Single-Phase Single-Stage Transformer less Grid-Connected PV System

2664 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 6, JUNE 2013

Single-Phase Single-Stage Transformer lessGrid-Connected PV System

Bader N. Alajmi, Khaled H. Ahmed, Senior Member, IEEE, Grain Philip Adam, and Barry W. Williams

Abstract—In this paper, a single-phase, single-stage currentsource inverter-based photovoltaic system for grid connection isproposed. The system utilizes transformer-less single-stage con-version for tracking the maximum power point and interfacingthe photovoltaic array to the grid. The maximum power point ismaintained with a fuzzy logic controller. A proportional-resonantcontroller is used to control the current injected into the grid. Toimprove the power quality and system efficiency, a double-tunedparallel resonant circuit is proposed to attenuate the second- andfourth- order harmonics at the inverter dc side. A modified carrier-based modulation technique for the current source inverter is pro-posed to magnetize the dc-link inductor by shorting one of thebridge converter legs after every active switching cycle. Simulationand practical results validate and confirm the dynamic perfor-mance and power quality of the proposed system.

Index Terms—Current source inverter (CSI), grid-connected,maximum power point tracking (MPPT), photovoltaic (PV).

I. INTRODUCTION

DUE to the energy crisis and environmental issues, renew-able energy sources have attracted the attention of re-

searchers and investors. Among the available renewable energysources, the photovoltaic (PV) system is considered to be a mostpromising technology, because of its suitability in distributedgeneration, satellite systems, and transportation [1]. In dis-tributed generation applications, the PV system operates in twodifferent modes: grid-connected mode and island mode [2]–[6].In the grid-connected mode, maximum power is extracted fromthe PV system to supply maximum available power into thegrid. Single- and two-stage grid-connected systems are com-monly used topologies in single- and three-phase PV applica-tions [7], [8]. In a single-stage grid-connected system, the PVsystem utilizes a single conversion unit (dc/ac power inverter)to track the maximum power point (MPP) and interface the PVsystem to the grid. In such a topology, PV maximum poweris delivered into the grid with high efficiency, small size, andlow cost. However, to fulfill grid requirements, such a topology

Manuscript received May 15, 2012; revised August 12, 2012 and September25, 2012; accepted October 25, 2012. Date of current version December 7, 2012.Recommended for publication by Associate Editor V. Agarwal.

B. N. Alajmi, G. P. Adam, and B. W. Williams are with the Depart-ment of Electronic and Electrical Engineering, University of Strathclyde,Glasgow G1 1XQ, U.K. (e-mail: [email protected]; [email protected]; [email protected]).

K. H. Ahmed is with the Department of Electrical Engineering, Fac-ulty of Engineering, Alexandria University, Alexandria 21526, Egypt (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.2012.2228280

requires either a step-up transformer, which reduces the sys-tem efficiency and increases cost, or a PV array with a high dcvoltage. High-voltage systems suffer from hotspots during par-tial shadowing and increased leakage current between the paneland the system ground though parasitic capacitances. Moreover,inverter control is complicated because the control objectives,such as MPP tracking (MPPT), power factor correction, and har-monic reduction, are simultaneously considered. On the otherhand, a two-stage grid-connected PV system utilizes two con-version stages: a dc/dc converter for boosting and conditioningthe PV output voltage and tracking the MPP, and a dc/ac inverterfor interfacing the PV system to the grid. In such a topology, ahigh-voltage PV array is not essential, because of the dc voltageboosting stage. However, this two-stage technique suffers fromreduced efficiency, higher cost, and larger size.

From the aforementioned drawbacks of existing grid-connected PV systems, it is apparent that the efficiency andfootprint of the two-stage grid-connected system are not at-tractive. Therefore, single-stage inverters have gained attention,especially in low voltage applications. Different single-stagetopologies have been proposed, and a comparison of the avail-able interface units is presented in [8], [9]. The conventionalvoltage source inverter (VSI) is the most commonly used in-terface unit in grid-connected PV system technology due toits simplicity and availability [10]. However, the voltage buckproperties of the VSI increase the necessity of using a bulkytransformer or higher dc voltage. Moreover, an electrolytic ca-pacitor, which presents a critical point of failure, is also needed.Several multilevel inverters have been proposed to improve theac-side waveform quality, reduce the electrical stress on thepower switches, and reduce the power losses due to a highswitching frequency [11]–[14]. However, the advantages areachieved at the expense of a more complex PV system. More-over, a bulky transformer and an unreliable electrolytic capacitorare still required.

The current source inverter (CSI) has not been extensivelyinvestigated for grid- connected renewable energy systems [15].However, it could be a viable alternative technology for PV dis-tributed generation grid connection for the following reasons:

1) the dc input current is continuous which is important fora PV application;

2) system reliability is increased by replacing the shunt inputelectrolytic capacitor with a series input inductor;

3) the CSI voltage boosting capability allows a low-voltagePV array to be grid interface without the need of a trans-former or an additional boost stage.

Grid-connected PV systems using a CSI have been proposed.The three-phase CSI for PV grid connection proposed in [16],

0885-8993/$31.00 © 2012 IEEE

ALAJMI et al.: SINGLE-PHASE SINGLE-STAGE TRANSFORMER LESS GRID-CONNECTED PV SYSTEM 2665

successfully delivered PV power to the grid, without sensingthe ac output current, with a total harmonic distortion (THD)of 4.5%. However, an ac current loop is essential in the grid-connected application in order to limit the current and quicklyrecover the grid current variation during varying weather condi-tions. A dynamic model and control structure for a single-stagethree-phase grid-connected PV system using a CSI is proposedin [17]. The current injected into the grid has a low THD andunity power factor under various weather conditions. However,the controller consists of only current loops, which affect systemreliability.

Unlike the three-phase grid-connected CSI, the single-phasesystem has even harmonics on the dc side, which affect MPPT,reduce the PV lifetime, and are associated with odd-order har-monics on the grid side [9], [18]. Therefore, eliminating theeven harmonics on the dc side is essential in PV applications.Various techniques have been proposed to reduce the even har-monic effects in CSI PV applications. The conventional solutionto the dc current oscillation is to use a large inductor, which iscapable of eliminating the even-order harmonics. Practically,the CSI inverter produces high dc current [17]; therefore, aninductor with a large value is usually bulky and large in size.Thus, this technique is practically unacceptable. To eliminatethe harmonics without using large inductance, two solutionshave been proposed in the literature, namely feedback currentcontrol and hardware techniques. Specially designed feedbackcurrent controllers intended to eliminate the odd harmonics onthe ac side without using large inductance are proposed in theliterature. In [19], the oscillating power effect from the gridis minimized by employing a tuned proportional resonant con-troller at the third harmonic. Nonlinear pulsewidth modulation(NPWM) has been proposed in [20] to improve harmonic miti-gation. NPWM is based on applying computational operations,such as a band-pass filter, a low-pass filter, a phase-shifter block,and various division operations to extract the second-order har-monic component from the dc-link current. In [21], the poweroscillating effect is mitigated by using a modification of the car-rier signal on pulse amplitude modulation (PAM). The carriersignal is varied with the second-order harmonic component inthe dc-link current to eliminate its effect on the grid current.These techniques [19]–[21] are not suitable for a single-stagegrid-connected PV system, because the dc current oscillationis large, which causes high system losses and reduces its life-time. In the hardware solution proposed in [22], second-orderharmonics are eliminated by using an additional parallel reso-nant circuit on the dc-side inductor. Even though the hardwaresolution adds costs, losses, and size, it is considered to be a prac-tical solution for CSI-based PV systems. Usually, the impact ofsecond-order harmonics in the dc-side current can significantlyaffect the ac-side current. Additionally, the fourth-order har-monic in the dc-side current could affect the ac-side current athigh modulation indices.

In this paper, a single-stage single-phase grid-connected PVsystem-based on a CSI is proposed. A doubled-tuned parallelresonant circuit is proposed to eliminate the second- and fourth-order harmonics on the dc side. Moreover, a modified carrier-based modulation technique is proposed to provide a continuous

Fig. 1. Single-phase grid connected current source inverter.

path for the dc-side current after each active switching cycle.The control structure consists of MPPT, an ac current loop, and avoltage loop. To demonstrate the effectiveness and robustness ofthe proposed system, computer-aided simulation and practicalresults are used to validate the system.

II. SYSTEM DESCRIPTION

A grid-connected PV system using a single-phase CSI isshown in Fig. 1. The inverter has four insulated-gate bipolartransistors (IGBTs) (S1–S4) and four diodes (D1–D4). Eachdiode is connected in series with an IGBT switch for reverseblocking capability. A doubled-tuned parallel resonant circuitin series with dc-link inductor Ldc is employed for smoothingthe dc link current. To eliminate the switching harmonics, a C–Lfilter is connected into the inverter ac side.

III. DOUBLE-TUNED RESONANT FILTER

In a single-phase CSI, the pulsating instantaneous power oftwice the system frequency generates even harmonics in thedc-link current. These harmonics reflect onto the ac side as low-order odd harmonics in the current and voltage. Undesirably,these even harmonics affect MPPT in PV system applicationsand reduce the PV lifetime. In order to mitigate the impact ofthese dc-side harmonics on the ac side and on the PV, the dc-link inductance must be large enough to suppress the dc-linkcurrent ripple produced by these harmonics. Practically, largedc-link inductance is not acceptable, because of its cost, size,weight, and the fact that it slows MPPT transient response.To reduce the necessary dc-link inductance, a parallel resonantcircuit tuned to the second-order harmonic is employed in serieswith the dc-link inductor. The filter is capable of smoothingthe dc-link current by using relatively small inductances. Eventhough the impact of the second-order harmonic is significantin the dc-link current, the fourth-order harmonic can also affectthe dc-link current, especially when the CSI operates at highmodulation indices. Therefore, in an attempt to improve theparallel resonant circuit, this paper proposes a double-tunedparallel resonant circuit tuned at the second- and fourth-orderharmonics, as shown in Fig. 2

In order to tune the resonant filter to the desired harmonicfrequencies, the impedance of C1 and the total impedance ofL1 , L2 , and C2 should have equal values of opposite sign. Forsimplicity, assume component resistances are small, and thus


Fig. 2. Proposed double-tuned resonant filter.

Fig. 3. Impedance versus frequency measurement for the doubled-tuned par-allel resonant circuit.

can be neglected in the calculation

ZC 1 + Zt = 0. (1)

From (1), the capacitances are represented by the followingequations:

C1 =L2C2 − 1

ω 2

ω2L1L2C2 − L1 − L2(2)

C2 =−L2

L2C1

− ω2L1L2+

1ω2L2

(3)

where C1 and C2 are the resonant filter capacitances, L1 andL2 are the resonant filter inductances, ZC 1 is C1 impedance, Zt

is the total impedance of L1 , L2 , and C2 , and ω is the angu-lar frequency of the second- or fourth-orders harmonics. Afterselecting the inductance values, which are capable of allowingthe maximum di/dt at rated current, the angular frequency of thesecond harmonics in (2) and the angular frequency of the fourthharmonic in (3) are used. The desired capacitances are calculatedby numerically solving (2) and (3). Fig. 3 shows the impedanceversus frequency measurement for the doubled-tuned parallelresonant circuit. The filter is capable of eliminating both thesecond- and fourth-order harmonics.

In order to obtain the relationship between the resonant in-ductances (L1 and L2), (1) and (2) are solved for C1 , (4) asshown at the bottom of the page.

Fig. 4. Characteristics of the double-tuned resonant filter: the resonant capac-itances (C1 and C2 ) as a function of the resonant inductances L1 and L2 .

Fig. 5. Proposed double-tuned resonant filter for eliminating n harmonics.

From (4), to avoid complex numbers in the solution, the rela-tionship between L1 and L2 should be

L2 ≤ 1.778L1 . (5)

To select the optimum values for the proposed filter com-ponents, the effects of varying resonant circuit inductance areanalyzed. Fig. 4 shows resonant capacitance (C1 and C2) as afunction of the resonant inductances L1 and L2 . It can be shownthat C1 is not significantly affected when varying L1 and L2 ,whereas C2 is affected mainly by L2 . As L2 decreases, the valueof C2 increases. Therefore, increasing the capacitance leads toreduced overall system weight and size by reducing the dc-linkinductance.

The proposed filter concept can be extended to eliminate anynumber of harmonics by employing the cascaded circuit shownin Fig. 5. In order to compute the filter passive components, (6)is numerically solved for C1 to Cn

L1ω1 +1

ω1C1+ Zt = 0

L1ω2 +1

ω2C1+ Zt = 0

...

L1ωn +1

ωnC1+ Zt = 0 (6)

C1 =

√L1(L1ω4

1 + L1ω42 − 2L1ω2

1ω22 − 4L2ω2

1ω22 ) + L1ω

21 + L1ω

22

2L21ω

21ω2

2 + 2L1L2ω21ω2

2(4)


Fig. 6. Proposed carriers-based PWM along with switching sequence for one fundamental frequency.

where Zt is the total impedance of the series–parallel circuitcomponents L2 to Ln and C2 to Cn and n is the harmonicorder. To clarify the proposed filter design for the mitigationof more harmonics, an example of eliminating three harmonicsis outlined. To eliminate the second-, fourth- and sixth-orderharmonics, (6) is rewritten, as (7)–(9) shown at the bottom ofthe page.

By numerically solving (7)–(9), and (9), the capacitances thateliminate the desired harmonics can be computed.

IV. MODIFIED CARRIER-BASED PULSEWIDTH MODULATION

Modified carrier-based pulsewidth modulation (CPWM) isproposed to control the switching pattern for the single-phasegrid-connected CSI. In order to provide a continuous path for the

dc-side current, at least one top switch in either arm and one bot-tom switch must be turned ON during every switching period.In conventional sinusoidal pulsewidth modulation (SPWM), theexistence of overlap time as the power devices change statesallows a continuous path for the dc current. However, the over-lap time is insufficient to energize the dc-link inductor, whichresults in increased THD. Therefore, CPWM is proposed toprovide sufficient short-circuit current after every active switch-ing action. CPWM consists of two carriers and one reference.Fig. 6 shows the reference and carrier waveforms, along withthe switching patterns. The carrier with the solid straight lineshown in Fig. 6 is responsible for the upper switches, whilethe dashed line carrier is responsible for the lower switches andis shifted by 180◦. To understand the switching patterns of theproposed CPWM, Fig. 6 is divided into ten regions (t1 − t10),

C1 =−(C2L2ω

22 + C2L3ω

22 + C3L3ω

22 − C2C3L2L3ω

42 − 1)

L1ω22 + L2ω2

2 + L3ω22 − C2L1L2ω4

2 − C2L1L3ω42 − C3L1L3ω4

2 − C3L2L3ω42 + C2C3L1L2L3ω6

2(7)

C2 =−(C1L1ω

24 + C1L2ω

24 + C1L3ω

24 + C3L3ω

24 − C1C3L1L3ω

44 − C1C3L2L3ω

44 − 1)

L2ω24 + L3ω2

4 − C1L1L2ω44 − C1L1L3ω4

4 − C3L2L3ω44 + C1C3L1L2L3ω6

4(8)

C3 =C1L1ω

26 + C1L2ω

26 + C1L3ω

26 + C2L2ω

26 + C2L3ω

26 − C1C2L1L2ω

46 − C1C2L1L3ω

46 − 1

C1L1L3ω46 − L3ω2

6 + C1L2L3ω46 + C2L2L3ω4

6 − C1C2L1L2L3ω66

(9)


TABLE ISWITCHING COMBINATION SEQUENCE

Fig. 7. Comparison between the proposed CPWM and conventional SPWM:(a) CSI output current using CPWM and (b) CSI output current usingSPWM.

and each region represents one carrier frequency period. Table Ishows the switch combination for each of the ten regions. Asshown in Fig. 6 and Table I, CPWM operates in two modes,a conductive mode and a null mode, and the switching actionof each IGBT is equally distributed during every fundamentalperiod. To validate the proposed CPWM, simulation results ofa CSI operated by both CPWM and SPWM are shown in Fig. 7.The CSI is operated in an island mode and has the followingspecification.

The dc voltage Vdc is 50 V; in the double-tuned resonant filterL1 = 10 mH, L2 = 5 mH, C1 = 125 μF, and C2 = 250 μF,the capacitor on the ac side is 20 μF, the inductance is 1 mH,the resistive load is 50 Ω, the output voltage is 110 V, and theswitch frequency is 4 kHz.

Fig. 7 shows that the proposed CPWM generates lowerswitching frequency harmonics in the ac output current whencompared with conventional SPWM. The THD is 1% with theproposed CPWM and 4.4% with conventional SPWM.

V. PROPOSED SYSTEM CONTROL TECHNIQUE

To design a grid-connected PV system using a CSI, the rela-tionship between the PV output voltage and the grid voltage isderived as follows.

By neglecting inverter losses, the PV output power is equalto the grid power

VPVIPV = 1/2Ig,peakVg,peak cos θ (10)

where θ is the phase angle, Vpv and Ipv are the PV output voltageand current, respectively, while Vg,peak and Ig,peak are the gridpeak voltage and current, respectively. The grid current is equalto the PV output current multiplied by the inverter modulationindex M

Ig,peak = MIPV . (11)

Substituting (11) into (10), assuming unity power factor, theequation describing the relationship between the PV output volt-age and the grid voltage is

VPV =12MVg,peak . (12)

Therefore, in order to interface the PV system to the gridusing a CSI, the PV voltage should not exceed half the gridpeak voltage.

The CSI is utilized to track the PV MPP and to interface thePV system to the grid. In order to achieve these requirements,three control loops are employed, namely MPPT, an ac currentloop, and a voltage loop.

To operate the PV at the MPP, MPPT is used to identifythe optimum grid current peak value. Any conventional MPPTtechnique can be used. However, to prevent significant losses inpower, the tracking technique should be fast enough to handleany variation in load or weather conditions. Therefore, a fuzzylogic controller (FLC) is used to quickly locate the MPP.

The inputs of the FLC are

ΔP = P (k) − P (k − 1) (13)

ΔIPV = IPV(k) − IPV(k − ‘1) (14)

and the output equation is

ΔIg,ref = Ig,ref (k) − Ig,ref (k − 1) (15)

where ΔP and ΔIPV are the PV array output power and currentchange, ΔIg,ref is the grid current amplitude change reference,Ig,ref is the grid current reference, and k is the sample instant.The variable inputs and output are divided into four fuzzy sub-sets: PB (Positive Big), PS (Positive Small), NB (Negative Big),and NS (Negative Small). Therefore, the fuzzy algorithm re-quires 16 fuzzy control rules; these rules are based on the regu-lation of the hill climbing algorithm, where the fuzzy rules areshown in Table II. To operate the fuzzy combination, Mamdani’smethod with Max–Min is used.

From the behavior of the controller inputs and output, theshapes and fuzzy subset partitions of the membership functionin both the inputs and output are shown in Fig. 8. A center of areaalgorithm (COA) is used in the defuzzification stage to convert


TABLE IIFUZZY LOGIC RULES

Fig. 8. Membership function: (a) input ΔP , (b) input ΔI , and (c) output ΔD.

Fig. 9. Block diagram of the FLC-based MPPT.

the fuzzy subset duty cycle changes into real numbers [6]

ΔIg,ref =

n∑

iμ(Ig,ref ,i)Ig,ref ,i

∑ni μ(Ig,ref ,i)

(16)

where ΔIg ,ref is the fuzzy controller output and Ig,ref ,i isthe center of max–min composition at the output membershipfunction.

To ensure synchronization between the grid current and volt-age, a sinusoidal signal generated by a phase-locked-loop (PLL)is multiplied by the MPPT output. Fig. 9 shows a block diagramof the MPPT structure.

For precise control of the single-phase inverter, proportional-resonant (PR) control is employed in the voltage and currentloop controllers. The basic principle of the PR controller is tointroduce an infinite gain at a selected resonant frequency inorder to eliminate steady-state error at that frequency. The PR

Fig. 10. Equivalent circuit of the CSI ac side.

controller transfer function is expressed as

y = Kpe + Kies

s2 + ω2o

(17)

where Kp is the proportional gain, Ki is the integral gain, e isthe signal error, and ωo is the fundamental angular frequency.

The transfer function of the PR controller is digitized usingthe following derivation.

Let

z(s) = Kis

s2 + ω2o

e(s). (18)

Rearrange (18) as

sz(s) +ω2

o

sz(s) = Kie(s). (19)

Let

w(s) =ω2

o

sz(s). (20)

By taking the derivative of (19) and (20) we have

dw(t)dt

= ω2o z(t) (21)

dz(t)dt

= Kie − w(t) (22)

where z and w are auxiliary control variables used to facilitatethe control design. In the following section, the subscripts i andv will be used with these control variables to signify the currentand voltage controllers, respectively.

From (17), (21), and (22), the output of the PR controller canbe rewritten as

y = kpe(t) + z(t). (23)

In order to compute the controller output (21), (22), and (23)are solved numerically as

W (k + 1) = W (k) + Tsω2o Z(k) (24)

Z(k + 1) = Z(k) + Ts(Kie(k) − W (k + 1)) (25)

y(k + 1) = Kpe(k) + Z(k + 1). (26)

From the equivalent circuit of the CSI ac side, which is shownin Fig. 10 and the PR controller equations, the ac current andvoltage loops are designed, where Iin is the CSI output current,Cf is the filter capacitor, Lf is the filter inductor, R is the


Fig. 11. AC current and voltage loops.

TABLE IIIDESIGN SPECIFICATIONS AND CIRCUIT PARAMETERS

inductor internal resistor, Ic is the current passing through thecapacitor, Ig is the grid current, and Vg is the grid voltage.

The differential equation that describes the ac-side dynamicvoltage is

dIg

dt= −R

LIg +

Vc − Vg

L. (27)

Let

u = Vc − Vg . (28)

From (27) and (28), by feeding the grid current error to thePR controller, the value of u is obtained from (23) as

u(t) = kpi(Ig,ref (t) − Ig (t)) + zi(t). (29)

Substituting (29) into (27)

digdt

=1L

(kpiIg,ref (t) − kpiIg (t) − RIg (t) + zi(t)) (30)

where

dzi(t)dt

+ ω20

∫zi(t)dt = kii(Ig,ref (t) − Ig (t)) (31)

and

wi(t) =∫

ω2o zi(t)dt (32)

where kpi is the current controller proportional gain and kii isthe current controller integral gain.

By taking the derivative of (31) and (32)

dzi(t)dt

= ki(Ig,ref (t) − Ig (t)) − wi(t) (33)

dwi(t)dt

= ω2o zi(t). (34)

From (30), (33), and (34), the state- space model of thecurrent-loop controller is obtained as

d

dt

⎛

⎝Ig (t)zi(t)wi(t)

⎞

⎠ =

⎛

⎜⎜⎝

−(R + Kpi)L

1L

0

−Kii 0 −10 ω2

o 0

⎞

⎟⎟⎠

⎛

⎜⎝

Ig (t)zi(t)wi(t)

⎞

⎟⎠

+

⎛

⎜⎜⎝

Kpi

LKii

0

⎞

⎟⎟⎠ Ig,ref (t). (35)

Similarly, the differential equation that describes the ac-sidedynamic current is

dVc

dt=

Iin − Ig

C. (36)

Let

λ = Iin − Ig . (37)

From (36) and (37), by feeding the grid current error into thePR controller, the value of u is obtained from (23)

λ = kpv(Vc,ref (t) − Vc(t)) + zv (t). (38)

Substituting (38) into (36)

dVc(t)dt

=1C

(kpvVc,ref − kpvVc(t) + zv (t)) (39)

where

dzv (t)dt

+ ω20

∫zv (t)dt = kiv (Vc,ref (t) − Vg (t)) (40)


Fig. 12. (a) PV output power, (b) PV output current, (c) grid voltage (factored by 10) and current, (d) CSI output current, and (e) grid active and reactive power.

and

wv (t) =∫

ω2o zv (t)dt. (41)

where kpv is the voltage controller proportional gain and kiv isthe voltage controller integral gain.

By taking the derivative of (40) and (41)

dzv (t)dt

= kiv (Vc,ref − Vc(t)) − wv (t) (42)

dwv (t)

dt= ω2

o zv (t). (43)

From (39), (42), and (43), the state- space model of the voltageloop controller is

d

dt

⎛

⎜⎝

Vc(t)zv (t)wv (t)

⎞

⎟⎠ =

⎛

⎜⎜⎝

−Kpv

C

1C

0

−Kiv 0 −10 ω2

o 0

⎞

⎟⎟⎠

⎛

⎜⎝

Vc(t)zv (t)wv (t)

⎞

⎟⎠

+

⎛

⎜⎜⎝

Kpv

LKiv

0

⎞

⎟⎟⎠ Vc,ref (t). (44)


Fig. 13. Simulation results of the proposed system under two radiation levels: 500 and 1000 W/m2 . (a) PV output power, (b) PV output current, (c) grid voltage(factored by 10) and current, (d) CSI output current, and (e) grid active and reactive power.

To obtain the overall state-space model of the controllers, (28)is rewritten as

Vc,ref (t) = u(t) + Vg (t) = kpi(Ig,ref (t) − Ig (t))

+ zi(t) + Vg (t). (45)By substituting (45) into (39)

dVc(t)dt

=1C

(−kpvVc(t) + zv (t) − kpvKiiIg (t) + zi(t)

+ kpvKiiIg,ref + kpvVg (t)) (46)

dzv (t)dt

= −kivVc(t) − kiv kpiIg (t) + kiv kpiIg,ref (t)

+ kiv zi(t) + kivVg (t) − wv (t) (47)

dwv (t)dt

= ω2o zv (t). (48)

Fig. 14. Proposed system efficiency as a function of PV output power.


Fig. 15. (a) Test rig photograph and (b) hardware diagram.

From (30), (33), (34), (46), (47), and (48), the system state-space model is

d

dt

⎛

⎜⎜⎜⎜⎜⎜⎜⎜⎝

Vc(t)zv (t)wv (t)Ig (t)zi(t)wi(t)

⎞

⎟⎟⎟⎟⎟⎟⎟⎟⎠

=

⎛

⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

−kpv

C

1C

0kpvkpi

C

kpv

C0

−kiv 0 −1 kiv kpi kiv 00 ω2

o 0 0 0 0

0 0 0−kpi

L

1L

0

0 0 0 −kii 0 −10 0 0 0 ω2

o 0

⎞

⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

×

⎛

⎜⎜⎜⎜⎜⎜⎜⎜⎝

Vc(t)zv (t)wv (t)Ig (t)zi(t)wi(t()

⎞

⎟⎟⎟⎟⎟⎟⎟⎟⎠

+

⎛

⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

kpvkpi

C

kpv

Ckivkpi kiv

0 0kpi

L0

kii 00 0

⎞

⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(Ig,ref (t)Vg (t)

). (49)

Equation (49) can be rewritten in short form as

dx(t)dt

= Ax(t) + Bu(t). (50)

Using the first-order Euler approximation, (50) can be writtenin discrete form as

x(k + 1) = (1 + TsA)x(k) + TsBu(k). (51)

Therefore, (49) can be expressed in discrete form as (52)shown at the bottom of the next page, where Ts is the controlsample time, which is selected to be to the reciprocal of thePWM switching frequency.

The overall control structure is shown in Fig. 11.

VI. SIMULATIONS

Ten series-connected PV modules with a total rated power of500 W are tested in the proposed system, for which the designspecification and circuit parameters are given in Table III. Theac-side filter capacitor is selected to attenuate high frequencyharmonics that are associated with switching frequencies andtheir sidebands, taking into account the rated ac and dc cur-rents. So that at rated power, the converter is able to supply the


Fig. 16. Comparison of even harmonic affects on CSI: (a) CSI with a large inductance at M = 0.5, (b) CSI with a resonant filter at M = 0.5, (c) CSI with alarge inductance at M = 0.9, and (d) CSI with a resonant filter at M = 0.9.

ac-side active and reactive power demands, and compensate forfilter capacitor and inductor reactive power, without sliding intoovermodulation. The parameters of the dc-side tuned filter areselected as described in Section III.

To validate the performance of the proposed system, sim-ulations are performed using MATLAB/Simulink. The resultsof the proposed system under normal weather conditions areshown in Fig. 12. The PV maximum power is extracted in arelatively short time with small oscillation in steady state, asshown in Fig. 12(a). Moreover, MPPT successfully locks the dccurrent to the optimum value, as shown in Fig. 12(b). On the acside, the PV maximum power is successfully injected into thegrid with low THD, high efficiency, and unity power factor. Thegrid voltage and current are shown in Fig. 12(c), where bothare synchronized and the THD of the grid current is only 1.5%.

Fig. 12(d) shows that the CSI output current is not violated,by allowing switching of one current level at the same time. Inaddition, the grid active power and reactive power are shown inFig. 12(f). The total system efficiency is 95%, and the powerfactor is almost unity.

To demonstrate the effectiveness of the proposed system un-der varying weather conditions, a simulation is carried out usingtwo radiation levels, 500 W/m2 and 1000 W/m2 . As shown inFig. 13(a), the PV MPP is extracted in a relatively short time,has a small oscillation around the MPP during steady state,and the new MPP is correctly extracted during varying weatherconditions. Also the MPPT maintains the PV output current atits optimum value during both weather conditions, Fig. 13(b)shows the current on the dc side. Fig. 13(c) shows that the gridcurrent has a small THD and unity power factor under both

⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎣

Vc(k + 1)Zv (k + 1)Wv (k + 1)Ig (k + 1)Zi(k + 1)Wi(k + 1)

⎤

⎥⎥⎥⎥⎥⎥⎥⎥⎦

=

⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

1 − Tskpv

CTs

1C

0 Tskpvkpi

CTs

kpv

C0

−Tskiv 1 −Ts Tskiv kpi Tskiv 00 ω2

0Ts 1 0 0 0

0 0 0 1 − Tskpi

LTs

1L

0

0 0 0 Tskii 1 −Ts

0 0 0 0 ω20T 1

⎤

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎣

Vc(k)Zv (k)Wv (k)Ig (k)Zi(k)Wi(k)

⎤

⎥⎥⎥⎥⎥⎥⎥⎥⎦

+

⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

Tskpvkpi

CTs

kpv

CTskiv kpi Tskiv

0 0

Tskpi

L0

Tskii 00 0

⎤

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

[Ig,ref (k)Vg (k)

]

(52)


Fig. 17. Experimental results of the proposed grid connected system.

weather conditions. Fig. 13(d) shows that the CSI output cur-rent is not violated by allowing switching of one current levelat the same time on both radiation levels. Moreover, Fig. 13(f)shows the active power and reactive power under both weatherconditions. From Fig. 13(a) and (f), the total system efficiencyis about 95% for each radiation level. For further validation ofthe proposed system efficiency, Fig. 14 illustrates the efficiencyas function of the input power under different radiation levels.

VII. EXPERIMENTAL RESULTS

The performance of the proposed grid-connected CSI is ver-ified experimentally with the hardware shown in Fig. 15. Theexperimental setup consists of an Agilent modular solar arraysimulator to emulate PV system operation; a CSI with a 4-kHzswitching frequency to boost the output voltage, track the max-imum power point, and interface the PV system to the grid; anda single-phase auto-transformer to emulate the power grid. AnInfineon TriCore TC1796 is used to generate the PWM signalsand realize the proposed feedback loop controllers.

A. Practical Validation of the Proposed Filter

To validate the effectiveness of the proposed system, the re-sults of the CSI with the double-tuned resonant filter are com-pared with those from the CSI with large dc- link inductance, L= 300 mH. Fig. 16 shows the input dc current and the output acvoltage and current of the CSI under both test conditions. FromFig. 16(a) and Fig. 16(b), the double-tuned resonant filter andthe large inductance filter successfully eliminate even harmoniceffects at low modulation indices. The THD at the ac side for theCSI with a resonant filter is 1.29%, whereas the THD for the CSIwith large link inductance is 1.92%. On the other converter side,Fig. 16(c) and (d) shows the harmonic effects of both cases witha high modulation index. The proposed double-tuned resonantfilter successfully eliminates the even-order harmonics in the dccurrent, reducing the THD on the ac side to 2.73%. However,the CSI with large inductance reduces the THD to 6.16%, whichdoes not meet the IEEE-519 harmonics standard. Since PV ap-plications operate over a wide range of modulation indices totrack the MPP, the proposed double-tuned filter system is bettersuited for PV applications.

B. Grid Connection Validation

I–V curves are programmed into the PV source simulator totest the experimental system. The results of the proposed grid-connected CSI are shown in Fig. 17. The optimum PV currentis attained in a relatively short time and has a small steady-stateoscillation. Also, the CSI successfully injects the PV currentinto the grid with low total harmonics distortion.

VIII. CONCLUSION

A single-stage single-phase grid-connected PV system usinga CSI has been proposed that can meet the grid requirementswithout using a high dc voltage or a bulky transformer. Thecontrol structure of the proposed system consists of MPPT, acurrent loop, and a voltage loop to improve system performanceduring normal and varying weather conditions. Since the systemconsists of a single-stage, the PV power is delivered to the gridwith high efficiency, low cost, and small footprint. A modifiedcarrier-based modulation technique has been proposed to pro-vide a short circuit current path on the dc side to magnetize theinductor after every conduction mode. Moreover, a double-tunedresonant filter has been proposed to suppress the second- andfourth-order harmonics on the dc side with relatively small in-ductance. The THD of the grid- injected current was 1.5% in thesimulation and around 2% practically. The feasibility and effec-tiveness of the proposed system has been successfully evaluatedwith various simulation studies and practical implementation.

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Bader N. Alajmi received the B.Sc. and M.Sc. de-grees from California State University, Fresno, in2001 and 2006, respectively. He is currently work-ing toward the Ph.D. degree in electrical engineer-ing from the Department of Electrical and electronic,Strathclyde University, Glasgow, U.K.

His research interests include digital controlof power electronic systems, microgrids and dis-tributed generation, photovoltaic inverters, and dc–dcconverters.

Khaled H. Ahmed (SM’12) received the B.Sc. (firstclass Hons.) and M.Sc. degrees from the Facultyof Engineering, Alexandria University, Alexandria,Egypt, in 2002 and 2004, respectively, and the Ph.D.degree in electrical engineering from the Universityof Strathclyde, Glasgow, U.K., in 2008.

Since 2009, he has been a Lecturer with Alexan-dria University, Alexandria, Egypt. He has authoredor coauthored more than 50 technical papers in refer-eed journals and conferences. His research interestsinclude digital control of power electronic systems,

power quality, microgrids, distributed generation, dc–dc converters, and HVDC.Dr. Ahmed is a Reviewer for the IEEE TRANSACTIONS and several

conferences.

Grain Philip Adam received the Ph.D. degree inpower electronics from the University of Strathclyde,Glasgow, U.K., in 2007.

He is a Research Fellow with the Institute ofEnergy and Environment, University of Strathclyde.His research interests include fault tolerant voltagesource multilevel converters for HVDC systems; con-trol of HVDC transmission systems and multitermi-nal HVdc networks; voltage source converter-basedFACTS devices; and grid integration issues of renew-able energies. He has authored or coauthored several

technical reports, journal, and conference papers in the area of multilevel con-verters and HVdc systems, and grid integration of renewable power.

Dr. Adam has contributed in reviewing process for several IEEE and IETTRANSACTIONS, and journals and conferences.

Barry W. Williams received the M.Eng.Sc. degreefrom the University of Adelaide, Adelaide, S.A., Aus-tralia, in 1978, and the Ph.D. degree from CambridgeUniversity, Cambridge, U.K., in 1980.

After seven years as a Lecturer at Imperial Col-lege, University of London, London, U.K., he becamea Chair of Electrical Engineering at Heriot–Watt Uni-versity, Edinburgh, U.K, in 1986. He is currently aProfessor at Strathclyde University, Glasgow, U.K.His teaching covers power electronics (in which hehas a free internet text) and drive systems. His re-

search interests include power semiconductor modeling and protection, con-verter topologies, soft switching techniques, and application of ASICs andmicroprocessors to industrial electronics.

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