC − VL = 0

Figure 4 Improved SL Z-source

Equivalent circuit of this mode is shown in Figure 6(b). When the switch S is off, the different states of the diodes Din , D1 , D2 , D3 , D4 , D5 and D6 are presented in Table. I. As the two diodes D1 and D2 are turned off and D3 is turned on, this makes the two inductors L1 and L3 to be connected in series. On the other side when the two diodes D4 and D5 are turned off and the diode D6 is turned on the two inductors L2 and L4 are connected in series, In this case the diode Din remains turned on.

VC1 = VC 2 = VC ,VL1 = VL 2 = VL3 = VL 4 = VL THE DIFFERENT STATES OF THE DIODES FUNCTION OF S STATE.

TABLE I.

S

Din

D1

D2

D3

D4

D5

D6

on

off

on

on

off

on

on

off

off

on

off

off

on

off

off

on

In this mode, the relation between the input voltage, capacitor voltage, the inductance voltage and the input DC voltage of the inverter can be presented by the following equations: −VC − 2VL = 0 Vin − Vdc − VL + VC − VL = 0

Figure 5 Equivalent Circuit of Improved SL Z-source Inverter.

(4) (5)

By applying the volt-second balance principle to the inductor voltage, the following expressions are obtained:

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INTERNATIONAL JOURNAL OF ADVANCED RENEWABLE ENERGY RESEARCH M.A.Ismeil et al., Vol. 1, Issue. 6, pp. 345-353, 2012

VC =

2D Vin 1 − 3D

(6)

Vdc =

1+ D Vin = BVin 1 − 3D

(7)

Thus; the boost factor of the SL Z-source impedance B is expressed as follows: T 1+ o 1+ D T B= = 1 − 3D 1 − 3To T

(8)

The resulting gain of the SL Z-source is then expressed as follows: Gmax = MB =

(2 − M ) 3M − 2

(9)

The detailed model of the non ideal case was presented in previous work [18].

1 Vdc .M 2

Non-Shoot-Through State

Figure 6 Equivalent Circuit of Improved SL Z-Source Inverter. (a) ShootThrough State. (b) Non-Shoot-Through State.

The peak AC voltage can be calculated by using (10) vac _ peak =

(b)

(10) IV. STRESS ANALYSIS The voltage stress across the capacitors in the initial topology of SL Z-source presented in [5] and given by: VC =

1− D Vin 1 − 3D

(11)

This expression is different from the one presented in (6) which is deduced from the improved topology proposed in this paper. A comparison between the curves of the voltage stress across the capacitors versus the duty cycle of the initial topology and the improved topology of the SL Z-source are shown in Figure 7. It is obvious that the voltage stress across the capacitors of SL Z-source is larger than the proposed topology. (a)

Shoot-Through State

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INTERNATIONAL JOURNAL OF ADVANCED RENEWABLE ENERGY RESEARCH M.A.Ismeil et al., Vol. 1, Issue. 6, pp. 345-353, 2012

10

Vc/Vin

8 6 Improved SL Z-source 4

SL Z-source 2 0 0

0.05

0.1

0.15 D

0.2

0.25

0.3

Figure. 7 Voltages Stress Against Duty Cycle.

On the other side, the voltage stress across the switches in the proposed topology Vs can be expressed as follows: Vs = BVin

(12) Figure 8. Waveforms and Switching Strategies of Simple Boost

This voltage can be rewritten as a function of the gain and the modulation index: Vs G = Vin M

VI. TWO- CONTROL METHODOLOGY A. Control of DC-Side

(13)

Using small signal analysis for non ideal topology, which is shown in Figure 9 where: L1 ,L2 ,L3 , L4 , C1 ,C2 are SL Z-source

V. SIMPLE BOOST CONTROL FOR SINGLE PHASE IMPROVED SL

impedance network, rL and rC are the stray resistance of

Z-SOURCE

inductors and the equivalent series resistance (ESR) of

This control strategy is based on the use of the two straight lines, line in the positive side and the other line in the negative side of the voltage axis. The value of the positive line has to be kept larger than or equal to the peak value of the reference voltages which is imposed to be balanced. Also, the negative line has to be less than or equal to the negative peak of the reference voltages as shown in Figure 8. The carrier signal is the same as in the classical carrier triangular based PWM. In this control strategy, the boost factor is constant and the maximum gain is presented in (9).

capacitors respectively, the dynamic vc can be obtained [16] as following: vC G do =

sb1 + b0 2

a 2 s + a1s + a0

Where:

The shoot through can be occurred when the triangular wave is greater/less than the reference signal or greater/less than the positive/negative straight lines. In the other situation, the control strategy will be the same as the classical triangular PWM.

b1 = (2L(I o − 3I L )) b0 = (K1( 1 − 3D )) + (I o − 3I L )((1 − 5D)rC + 2rL ) K1 = ((5rC − 2rL )I L + 3VC + 2Vin − I o rC ) a2 = 2CL ; a1 = (2rL − ( 5D − 1 )rC ) ; a0 = (1 − 3D )2 I o : Equivalent load current

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INTERNATIONAL JOURNAL OF ADVANCED RENEWABLE ENERGY RESEARCH M.A.Ismeil et al., Vol. 1, Issue. 6, pp. 345-353, 2012

D,I o ,VC1 = VC 2 = VC ,I L1 = I L2 = I L are the DC steady state values.

As shown in Figure 10, the system has a zero in the right half side of the S plane, so the system is unstable. By using PI controller with Kp= 9.533e-5 and KI =2.1856e-5, the system has been changed from instability state to stability state with phase margin is over 45o (90.9o). This means that, the proposed system and controller is stable and has a good performance.

40 20 Magnitu de (dB )

0 -20 -40 -60 -80 -100

G.M.: 18.1 dB Freq: 24.3 Hz Stable loop

-120 360

P h ase (deg )

315 270 225 180 135

P.M.: 90.9 deg Freq: 0.0105 Hz

90 -4 10

10

-3

10

-2

10

-1

0

10 10 Frequency (Hz)

1

10

2

10

3

10

Figure 9 System configuration of Improved SL Z source with proposed control method Figure 11 Bode plot for transfer function of DC side after PI compensation

By using the parameter in Table II, bode plot of DC side can be obtained as shown in Figure 10 The steady state value of shoot-state time (Do) can calculate from (6) as following:

Open-Loop Bode Editor for Open Loop 1 (OL1) 100

Magnitude (dB)

80 60

Do =

40

2Vin + 3VCref

(15)

20

Where VCref is the reference capacitor voltage and Vin is the

G.M.: -63.9 dB Freq: 47.8 Hz Unstable loop

0

imposed DC input voltage. Using the reference and the measured capacitor voltages, the shoot-state duration (D) is regulated using the DC-side PI controller as the following diagram:

-20 360

Phase (deg)

VCref

270

180 P.M.: -74.6 deg Freq: 2.04e+003 Hz 90 0

10

1

10

2

10 Frequency (Hz)

3

10

10

Figure 10 Bode plot the open loop transfer function of DC side

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INTERNATIONAL JOURNAL OF ADVANCED RENEWABLE ENERGY RESEARCH M.A.Ismeil et al., Vol. 1, Issue. 6, pp. 345-353, 2012

VII. SIMULATION RESULTS To validate the theoretical advantages of the use of the improved SL Z-source inverter, the whole system is simulated using Matlab/Simulink/Sim-Power Software Environment. In this simulation test, the DC input voltage is constant and the load is changed from 311Ω to 155.5Ω. The used system parameters for this test are shown in TABLE II Figure 13 shows the capacitor voltage of the SL Z –source inverter under the load changes. THE PARAMETERS OF THE SL Z- SOURCE

TABLE II. Figure 12 Control block diagram of the voltage regulator for DC Side Input voltage

Filter parameter

A- AC-side control

3mH

Cf

100µF

311Ω 0.495 A

C1 = C2

0.8mF

Switching frequency

fs

10kHz

equivalent series resistance (ESR) of capacitors

rC

0.003Ω

Inductor stray resistance

rL

0.005Ω

Duty cycle

D

0.3

Where Vref is the required output voltage, Vin is the input DC voltage, and B is the boost factor. The boost factor B is calculated from equation (8) using the output of the DC-side controller (D). Then, using the PI controller, the difference between the reference voltage signal (Vref) and the measured output voltage (Vo) is used to compensate and regulate the value of the Modulation index (M) to be applied to the system as shown in the following diagram:

1mH

L3 = L4

Improved SL ZSI

(16)

BVin

Lf

L1 = L2 =

First, the steady state value of Modulation index (Mo) is calculated by using (10) as following: Vref

35V

resistive load Io

The AC output voltage is controlled by regulating the Modulation index (M).

Mo =

Vin

300

250

200

150

‫܌܉ܗۺ܄‬ 100

‫܎܍܀ି܋ۯ܄‬ 50

0 0.4

0.6

0.8

1

1.2

Figure 13 Capacitor voltage under load change Figure 13 Control block diagram of the voltage regulator for AC Side

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1.4

1.6

1.8

2

INTERNATIONAL JOURNAL OF ADVANCED RENEWABLE ENERGY RESEARCH M.A.Ismeil et al., Vol. 1, Issue. 6, pp. 345-353, 2012

With load changing, the controller success to achieve the required output voltage as shown in Figure 14. Also, the inductor current of the improved SL Z-Source is shown in Figure 15.

improved. The designed PI controllers achieve the required response for both sides, DC and AC. Where, the AC side voltages and currents are fully regulated and stabilized under load changes. The PI controller ensures a robust, stabilized operation and efficient energy conversion.

400

Load Current*100

REFERENCES

Load Voltage

[1] Babak Farhangi, Shahrokh Farhangi “Application of Z-Source

300 200 100 0 -100 -200 -300 -400 0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1.2

1.3

1

Figure 14 Output voltage and current under load change

20 18 16

IL

14 12 10 8 6 4 2 0.6

0.7

0.8

0.9

1

1.1

1.4

Figure 15 Inductor current of the improved SL Z-Source

VIII. CONCLUSION This paper deals with the presentation of a new and improved topology of the SL Z-source inverter. The main goal is to improve the behaviors quality of the Z-source inverter. Especially to solve the major drawbacks of previous topologies, Such as voltage stress across the capacitors, voltage stress across the inverter switches, and the inrush current. In addition the quality of the boost factor is

Converter in Photovoltaic Grid-Connected Transformer-Less Inverter” Electrical Power Quality and Utilisation, Journal Vol. XII, No. 2,2006. [2] Dong-Choon Lee; G-Myoung Lee “A Novel Overmodulation Technique for Space-Vector PWM Inverters” Power Electronics, IEEE Transactions on , 1998 , Vol. 13, PP: 1144 – 1151. [3] F. Z. Peng, “Z-source inverter,” IEEE Trans. Ind. Applicat., vol. 39, no.2, pp. 504–510, Mar. 2003. [4] P. C. Loh, D. M. Vilathgamuwa, Y. S. Lai, G. T. Chua, and Y. Li, “Pulsewidth modulation of Z-source inverters,” in Rec., 39th IAS Annu. Meeting, 2004, pp. 148–155. [5] F.Z. Peng, M. Shen, and Z. Qian, “Maximum boost control of the Zsource inverter,” IEEE Trans. Power Electron. vol. 20, no. 4, pp.833838, Jul. 2005 [6] Shen, M.; Jin Wang; Joseph, A.; Peng, F.Z.; Tolbert, L.M.; Adams, D.J.” Maximum constant boost control of the Z-source inverter” Industry Applications Conference, 2004. 39th IAS Annual Meeting. Conference Record of the 2004 IEEE, 3-7 Oct. 2004. [7] U. Shajith Ali, V. Kamaraj, “A Novel Modified Space Vector Pulse Width Modulation Technique for High Performance Z-Source Inverter”, International review of electrical engineering IREE, Vol. 6. n. 2, pp. 618623 [8] O. Abutbul, A. Gherlitz, Y. Berkovich, and A. Ioinovici, “Step-up switching mode converter with high voltage gain using a switchedcapacitor circuit,” IEEE Trans. Circuits and Systems I: Fundamental Theory and Applications, vol. 50, no. 8, pp. 1098-1102, 2003. [9] A. Ioinovici, “Switched-capacitor power electronics circuits,” IEEE Circuits and Systems Magazine, vol. 1, no. 4, pp. 37-42, 2001. [10] M. Prudente, L.L. Pfitscher, G. Emmendoerfer, E.F. Romaneli, and R.Gules, “Voltage multiplier cells applied to non-isolated dc-dc Cconverters,” IEEE Trans. Power Electron., vol. 23, no. 2, pp. 871-887, Mar. 2008. [11] M. Zhu, F.L. Luo and Y. He, “Remaining inductor current phenomena of complex dc-dc converters in discontinuous conduction mode: general concepts and case study,” IEEE Trans. Power Electron., vol. 23, no. 2,pp. 1014-1019, Mar. 2008. [12] M. Zhu and F.L. Luo, “Voltage-lift-type Cûk converters: topology and analysis,” IET Power Electron., vol. 2, no. 2, pp. 178-191, Mar. 2009. [13] M. Zhu and F.L. Luo, “Series SEPIC implementing voltage lift technique for dc-dc power conversion,” IET Power Electron., vol. 1, no.1, pp. 109121, Mar. 2008. [14]M. Zhu and F.L. Luo, “Super-lift dc-dc converters: graphical analysis modelling,” J. of Power Electron., vol. 9, no. 6, pp. 854-864, Nov. 2009 [15] Miao Zhu; Kun Yu;Fang Lin Luo” Topology analysis of a switchedinductor Z-source inverter” Industrial Electronics and Applications (ICIEA), 2010 the 5th IEEE Conference on Issue Date: 15-17 June 2010 On page(s): 364 – 369 [16] Shaojun Xie; Yu Tang; Chaohua Zhang “Research on third harmonic injection control strategy of improved Z-Source Inverter“Energy Conversion Congress and Exposition, 2009. ECCE 2009. IEEE , Page(s): 3853 – 3858 [17] Shen, M.; Jin Wang; Joseph, A.; Peng, F.Z.; Tolbert, L.M.; Adams, D.J.” Maximum constant boost control of the Z-source inverter”

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Industry Applications Conference, 2004. 39th IAS Annual Meeting. Conference Record of the 2004 IEEE, 3-7 Oct. 2004. [18] Mohamed A. Ismeil, Abdallah Kouzou, Ralph Kennel, Abdalla A. Ibrahim ,Mohamed Orabi, Mahrous E. Ahmed “Modeling of non-ideal Improved

Switched Inductor (SL) Z-source Inverter” ACEMP electromotion 2011, 8-10 September 2011 Istanbul Turkey, Page(s): 481- 486

Ralph M. Kennel was born in 1955 at Kaiserslautern (Germany). In 1979 he got his diploma degree and in 1984 his Dr.-Ing. (Ph.D.) degree from the University of Kaiserslautern. From 1983 to 1999 he worked on several positions with Robert BOSCH GmbH (Germany). Until 1997 he was responsible for the development of servo drives. Dr. Kennel was one of the main supporters of VECON and SERCOS interface, two multi-company development projects for a microcontroller and a digital interface especially dedicated to servo drives. Furthermore he took actively part in the definition and release of new standards with respect to CE marking for servo drives Between 1997 and 1999 Dr. Kennel was responsible for "Advanced and Product Development of Fractional Horsepower Motors" in automotive applications. His main activity was preparing the introduction of brushless drive concepts to the automotive market. From 1994 to 1999 Dr. Kennel was appointed Visiting Professor at the University of Newcastle-upon-Tyne (England, UK). From 1999 - 2008 he was Professor for Electrical Machines and Drives at Wuppertal University (Germany). Since 2008 he is Professor for Electrical Drive systems and Power Electronics at Technische Universtaet Muenchen (Germany). His main interests today are: Sensorless control of AC drives, predictive control of power electronics and Hardware-in-the-Loop systems. Dr. Kennel is a Senior Member of IEEE, a Fellow of IEE and a Chartered Engineer in the UK. Within IEEE he is Treasurer of the Germany Section as well as Vice President Meetings of the Power Electronics society (PELS).

M. A. Ismeil was born in Qena, Egypt on October ,1977. He received his B .S and M .S. In electrical engineering from the South Valley University in 2002, 2008 respectively. He is currently working toward the Ph.D. Degree. From October 2010 until now he is a PHD student in Department of Electrical Drive Systems and Power Electronics, Technical University of Munich, Germany.

Ayman Francees is a PhD student at Dept. of Electrical Drive Systems and Power Electronics, Technical University of Munich, Munich, Germany. He received his BSc in Industrial Electronics and Control Engineering, Menofia Universiy, Egypt, 2006. He received his MSc in Electrical Power and Machines, Cairo University, Egypt, 2009. His research interests are renewable energy, power elctronics, modern control systems including fuzzy systems, neural networks, and predictive control.

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