New Extendable Single-Stage Multi-input DC–DC/AC Boost ...

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 2, FEBRUARY 2014 775

New Extendable Single-Stage Multi-inputDC–DC/AC Boost Converter

Saeed Danyali, Seyed Hossein Hosseini, Member, IEEE, and Gevorg B. Gharehpetian, Senior Member, IEEE

Abstract—This paper presents a new extendable single-stagemulti-input dc–dc/ac boost converter. The proposed structure com-prises of two bidirectional ports in the converter’s central part tointerface output load and battery storage, and several unidirec-tional input ports to get powers from different input dc sources.In fact, the proposed topology consists of two sets of parallel dc–dc boost converters, which are actively controlled to produce twoindependent output voltage components. Choosing two pure dc ortwo dc-biased sinusoidal values as the converter reference volt-ages, situations of the converter operating in two dc–dc and dc–acmodes are provided, respectively. The proposed converter utilizesminimum number of power switches and is able to step up thelow-level input dc voltages into a high-level output dc or ac voltagewithout needing any output filter. The converter control systemincludes several current regulator loops for input dc sources andtwo voltage regulator loops for generating the desired output volt-age components, resulting in autonomously charging/dischargingthe battery to balance the power flow. Due to the converter inher-ent multi-input multioutput control system, the small signal modelof the converter is extracted and then the pole-placement controlstrategy via integral state feedback is applied for achieving the con-verter control laws. The validity and effectiveness of the proposedconverter and its control performance are verified by simulationand experimental results.

Index Terms—Hybrid systems, multiinput converter, single-stage converter, small-signal modeling, state feedback.

NOMENCLATURE

PO1 , Pi1 , PB 1 Output, input, and battery powers at the con-verter first side.

PO2 , Pi2 , PB 2 Output, input, and battery powers at the con-verter second side.

VO , IO , PO Converter output voltage, current, and power.VB , IB , PB Battery voltage, current, and power.PC 1 , PC 2 Instantaneous powers of the converter

capacitors.VO1 , VO 2 Converter first and second sides output

voltages.

Manuscript received August 5, 2012; revised September 20, 2012, November20, 2012, and March 10, 2013; accepted March 21, 2013. Date of current versionAugust 20, 2013. Recommended for publication by Associate Editor F. L. Luo.

S. Danyali and S. H. Hosseini are with the Faculty of Electrical and Com-puter Engineering, University of Tabriz, Tabriz 51666-16471, Iran (e-mail:[email protected]; [email protected]).

G. B. Gharehpetian is with the Department of Electrical Engineering, Amirk-abir University of Technology, Tehran 15875-4413, Iran (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2013.2256468

Vm , Im Converter output voltage and current peakvalues.

Vi , ILi Input voltage and current at the ith input port.VL , VH Lowest and highest values of the converter in-

put voltages.DL , DH Lowest and highest values of the converter duty

ratios.x, x, X Converter state variables vector, its ac and dc

parts.ΦC , ΦC Controllability matrixes.Kx , Kq State feedback gains matrixes.u, y Input and output vectors of the control system.C1 , C2 Converter output capacitors.ri , Li Resistance and inductance of the ith input port.Vstr Voltage stress of the converter power switches.Vdc DC bias value of the converter output voltages.di Duty ratio of ith boost cell of the converter.RL Load resistance.ω Converter output voltage angular frequency.fs Switching frequency.

I. INTRODUCTION

ENERGY sources like wind turbines and photovoltaic (PV)systems are intermittent and unpredictable; therefore, they

are not highly reliable. In order to address this issue, renew-able resources are either combined with each other or fuel cells(FCs) and energy storage systems (ESSs). Nowadays, the con-cept of multiple-input converters (MICs) has been proposed toaccommodate several renewable energy resources. These con-verters provide simple circuit topologies, centralized control,high reliability, low manufacturing cost, and size. The system-atic approaches of generating and synthesizing MICs have beenintroduced in [1]–[4]. In general, all various MICs are responsi-ble to accept dc voltage sources at their input ports, while fromthe output point of view they can be broken into two categories:dc–dc MICs and dc–ac MICs.

For the first category, in [5]–[7], three multi-input convert-ers have been proposed based on the structure of the dc boostconverter. The three-input dc–dc boost converter proposed bythe authors in [7] benefits from simple unified structure andminimum numbers of power switches. A family of multiportdc–dc converters based on the combination of dc-link voltagesby magnetic coupling of half-bridge boost converters has beenpresented in [8]. In [9] and [10] two hybrid dc–dc systemswere introduced and their control strategies have been plannedbased on decoupling method to separately compensate the cross-coupled control loops. In [11], a systematic approach is proposedfor the derivation of nonisolated three-port converter topologies.

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776 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 2, FEBRUARY 2014

Fig. 1. Proposed converter structure.

A three-port dc–dc converter integrating PV and battery powersfor high step-up applications is proposed in [12].

For the second category, i.e., dc–ac MICs, in [13], an isolateddc–ac bidirectional multi-input converter has been controlledby the input-output feedback linearization method. An isolatedthree-port full-bridge topology has been proposed in [14] forhybrid FC/Battery systems, which aims at feeding a small au-tonomous load. A line-interactive FC power supply has beenintroduced in [15], which can operate in both stand-alone andgrid-connected modes. A grid connected multi-input inverterhas been proposed in [16] to form a hybrid PV/wind powersystem.

Although dc–ac MICs gain several advantages, all of themutilize at least two conversion stages and need an output filterto support ac loads. Accordingly, for all MICs, multiple powerconversion stages may result in increasing the count of devices,system power losses, size, weight, and cost of hybrid systems.

In this regard, single-stage topologies, which integrate per-formance of each stage of multistage power converters, are be-coming more attractive. Although they may cause control com-plexity, they offer higher efficiency and reliability, and lowercost and size. In [17], a single-stage single-input z-source in-verter with coupled inductor, which is able to step-up low-levelinput dc voltages into a high-level output ac voltage, has beenproposed. In [18], two dc sources are embedded in the x-shapeimpedance network of the z-source inverter. This circuit lacksenough degrees of freedom for the control system and does notprovide acceptable current ripple for the input sources. Con-ventional single-stage boost inverter [19] has been utilized bythe authors as a series grid-connected single-stage PV inverterin [20], which also plays the role of grid voltage compensatorfor an ac load. Unfortunately, all single-stage inverters are notmulti-input and therefore not suitable for hybrid systems. As dis-cussed previously, it can be said that for multisource systems,better performances can be accessed providing that a single-stage multiinput converter is utilized. Such a converter becomesmore attractive if it can operate in both dc–dc and dc–ac modes,without any changes in the converter structure.

In this paper, a new extendable single-stage multi-input boostconverter is proposed which can operate in both dc–dc and dc–ac modes. The proposed converter integrates two bidirectionalports for battery storage and output load and several unidirec-

tional ports for different input dc sources. The proposed con-verter is able to directly step up the low-level input dc voltagesinto a high-level output dc/ac voltage and does not need anyoutput filter, while it only uses the minimum number of powerswitches. The load voltage is differentially obtained from theconverter two output voltage components. For dc–dc mode op-eration, these voltages are regulated at two different dc values,while in dc–ac mode they are controlled to be two 180◦ out-of-phase dc-biased sinusoidal voltages. Owing to the multi-inputstructure of the converter, the integral state feedback strategy ofmulti-input multioutput (MIMO) control systems is applied tothe converter small signal model to achieve its control laws. Asa result, several input current regulator loops for the input dcsources and two output voltage control loops are designed forthe proposed converter. Finally, the effectiveness of the proposedconverter and its control performance are studied and verifiedby simulation and experimental results.

In comparison with other multi-input double-stage dc–ac con-verters, the proposed converter applies only one power conver-sion stage and also is able to operate in both dc–dc and dc–acmodes without using any output filter. To be more precise, itutilizes less number of power switches and passive elements.Moreover, compared to a system that utilizes the same num-ber of active and/or passive elements, the proposed system hassuperiority over minimizing voltage ratings and sizes of theelements.

II. PROPOSED CONVERTER AND OPERATION MODES

The structure of the proposed extendable single-stage multi-input dc–dc/ac boost converter is illustrated in Fig. 1. As indi-cated in the figure, in the converter central part, two bidirectionalports are provided to connect the output load and battery stor-age. The output load is connected between two dc-link voltagesVO1 and VO2 , which are unipolar and independently obtainedfrom the voltages across two common output capacitors of sev-eral parallel dc boost converters. The middle boost convertersare current bidirectional and connected to the dc-link of thecommon battery, while the other ones (i.e., i = 3, . . . , n) arecurrent unidirectional and fed from separate input dc sources(i.e., Vi3 , . . . , Vin ). The first aim of using the battery storageis to supply or absorb the power difference between the total

DANYALI et al.: NEW EXTENDABLE SINGLE-STAGE MULTI-INPUT DC–DC/AC BOOST CONVERTER 777

generated dc power by the input dc sources and the load power.In this hybrid system, all kind of rechargeable batteries and alsoultracapacitors are applicable as ESS.

For the proposed system, the single power switch of eachunidirectional boost converter is controlled to regulate the dcpower of its corresponding input source, while in the convertercentral part both upper and lower power switches of the bidirec-tional boost converters are complementary switched to producetheir corresponding output reference voltages. Thus, n differ-ent duty ratios (d1 , . . . , and dn ) are introduced to control theconverter power switches S1 , S

∗1 , S2 , S

∗2 , S3 , . . . , and Sn , re-

spectively. These duty ratios are the converter controlling vari-ables that facilitate current and voltage regulation goals of theproposed system.

For the proposed system, the input dc sources Vi3 , . . . , Vinshould deliver n-2 ripple free dc currents, i.e., IL3 , . . . , ILn ,respectively. Thus, the total generated dc powers at the bothsides of the converter are expressed as follows:

Pi1 =n/2∑

k=2

Vi2 k −1 IL2 k −1 , Pi2 =n/2∑

k=2

Vi2 kIL2 k

. (1)

The proposed converter can work in both dc–dc and dc–acmodes. Following sections will try to demonstrate operationprinciples of the proposed converter in these operation modes.

A. DC–DC Mode

If two different dc values are chosen as the converter outputreference voltages, then a pure dc voltage appears across theoutput load as follows:

Vo1 = V1 , Vo2 = V2 , Vo = V1 − V2 . (2)

For an output resistive load the consumed power can be ex-pressed by the following equations:

Io = (V1 − V2)/RL

Po = VoIo = (V 21 − 2V1V2 + V 2

2 )/RL. (3)

Now, we obtain the converter first- and second-side powersPo1 and Po2 delivered to the load as follows:

Po1 = Vo1 Io = (V 21 − V1V2)/RL

Po2 = −Vo2 Io = −(V1V2 − V 22 )/RL. (4)

As seen in (4), first side of the converter delivers the positivepower amount PO1 , while the negative power amount of PO2is absorbed by the converter second side. These powers areconstant values that only depend on the converter both sidevoltages. By neglecting converter power losses, the battery’sboth sides powers are obtained as follows:

PB1 = Po1 − Pi1 =(V 2

1 − V1V2)RL

−n/2∑

k=2

Vi2 k −1 IL2 k −1

PB2 = Po2 − Pi2 = − (V1V2 − V 22 )

RL−

n/2∑

k=2

Vi2 kIL2 k

. (5)

The summation of PB 1 and PB 2 gives the battery total ex-changed power as follows:

PB = PB1 + PB2 = Po −n∑

k=3

VikILk

. (6)

As (6) shows, the battery source supplies or absorbs the powerdifference between the load power and the total generated inputpower. The battery current IB and its both side inductor currentsIL1 and IL2 are determined as follows:

⎧⎪⎪⎨

⎪⎪⎩

IL1 =PB1

VB=

Po1 − Pi1

VB

IL2 =PB2

VB=

Po2 − Pi2

VB

; IB =Po

VB−

n∑

k=3

VikILk

VB.

(7)

B. DC–AC Mode

If the converter reference voltages are chosen as (8), then theproposed converter will operate in the dc–ac mode as

Vo1 (t) = Vdc +Vm

2Sin ωt

Vo2 (t) = Vdc −Vm

2Sin ωt (8)

where their dc parts are the same as Vdc and the modulation ofeach sinusoidal part is 180◦ out of phase with the other one. Thisconcept results in generating a pure sinusoidal voltage acrossthe load as follows:

Vo(t) = Vo1 (t) − Vo2 (t) = Vm Sin ωt. (9)

Instantaneous current and power of an output resistive loadcan be expressed by the following equations:

Io(t) = Im Sin ωt, Im = Vm /RL

Po(t) = Vo(t)Io(t) = Po + Po =−Vm Im

2Cos 2ωt+

[Vm Im

2

].

(10)

In (10), the average quantity (Vm Im )/2 corresponds to theload average power Po , while the alternative term at the angularfrequency of 2ω denotes the pulsation component of the loadpower. Now, the converter first- and second-sides instantaneouspowers delivered to the load are obtained as follows:

Po1 = Vo1 (t)Io(t) = VdcIm Sin ωt +Vm Im

2Sin2ωt

= VdcIm Sin ωt − Po

2Cos 2ωt +

[Po

2

]

Po2 = −Vo2 (t)Io(t) = −VdcIm Sin ωt − Po

2Cos 2ωt +

[Po

2

].

(11)

As (11) shows, the average powers delivered to the load atthe both sides of the converter are the same and equal to the half


of the load average power for all power operation conditions.Also, the instantaneous powers associated with the convertercapacitors C1 and C2 (XC 1 = 1/C1ω and XC 2 = 1/C2ω) areobtained as follows:

PC1 = Vo1 IC1 =(Vdc +

Vm

2Sin ωt

)C1d

dt

(Vdc +

Vm

2Sin ωt

)

=VdcVm

2XC1

Cos ωt +V 2

m

8XC1

Sin 2ωt

PC2 = Vo2 IC2 = −VdcVm

2XC2

Cos ωt +V 2

m

8XC2

Sin 2ωt. (12)

Neglecting the converter power losses and the stored energyin the converter inductors, the battery’s both side powers areobtained as follows:

PB1 = Po1 + PC1 − Pi1 = VdcIm Sin ωt +VdcVm

2XC1

Cos ωt

− Po

2Cos 2ω +

V 2m

8XC1

Sin 2ωt

+

⎡

⎣ Po

2−

n/2∑

k=2

Vi2 k −1 IL2 k −1

⎤

⎦

PB2 = Po2 + PC2 − Pi2 = −VdcIm Sin ωt − VdcVm

2XC2

Cos ωt

− Po

2Cos 2ωt +

V 2m

8XC2

Sin 2ωt +

⎡

⎣Po

2−

n/2∑

k=2

Vi2 kIL2 k

⎤

⎦.

(13)

Summing PB 1 and PB 2 and assuming XC 1 = XC 2 = XC

gives the total instantaneous battery power as follows:

PB = PB + PB = −PoCos 2ωt +V 2

m

4XCSin 2ωt

+ [Po − Pi1 − Pi2 ] (14)

where PB represents the battery average power, which is equalto the system power difference between the total generated dcpower and the average load power. Besides, the power compo-nent PB is the summation of the pulsation component of the loadpower and the total reactive power associated with the convertercapacitors. Now, neglecting the saved energy in the converterinductors, the battery current and its both side inductors currentsare obtained

IL1 =PB1

VB=

VdcIm

VBSin ωt +

VdcVm

2VB XCCos ωt

− Po

2VBCos 2ωt +

V 2m

8VB XCSin 2ωt +

[Po − 2Pi1

2VB

]

IL2 =PB2

VB= −VdcIm

VBSin ωt − VdcVm

2VB XCCos ωt

− Po

2VBCos 2ωt+

V 2m

8VB XCSin 2ωt+

[Po − 2Pi2

2VB

](15)

IB =PB

VB= − Po

VBCos 2ωt +

V 2m

4VB XCSin 2ωt

+[Po − Pi1 − Pi2

VB

](16)

As seen in (15), two currents IL1 and IL2 contain two similaralternative terms with the angular frequencies of ω and 2ω andtwo different dc terms that depend on the total generated powerby their corresponding input dc sources. Moreover, the batterycurrent in (16) is a dc-biased sinusoidal waveform at the angularfrequency of 2ω, which guarantees supplying the expected dcand ac power components of the battery.

III. DYNAMIC MODELING OF THE PROPOSED CONVERTER

As depicted in Fig. 1, the proposed converter includes n + 2passive elements, i.e., C1 , C2 , L1 , L2 , . . . , Ln , introducing n + 2different state variables VO1 , VO2 , IL1 , IL2 , . . . , and ILn . Goalsof the converter control system are defined to produce the de-sired output voltage components and regulate currents of the in-put dc sources. Thus, n state variables VO1 , VO2 , IL3 , IL4 , . . . ,and ILn need to be directly controlled, while two other statevariables related to the battery source (IL1 and IL2) are notdirectly controllable and automatically adjusted considering theconverter power operating point. Besides, the proposed con-verter provides n independent duty ratios i.e., d1 , . . . , dn , toregulate the mentioned controllable state variables through ndifferent control loops. For this purpose, small signal model ofthe converter should be extracted first. The small signal model isusually obtained from the converter state space averaged model,which is presented as follows:

C1dVo1

dt=

n/2∑

k=1

(1 − d2k−1)IL2 k −1 −(Vo1 − Vo2 )

RL

C2dVo2

dt=

n/2∑

k=1

(1 − d2k )IL2 k− (Vo2 − Vo1 )

RL

L1dIL1

dt= d1VB + (1 − d1)(VB − Vo1 ) − r1 IL1

L2dIL2

dt= d2VB + (1 − d2)(VB − Vo2 ) − r2 IL2

L3dIL3

dt= d3Vi3 + (1 − d3)(Vi3 − Vo1 ) − r3 IL3 .

...

LndILn

dt= dnVin + (1 − dn )(Vin − Vo2 ) − r

nILn

(17)

The design procedure to obtain the converter small signalmodel from (17) can be found in [21]. Based on this method,the state variables and the duty ratios contain two components:dc values (X, D) and perturbations (x, d). Substituting sum-mation of these components for x, and d variables in (17),results in achieving the small signal model of the proposed con-verter, which is still nonlinear. Its nonlinearity aspect is due tothe fact that it contains the second-order terms of perturbations


variables (x · d). However, for power electronic converters, itis also assumed that the perturbations components are smalland do not significantly vary during one switching period (i.e.,x � X, d � D). Therefore, by neglecting the second-orderterms, an approximated linear small signal model of the con-verter is obtained as (18) that can demonstrate the converterdynamic behavior and stability and facilitates proper design ofits controllers

C1dvo1

dt=

n/2∑

k=1

(1 − D2k−1 )iL2 k −1 −n/2∑

k=1

d2k−1 IL2 k −1

− (vo1 − vo2 )RL

C2dvo2

dt=

n/2∑

k=1

(1 − D2k )iL2 k−

n/2∑

k=1

d2k IL2 k− (vo2 − vo1 )

RL

L1diL1

dt= (D1 − 1)vo1 + d1 Vo1 − r1 iL1

L2diL2

dt= (D2 − 1)vo2 + d2 Vo2 − r2 iL2

L3diL3

dt= (D3 − 1)vo1 + d3 Vo1 − r3 iL3 .

...

LndiLn

dt= (Dn − 1)vo2 + dn Vo2 − r

niLn

(18)

This linear model can be represented by the state-space matrixform as follows:

˙x(t) = Ax(t) + Bu(t)

y(t) = Cx(t) + Du(t) (19)

A =⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

−1RLC1

1RLC1

1 − D1

C10

1 − D3

C1· · · 0

1RLC2

−1RLC2

01 − D2

C20

1 − Dn

C2

D1 − 1L1

0−r1

L10 0 0

0D2 − 1

L20

−r2

L20 0

D3 − 1L3

0 0 0−r3

L30

.... . .

0Dn − 1

Ln0 0 0

−rn

Ln

⎤

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(20)

B =

⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

−IL1

C10

−IL3

C1· · · 0

0−IL2

C20

−ILn

C2

Vo1

L10 0 0

0Vo2

L20 0

0 0Vo1

L30

.... . .

0 0 0 · · · Vo2

Ln

⎤

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

x =

⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

vo1

vo2

iL1

iL2

iL3

...

iLn

⎤

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

, u =

⎡

⎢⎢⎢⎢⎢⎢⎢⎣

d1

d2

d3...

dn

⎤

⎥⎥⎥⎥⎥⎥⎥⎦

(21)

where x, u, and y are state variables vector, control variablesvector, and system outputs vector, respectively. A is the statematrix, B is the input matrix, C is the output matrix, and D is thefeed-forward matrix. The converter control system is aimed toregulate the state variables Vo1 , Vo2 , IL3 , IL4 , . . . , ILn

throughtheir corresponding controlling variables d1 , d2 , d3 , d4 , . . . , dn ,respectively, so C and D matrixes are defined as follows:

y =

⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

Vo1

Vo2

IL3

IL4

...

ILn

⎤

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

, C =

⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

1 0 0 0 0 0 · · · 0

0 1 0 0 0 0 0

0 0 0 0 1 0 0

0 0 0 0 0 1 0...

. . .

0 0 0 0 0 0 0 1

⎤

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

, D = 0.

(22)

IV. POLE-PLACEMENT CONTROL APPROACH

As mentioned, the proposed converter control system includesn control loops, i.e., two output voltage control loops and n–2input dc current regulator loops. The converter small signalmodel (20)–(22) introduces a linear MIMO control system,which has several interacting control loops. Designing classicalcontrol compensators, i.e., PI and PID, for this system needsto find n decoupled SISO transfer functions of the system. Ob-taining these decoupled transfer functions becomes more com-plex when the system order goes more than three. So designingthe converter closed-loop controllers should be directly accom-plished by MIMO systems control methods. A useful MIMOcontrol method is pole-placement approach via integral state


feedback [22]. This method directly deals with the state vari-ables to design control compensators. As a result, it is prop-erly applicable to power switching converters, where all statevariables are accessible. It can be shown that if the consideredsystem is completely state controllable, then poles of the closed-loop system can be placed at any desired locations by means ofan appropriate state feedback gain matrix. The most frequentlyused approach to choose locations of desired closed-loop polesis based on experience in the root-locus design, placing a dom-inant pair of closed-loop poles and choosing other poles at itsleft side enough far from the jω-axis. Considering the (20) and(21), the system controllability matrix is expressed as follows:

ΦC = [B... AB

... A2B... · · ·

... An+1B]. (23)

For the proposed system, if the rank of the controllabilitymatrix is complete (rank(ΦC ) = n + 2), then the system becomescompletely state controllable. Now, n additional integral statesare defined as follows:

q1(t) = r1(t) − y1(t) = r1(t) − vo1 (t)

q2(t) = r2(t) − y2(t) = r2(t) − vo2 (t)

q3(t) = r3(t) − y3(t) = r3(t) − iL3 (t)

...

qn (t) = rn (t) − yn (t) = rn (t) − iLn(t). (24)

The state and output equations of the system, considering thenew integral states, are rewritten as follows:

⎡

⎣˙x(t)· · ·q(t)

⎤

⎦ =

⎡

⎢⎢⎣A

... 0

· · ·... · · ·

−C... 0

⎤

⎥⎥⎦ x(t) +

⎡

⎣B· · ·0

⎤

⎦ u(t) +

⎡

⎣0· · ·I

⎤

⎦ r(t)

y(t) =[

C... 0

]⎡

⎣x(t)· · ·q(t)

⎤

⎦ (25)

where r(t) is the input reference vector of the control system asfollows:

r(t) = [Vo1 ref Vo2 ref IL3 r e f · · · ILn r e f ]T . (26)

The system (25) should be also completely controllable.Hence, by defining A and B

A =

⎡

⎢⎢⎣A

... 0

· · ·... · · ·

−C... 0

⎤

⎥⎥⎦ , B =

⎡

⎣B· · ·0

⎤

⎦ . (27)

The controllability matrix of (25) ΦC can be written by thefollowing matrix:

ΦC = [B... AB

... A2 B... · · ·

... An B... An +1 B] =⎡

⎢⎢⎣B

... AB... A2B

... · · ·... An B

... An +1B· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·0

... − C... − CAB

... · · ·... − CAn−1B

... − CAn B

⎤

⎥⎥⎦

(28)

and then ΦC can be arranged as follows:

ΦC =

⎡

⎢⎢⎣B

... AΦC

· · ·... · · ·

0... −CΦC

⎤

⎥⎥⎦

=

⎡

⎢⎣B

... A· · · · · · · · ·0

... −C

⎤

⎥⎦

︸︷︷︸M

⎡

⎢⎢⎣I

... 0

· · ·... · · ·

0... ΦC

⎤

⎥⎥⎦ . (29)

Considering that the rank of ΦC is complete, the system (25)is completely state controllable if and only if rank (M) = 2n +2. This fact guaranties that there is a matrix K, which satisfiesthe pole-placement problem. Considering the following statefeedback control:

u(t) = [Kx

... Kq]

︸︷︷︸K

⎡

⎣x(t)· · ·q(t)

⎤

⎦ (30)

where, Kx and Kq are:

Kx =

⎡

⎢⎢⎢⎢⎣

K11 K12 · · · K1(n+2)

K21 K22 · · · K2(n+2)...

......

...

Kn1 Kn2 · · · Kn(n+2)

⎤

⎥⎥⎥⎥⎦

Kq =

⎡

⎢⎢⎢⎢⎣

K ′11 K ′

12 · · · K ′1n

K ′21 K ′

22 · · · K ′24

......

......

K ′n1 K ′

n2 · · · K ′nn

⎤

⎥⎥⎥⎥⎦. (31)

By substituting (30) in (25), we attain the whole system state-space control model as follows:

⎡

⎣˙x(t)· · ·q(t)

⎤

⎦ =

⎡

⎢⎢⎣

A + BKx

... BKq

· · ·... · · ·

−C... 0

⎤

⎥⎥⎦ x(t) +

⎡

⎣0· · ·I

⎤

⎦ r(t)

˙x(t) = Ax(t) + Br(t) (32)

Now, the problem is to find the controlling signal u(t) via statefeedback gain matrix K, so that the closed-loop system eigenval-ues are placed at the desired locations. There are several methodsto determine the system controller matrix K = [Kx Kq ]. Thecontrol systems toolbox of the MATLAB software provides auseful pole-placement function [23], which inputs the system(25) and the desired eigenvalues locations to find the state feed-back gain matrixes.

V. CONVERTER DESIGN

The five-input structure of the proposed converter is shownin Fig. 2. As is seen in the figure, eight passive elements C1 , C2 ,L1 , L2 , . . . , L5 , and L6 exist in the converter structure (n = 6).All these passive elements values can be determined in such a


Fig. 2. Five-input structure of the proposed converter.

way that the desired current and voltage ripples are satisfied forthe converter. It can be easily shown that in order to have themaximum current and voltage ripples of ΔImax and ΔVmax forthe system inductors and capacitors, respectively, they shouldbe chosen bigger than the following minimum values:

Li min =DmaxVi

ΔImaxfs, Cmin =

DmaxVm

RLΔVmaxfs(33)

where Dmax is the converter predefined maximum duty ratio(comes from the converter stability consideration), fs is theconverter switching frequency, Vi is the input dc voltage con-nected to the ith inductor, RL is the load resistance, and Vm isthe peak value of the load sinusoidal voltage. Hence, for the in-put and output voltage ranges in the simulation section, Dmax =0.8, fs = 30 kHz, ΔImax = 1 A for L3 to L6 , ΔImax = 7 Afor L1 and L2 and ΔVmax = 10 V for C1 and C2 the fol-lowing minimum values are obtained for the converter passiveelements:

L1 min = L2 min = 0.35 mH, L3 min ...L6 min = 2.5 mH

Cmin = 30μF. (34)

As is mentioned in the dc–ac operation mode, the proposedconverter power switches experience the voltage stress of Vstr =Vdc+Vm /2. This voltage stress can be possibly minimized if thevoltage Vdc is minimized. Therefore, assuming that all inputdc voltages and the converter duty ratios take values in thefollowing ranges:

VL ≤ Vi ≤ VH

DL ≤ di ≤ DH , DL,DH ∈ [0, 1). (35)

It can be shown that, if the lowest and highest duty ratiosare set at zero and the predefined value Dmax , respectively,the voltages Vdc and Vstr are minimized, while a minimumacceptable value VL min is dictated to input dc voltages as

Vdc |min = VH + Vm /2

Vstr |min = VH + Vm

VL |min = (1 − Dmax)(VH + Vm ). (36)

For example, if the minimum and maximum values of theconverter duty ratios are designed to be DL = 0, Dmax = 0.8and with VH = 100 V, and Vm = 280 V, using (36) gives thefollowing voltage design considerations for the system:

Vdc |min = 240 V; Vstr |min = 380 V; VL |min = 76 V.(37)

TABLE ISIMULATION PARAMETERS

For the five-input converter in Fig. 2, with the circuit param-eters listed in Table I and using (20)–(22), small signal modelmatrixes are obtained first. Afterward, the rank of controllabil-ity matrix ΦC is ensured to be n + 2 = 8 and then the rank ofmatrix M is obtained 2n + 2 = 14. Fourteen eigenvalues of thestate matrix A are obtained as follows:

λ = 0, 0, 0, 0, 0, 0

− 1545 ± 2948j, −126 ± 3216j

− 68, −71, −35,−35.

As seen, there are six dominant eigenvalues at origin (S = 0),which are resulted from the additional integral states (q1 , . . . ,q6). Now, in order to assure the converter to operate in the stableregion, all the converter eigenvalues are left shifted on σ axisto achieve the desired locations for the converter closed-loopeigenvalues (i.e., λi = λi − 4000; i = 1, . . . , 14)

λ = −4000, −4000, −4000, −4000, −4000, −4000

− 5545 ± 2948j, −4126 ± 3216j

− 4068, −4071, −4035, −4035.

Then Kx and Kq matrixes, which satisfy this pole-placementperformance, are obtained as follows:

Kx =⎡

⎢⎢⎢⎢⎢⎣

−8.8 −2.3 −19 −0.4 −38.2 −5.2 −50 −4.2−1.9 −8.7 −0.7 −19 −1.71 −54 −1.3 −43−5.7 −0.9 −9.7 3.21 −129 8.9 −41 7.286.3 17.1 3.20 20.4 11.6 −47 15.3 77.823.6 5.82 33.0 −2.2 105 −5.7 3.69 4.813.22 3.81 3.00 4.82 11.1 16.6 15.2 99.1

⎤

⎥⎥⎥⎥⎥⎦

× 10−3

Kq =

⎡

⎢⎢⎢⎢⎢⎣

27.3 −1.1 34.9 15.9 53.3 12.8−2.8 27.1 0.56 60.7 −2.4 44.6520.7 0.06 735 0.47 63.7 0.65−7.8 −40.1 −20.2 545 −28.4 −121−57.9 −2.54 −147 −1.96 644 −1.3−6.29 −3.05 −19.3 −11.5 −29.5 488

⎤

⎥⎥⎥⎥⎥⎦

Fig. 3 shows six integral state feedback loops for the proposedconverter. This system has poles which have been assigned bythe matrix Kx and Kq at the desired places and tracks the inputreferences VO1ref , VO2ref and IL3ref , . . . , IL6ref . As is clear thedesigned control system is type one and it can be shown thatin dc-ac mode there will be a very small phase delay (about3–5 degrees) between the generated output sinusoidal voltage


Fig. 3. Proposed converter integral state feedback control loops: Voltage regulator loops of (a) first capacitor and (b) second capacitor and current regulator loopsof (c) input source Vi3 , (d) input source Vi4 , (e) Input source Vi5 , and (f) Input source Vi6 .

and its reference signal which can be fully compensated withconsidering an initial phase shift for the reference voltage signal.

VI. CONVERTER STABILITY AND SENSITIVITY STUDY

In the dc–ac mode, operating point of the proposed con-verter and consequently its small-signal model change due toperiodically variations of the converter output voltages in therange of [Vdc − Vm /2 Vdc + Vm /2]. Hence, the converter eigen-values may move from the desired locations to other placeson the S page. For this reason, the converter stability shouldbe ensured throughout all the output voltages range. In this re-spect, after determining the system state feedback matrixes Kx

and Kq , several different possible operating points are definedfor the converter output voltages. Afterward for each operatingpoint, converter small signal model and its eigenvalues are ob-tained from matrix A. For each case, the nearest real part ofthe ejgenvalues to the jω-axis shows the converter stability mar-gin (SM) in the operating point. Depicting all stability marginsof the defined operating points in a same graph introduces theconverter SM curve, which helps to study the converter controlsystem stability. This procedure has been made for fifteen differ-ent operating points, evenly distributed throughout the converteroutput voltages in a typical range of [100 V 380 V]. The resultedSM curve (dR = dL = dC = 0%) has been shown in Fig. 4. Asseen in the figure, we have also considered sensitivity of theobtained SM curve to the variations of the converter circuitparameters. In this regard, the converter SM curve has been de-picted in the presence of the maximum parameters variationsof ±50% for the all converter resistances, inductances, and ca-pacitances values. From the curve of dR = dL = dC = 0%,since OP8 is the operating point that the converter control sys-tem has been designed for, the converter SM becomes exactly4000, which is equal to the left shift level between the converterlocated desired eigenvalues and the primary eigenvalues. It canbe also seen that for every SM curve, the worst operating point

Fig. 4. SM curves for the five-input structure of the proposed converter.

Fig. 5. SM curves for a nine-input structure of the proposed converter.

of the converter occurs at the operating points of OP1 or OP15 ,which correspond to the moments that one of the converter out-put voltages VO1 or VO2 is set at its maximum value (Vdc +Vm /2). Moreover, considering ±50% variations in the converterresistances values does not have significant impacts on the con-verter SM curve. However, when the converter inductances andcapacitances values are considered to have −50% variations,the converter SM curve has obviously changed. As clear fromthe figure, the higher values of the system inductances and ca-pacitances result in moving the system eigenvalues towards thejω axis and hence achieving less SM values, so that the worst


SM curve is obtained for dL = +50%, which denotes that thedominant eigenvalues are generally correspond to the systeminductors.

Besides, the worst operating point on this curve shows alsothe minimum SM about 1000, which guarantees successfullyoperation of the converter control system even in the presenceof +50% variations in the converter inductances values. Such asecure SM is indebted from the fact that the converter primaryeigenvalues have been enough left shifted on σ axis to achievethe desired eigenvalues.

Furthermore, when the converter circuit in Fig. 2 is extendedto support two more input dc ports at each side, a nine-inputstructure of the proposed converter is constructed (n = 10). Byconsidering similar ranges for the converter circuit parameters,the converter SM curves in the presence of ±50% parametersvariations is obtained as shown in Fig. 5. This figure gives aminimum SM about 1000 in the worst operating point and evenin the presence of dL = +50%. As a result, when the proposedconverter is designed with more number of input sources andalso similar ranges for the circuit parameters, its control systemcan still work successfully and gain a secure SM for the worstoperating points of the converter.

For the worst operating points, each boost cell of the pro-posed converter takes its highest duty ratio to adapt its inputvoltage to the corresponding output voltage. So, it is reasonableto predefine a maximum value of Dmax for all the converterduty ratios, with the purpose of stability consideration to use inthe converter designing stage.

VII. SIMULATION RESULTS

In this section, the introduced converter in Fig. 2 is simu-lated by PSCAD/EMTDC software to show its operation per-formances in both dc–dc and dc–ac modes. The simulation pa-rameters for the converter circuit are listed in Table I. In addition,a changeable resistive load is connected to the output port. Insimulations, using the obtained input/output voltages in (37)and considering the voltage drops across passive and active ele-ments, the voltages of input dc sources, battery storage, and themaximum and dc-bias values of the converter output voltage areset at following values:

Vi3 = 80V, Vi4 = 95V, Vi5 = 90V, Vi6 = 85V

VB = 96V, Vm = 280V, Vdc = 240V.

A. DC–DC Mode

In this mode, the load voltage is desired to be VO = 200 V.And for this matter, the converter output voltages VO1 and VO2are regulated at the reference dc voltages of VO1ref = 340 Vand VO2ref = 140 V, respectively. The reference currents of theinput dc sources are considered to be variable, which will resultin providing three different periods of simulation. These test-ing periods are obviously seen in the Figs. 6–8. Fig. 6 depictsboth output generated voltages alongside the load voltage, wellproduced at 340 V, 140 V, and 200 V, respectively. The drawncurrents from the input dc sources are illustrated in Fig. 7, whichare well regulated at their reference values with the current rip-

Fig. 6. Converter output voltages in the dc–dc mode.

Fig. 7. Drawn currents from the input dc sources in the dc–dc mode.

Fig. 8. IB , IL 1 , and IL 2 in the dc–dc mode.

ple less than 5%. In Fig. 8, the battery current IB alongside theinductors currents IL1 and IL2 are depicted. As is clear from thefigure, IL1 and IL2 take positive and negative values, respec-tively, denoting the delivering and absorbing two powers PO1and PO2 at the both side of the converter. The theoretical aver-age value of the battery current is IB .ave = (Po–Pi1–Pi2)/VB

and due to supplying the converter power losses, it will be setat a value a little more than the theoretical value.

In the first period (0 < t < 0.2 s), the load resistance absorbsa power about PO = 2.5 kW (RL = 16 Ω) and the currents ofthe input sources are set at the following reference values:

IL3ref = 0A, IL4ref = 14A, IL5ref = 8Aand IL6ref = 0A.

In this condition, the proposed converter works only withtwo input sources that generate the total input power of Pi =2.05 kW, which is less than the load power. So, the battery isautonomously discharged with the power deficiency of 0.45 kWin addition to the converter power losses, which leads to set thebattery average current at IB .ave = 7 A.

For the second period (0.2 < t < 0.4 s), the reference currentsIL3ref and IL6ref are increased to 12 A and 5 A, respectively,


Fig. 9. Converter output voltages and current in the dc–ac mode for (a) first and second periods and (b) second and third periods.

while the load power and the other reference currents IL4ref andIL5ref still persist at their previous values. This condition resultsin working the proposed converter with the all four input voltagesources, simultaneously. In this state, the total generated inputpower of Pi = 3.43 kW is more than the load power (PO =2.5 kW). Hence, the average value of the battery current is setabout −7 A to absorb the generated extra power of 0.93 kWminus the converter power losses.

Finally, in the last simulation period (0.4 < t < 0.6s), the loadpower is decreased to PO = 1.5 kW (RL = 27 Ω) at the sametime with decreasing the reference currents IL4ref and IL5ref tothe values of 2 A and 0 A, respectively. Thus, the total inputpower of Pi = 1.58 kW is extracted from the only three of inputsources. In this case as seen in Fig. 8, the battery average currentis about zero, showing equality of the converter power lossesand extra generated input power.

B. DC–AC Mode

In this mode, the output voltage of the converter is desired tobe a 50 Hz sinusoidal waveform with an rms-value equals to theload voltage in the dc–dc mode Vrms = 200 V (Vm = 280 V).Thus, the parameters of the two output dc-biased sinusoidalvoltages VO1 and VO2 are chosen to be Vm /2 = 140 V and Vdc =240 V. With the intention of achieving similar results, the loadpower, the input dc sources Vi3 to Vi6 and their reference currentsvalues are chosen to be as the same as those in the dc–dc mode.Therefore, three similar periods are provided for the system.Fig. 9(a) and (b) depict the both dc-biased sinusoidal voltagesbeside the load voltage and current, before and after applyingthe system step changes at the moment of 0.2 s and 0.4 s,respectively. As is clear the load voltage is perfectly generatedsinusoidal (THD < 3%) and does not experience any voltagequality problems, i.e., voltage sags/swells, coming from the factthat the battery is immediately charged/discharged to supportinput sources in online producing the desired output voltages.

The drawn currents from the input dc sources IL3 to IL6 areillustrated in Fig. 10, respectively. As seen in the figure, thesecurrents are well regulated at their reference values and also withacceptable ripple components. The battery current IB and itsboth side inductors currents IL1 and IL2 are shown in Figs. 11and 12, before and after applying the system step changes atthe moment of 0.2 s and 0.4 s, respectively. As is clear fromFig. 11(a) and (b), the battery current is a dc-biased sinusoidal

Fig. 10. Drawn currents from the input dc sources in the dc–ac mode.

waveform at the angular frequency of 2ω and with differentaverage values of 7 A, −7 A and 0 A for the three respectivebattery utilization modes of discharge, charge and stand-by (zeroexchange power). Moreover for the last simulation period, dueto changing the load power, amplitude of the battery currenthas also simultaneously decreased regarding to decreasing theload power. Besides, as obviously seen in the Fig. 12(a) and(b), the currents IL1 and IL2 have similar current waveformsand take different dc levels due to receiving different powersfrom their corresponding input dc sources. In Fig. 13(a), (b),and (c), all the converter duty ratios have been illustrated for thesecond simulation period that they instantaneously vary to tracethe control system reference values.

As shown for both dc–dc and dc–ac modes, the converter de-signed closed-loop control system is highly stable and does notexperience any tough transient response for the shown operatingpoints and against the applied step changes in the load and inputdc powers.

The power switches of the unidirectional boost cells at theboth sides of the converter require current ratings as the sameas those for the conventional dc boost converters. On the otherhand, the power switches in the converter central part conductthe inductor currents IL1 and IL2 , which contain peak valuesabout 3–4 times bigger than their average values for few mil-liseconds. Although all existing power switches in market caneasily tolerate pulsed currents about 4–5 times bigger than theircurrent ratings for few milliseconds, it may cause increase con-duction losses for the power switches and consequently decreasethe converter power efficiency. Therefore, a tradeoff betweenchoosing the current ratings and decreasing conduction lossesof these power switches should be made.


Fig. 11. Battery current in the dc–ac mode for (a) first and second periods and (b) second and third periods.

Fig. 12. IL 1 and IL 2 in the dc–ac mode for (a) first and second periods and (b) second and third periods.

Fig. 13. Proposed converter duty ratios in dc–ac mode (a) d1 and d2 , (b) d3 and d4 , and (c) d5 and d6 .

Fig. 14. Prototype converter.

VIII. EXPERIMENTAL RESULTS

In order to verify the proposed converter performance, a lowpower three-input prototype converter was built as shown inFigs. 14 and 15. The circuit parameters are written on Fig. 15.The proposed control scheme is implemented by the Texas In-strument TMS320F2812 DSP. Two different dc voltage sourcesof Vi3 = 40 V and Vi4 = 50 V, with the maximum deliver-able currents of 5 A, are utilized as the converter input sources.Moreover, a 48 V battery consisting of four-series 12 V lead-acidbatteries is employed in this prototype as the ESS. In order tovalidate practical performances of the proposed converter, three

Fig. 15. Three-input converter studied in the experimental section.

different conditions are scheduled for the system by changingthe reference currents of the input sources and the load resis-tance. All the experimental figures have been captured with thescale of 0.1.

A. DC–DC Mode

For dc–dc mode, the output dc voltage of the converter isdesired to be Vo = 100 V. Thus, two dc reference voltages ofVO1ref = 170 V and VO2ref = 70 V are chosen for the converter.The converter output voltages are illustrated in Fig. 16, well


Fig. 16. Converter output voltages in the dc–dc mode (50 V/div).

Fig. 17. Drawn currents from the input sources in the dc–dc mode (1 A/div).

Fig. 18. IB , IL 1 , and IL 2 in the dc–dc mode (2 A/div).

regulated at their reference values and also Fig. 17 shows bothdrawn currents from input sources Vi3 and Vi4 (IL3 and IL4),showing very low current ripples. The currents IL1 and IL2 andthe battery current IB are also depicted in Fig. 18.

In the first operation condition, the load power is about PO =200 W (RL = 50 Ω) and the reference currents of the input dcsources are chosen to be IL3ref = 4.25 A and IL 4ref = 1 A.With these reference values, the total generated input powerbecomes 220 W. As is seen in Fig. 18, the average value ofthe battery current is about zero, which means that the totalgenerated input power has completely supplied the load and itsextra power (20 W) is approximately adequate to supply the

Fig. 19. Converter output voltages in the dc–ac mode (50 V/div).

converter power losses. In this condition the proposed converterefficiency is about 91%.

For the second operation condition, the reference currentIL3ref is suddenly decreased to 1 A, while the load power andthe reference current IL4ref do not change and still remain attheir previous. These reference values generate the total inputpower of 130 W. This amount of power cannot completely sup-ply the load and therefore, the battery source is autonomouslydischarged to balance the converter power flow. So, as seen inthe Fig. 18, the average current of the battery has been set about1.7 A, which draws 82 W power from the battery to supply thesystem power deficiency of 70 W and the converter power lossesof 12 W. This condition achieves 94% power efficiency for theproposed converter.

At the end, in the third experimental period the load power issuddenly decreased to PO = 100 W (RL = 100 Ω) and the refer-ence current IL4ref increases to 3 A, while the reference currentIL3ref persists at its previous value of 2 A. With these referencevalues, the total generated power by the input sources is about230 W. This amount of power can completely supply the load,and its extra power (130 W) will supply the converter powerlosses and charge the battery. Therefore, as seen in Fig. 18, theaverage value of the battery current has been set about –2.2 A,which shows 106 W charging power to the battery and 24 Wpower losses of the converter. In this condition, the converterpower efficiency is about 90%.

B. DC–AC Mode

In this mode, the output voltage of the converter is desiredto be a 50 Hz sinusoidal waveform with an rms-value equalsto the load voltage in the dc–dc mode Vrms = 100 V (Vm =140 V). Thus, the parameters of the two output dc-biased si-nusoidal voltages VO1 and VO2 are chosen to be Vm /2 = 70 Vand Vdc = 120 V. Also, with the intention of achieving similarresults, the load power, the input dc sources Vi3 and Vi4 , andtheir reference currents values IL3ref and IL4ref are chosen tobe exactly similar to those in the previous dc–dc experimenta-tion. Therefore, three similar experimental periods are providedto the system to show the proposed converter performance inthe dc–ac mode. Both generated dc-biased sinusoidal voltagesalongside the load voltage are shown in Fig. 19. As seen in the


Fig. 20. Drawn currents from the input sources in dc–ac mode (1 A/div).

Fig. 21. IB , IL 1 , and IL 2 for first and second periods (5 A/div).

Fig. 22. IB , IL 1 , and IL 2 for second and third periods (5 A/div).

figure, the desired output voltage has been produced in a high-quality sinusoidal wave shape, without using output filter. Also,Fig. 20 shows both drawn currents from the input dc sourcesVi3 and Vi4 , well regulated at their reference values. The bat-tery current IB and its both side inductors currents IL1 and IL2are also depicted in Figs. 21 and 22, before and after applyingsystem step changes. As seen in the figures, the battery currentoscillates with the angular frequency of 2ω and takes differentaverage values about 0 A, 1.7 A, and –2.2 A, respectively. Forthe third experimental period, amplitude of the battery currenthas obviously diminished due to decreasing the load power.Moreover, the inductors currents IL1 and IL2 have similar cur-rent waveforms for all three simulation periods, while they take

different dc levels due to receiving different powers from theircorresponding input sources.

The proposed converter gains the average efficiencies about91.6% and 92.3% in dc–dc and dc–ac modes, respectively, thatare satisfactory in comparison to the obtained efficiencies of81%, 95%, and 80% in [7], [11] and [12], respectively, dealingwith dc–dc MICs and the obtained efficiency of 83.4% in [17]as a single-stage dc–ac inverter.

IX. CONCLUSION

A new single-stage multi-input boost converter which canwork in both dc–dc and dc–ac modes has been introduced inthis paper. The proposed converter is extendable to accept morenumber of input dc sources, which utilizes minimum numberof power switches and small passive elements and does notneed any output filter. In the central part of the converter struc-ture battery storage is autonomously charged or discharged tobalance the power flow. Two output voltages and several inputdc currents control loops have been designed for the proposedconverter via integral state feedback control method. The statefeedback gain matrixes (Kx and Kq ) are so determined that theconverter closed-loop eigenvalues are placed far from jω-axis,make the system highly stable and achieve desired dynamicbehavior and acceptable transient response. Simulation resultsshow all the converter capabilities such as low-current ripplesfor input dc sources, autonomous battery charging/discharging,and producing high-quality dc or ac output voltages. A proto-type has been also built, which its experimental results verifytheoretical and simulation studies.

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Saeed Danyali was born in Abdanan, Ilam, Iran, in1983. He received the B.Sc. degree in electronic en-gineering from the University of Yazd, Yazd, Iran, in2005 and the M.Sc. degree in electrical power engi-neering from the University of Tabriz, Tabriz, Iran, in2008. He is currently working toward the Ph.D. de-gree in electrical power engineering from the Facultyof Electrical and Computer Engineering, Universityof Tabriz, Tabriz, Iran.

His research interests include renewable energysystems, power electronic converters, and brushless

dc motor drives and generators. Mr. Danyali currently focuses on single stagemultiinput dc–dc and dc–ac converters.

Seyed Hossein Hosseini (M’93) was born in Marand,Iran, in 1953. He received the M.S. degree from theFaculty of Engineering, University of Tabriz, Tabriz,Iran, in 1976, the DEA and Ph.D. degrees from INPL,France, in 1978 and 1981, respectively, all in electri-cal engineering.

In 1982, he joined the University of Tabriz, Iran,as an Assistant Professor in the Department of Elec-tric Engineering, where he was an Associate Pro-fessor from 1990 to 1995, and has been a Profes-sor since 1995. From September 1990 to September

1991, he was a Visiting Professor in the University of Queensland, Australia.From September 1996 to September 1997, he was a Visiting Professor in theUniversity of Western Ontario, Canada. His research interests include powerelectronic converters, matrix converters, active and hybrid filters, application ofpower electronics in renewable energy systems and electrified railway systems,reactive power control, harmonics, and power quality compensation systemssuch as SVC, UPQC, FACTS devices.

Gevorg B. Gharehpetian (M’00–SM’08) receivedthe B.S., M.S., and Ph.D. degrees in electrical engi-neering in 1987, 1989, and 1996, from Tabriz Uni-versity, Tabriz, Iran, Amirkabir University of Tech-nology (AUT), Tehran, Iran, and Tehran University,Tehran, Iran, respectively, graduating all with FirstClass Honors. As a Ph.D. student, he has receivedscholarship from DAAD (German Academic Ex-change Service) from 1993 to 1996 and he was withHigh Voltage Institute of RWTH Aachen, Aachen,Germany.

He has been holding the Assistant Professor position at AUT from 1997to 2003, the position of Associate Professor from 2004 to 2007 and has beenProfessor since 2007. He was selected by the ministry of higher education asthe distinguished professor of Iran and by IAEEE (Iranian Association of Elec-trical and Electronics Engineers) as the distinguished researcher of Iran and wasawarded the National Prize in 2008 and 2010, respectively. He is the author ofmore than 600 journal and conference papers. His teaching and research interestinclude power system and transformers transients and power electronics appli-cations in power systems.

Prof. Gharehpetian is a Distinguished member of the IAEEE, and a Memberof the Central Board of IAEEE.

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