AC Small Signal Modeling, Analysis and Control of Quasi-Z-Source Converter

Yuan Li Sichuan University

Dept. of Electrical Engineering & Information Chengdu, 610065, China

yli@scu.edu.cn

Fang Z. Peng Michigan State University

Dept. of Electrical & Computer Engineering Lansing, 48824, US

fzpeng@msu.edu

Abstract—This paper addresses the ac small signal modeling of the quasi-Z-Source Converter (qZSC). The linearized control/disturbance-to-system-variable transfer functions of the voltage-fed type quasi-Z-source network are derived, indicating the existence of right half plane (RHP) zero, which could impose limitation on controller design. Analysis on the dynamics introduced by the shoot-through state of the quasi-Z-source network is presented based on the ac small signal model, which is compared with the detailed circuit model for validation. Considering system dynamic characteristics, the qZSC design guidelines for passive component sizing is investigated by parameter sweeping of the small signal model based transfer functions. As another application of the ac small signal modeling, a PI compensator with feed forward control loop is developed for the qZSC in stand-alone operation. Experimental result is provided to validate the effectiveness of the closed-loop control.

Keywords-small signal model, quasi-Z-source converter (qZSC), dynamic response, closed-loop control.

I. INTRODUCTION A class of quasi-Z-source inverter (qZSI) was firstly

proposed in 2007 [1]. As a derivate from the conventional Z-source inverter (ZSI) [2], the qZSI gets impedance network to couple the voltage source or current source with the inverter bridge as well, which makes it possible to introduce shoot-through state and accomplish buck or boost operation in either voltage-fed or current-fed mode. Besides, the qZSI features further advantages compared to the traditional ZSI, such as continuous input current (the voltage-fed type), and reduced passive component (capacitor) rating. With the potential economical advantages and improved reliability following by the allowance of shoot-through state, the qZSI is attractive in many applications where a large range of voltage gain is needed, such as photovoltaic inverter, wind power generation, and hybrid electric vehicles, etc [3]-[5].

Modified pulse-width modulation (PWM) that has been explored for traditional ZSI can be transplanted to the qZSI seamlessly. The derivations of the control of shoot-through duty ratio to the output voltage in steady state are contributed in literatures. Several ways to boost the voltage by introducing shoot-through states into conventional PWM are presented in [6]-[7], namely simple boost, maximum boost and maximum constant boost, where the maximum constant boost achieves the maximum voltage gain at any given modulation index

without low frequency ripple. And [8] presents a detailed analysis of ways to modify conventional carrier-based PWM strategies for the ZSI. Required by the advanced control in various applications, modeling, transient analysis and closed-loop controller is contributed in literatures [9]-[10].

Recently, many researchers further investigate circuit with quasi-Z-source network to accomplish DC-DC, AC-DC or AC-AC conversions [11]-[13], which together with qZSI are generically quasi-Z-source converters (qZSC). Particularly, the voltage-fed type quasi-Z-source network with continuous input current is presented most frequently in the lately studied qZSC. Therefore it is necessary to learn more about the system characteristics of the quasi-Z-source network, such as dynamic response to the control, guidelines of passive components size, system limits and solutions. This paper extends the steady state derivation to dynamic modeling of the voltage-fed type quasi-Z-source network by state space averaging. Considering the asymmetric circuitry, a fourth-order ac small signal model in continuous conduction mode (CCM) is established and investigated. The linearized transfer functions are derived accordingly, based on which analysis about the dynamic response of the capacitors and inductors in the quasi-Z-source network are carried on. Parameter sweeping is applied to study the system limits and qZSC design issues. In the end, a closed-loop controller for stand-alone three-phase qZSI is developed based on the ac small signal model. Simulation and experimental results are both presented for validation of the theoretical analysis.

II. GENERAL VOLTAGE-FED TYPE QUASI-Z-SOURCE CONVERTER

Fig. 1 shows the general structure of the voltage-fed type qZSC investigated in this paper. Since there is inductor L1 at the input of the two-port impedance network, the input current of the qZSC is continuous. The employed quasi-Z-source network couples the converter to the voltage source, load, or another converter. The voltage source can be one or a combination of follows: a battery, photovoltaic panel, fuel cell, diode rectifier, a capacitor or an ac voltage source, etc. Switches involved in the qZSC can be unidirectional for single- direction power flow or bidirectional for dual-direction power flow. For the output of the qZSC, there can be passive load or source, either in dc or ac form, which is commonly coupled by

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2012 IEEE 7th International Power Electronics and Motion Control Conference - ECCE Asia June 2-5, 2012, Harbin, China

978-1-4577-2088-8/11/$26.00 ©2012 IEEE

Figure 1. General structure of the voltage-fed type qZSC with continuous

input current

the smooth inductor.

The buck operation is normally accomplished by conventional switch of the converter, where S2 is equivalently OFF and S1 is ON. Taking a voltage-fed qZSI as an example, the OFF state of S2 implies none of the inverter phase legs is shorted. In steady state we have vC2 = 0 V, vin = vC1 = vPN. The output voltage of qZSC depends on the switching duty cycle of the conventional converter. The boost operation can be achieved by introducing shoot-through states into switch S2, e.g. S2 is ON in a short interval T0 of one switch duty cycle Ts. Accordingly switch S1 is OFF either due to the circuit (for example a diode is used as S1) or active control. By defining the shoot-through duty ratio d0 = T0/Ts, we have following voltage equations of the qZSC in steady state [1]:

01

0

11 2C in

dv v

d−

=−

; (1)

02

01 2C ind

v vd

=−

; (2)

1 20

1ˆ1 2PN C C in inv v v v Bv

d= + = =

−. (3)

where ˆPNv is the peak voltage of the qZSC output; and B is defined as the voltage boost factor.

III. AC SMALL SIGNAL MODELING OF THE QUASI-Z-SOURCE NETWORK

A. AC Small-Signal Model for the Quasi-Z-Source Network and Transfer Functions This paper focuses on the boost operation in the continuous

conduction mode (CCM) of the qZSC, which is the unique operation status and performed in all the qZSC applications. The ac small-signal modeling and analysis is established based on dc-dc conversion for general analysis purpose. For the dc side modeling, other forms of conversion such as dc-ac inverter or ac-ac converter can be represented by the single switch S2 and current source connected in parallel [9]-[10].

Fig. 2(a) shows the equivalent circuit of the quasi-Z-source network in shoot-through state, where the S2 is ON and the load is shorted by the converter bridge. Input voltage vin is one system input. Given the fact that the real source such as PV

(a)

(b)

Fig. 2. Equivalent circuit of quazi-Z-source network when in the (a) shoot-through and (b) non-shoot-through states.

panels or fuel cells doesn’t have as stiff output characteristics as an idea voltage source in many applications, the input current iin could be one function of vin, which is determined by the specified energy source nature. Fig 2(b) shows the equivalent circuit of the quasi-Z-source network in non-shoot-through state, where the S2 is OFF and load current iload flow through the qZSC. Considering the asymmetric quasi-Z-source network, there are four state variables: the current through two inductors iL1, iL2; the voltage across the capacitors vC1, vC2. The load current iload serves as another input (disturbance) of the quasi-Z-source network. To simplify the analysis, assume that C = C1 = C2, L = L1 = L2, the stray resistances of inductors r = r1 = r2, and the equivalent series resistances (ESR) of capacitors R = R1 = R2.

At the shoot-through state shown in Fig. 2(a), capacitors transfer their electrostatic energy to magnetic energy stored in inductors. The dynamic state equations of the quasi-Z-source network are given as (4)

ddt

= +1 1x A x B u (4)

where 1 2 1 2[ ]L L C Ci i v v ′=x ,

( ) 10 0

( ) 10 0

10 0 0

1 0 0 0

r RL L

r RL L

C

C

− +⎡ ⎤⎢ ⎥⎢ ⎥

+⎢ ⎥−⎢ ⎥= ⎢ ⎥⎢ ⎥−⎢ ⎥⎢ ⎥⎢ ⎥−⎣ ⎦

1A,

0 0 0 01/ 0 0 0L

′⎡ ⎤= ⎢ ⎥⎣ ⎦1B , [ ]load ini v ′=u .

At the non-shoot-through states shown in Fig. 2(b), the dc power source as well as inductors charges capacitors and powers the external ac load, boosting the dc voltage across the inverter bridge. The dynamic state equations are shown as (5)

1849

2 2ddt

= +x A x B u (5)

where ( ) 10 0

( ) 10 0

1 0 0 0

10 0 0

r RL L

r RL L

C

C

− +⎡ ⎤−⎢ ⎥⎢ ⎥

+⎢ ⎥− −⎢ ⎥= ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

2A ,

/ 1// 0

1/ 01/ 0

R L LR L

CC

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥−⎢ ⎥−⎣ ⎦

2B .

Using state space averaging, the dc-side model of qZSI can be obtained as shown in (6).

ddt

= +

= +

x Ax Bu

y Cx Du (6)

where 0 1 0 2(1 )d d= + −A A A , 0 1 0 2(1 )d d= + −B B B , 1

1

C

L

vi⎡ ⎤

= ⎢ ⎥⎣ ⎦

y ,

0 0 1 01 0 0 0⎡ ⎤

= ⎢ ⎥⎣ ⎦

C , and 00⎡ ⎤

= ⎢ ⎥⎣ ⎦

D .

To model the qZSC small signal dynamics, perturbation is applied to vin and d0. Substituting ˆx X x= + (where X and x̂ are the dc terms and perturbations of the variable 0x d= , inv ,

loadi , 1Li , 2Li , 1Cv and 2Cv ) into (3), the Laplace-transformed transfer functions of the multi-input multi-output quasi-Z-source network can be derived. The transfer functions from d0 to capacitor voltage vC1 and vC2 are identical, denoted as

0

ˆˆ ( )Cvd

G s in (7).

0

ˆˆ

ˆ ( ) 00ˆ ( ) 0

1 2 0 1 22 2

0

ˆ ( )( ) ˆ ( )

( )(1 2 ) ( )( )( ) (1 2 )

C

load

in

v Cd

i sv s

C C load load L L

v sG s

d s

V V RI D I I I Ls r RLCs C r R s D

==

=

+ − − + − − + +=

+ + + −(7)

One can tell that term 1 2 0( )(1 2 )C C loadV V RI D+ − − and

1 2( )load L LI I I− − are positive giving the fact that R and r is the parasitic resistance, which can be ignored with respect to the other parameters. Therefore the zero places on the right half plane (RHP), indicating a non-minimum phase system, which will be validated by both root loci and simulation in next subsection.

Other transfer functions from vin to the state variables are documented as following: 1ˆ

ˆ ( )C

in

vvG s , 2ˆ

ˆ ( )C

in

vvG s , 1

ˆˆ ( )L

in

ivG s , 2

ˆˆ ( )L

in

ivG s

are fourth order, indicating the asymmetric structure of the quasi-Z-source network. However, 1 2ˆ ˆ

ˆ ˆ( ) ( )C C

in in

v vv vG s G s+ and

1ˆˆ ( )L

in

ivG s + 2

ˆˆ ( )L

in

ivG s (denoted as ( )ˆ

ˆ ( )C sum

in

vvG s and ( )

ˆˆ ( )L sum

in

ivG s ) will

result in second-order transfer functions ( )

0

ˆ ( ) 0ˆ 2 2ˆ ( ) 0 0

ˆ ( ) 0

ˆ ( ) 1 2( )ˆ ( ) ( ) (1 2 )

C sum

in

load

v C sumv

d sini s

v s DG sv s LCs C r R s D=

=

−= =

+ + + − (8)

and

( )

0

ˆ ( )ˆ 2 2

ˆ ( ) 0 0ˆ ( ) 0

ˆ ( )( )

ˆ ( ) ( ) (1 2 )L sum

in

load

i L sumv

d sini s

i s sCG sv s LCs C r R s D=

=

= =+ + + −

. (9)

This can be explained by the symmetric energy exchanging process between two capacitors together and two inductors together when shoot-through and non-shoot-through states are alternating. The transfer functions from 0d to inductor current

iL1 and iL2 are identical, denoted as 0

ˆˆ ( )Lid

G s in (10). The

transfer functions from load current iload to capacitor voltage and inductor current are shown in (11) and (12), respectively. Among these equations, D0, Iload, VC1, VC2, IL1, IL2 represents a given equilibrium point nearby which the system can be linearised.

0

ˆˆ

ˆ ( ) 00ˆ ( ) 0

1 2 1 2 02 2

0

ˆ ( )( ) ˆ ( )

( ) ( )(1 2 )( ) (1 2 )

L

load

in

i Ld

i sv s

C C load load L l

i sG sd s

V V RI Cs I I I DLCs C r R s D

==

=

+ − − − − −=

+ + + −

(10)

0

ˆ 0 0 0ˆ 2 2ˆ ( ) 0 0

ˆ ( ) 0

ˆ ( ) (1 )(1 2 ) (1 )( )( ) ˆ ( ) (1 2 )( )

C

load

in

v Ci

d sloadv s

v s R D D D Ls r RG s

LCs C r R s Di s ==

− − − − + += =

+ + + −

(11)

0

ˆ 0 0 0ˆ 2 2ˆ ( ) 0 0

ˆ ( ) 0

ˆ (1 ) (1 )(1 2 )( )( ) ˆ ( ) (1 2 )( )

L

load

in

i Li

d sloadv s

R D Cs D Di sG s

LCs C r R s Di s ==

− + − −= =

+ + + −

(12) B. Dynamic Characteristics of the Quasi-Z-Source Network

Based on these equations, the characteristic equation of the quasi-Z-source network can be obtained as (13).

22 0(1 2 )

0Dr Rs s

L LC−++ + = . (13)

Equation (13) can be written as the normalized form 2 22 0n ns sξω ω+ + = , (14)

where the natural frequency is 01 2

nD

LCω −

=

and the damping ratio is

02(1 2 )r R C

D Lξ +=

−.

It can be indicated from the characteristic equation that D0 effects on the system dynamic characteristics as well as passive components. Besides, notice that increase in C would increase the damping ratio; while increase in L would reach the opposite effect.

Practically, d0 has to be controlled to span its permissible range for voltage boost. Therefore root loci of the transfer function

0

ˆˆ ( )Cvd

G s are studied by parameter sweep to make a

clear map of the dynamic characteristics of the quasi-Z-source network. The system specifications are as follows: L = 500μ

1850

H, C = 400μF, R = 0.03Ω, r = 0.47Ω, D0 = 0.25, Iload = 9.9 A and Vin = 130 V.

Fig. 3 shows the pole and zero trajectories of 0

ˆˆ ( )Cvd

G s with L,

D0 and C variations, respectively. It is observed that there is a right-half-plane (RHP) zero in

0

ˆˆ ( )Cvd

G s , which is implied by (4)

as well. The RHP zero indicates the quasi-Z-source network is a non-minimum phase system, which is learned to imply high- gain instability and impose control limitations. It also can be observed from Fig. 3(a) that along with increasing in L, zeros are pushed from the right half plane toward the origin along the real axis, indicating an increasing degree of non-minimum- phase under-shoot (e.g. capacitor voltage dips before it rises

-0.5 0 0.5 1 1.5 2 2.5 3

x 104

-1500

-1000

-500

0

500

1000

1500

Real Axis

Imag

inar

y A

xis

200L Hμ=1600L Hμ=

200L Hμ=

1600L Hμ=

(a)

-0.5 0 0.5 1 1.5 2 2.5

x 104

-2000

-1500

-1000

-500

0

500

1000

1500

2000

Real Axis

Imag

inar

y A

xis

0 0.05D =0 0.35D =

0 0.05D =

0 0.35D =

(b)

-2000 0 2000 4000 6000 8000 10000 12000-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Real Axis

Imag

inar

y A

xis

100C Fμ=

800C Fμ=

100 ~ 800C Fμ=

(c)

Fig. 3. Pole-zero map of transfer function0

ˆˆ ( )Cvd

G s , with parameter sweep of

(a) L, (b) D0 and (c) C.

on a response of d0 rising). Similar conclusion can be reached with an increase in d0, which means that a deeper voltage dip will turn out with a heavier voltage boost operation. However, the variation of C has no influence on the RHP zeros seen from Fig. 3(c).

Additionally, the conjugated pole pairs are observed to move towards the origin along with the increase in L, as shown in Fig. 3(a). Thus the feedback control performance is predicted deteriorated with the increase in L. Moreover, increasing in L causes smaller damping ratio and decreasing natural frequency, which is consistent with (14). On the other side, the conjugated pole pairs can be seen shifting towards the real axis with increase in d0 or C, implying increasing system settling time and decreasing natural frequency, which is consistent with (14), too.

Passive components sizing of L and C can be conducted accordingly to the system operation conditions. The steady-state current/voltage ripple is one of the main considerations for the inductance/capacitance decision. Besides, the placement of poles and zeros gives an important guideline for components sizing to accomplish satisfactory system transient responses. To the end, trade-off needs to be made among the steady-state performance, dynamic response as well as the costs.

C. Small signal model validation

Above derivation of the small signal model can be validated by detailed circuit model. Fig. 4 gives the qZSC structure simulated by Matlab/Simulink using detailed switching model. The system specifications are as follows: L = 500μH, C = 100μF, load resistance RL = 8Ω, load inductance LL = 2 mH, Vin = 130 V and switching frequency fs = 20 kHz.

Fig. 4 qZSC structure for small signal model validation

Fig. 5 shows the under-shoot and overshoot of capacitor

voltage when a step change of d0 is given. It is observed that the capacitor voltage dips before it rises; while raises before it drops. This is known as a typical non- minimum-phase nature that has been predicted by the RHP zero of

0

ˆˆ ( )Cvd

G s .

Table I and Table II list the under-shoot ofΔV and Δiload with the shoot-through duty ratio d0 subject to a step change from 0.1 to 0.4. It can be seen that with the inductance increasing, the under-shoot will extend obviously, which gives rise to the under-shoot of the load current iload. This result consists to the root loci analysis. However, change of capacitance does not lead to larger under-shoot. To the contrary, ΔV is suppressed by larger capacitance, which is probably because it is easier to satisfy the load demand during a transient with a bigger capacitor.

1851

VΔ

(a)

(b)

Fig. 5 Non-minimum-phase response of capacitor voltage when a step increase of d0 is given: (a) undershoot and (b) overshoot.

Table I Under-shoot of capacitor voltageΔV/V

C/L 200μH 500μH 1000μH 1600μH 100μF 1.2 2 4 5 200μF 1.2 1.3 2.1 2.8 500μF 0.6 0.6 0.8 1.1 1000μF 0.3 0.3 0.4 0.5

Table II Under-shoot of load currentΔiload/A

C/L 200μH 500μH 1000μH 1600μH 100μF 1.6 2 2.6 2.9 200μF 1.7 2.2 2.6 2.8 500μF 2 2.4 2.6 2.8 1000μF 2 2.5 2.7 2.8 Properly passive components sizing can achieve good

transient performance. Fig. 6 shows the simulation results of dynamic response subject to step change of d0 with various quasi-Z-source network parameters: (a) L = 500μH, C = 200μF; (b) L = 1200μH, C = 200μF; and (c) L = 1200μH, C = 600μF. Option (b) gets the least overshoot and settling time; whereas less inductance or more capacitance would lead to more overshoot and probably system oscillation when in a closed-loop control.

I. CONTROL OF THE QUASI-Z-SOURCE INVERTER IN STAND-ALONE MODE

As an application of the small signal modeling of the qZSC, this subsection presents one way to control the quasi-Z-source

500 ; 200L H C Fμ μ= =1200 ; 200L H C Fμ μ= =1200 ; 600L H C Fμ μ= =

(a)

500 ; 200L H C Fμ μ= =1200 ; 200L H C Fμ μ= =1200 ; 600L H C Fμ μ= =

(b)

Fig. 6. Step response of (a) capacitor voltage and (b) inductor current when the shoot-through duty ratio d0 subject to a step change with various L and C.

inverter in a photovoltaic (PV) power condition system (PCS), which operates in stand-alone mode. Fig. 7 shows the system configuration, where Lf, Cf, and Rf are inductance, capacitance and stray resistance of the filter, respectively; voj, iCj, vij, iLj, ioj are output voltage, capacitor current of filter, output voltage of inverter, inductor current of filter and load current, respectively, all in three phase ( j = a, b, c). Through the decoupling capacitor, control of dc side and ac side is executed separately, as shown in Fig.8. Pulses generated by the dc-side controller and the ac-side controller are combined together by logical ‘OR’ to fire six IGBTs, assuming ‘1’ is ON and ‘0’ is OFF.

For the dc-side control, capacitor voltage vC1 is measured and fed back. The dynamics of vC1 caused by d0 can be obtained via (7). Linear approximation of the PV output characteristics can be accomplished by the small signal modeling. A normal operation for voltage control generally starts from the open circuit voltage of PV panels Voc, and stays at operating points where VPV > VMPP, where VMPP is the voltage at the maximum power point. Based on the linear approximation, proportional-integral (PI) controller assisted with a feed forward d0 is used as the shoot-through compensator. The feed forward d0 is determined according to the inherent relationship of vC1 and v’in in steady state:

10

12C in

C in

v vdv v

−=−

* '

* ' . (15)

where v’in is the input voltage vin after a low-pass filter. Based on the small signal modeling, PI parameters for vC1 control loop can be decided. In order to prevent the clashes between the dynamics of ac- and dc-sides, the dc-side

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Fig. 7. System configuration of stand-alone qZSI based PV PCS.

1Cv*

ojv*

1Cv

11

I CP C

KKs

+ __

inv 1

12C in

C in

v vv v

−−

* '

* '

inv'

0

CvdG sˆˆ ( )

0d

SPWM

ijv

Fig. 8 Two-stage control method for stand-alone qZSI based PV PCS.

1fC s

ijv 1f fL s R+

oji

Lji Cji ojvojv

2pK11

ip

KKs

+

ojv

ojv*

Cji

Cji*

Fig. 9. Control block diagram of the voltage regulator.

dynamics should be made considerably slower. This could

be supported by having a relatively lower bandwidth in the dc-side voltage loop. According to the qZSI network specification (L = 500μH, C = 400μF, R = 0.03Ω, r = 0.47Ω, D0 = 0.25, Iload = 9.9 A and Vin = 130 V), the crossover frequency of the PI controller and low-pass filter are both set to 25 Hz, where KP_C1 = 1e-4, KI_C1 = 0.8.

For the ac-side control, traditional methods explored for voltage regulation are applicable to stand-alone PV PCS. This paper employs a typical multi-loop controller in stationary frame as the voltage regulator, as shown in Fig. 9. A proportional compensator is used with the inner current loop, which gives a faster response and stabilizes the output for a current disturbance. Filter capacitor current iCj is fed back instead of filter inductor current iLj for better disturbance rejection and active oscillation damping. PI compensator is used with the outer voltage loop, which gives good reference tracking and stabilized slower variations. In this implementation, Kp2 was selected based on the principle that to keep the closed-loop gain 0 dB from system output frequency (60 Hz) to half of the switching frequency. Considering the time delay caused by the digital implementation, Kp2 would be less in practice to maintain a sufficient phase margin for stable performance. The outer voltage loop control parameters Kp1, Ki1 are selected with the compromise that the crossover frequency is low enough to remove the switching harmonics

but a sufficiently high bandwidth is remained to have fast response and perfect reference tracking.

II. EXPERIMENTAL RESULTS Experiments were executed in stand-alone operation. Fig.

10 shows the steady state waveforms of the closed-loop controlled stand alone qZSI, with 2.16 kW load and 1.08 kW load respectively. The total harmonic voltage distortion of the output voltage in each case is 1.57% and 1.67%, respectively. Fig. 11 shows the transients when load changed between 1.08 kW and 2.16 kW, where the peak ac voltage vp_peak = 85 V. The input PV voltage is 190 V for light load and 145 V for heavy load, respectively. With proposed control approach, the capacitor voltage was maintained at 190 V. It can be observed that in the steady state the output voltage accomplished satisfactory quality; while in the transient, a stable performance and good disturbance rejection can be achieved as well.

(a)

(b)

Fig. 10. Steady state waveforms of the closed-loop controlled stand alone qZSI, with (a) 2.16 kW load and (b)1.08 kW load.

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iload, 10 A/div

vC1, 100 V/div

vin, 100 V/div

vout-ll, 100 V/div

(a)

iload, 10 A/div

vC1, 100 V/div

vin, 100 V/divvout-ll, 100 V/div

(b)

Fig. 11 Experimental results of the transients when vo(l-l) = 104 V rms, vC1 = 190 V with step change from (a) 2.16 kW to 1.08 kW and (b) 1.08 kW to 2.16

kW.

III. CONCLUSION This paper presents ac small signal modeling, analysis and

control of the qZSC. Based on the small signal model, the right-half-plane zero is observed in the quasi-Z-source network. Parameter sweeping is conducted to investigate the dynamics of the qZSC, which shows that increase of the

inductance of the qZSC network will result in increase degree of non-minimum-phase system; whereas increase of capacitance has little effect on the non-minimum-phase under-shoot but a slower dynamic response. The analysis is verified by detailed circuit model using computer simulation. Based on the small signal model, a control method for qZSI based PV PCS is presented, experimental result of which confirms the effectiveness of the controller.

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