2092 ieee transactions on industrial electronics, vol. … · is a dc/ac converter [1]–[4]. in...

2092 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 64, NO. 3, MARCH 2017

Dynamic Performance Improvement of aGrid-Tied PV System Using a Feed-Forward

Control Loop Acting on the NPCInverter Currents

Leonardo Bruno Garcia Campanhol, Sergio Augusto Oliveira da Silva, Member, IEEE,Azauri Albano de Oliveira, Jr., and Vinıcius Dario Bacon

Abstract—This paper presents a three-phase grid-connected photovoltaic (PV) system, which is implementedusing the neutral-point-clamped (NPC) inverter. A currentfeed-forward control loop (FFCL) is proposed to improvethe PV system dynamic behavior, due to the PV array beingconstantly subjected to sudden solar irradiance change,which causes voltage oscillations in the dc bus and, hence,interferes in proper PV system operation. As the currentFFCL acts to speed up the calculation of the invertercurrent references, the dynamic response of the currentsinjected into the grid is improved. As a consequence, thedynamic behavior of the dc-bus voltage is also enhanced,reducing both settling time and overshoot. Besides theinjection of active power into the grid, the PV system isalso controlled to perform active power-line conditioning,so that load harmonic currents are suppressed, as wellas load reactive power is compensated. However, the NPCinverter must be properly designed to guarantee that itspower rating will not be exceeded, since both fundamentaland nonfundamental current components flow through thegrid-tied inverter. Extensive experimental results basedon a digital signal processor are presented in order toevaluate the effectiveness, as well as the static and dynamicperformance of the PV system.

Index Terms—Active power-line conditioning, feed-forward control loop (FFCL), photovoltaic (PV) system,three-level neutral-point-clamped (NPC) inverter.

I. INTRODUCTION

IN RECENT years, the generation of electric energy based onrenewable energy sources (RES) has risen significantly, due

Manuscript received April 27, 2016; revised June 30, 2016 and August19, 2016; accepted October 7, 2016. Date of publication November 7,2016; date of current version February 9, 2017. This work was supportedin part by CNPq under Grant 471825/2009-3.

L. B. G. Campanhol is with the Department of Electrical Engineering,Federal University of Technology (UTFPR-AP), Apucarana 86812-460,Brazil (e-mail: [email protected]).

S. A. O da Silva and V. D. Bacon are with the Departmentof Electrical Engineering, Federal University of Technology (UTFPR-CP), Cornelio Procopio 86300-000, Brazil (e-mail: [email protected];[email protected]).

A. A. de Oliveira, Jr., is with the Department of Electrical and Com-puting Engineering, Sao Carlos Engineering School, University of SaoPaulo, Sao Carlos 13566-590, Brazil (e-mail: [email protected]).

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

Digital Object Identifier 10.1109/TIE.2016.2625779

to growing demand for electricity, as well as reaching goals re-lated to a reduction in the environmental and economic impactsintroduced by conventional power generation pollutant sources.Thereby, the traditional setting of power generation has changed,highlighting the use of RES, such as hydro, biomass, wind, solar,and others.

Concerning the use of solar energy, this has been employedthrough the conversion of photovoltaic (PV) energy into elec-trical energy. In addition, this form of energy production canbe considered clean, producing reduced environmental impacts,since the waste is generated only in the manufacturing processor in the disposal. For this reason, the generation of electricityby means of PV systems is considered promising among thevarious existing RES.

Usually, one or two power conversion stages are requiredto compose a grid-connected PV system. In double-stage PVsystems, one power stage is a dc/dc converter and the otheris a dc/ac converter [1]–[4]. In this case, the dc/dc converterperforms the maximum power point tracking (MPPT) control,while the dc/ac converter connects the PV system to the gridand performs the current control.

On the other hand, in single-stage grid-tied PV systems [5]–[12], the control loops of the MPPT and inverter currents are,simultaneously, carried out in one power conversion stage. As aresult, the power loss decreases, and hence, the system efficiencyincreases [7]. Furthermore, the speed of the MPPT control loop(dc-bus control loop) must be much slower than that of thecurrent control loop, in order to ensure undistorted currentsinjected into the grid [12].

Nonuniform insolation and/or temperature variation interferein the amount of energy generated by the PV system. Thus, inde-pendent of the PV system arrangement, techniques for achievingMPPT have been developed [12]–[15], where the tracking factor[15], complexity, and dynamic response are some of the mainfactors used to evaluate and/or compare MPPT algorithms.

PV arrays are also subjected to sudden solar radiationchanges. In this case, the dc-bus voltage amplitude varies, andoscillations in the dc-bus voltage can occur. As a consequence,the performance of the PV system can be affected, since thedc-bus power balance is used to control the amplitude of theinverter currents injected into the grid. In other words, large

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CAMPANHOL et al.: DYNAMIC PERFORMANCE IMPROVEMENT OF A GRID-TIED PV SYSTEM USING A FFCL 2093

voltage variations in the dc-bus interfere in the calculation ofthe grid-tied inverter current references during transients.

Most of the MPPT techniques presented in the literature donot consider or discuss the effects of abrupt variations in solarirradiance on the PV system performance. In [5], a feed-forwardcurrent (FFC) control loop was proposed to make the PV systemdynamics independent from those of the distribution networkand the loads. However, the effects of abrupt solar radiationvariations on the PV system performance have not been treated.In [7], MPPT techniques were implemented taking into accounta single-stage PV system operating under partial shading. Al-though the performance of the MPPT techniques was evaluated,no procedure was adopted to mitigate problems related to fastirradiance variations. A function-based MPPT method was pro-posed in [13], in order to evaluate the performance of the methodwith regard to start-up, steady-state, and dynamic response, con-sidering abrupt solar radiation changes. The mentioned functionis used to determine the duty cycle of the dc/dc converter em-ployed to achieve the MPPT. On the other hand, the dynamicbehavior of the dc-bus voltage has not been evaluated due tothe proposed MPPT algorithm not having been tested, eitherusing simulations or experimentation, in practical grid-tied PVsystems. In [12], a modified incremental conductance MPPTalgorithm is proposed to improve the stability of the MPPTmethod, when a single-stage grid-tied PV system is subjectedto sudden insolation changes. Although this modified MMPTmethod acts detecting the fast decreasing of the PV array outputpower when abrupt insolation occurs, large dc-bus voltage os-cillation is still observed during the aforementioned transient. Inaddition, this MPPT method is not able to detect fast increasingof the PV array output power when sudden isolation occurs.

This paper proposes implementation of a current feed-forward control loop (FFCL), which acts to speed up thecalculation of the inverter current references and, hence,contributes to overcome problems associated with sudden in-crease and decrease solar radiation changes in grid-connectedPV systems. The FFCL, which is not tied to any MPPT tech-nique, acts in conjunction with the inverter dc-bus voltage con-troller, improving the dynamic response of both dc-bus voltageand inverter currents. As a consequence, the settling time andovershoot/undershoot are reduced during transient conditions.In addition, since the inverter dc-bus voltage oscillations areattenuated, the risk of over voltage rating in the power semicon-ductors is also reduced.

In this paper, besides the injection of active power into thegrid, the PV system performs the active power-line condition-ing task, which includes load harmonic current suppression andload reactive power compensation [3], [6], [16]–[18]. In thiscase, the PV system handles, simultaneously, the active en-ergy produced by the PV array and both nonfundamental and/orfundamental nonactive energy, which are caused by harmoniccurrents/voltages or reactive currents, respectively [19]. In otherwords, the PV system is also able to carry out the parallel activepower filter function, such that an effective power factor (PF)correction is performed.

Thus, in order to mitigate power quality problems and in-crease the system efficiency, the three-phase transformerless

grid-tied PV system presented in this paper uses a single-stagedc/ac power conversion, which is implemented using the three-level neutral-point-clamped (3L-NPC) inverter [16], [20].

A current reference generator (CRG) algorithm calculatesthe reference current that will be synthetized by the grid-tiedinverter. Once the active power-line conditioning is also takeninto account, the following tasks are allowed:

1) injection of active power into the grid from the energyproduced by the PV array;

2) compensation of the load reactive power;3) suppression of the load harmonic currents.

However, due to the active conditioning operation, controlof the ac current amplitude must be performed to avoid theoccurrence of over power rating in the grid-tied inverter [6], [7].

The algorithm used to generate the references of the nonactivecurrents (harmonic and reactive components) is implementedbased on the synchronous reference frame (SRF) method. Fur-thermore, the synchronous unit vector coordinates, sin(θ) andcos(θ), are calculated using the estimated utility voltage phaseangle (θ), which is obtained from a phase-locked loop (PLL)system.

This paper is organized as follows. In Section II, the PV sys-tem description is presented, including the SRF-based CRG al-gorithm and the inverter current and dc-bus voltage controllers.Section III presents the FFCL and three-phase power-based PLLsystem (3pPLL) description. Section IV presents the controllerdesign of the 3L-NPC inverter, where the open-loop and closed-loop transfer functions (TFs) of the current and voltage controlloops are achieved. In addition, the procedures used to com-pute the voltage and current controller gains are presented. InSection V, the performance and feasibility of the single-stagethree-phase grid-tied PV system are evaluated by means of ex-tended experimental results. Finally, Section VI presents theconclusions.

II. PV SYSTEM DESCRIPTION

Fig. 1 presents the complete scheme of the three-phase trans-formerless grid-tied PV system studied in this paper. As canbe seen, the PV system is connected to the three-phase four-wire system, where, besides the injection of active energy intothe grid, the active power-line conditioning is also carried out.As can be observed in Fig. 1, the single-stage PV system isimplemented using the grid-connected 3L-NPC inverter, whichhas been widely used in applications involving PV systems [2],[8], [10].

Since single-stage power conversion is used in the PV system,the PV array is directly linked to the inverter dc-bus. The series-connected PV array string is composed of 20 series-connectedsolar panels. Under standard test conditions, the voltage of eachpanel at maximum power point (MPP) is around 30.8 V, resultingin a total dc-bus voltage of around 616 V at the PV array outputterminals. Thus, the direct connection between the PV array andthe inverter dc-bus is possible, and the use of any dc/dc step-up converter is not required. Therefore, the energy efficiencyinvolving the power conversion stages increases and the overallsystem cost decreases.


Fig. 1. Complete scheme of the single-stage three-phase grid-tied PV system.

Fig. 2. Block diagram of the SRF-based CRG algorithm.

The NPC inverter is connected to the utility grid by meansof inductive coupling filters (L-filters). As the NPC inverter iscurrent controlled, its current references are computed in thecontrol system shown in Fig. 1. All the algorithms employed togenerate the inverter current references (SRF-based current andPLL), as well as the ac-current control loop and the other twodc-bus voltage control loops, will be properly described in thenext subsections.

A. CRG Algorithm

In this subsection, the CRG, which is represented by the algo-rithm shown in Fig. 2, is described. It is employed to compute theproper grid-tied inverter current references (i∗ca , i∗cb , i∗cc ), whichinvolve both the active and nonactive current components. InFig. 2, the active current components are represented by idc andiff , while iLdh

, iLq and iL0 represent the nonactive components.The algorithm presented in Fig. 2 is based on the SRF method.

In this SRF-based algorithm, the load currents are measuredand transformed from a three-phase stationary frame (abc-axes)into a two-phase stationary frame (αβ0 -axes). Next, these cur-rents are transformed into a two-phase SRF (dq-axes). These

transformations are given by (1) and (2), respectively,

⎡⎣

iLα

iLβ

iL0

⎤⎦ =

√23

⎡⎢⎢⎢⎢⎢⎢⎢⎣

1 −12

−12

0√

32

−√

32

1√2

1√2

1√2

⎤⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎣

iLa

iLb

iLc

⎤⎦ (1)

[iLd

iLq

]=

[cosθ sinθ−sinθ cosθ

] [iLα

iLβ

]. (2)

In the dq-axes, the current iLd is composed of both con-tinuous and alternate components. The continuous component(iLdd c ) represents the load fundamental active currents, whilethe alternate component (iLdh

) represents the load harmonic cur-rents, both in the d-axis. The quantity iLdh

is extracted using ahigh-pass filter (HPF), where its implementation makes use of alow-pass filter (LPF), as shown in Fig. 2. In addition, the currentiLd represents the sum of the load fundamental reactive compo-nent with the harmonic components in the q-axis, whereas iL0represents the zero-sequence component of the neutral wire inthe αβ0 -axes. Therefore, in order to guarantee, in theory, unityPF, both iLq , iL0 and iLdh

quantities must be compensated.As aforementioned, the inverter handles both active and non-

active currents. Thus, to guarantee that all active energy pro-duced by the PV generator is injected into the grid withoutinverter over power rating, the amplitude of compensation cur-rents, represented by iLdh

, must be controlled. For this purpose,the strategy employed in [6] was adopted in this paper.

The inverse transformations from the rotating reference framedq into the αβ reference frame and from the αβ0 referenceframe into the abc reference frame are given by (3) and (4), re-spectively. Hence, the final grid-tied inverter current references


Fig. 3. Block diagram of the current and dc-bus control loops.

(i∗ca , i∗cb , i∗cc ) are obtained[

icα

icβ

]=

[cosθ −sinθsinθ cosθ

] [iLdh

+ iff − idciLq

](3)

⎡⎢⎣

i∗ca

i∗cb

i∗cc

⎤⎥⎦ =

√23

⎡⎢⎢⎢⎢⎢⎢⎢⎣

1 01√2

−12

√3

21√2

−12

−√

32

1√2

⎤⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎣

icα

icβ

iL0 − idcu

⎤⎦ . (4)

The currents idc and idcurepresented in (3) and (4), respec-

tively, are extracted from their respective dc-bus voltage con-trollers, as shown in Fig. 3. In addition, the FFC iff representedin (3) is obtained from the FFCL. The difference between iff andidc (iff − idc) shown in Fig. 3 performs the dc-bus active powerbalance of the PV system, as well as controls the active powerdemanded to regulate the dc-bus voltage, considering the com-pensation of the power loss related to the L-filters and switchingdevices. Details related to the FFC control action are discussedin Section III.

B. Current Controller

The current controller (proportional-integral multiresonant—PI-MR) used in the abc phases of the PV system is shown inFig. 3, where the physical system is represented by the induc-tances (Lf a,b,c ) and resistances (RLf a,b,c ) of the L-filters (seeFig. 1), in conjunction with the dc-bus voltage (vdc/2). TheNPC inverter pulse width modulation (PWM) static gain is rep-resented by KPWM , which is calculated taking into account thepeak value of the PWM triangular carrier [22].

Since only alternate components compose the inverter currentreferences (i∗ca , i∗cb , i∗cc ), the conventional proportional-integral(PI) controller does not guarantee null error in steady state.Thus, the PI-MR controller is adopted. The TF of the PI-MRcontroller is given by (5), in which, due to the infinite open-loopgain at the resonant frequency (ωo ), zero steady-state error isachieved

GPI−MR(s) = kP i +kI i

s+

n∑m=1

km s

(s2 + (mω1)2)

= GPI(s) +n∑

m=1

GMR(m )(s). (5)

In (5), kP i and kI i represent the respective proportional andintegral gains of the current PI-MR controller; the resonant gain

at a specific resonant frequency (ωo = mω1) is represented bykm ; ω1 is the fundamental utility frequency; and as m = 1, 3,5, 7, and 9, the first, third, fifth, seventh, and ninth compo-nents were chosen as resonant terms. The first-order component(m = 1) represents both the fundamental active components in-jected into the utility grid and the fundamental load reactivecomponents.

On the other hand, the multiresonant PI controllers (see Fig. 3)are tuned so that the resonant terms present 0 dB gain at theirrespective crossover frequencies (ωcm ). Thus, the multiresonantcontroller gains (km ), presented in (5), are achieved to guaranteethat the multiresonant crossover frequencies will be equal to theadopted crossover frequency defined in the design specificationsof the current PI controllers (ωci), such that ωcm = ωci .

C. DC-Bus Controllers

As can be seen, two dc-bus voltage PI controllers are alsopresented in Fig. 3. The first, denominated PIvd c , is used tocontrol the total dc-bus voltage at a constant reference v∗

dc . Thereference voltage v∗

dc is obtained from the perturb and observe(P&O)-based MPPT technique [6], as shown in Fig. 1. The out-put signal of this controller is represented by idc , where thisquantity represents the total energy produced by the PV sys-tem plus the energy demanded by the PV system to compensatethe losses related to the filtering inductors and semiconduc-tor devices. The current idc is included in (3) and representedin Figs. 2 and 3. The second dc-bus controller, denominatedPIvd c u

, is used to compensate the dc-bus voltage unbalances.In this case, the difference between the dc-bus voltages (vdc1 −vdc2 ) is measured and compared to zero reference, as shown inFigs. 1 and 3. The PIvd c u

output signal (idcu) is included in (4)

and also represented in Figs. 2 and 3.

III. CURRENT FFCL

Atmospheric conditions related to solar radiance and/or tem-perature imply in distinct amounts of energy available in thePV array. In particular, abrupt solar radiation changes result involtage oscillations in the inverter dc bus, affecting computationof the inverter current references, and interfering in the properoperation of the PV system.

The FFCL proposed in this paper aims to reduce the ampli-tude oscillations that can occur in the dc-bus voltage due to theoccurrence of disturbances, such as sudden insolation changes.This control action is represented by the FFC (iff ) shown inFig. 2.

The FFCL is based on the dc-bus power balance. Althoughmaintaining the dc-bus voltage by means of only the dc-busvoltage controller could ensure PV system power balance, thiscontroller is not fast enough to avoid voltage oscillations whensudden insolation changes occur. In other words, the speed ofthe dc-bus voltage control loop must be adequately designedto be slower than the current control loops to guarantee nointerference with each other, which could affect the quality ofthe current waveform injected into the grid.

Therefore, the FFCL acts through the CRG. In other words,the FFCL previously estimates the energy available in the PV


array and, hence, helps when computing the inverter active cur-rents that will be injected into the grid. Thus, this control actioncontributes to reducing the settling time and overshoot that occurin the dc-bus voltage, as well as in the inverter currents duringtransients.

The active power generated by the PV array (Ppv ) is calcu-lated as follows:

Ppv = vpv ipv = (vdc1 + vdc2 )ipv (6)

where vpv and ipv represent the PV array voltage and current,respectively, and vdc1 and vdc2 are the dc-bus voltages.

Assuming that the PV system handles only active energy andthe grid-tied inverter currents are balanced, the active power(Pac) injected into the grid is given by

Pac = 3Vsrm s Isrm s =3Vsp

Isp

2(7)

where Vsrm s and Isrm s represent the rms values of the funda-mental utility voltage and current, respectively, and Vsp

and Isp

are their respective peak amplitudes.It is supposed that the PV system operates in ideal conditions,

such that the system losses can be disregarded. In this case, thetotal active power extracted from the PV array is provided tothe grid, such that Pac = Ppv .Therefore, from (6) and (7), theutility peak current (Isp

) can be estimated by

Isp=

2vpv ipv

3Vsp 1

(8)

where vpv and ipv are measured, while Vsp 1 is estimated bya PLL system and represents the peak amplitude of the utilityvoltage positive-sequence component.

As can be seen in Fig. 2, the iff is represented in the syn-chronous rotating frame. Thus, when Isp

is transformed fromthe abc-axes into the dq-axes, iff can be computed by

iff =√

3/2Isp. (9)

Therefore, iff is used in (3) to calculate the currents icα andicβ . By means of (3), the inverter reference currents (i∗ca , i∗cb , i∗cc )are computed by (4). Thus, as can be noted, iff acts to acceleratethe calculation of the inverter reference currents. As a result, iffcontributes to improve the dynamic responses of both the dc-busvoltage and grid-tied inverter currents.

As can be noted, to implement the FFCL, no additional volt-age or current transducers are needed, since the quantities thatcompose iff have been previously measured or estimated.

A. PLL Scheme

Fig. 4 presents the there-phase PLL scheme implemented inthis paper. The PLL system called AF-PSD-3pPLL is com-posed of three nonautonomous adaptive filters (AFs) and apositive-sequence detector (PSD) operating in conjunction withthe 3pPLL [21]. Besides high rejection against voltage harmon-ics and voltage unbalances, the AF-PSD-3pPLL presents fastphase-locking.

The PLL PI controller gains (kP pll , kIpll), as well as the AFgain (Kc ) shown in Fig. 4, are designed taking into accountthe well-known frequency response analysis [23], together with

Fig. 4. Block diagram of the AF-PSD-3pPLL system.

the stability analysis presented in [21]. The gains kP pll andkIpll and Kc = μ/Ta are presented in Table I, where Ta isthe digital signal processor (DSP) sampling time and μ is theadaptation step size of the AFs. The gain A =

√z2

1 + z22 is

the positive-sequence peak amplitude of the three-phase utilityvoltage (A = Vsp 1 ), such that z1 = (w1a + w1b + w1c)/3 andz2 = (w2a + w2b + w2c)/3, where w1a,b,c and w2a,b,c are theAF weights in the abc stationary reference frame.

IV. CONTROLLER DESIGN OF THE NPC INVERTER

This section presents the mathematical development for ob-taining the controller design of the 3L-NPC inverter, where boththe TFs of the current and voltage control loops are presented.

A. Current Control Loop

The current controllers of the 3L-NPC inverter are imple-mented in the three-phase stationary reference frame (abc-axes).The mathematical development is accomplished consideringthat the filtering inductances and their respective resistancesare identical, such that Lf a = Lf b = Lf c and RLf a = RLf b =RLf c . Thus, by means of circuit analysis performed in the in-verter scheme shown in Fig. 1, the following equations can befound:

uan pwm = vLf a+ vRL f a

+ vsa (10)

ubn pwm = vLf b+ vRL f b

+ vsb (11)

ucn pwm = vLf c+ vRL f c

+ vsc (12)

where uan pwm , ubn pwm , and ucn pwm are the respective PWMoutput voltages at the parallel NPC inverter terminals; vLf a

,vLf b

, and vLf care the filter inductance voltages; vRL f a

, vRL f b,

and vRL f care the resistance voltages of the filter inductors; and

vsa , vsb , and vsc are the utility voltages.Thereby, after some mathematical manipulations in (10)–

(12), the open-loop TF of the physical system (Gps ) isgiven by

Gpsa , b , c(s) =

vdc

21

Lf a,b,cs + RLf a,b,c. (13)

On the other hand, based on the current control loop presentedin Fig. 3, the closed-loop TF considering the PI controllers is


TABLE IPARAMETERS ADOPTED IN THE EXPERIMENTAL TESTS

Apparent power Sa = 860 VA,of the unbalanced Sb = 750 VA,

three-phase nonlinear loads Sc = 470 VA

Nominal utility voltages (rms) Vs = 127.27 VInverter inductive filters Lf s = 1.7 mHResistance of the inverter inductive filters RL f s = 0.2 ΩEquivalent dc-bus capacitance Cd c = 2350 μF

MPP dc-bus voltage Vd c = 616 VSwitching frequency of the NPC inverter fsw = 20 kHzSampling frequency of the DSP A/D converter fa = 60 kHzP&O-based MPPT step-size voltage Δv = 1 VP&O-based MPPT sampling time T sM P P T = 166.67 msPWM gain KP W M = 2 × 10−3

Unbalanced nonlinear loads

Loads Phase A Phase B Phase CSingle-phase R = 12.5 Ω R = 19.5 Ω R = 58 ΩFull bridge rectifiers L = 15.6 mH L = 24.2 mH C = 940 μFfollowed by RL and RC load LL a = 1.3 mH LL b = 3 mH LL c = 6.1 mH

represented by

ica,b,c(s)i∗ca,b,c(s)

=X1(kP is + kI i)

Lf a,b,cs2 + (RLf a,b,c + X1kP i)s + X1kI i

(14)where X1 = KPWMvdc/2, kP i and kI i are the proportional andintegral gains of the PI current controllers, and i∗ca,b,c(s) are thecurrent references in the abc-axes.

B. DC-Bus Voltage Control Loops

The TFs of the dc-bus voltage control loop take into accountthe theoretical development presented in [24]. As a result, theopen-loop TF of the dc-bus voltage (Gvd c ) can be representedby

Gvd c (s) =vd

vdcCdcs(15)

where vd represents the utility voltage into the synchronousrotating frame (d-axis), vdc is the dc-bus voltage, and Cdc is thedc-bus equivalent capacitance.

Considering the dc-bus voltage PI controller (PIvd c ), theclosed-loop TF can be represented by

vdc(s)v∗

dc(s)=

kP vd c vds + kIvd c vd

vdcCdcs2 + kP vd c vds + kIvd c vd(16)

where kP vd c and kIvd c are the PI controller gains (see Fig. 3).In addition, the inherent voltage unbalances of the split ca-

pacitors placed in the inverter dc bus must be compensated. Inother words, a specific dc-bus controller must be used to over-come this problem, as shown in Fig. 3. The currents that flowthrough the capacitors Cdc1 and Cdc2 are considered to obtainthe mathematical model of this plant, as

iCd c 1 , 2= Cdc1 , 2

dvdc1 , 2

dt. (17)

Applying the Laplace transform and considering Cdc1 =Cdc2 , the open-loop TF of the unbalanced dc-bus voltage

Fig. 5. Prototype setup.

controller loop (Gvd c u) is given by

Gvd c u(s) =

vdc1 (s) − vdc2 (s)ic(s)

=3

2Cdc1 s. (18)

Thus, considering the unbalanced voltage PI controller (PIvd cu),

the closed-loop TF is represented by

vdc1 (s) − vdc2 (s)v∗

dc1(s) − v∗

dc2(s)

=3kP vd c u

s + 3kIvd c u

2Cdc1 s2 + 3kP vd c u

s + 3kIvd c u

(19)

where kP vd c uand kIvd c u

are the PI controller gains (see Fig. 3).Once the open-loop TFs (Gps , Gvd c , and Gvd c u

) are obtained,the current and voltage PI controllers can be tuned. The proce-dure used for tuning all the controllers was based on the fre-quency response method, via Bode diagram, presented in [23].In this method, the design specifications are the phase-margin(PM) and the crossover frequency at 0-dB gain. Thus, the PIcontrollers will provide the angular contributions to meet thespecified PMs and the proper gains to ensure that the com-pensated systems present the specified crossover frequencies at0 dB.

V. EXPERIMENTAL RESULTS

The experimental setup of the PV system was constructedbased on the scheme shown in Fig. 1 and is shown in Fig. 5.The digital implementation was performed by using the DSP(TMDXCNCD28377D—Texas Instruments), in which the cur-rent and dc-bus voltage controllers were embedded, as wellas the FFCL, P&O-based MPPT, CRG, and PLL algorithms.The 3L-NPC inverter was implemented using six insulated-gate bipolar transistor modules (SKM100GB 12T4—Semikron),with their proper drivers, and six fast recovery diodes (DSEI 6006A—IXYS). The LEM LA 100-Pand LEM LV 25P transduc-ers were used to measure the PV system currents and voltages,respectively, whereas the PV array string is composed of 20series-connected PV panels (SW 245—SolarWorld).

The main parameters employed in the experimental tests arepresented in Table I, while Table II presents the design specifica-tions of the PI controllers (PMs and the crossover frequencies),and all the PI controller gains.


Fig. 6. Utility voltage (vsa ), load currents (iL a , iL b , iL c ), and compensated source currents (isa , isb , isc ) of the PV system (50 V/div, 10 A/div,5 ms/div). (a) Utility voltage and load currents. (b) OPM 1: only active power-line conditioning ( Ppv = 0 W). (c) OPM 2: active power injection plusactive power-line conditioning (Ppv ∼= 3600 W). (d) OPM 3: total active power injection into the grid (Ppv ∼= 3600 W and PL = 0 W).

TABLE IIDESIGN SPECIFICATIONS AND GAINS OF THE PI CONTROLLERS

PI-MR current controllers

PIi crossover frequency ωc i = 1.2566e4 rad/sPIi phase margin PM i = 85◦

PIi current controller gains kP i = 351.29 kI i = 4.2717e5

Crossover frequencies of the CurrentMR controller

ωc 1 = ωc 3 = ωc 5 = ωc 7 = ωc 9 =1.2566e4 rad/s

Current MR controller gains k1 = 12555; k3 = 12465; k5 = 12284;k7 = 12012; k9 = 11650

dc-bus voltage controllers

PIv d c crossover frequency ωv d c = 28.274 rad/sPIv d c phase margin PM v d c = 75◦

PIv d c voltage controller gains kP v d c = 0.1797 kI v d c = 1.3615PIv d c u

crossover frequency ωv d c u= 14.5932 rad/s

PIv d c uphase margin PM v d c u

= 82◦

PIv d c uunbalance controller gains kP v d c u

= 0.0453 kI v d c u= 0.0929

PLL parameters and controller gains

PIp l l controller gains kP p l l = 141.7; kI p l l = 7777.4AF gain Kc = 300AF adaptation step size μ = 0.005

Fig. 6 shows the static behavior of the PV system taking intoaccount three different operation modes (OPMs), which aredescribed as follows: OPM 1 performs only active power-lineconditioning; OPM 2: performs active power injection plus ac-tive power-line conditioning; and OPM 3: performs only activepower injection. In Fig. 6, the following quantities are shown:phase “a” utility voltage (vsa ), compensated source currents(isa , isb , isc ), and load currents (iLa , iLb , iLc ).

Fig. 6(a) shows the load currents related to the nonlinear andunbalanced loads presented in Table I, in conjunction with thephase “a” utility voltage (vsa ). Fig. 6(b) presents the experimen-tal results for the OPM 1, where Ppv is zero and the nonlinearloads are connected to the grid. In this case, the PV system per-forms only the active power-line conditioning. As can be seen,the compensated source currents are always sinusoidal and inphase with the utility voltage. In OPM 2, Ppv is higher than theload active power PL . In this case, Ppv is consumed by the loadand the remaining power is injected into the grid, as shown inFig. 6(c). OPM 3 is shown in Fig. 6(d), where the total activepower produced by the PV array is injected into the grid (Ppv isaround 3600 W). As can be seen in Fig. 6(c) and (d), the sourcecurrents are sinusoidal and in opposite phase with the respectiveutility voltages.

TABLE IIITHDS AND RMS VALUES OF THE LOAD AND SOURCE CURRENTS AND PFS

Operation Modes Total harmonic distortions (THD %)

is a is b is c iL a iL b iL c

OPM 1 4.1 2.6 2.6 26.5 23.3 56.1OPM 2 8.2 6.6 3.8 26.5 23.3 56.1OPM 3 1.7 1.5 1.5 — — —

rms Currents (A)

OPM 1 5.23 5.11 4.95 6.91 5.99 3.72OPM 2 3.47 3.17 3.30 6.91 5.99 3.72OPM 3 8.07 8.01 8.04 — — —

Power Factor

OPM 1 1.0 1.0 1.0 0.93 0.92 0.78OPM 2 0.99 0.99 0.99 0.93 0.92 0.78OPM 3 1.0 1.0 1.0 — — —

Table III presents the total harmonic distortion (THD) of thecompensated source currents and load currents. As can be noted,in all OPMs, the THDs of the compensated source currents weresignificantly reduced. Table III also shows the rms currents andPFs with and without active power-line compensation. As canbe observed, an effective PF correction was carried out.

Fig. 7 presents the dynamic response of the dc-bus voltages(vdc , vdc1 , vdc2 ) and the source current (isa ), when the PV arrayis abruptly connected and disconnected from the inverter dc bus,which represents a sudden solar radiation change.

In Fig. 7(a) and (c), the PV array remains disconnected fromthe dc bus for up to 50 ms. After that, the PV array is connectedagain. As can be seen, the dynamic response of the PV systemwithout the FFCL [see Fig. 7(a)] is lower than observed when thePV system is operating with the FFCL [see Fig. 7(c)]. The samedynamic behavior can be observed in Fig. 7(b) and (d), wherethe PV array remains connected for up to 50 ms, and after that itis disconnected again. Fig. 7(b) shows the PV system dynamicresponse without the FFCL, while in Fig. 7(d), the PV system isoperating with the FFCL. Furthermore, Fig. 7(c) and (d) showthat use of the FFCL contributes to increasing the speed of thetransient responses of the compensated source current (isa ), aswell as assuring that there is no oscillation in the dc-bus voltagesduring the PV array transients. Fig. 7 also shows that there isno voltage unbalance in the dc-bus capacitors, meaning that thedc-bus voltage unbalance controller is operating properly.


Fig. 7. DC-bus voltages (vdc , vdc1 , vdc2 ) and source current (isa ) considering OPM 3 (100 V/div, 20 A/div, 50 ms/div). (a) PV array connectionwithout FFCL. (b) PV array disconnection without FFCL. (c) PV array connection with FFCL. (d) PV array disconnection with FFCL.

Fig. 8. DC-bus voltage (vdc ), FFC (iff ), dc-bus controller current (idc ), and PV array power (Ppv ) for abrupt solar radiation change consideringOPM 3 with FFCL (50 V/div, 14 A/div, 2 kW/div). (a) Solar radiation transient (5 s/div). (b) Solar radiation step down (100 ms/div). (c) Solar radiationstep up (100 ms/div).

Fig. 9. DC-bus voltage (vdc ), FFC (iff ), dc-bus controller current (idc ), and PV array power (Ppv ) for abrupt solar radiation change consideringOPM 3 without FFCL (50 V/div, 14 A/div, 2 kW/div). (a) Solar radiation transient (5 s/div). (b) Solar radiation step down (100 ms/div). (c) Solarradiation step up (100 ms/div).

Fig. 8 shows the FFC acting to improve the dynamic re-sponse of the PV system. Up to 10 s, the PV system is operatingnormally. At this moment, the PV array is disconnected and re-connected again after 20 s. Details related to the transients canbe observed in Fig. 8(b) and (c), where no oscillation is observedin the dc-bus voltage. During this time interval, in which the PVarray is disconnected, the PV system operates in OPM 1 and thedc-bus voltage reference is set to v∗

dc = 460 V. When the PVarray is reconnected, the MPP is reached in around 8 s, such thatv∗

dc = 525 V. Now, v∗dc is defined again by the MPPT algorithm.

Fig. 9 shows the results obtained when the FFCL is not con-sidered. As can be observed, the dynamic response of the PVsystem is slower. This happens because the dc-bus voltage con-trol loop must necessarily be designed to be slower than thecurrent control loops, as previously discussed in Section II.

Fig. 10 presents the results when step loads are performed(100% to 0% and 0 to 100%). It can be noted that even whenthe FFCL is acting, the PV system dynamic response is not

improved. This happens due to the FFCL acts only on the atmo-spheric disturbances to which the PV array is subjected.

VI. CONCLUSION

This paper presented a single-stage three-phase grid-tied PVsystem using the three-level NPC inverter. In order to improvethe PV system dynamic response, a current FFCL acting tospeed up the computation of the inverter current referenceswas proposed. Thus, improved PV system performance wasachieved when the PV array was subjected to climatic vari-ations, such as sudden insolation changes. As a result, boththe dc-bus voltage and grid-tied inverter currents dynamic be-haviors were improved with respect to the setting time andovershoot/undershoot). In addition, the PV system static behav-ior operating with active power-line conditioning was verified,where an effective PF correction was achieved. The performanceand feasibility of the PV system were evaluated by means of


Fig. 10. DC-bus voltage (vdc ) and load currents (iL a , iL b , iL c ) for stepload (100 V/div, 50 A/div, 500 ms/div). (a) OPM1/FFCL. (b) OPM2/FFCL.

extensive experimental results, validating the theoretical devel-opment.

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Leonardo Bruno Garcia Campanhol was bornin Rolandia, Brazil, in 1986. He received the B.S.degree in industrial automation technology andthe M.S. degree in electrical engineering fromthe Federal University of Technology, CornelioProcopio, Brazil, in 2009 and 2012, respectively.He is currently working toward the Ph.D. degreeat the Sao Carlos Engineering School, Univer-sity of Sao Paulo, Sao Carlos, Brazil.

Since 2013, he has been with the Depart-ment of Electrical Engineering, Federal Univer-

sity of Technology, Apucarana, Brazil, where he is currently an AssociateProfessor of electrical engineering. His research interests include powerelectronics applications involving unified power quality conditioner sys-tems, active power-line filters, photovoltaic systems, power quality, anddigital signal processing and applications.

Mr. Campanhol is a member of the Brazilian Power ElectronicsSociety.


Sergio Augusto Oliveira da Silva (M’13) wasborn in Joaquim Tavora, Brazil, in 1964. Hereceived the B.S. and M.S. degrees in electri-cal engineering from the Federal University ofSanta Catarina, Florianopolis, Brazil, in 1987and 1989, respectively, and the Ph.D. degreefrom the Federal University of Minas Gerais,Belo Horizonte, Brazil, in 2001.

Since 1993, he has been with the Departmentof Electrical Engineering, Federal University ofTechnology, Cornelio Procopio, Brazil, where he

is currently a full Professor of electrical engineering and Coordinatorof the Power Electronics, Power Quality and Renewable Energies Lab-oratory. His research interests include power electronics applicationsinvolving uninterruptible power supply systems, active power-line filters,photovoltaic systems, control systems, and power quality.

Prof. da Silva is a member of the Brazilian Power Electronics Societyand the IEEE Industrial Electronics Society.

Azauri Albano de Oliveira, Jr. was born in1955. He received the B.S and M.S. degreesin electrical/electronic engineering from the SaoCarlos Engineering School (EESC), Universityof Sao Paulo (USP), Sao Carlos, Brazil, in 1977and 1984, respectively, and the Ph.D. degreein electrical engineering from the PolytechnicSchool, University of Sao Paulo, in 1991.

Since 1978, he has been with the Depart-ment of Electrical and Computing Engineering,EESC, USP, where he is currently a Professor

of electrical engineering and the Coordinator of the Power Electronicsand Control Laboratory. His research interests include power electron-ics, electric machinery drives, wireless power transfer, and engineeringeducation.

Vinıcius Dario Bacon was born in Arapongas,Brazil, in 1991. He received the B.S. and M.S.degrees in electrical engineering in 2013 and2015, respectively, from the Federal Universityof Technology (UTFPR-CP), Cornelio Procopio,Brazil, where he is currently working toward thePh.D. degree.

Since 2016, he has been with the Departmentof Electrical Engineering, UTFPR-CP, where heis currently an Adjunct Professor of electrical en-gineering. His current research interests include

power quality, active power filters, renewable energies, and digital signalprocessing and applications.

Mr. Bacon is a member of the Brazilian Power Electronics Society.

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