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8/11/2019 Artigo Para Ser Traduzido Para o Ingls

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ELECTRONIC PROCESSING OF PHOTOVOLTAIC SOLAR ENERGY IN SYSTEMS

CONNECTED TO THE POWER GRID

[email protected]

[email protected]

UniversidadeTecnolgicaFederaldoParan

Av.MonteiroLobato,km04,PontaGrossa,Paran-CEP:84.016-210

UniversidadeFederaldeSantaCatarina,INEP

Caixapostal5119,Florianpolis, SantaCatarina-CEP:88.040-970

ABSTRACT

This article presents a photovoltaic system connected to the

commercial power grid in a centralized position and built

with a three-phase inverter with two stages which are capable

of extracting the maximum potential of photovoltaic panels.

The P&O algorithm is adopted as a technique of MPPT. The

isolation is made by a high frequency transformer. The

converter that composes the CC-CC stage dispenses thecontrol structure because it works with a ciclical reason and a

constant frequency within all of its operating range. This

makes the use of resonant CC-CC converters a good option

whose output is elevated in high frequencies favoring the

compression of power stucture. This way, the three-phase

converter with a resonant series is chosen to be part of this

stage. The MPPT is transferred to the CC-CA stage, that has a

electric current controler to the current injected in the electric

grid. The PWM three-phase inverter fed in tension, that

composes the CC-CA stage is controled and modulated in a

vectorial manner. The vectorial control imposes the Park

transformation to the line currents, from which results thedirect axis current. The MPPT uses the same variables from

the electronic current controler and maximizes the direct axis

current that reflects the power extracted from the photovoltaic

arrangement. This way, no specific measuring for the MPPT

is made, resulting in an economy of sensors.

Artigosubmetidoem29/10/2008(Id.:00914)Revisadoem19/03/2009,05/08/2009

AceitosobrecomendaodoEditorAssociadoProf.DarizonAlvesdeAn-drade

ABSTRACT

ElectronicProcessingofthePhotovoltaicSolarEnergyInGridConnectedSystems

Thispaperpresentsagrid-connectedphotovoltaicsystemin

centralizedconfigurationandconstructedwithathree-phase

dual-stageinverterabletoextractthemaximumpowerof

thePVmodules.TheP&Oalgorithm isadoptedasMPPT

technique.

The

isolation

is

achieved

by

a

high-frequencytransformer.

TheconverterusedintheDC-DCstagedis-

pensescontrol-loop, itsduty-cycleandswitchingfrequency

areconstantsthroughoutthepoweroperationrange.Thisen-

ablestheapplicationofDC-DCresonantconverters,whose

efficiency ishighathigh frequencies,favoringcompaction

of thepower circuit.Thus,the three-phaseseries resonant

converterischosentointegratethisstage.TheMPPTis

transferredtotheDC-ACstage,which,invariably,hasagrid

currentcontroller.Thethree-phasePWMvoltage-source in-

verter,intheDC-ACstage,usesvectorcontrolandspace

vectormodulation.ThevectorcontrolrequiresaParks

transformation

from

the

grid-currents

which

yield

the

directaxis

current.

The

MPPT

uses

the

same

variables

of

the

grid

currentcontrollerandmaximizethedirectaxiscurrentwhich

reflectsthepowerfluxfromthePVarray.Thus,anyspecific

measurementtorealizetheMPPTisnotneeded,resultingin

asmallcountofsensors.


2/13

KEYWORDS:

photovoltaic

system,

three-phase

dual-stageinverter,three-phaseseriesressonantconverter,MPPT.

1 INTRODUO

In this study a modified two-stage inverter is presented, which

is used in the processing of photovoltaic solar energy in

systems connected to the power grid. This is a innovative

equipment in many aspects whose conception emphasized the

reduction of costs, volume and weight. In this conception,

only commercially viable questions were addressed although

this application still isnt allowed by law in Brazil.

The direct conversion of solar energy to electricity is made by

photovoltaic modules. The cost of these equipments is the

main factor that defines the option for other generating

sources. A photovoltaic system does not produce toxic waste

as nuclear plants do, dont pollute the environment as

thermoelectric, coal or gas plants and dont involve any

environmental or social impact as do hydroelectric plants.

This way, the fundamental justification for the development

of this job are the great expectations for the reduction in the

cost of constructing solar cells, projecting something below

US$0,40/watt against the current US$4,00/watt

(Burger,2008). This reduction will proportionally lead to therise in the weight that the inverter exercises in total cost of the

system. Figure 1 shows a graph elaborated from data obtained

from the consultation to many inverter resellers for the

European and North-American markets, e.g. Alter Systems

(2008).

Seeing as the medium cost for the generation of

hydroelectricity is of US$1,00/watt, this same investment re-

Figure 1: Medium price announced of inverters connected to the power grid with

power up to 40kW.

relation per watt verified for an inverter of 10kW, the needfor a technological improvement of the inverters connectedto the grid becomes clear.

1.1 Brazilian Energetical Context

The system for production and transmission of electricity inBrazil is a hydrothermal system of great proportions with astrong predominance of hydroelectric plants that currentlysupport 80% of the electricity generated in Brazil.

To compensate the lack of investments in hydroelectric plants,the federal government created a program for theconstruction of gas powered thermoelectrics. In periods ofunfavorable hidrological conditions, these contribute to thecompliance to the consuming market in a complimentarymanner (Agency, 2005).

In the year of 2007, it was registered the greatest amount inthe consuming of electricity in the decade, about 5%. Thisgrowth is credited to sustainable growht of Brazil. Therationing, though, thanks to the low level of water reservoirswas evaded thanks to the activation of the thermoelectric

plants. But the largest part of the gas available in the marketis compromised with companies that, in the past few yearshave been using insume and with a growing fleet of vehiclesthat are moved by gas. Recent tests made by the Brazilian

National Operator of the Electrical System showed thatabout half of the capacity of the thermoeletric plants couldnot be reached due to the lack o fuel (O Racionamento,2007).

There will only be a sustainable development withinvestments in the generation of energy coming fromrenewable, in other words, those that dont consume fuelsand dont produce harmful wastes. This way, theconservation of the energy that is provided byhydroelectrical plants, role that is performed bythermoelectrical plants, could be auxiliated by photovoltaicsolar systems that are quite adequate to the integration withthe general urban environment.

Brazil has a high daily medium rate of solar radiation,reaching more than 5kWh/m per day in some regions(Agncia, 2005). By using photovoltaical modules with 40%efficiency that are in a initial phase of industrialization(Clula, 2007), 2kWh/m would be generated daily. This way,less than 10m on average, would be enough to supply oneconsuming unit of Santa Catarina whose average consuming

is of 503kWh per month, the largest of the south of thecountry (Celesc, 2008). This state has an average of 2,7inhabitants per consuming unit, in other words, permeasuring point.


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1.2 Photovoltaic Systems

Photovoltaic systems use tension inverters keyed to the

conditioning and synchronism of the exit of the

photovoltaic arrangement with the electrical grid. The

control exercises two main functions, tracking the point of

maximum power operation (MPPT) of the photovoltaic

arrangement and injects a sinusoidal current on the grid,

with a power factor close to the unitary.

There are three topologies of inverters that are connected to

the electrical grid (Carrasco et alii, 2006):

One stage inverters: in just one processing stage

the MPPT and the control of the current injected on

the grid are made.

Figure 2: Inverter with just one energy processing stage.

Two stage inverters: a CC-CC makes the MPPT

while a CC-CA converter is responsible for the

control of the current injected on the grid.

Figure 3: Inverter with two energy processing stages.

Multi-stage inverter: Many CC-CC converters

respond by the MPPT and one CC-CA converter

takes care of the current injected on the network.

Figure 4: Inverter with multiple energy processing stages.

The ways by which the photovoltaic modules are combined with the

topologies of inverters present themselves in four different

configurations.

Centralized inverter: Photovoltaic modules are

connected in series to form a row. Rows are connected

in parallel to form the arrangement, that provides

energy to the CC bus of na inverter. Seen in figure 5.

Parallel CC: Rows or arrangements are connected to

CC-CC converters. Just one internal CC bus feeds a

CC-CA converter. Seen in figure 6.

Parallel CA: Rows or arrangements are connected to

individual inverters. These inverters exits are

connected internally in parallel at the side of the CA.

Seen in figure 7.

Integrated inverter: each photovoltaic module has a

small inverter. These inverters are connected in parallel

at the side of the CA. Seen in figure 8.

Table 1 relates the topologies of inverters connected to the grid

with the possible configurations of photovoltaic systems.

1.3 Considerations

In some countries, like the U.S.A, the galvanic isolation between

the photovoltaic arrangement and the electrical power grid is

mandatory. Hence, thats why modern inverters tend to use a

high frequency transformer (Carrasco et alii, 2006). This

happens because the low frequency transformer is bigger,

heavier, more expensive and less efficient (Rashid, 2001). For a

high frequency transformer to be able to integrate the topology

of the inverter that is used in a photovoltaic system, the CC-CC

stage becomes indispensable.


4/13

Table 1: Options of implementation of a photovoltaic system

Figure 5: Centralized inverter conected to a photovoltaic arrangement.

Figure 6: Modules and inverter in a parallel CC configuration.

Figure 7: Modules and inverter in a parallel CA configuration.

Figure 8: Inverters integrated to their respective photovoltaic

modules.

According to Carrasco et alii (2006), in his considerations about

future tendencies, for the reduction in the cost per watt of inverters

connected to the electrical grid we would need to adopt a

centralized configuration. Besides, this configuration is pointed as

being the most appropriate for powers above 10kW, for being of

high efficiency and of low specific cost.

hhh Topologieshhhh

Configurations

hhhhhhh

Inverter

of one

stage

Inverter

of two stages

Inverter

of multiple

stages

Centralized inverter X

Parallel CC X X

Parallel CA X

Integrated inverter X


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From these considerations, you can direct the atention to the

two-stage inverter with a high frequency isolation which is

configured in a centralized plant of medium power. According

to Carletti et alii (2005), a medium power plant will operate

between 10kW to 500kW. A study about the structures that

could be employed on the two stages of the inverter will be

made next.

Carrasco et alii(2006) presents the Full-Bridge converter as the

most well employed representative of the CC-CC stage in

powers above 750W thanks to its good factor of transformer

usage. But in Ziogas et alii(1988), it is demonstrated that the

three-phase inversion is advantegeous when compared to a

monophasic one. Generally speaking, it is possible to see a

better distribution of losses in three-phase structures such as

that you can see that the components are forced to withstand a

relatively smaller effort. Capacitive or inductive filters have

their volume sensitively reduced because the current that goes

through them has a frequency which is higher compared to a

monophasic converter. Speaking specifically of the CC-CC

stage, Ziogas et alii (1988) demonstrated a reduction in the

volume of the high frequency three-phase inverter if compared

to a Full-Bridge. The combination of these advantages leads to

a improvement in the dynamic behavior, with faster answers.

Table 2 was elaborated by consulting the catalogs of some of

the main representatives of the market of inverters which are

connected to grid in the world. Its purpose is to maintain a

close relationship between this work and the commercial line.

All inverters are three-phase ones beyond 8kW. Non-isolated

equipments are the majority up to 10kW. They are light and

compact. From 5 to 10kW the parallel CC configuration is

preffered. With two to three CC-CC converters at the entrance,

there is more flexibility in the assembly of the photovoltaic

arrangement. Beyond 10kW all structures tend to be isolated.

The low frequency transformers are the most common ones,

which are installed in bulky and heavy inverters. The parallel

CA configuration is quite adopted to allow the use of high

frequency transformers. Some manufacturers even use fifteenCC-CA converters in a parallel CA configuration. The

centralized configuration with a high frequency isolation is the

combination that conducts electricity to the lighter equipments.

The MPPT is made at the CC-CC stage in all inverters that are

connected to the grid and that have a CC-CC stage, specially those

that are high frequency isolated.

The 15kW output seems to be the most promissing one in Brazil.

Even though the cost/watt tends to reduce, there are two practicallimitations for higher outputs. There could be a difficulty to find

areas that are big enough for the instalation of the photovoltaic

modules (an estimated amount of 130 of area would be needed for

15kW panels of our current technology) and not all secondary

three-phase transformers would accept the inverters connection

(generally, the smallest of the three-phase transformers are of

15kVA). It is is worth pointing that the inverter proposed in this

study is destined to urban areas, integrated to constructions. The use

of rooftops and windows would be an interesting starting point.

As conclusion, this study seeks to propose a two-stage inverter with

a high frequency isolation, configured in a centralized plant,

adequate to the processing of 15kW of outpot and that employs

three-phase inverters both in the CC-CC stage, and the CC-CA

stage.

2 MODIFIED TWO STAGE INVERTER

Although it is possible to consider the development of what was

proposed to this point as a contribution, questions related to control

still werent addressed. In this theme, this study proposes solutions

that give value to the inverter related to the state of the art.

In first place, one should keep in mind that both the MPPT and the

injected current controler of the grid are implemented in a digital

signal processor, which favors the usage of the vectorial control and

vectorial modulation. The realization of the MPPT frequently

passes by one or two fundamental methods which are known as

disturbance and observation (D&O) and incremental conductance

(IncCond). Of these, D&O are preffered specially in systems that

are are connected to the network and of high output (Hua et alii,

1998; Jing et alii, 2005).

In this study, it is proposed that the D&O is executed at the CC-CA

stage, in a way to make use of the processing capacity involved in

the control of the injected current in the electrical network, giving

origin to the Modified Two Stage Inverter, seen in figure 9.

This modified two stage inverter uses the same variables used in the

control of the injected current in the network to execute the D&O,


6/13

2

Ld

provoking a sensible economy of sensors. This way, with no

specific measurings for the D&O, it is possible to maximize the

output of the inverter and force the photovoltaic arrangement to

operate in the maximum power point, MPP.

The strategy for this to work is fundamented in a characteristic

that can be observed in CC-CC converters that makes them

reproduce in their exit terminals the same behavior of the

photovoltaic arrangement, when they are connected to it. A

very interesting aspect is that for the CC-CC converter to have

a behavior which is correspondent to the photovoltaic

arrangement, it must operate with constant ciclical reasons and

frequencies. It is demonstrated that this aspect makes

converters, in unfeasible aspects, to work with extreme

efficiency by all the operating range of the MPPT.

Figure 9: Two stage inverter with the MPPT being done on the CC-CA

stage.

2.1 CC-CC Stage

The most attractive three-phase CC-CC converters are those

that present smooth comutation since they can operate with

high keying frequencies which leads to significant reduction in

capacitive and magnetic elements. There arent many

three-phase CC-CC converters with smooth comutation

available in literature. A few of them (Doncker et alii, 1911;

Prasad et alii, 1991; Bhat e Zheng, 1996, Oliveira Jnior e

Barbi, 2005; Jacobs et alii,2004) were evalutated concerningtheir efficiency, number of components, emission of

electromagnetic interference, performance in assimetrical

operating conditions and aptitude to elevated outputs. The

structure presented in figure 10, obtained from Jacobs et alii

(2004), has showed itself as being insuperable in all aspects.

The transformer was echanged for its dispersion indutancies.

The transistors of one arm are activated in a complimentary

way. Between each arm there is a discrepancy of 120 in the

command pulses. When the keying frequency, f1, equals to the

resonance, fr, the converter operates in ZCS. If f1 > fr, the

converter will operate in ZVS. In this operating mode, a

reduction in the entry power, which is a normal opertating

condition of the arrangement, the converters efficiency reduces

drastically (Jacobs et alii, 2004). This way, for the ZCS mode, it is

possible to produce (1) and (2).

f

1

=fr=

1

In which: Iinav, VinavOutput and medium tension in the entry of

the CC-CC converter

IpaCurrent in the exit terminals of the photovoltaic arrangement.

Vdcav Medium tension in the exit of the CC-CC converter,

refered to the primary of the transformer.

RlossRepresents all the losses on the SRC3.

Although it has many advantages, the SRC3 has one deficiency

which makes it unfit to do the MPPT. Its keying frequency and its

ciclic reason are fixed variable (Jacobs et alii, 2004). So

concentrating all the control grids on the CC-CA stage is one of the

greatest merits of this study. This technique allows for such

defieciencies to be neglected.

2.2 CC-CA Stage

Photovoltaic arrangements have a behavior that is very similar to

that of a source of power. Hence why most of the CC-CA converters

that are connected to a network are fed in tension (Rashid, 2001), in

other words, have a CC bus in their entry, as shown in figure 11. The

high tension in the bus generally imposes the use of IGBTs in the

composition of the bridge of transistors.

The vectorial modulation, SVM, is employed in the deployment oftransistors in a way to minimize the THD of the current of the line.

A simetrical sequence is used to generate these trigger pulses. With

this, significant harmonic components only appear from keying

frequencies. The 5% limit of the THD which was established by

international laws is atended with the L filter of first order in the

connection with the electric grid. The combination of the vectorial

modulation with the use of the L filter of first order ended up with a

greater compactation and a reduced costs since the line inducers

were built with cores of iron and silicon. The ferrite is more

expensive and has a low density of magnetic flow.


7/13

From figure 11, it is possible to see that the Park transformation

(vectorial control) is used in the modeling of the converter,

from which results the direct axis current, Id.

3 CONTROL STRATEGY

The direct axis current Id represents the medium output which

has been injected in the electric grid, which is maximized by

the D&O algorithm. In it, the tension the bus CC, Vdc, is

disturbed while theId current is observed. The logic of the

D&O algorithm is described in table 3, whose mathematical

representation is in (3).

Vdc(k + 1)= Vdc(k) +

V

sign

[Vdc

(k)

Vdc

(k

1)]sign

[Id

(k)

Id

(k

1)]

(3)

The V greatness corresponds to the amplitude of the disturbance

which is applied in Vdc. This disturbance, as well as the period of its

application are adequately dimensioned in a way to evade the

instability of control (Fermia et alii, 2005)

Thesignfunction, that appears in (3), only extracts the signal of the

calculation made in its argument.

The system of figure 11 has more than one control entry, which led to

the abandoning of the theory of classic control favoring the theory of

control based in the space of states. Thus, the project of a servossystem

with state feedback and full control was developed (Ogata, 2003). The

state variables are generated from only two current sensors and one

tension sensor.. For the MPPT, no additional measuring is needed.

The dynamic model of the converter from figure 11 is presented in (4)

in a way to give better evidence to the state variables.

--It was not possible to import (4)

Id, Iq, VdcState variables.

Iquaxis current in quadrature.

Dd, DqControl entries.

VgTension of efficient phase of the electric grid.

WAngular frequency of the electric grid.

L, RIndutance and intrinsic resistance of the line inducers.

C2Capacitor of the CC bus.

Idc Resulting current from the division between the output

delivered to the CC bus and its tension, Vdc.

4 PROJECT PROCEDURE

Figure 12 presents the output structure of the modified two stage

inverter positioned between the photovoltaic arrangement and the

three-phase electric grid.

Although it has been established that the nominal output of 15kW is

the most adequate for the brazilian energetic context, a prototype of

4kW is projected in function of the availability of photovoltaic

modules in laboratory. The photovoltaic arrangement is composed

of 20 modules (two lines) KC200GT from Kyocera, in a total of

4kWp. The kWp unit represents the maximum potential that can be

extrracted from the photovoltaic arrangement, that is, the output in

STC (Standard Test Conditions Solar radiation of 1kW/m,

spectrum of 1,5 of air mass and temperature of photovoltaic cells at

25C). The specifications for the project of the inverter are:

Pin=4kW ; Vinav = 263V ; Iinav = 15,21 ; f1= 40kHz ; f2

=20kHz ; Vin=1%;Vg=220V

Perturbao

emVdcVariaodeId

Prxima

perturbao

+V Crescente +V

+V Decrescente -V

-

V Crescente -

V

-V Decrescente +V

Figure 10:Resonant three-phase CC-CC converter (SRC3)


8/13

215

1

V

In which:

PinNominal entry output of the CC-CC stage.

F2Keying frequency of the CC-CA stage

Vin - Tension ondulation in the photovoltaic

arragements terminal.

The SRC3s efficiency is estimated to be in n1=0,97 (Jacobs et

alii, 2004). It is then possible to calculate the output which was

delivered to the CC bus, as well as its tension, as seen in (5) and

(6). Vdcav is elevated to 816V due to the turn ratio of the

transformer.

P

dc

=

1

P

in

=

3880W

(5)

Vdcav

= 1Vinav= 255V (6)

The capacitor docked to the photovoltaic arrangement is

calculated in (7). A polyester capacitor of 680nF was used.

C1=Iinav

From (8) it is possible to obatin the value of the capacitor of the CC

bus, C2. The undulation over this capacitor,VC2=0,2V,

corresponds to a percentage of V. The value of C2 = 333uF is

adopted. This is the commercial value resulting from the association of

three electrolytic capactior of 1000uF. It is worth noticing that the tension in

this bus can approach 1000V.

C2 P dc / (12

2

Vg

VC2

f

2)

From three-phase transformer, built from three monophasics, a dispersion

of value Ld = 1,64uH was resulted. This way, each resonant capacitor

equals Cr= 9,9uF. This value, calculated in (1) is obtained by the parallel

association of three capacitors of polypropylene of 3,3uF.

The line inducers are calculated by (9), resulting in L = 9,3mH. The

undulation in the line of current is worthIL=0,42A which

corresponds to 5% of the current in the line of peak.

2

VgL = 4

f

2

IL

5 THEORETICAL RESULTS

The losses in the CC-CC stage are calculated in 0,32 isolatingRlossin (2).

By exchanging Rloss and (6) in (2), it is possible to trace the entry

characteristics of the SRC3, shown in figure 13. The parameters that

define this feature are its inclination and position. The inclination depends

on the losses. The position, of Vdc. This tension is controlled by the

Figure 11: Three-phase CC-CA converter fed in tension with the MPPT variables

Figure 12: Modified two stage inverter.


9/13

CC-CA converter. This way, the displacement in the I-V characteristic

of entry of the CC-CC converter is made by the CC-CA converter.

Figure 14 shows that the crossings between the curves that are

characteristics of the CC-CC converter and that of the photovoltaic

arrangement of 4kWp occurs practically over the points of maximum

output for various levels of radiation.

If the temperature varies, the CC-CA converter, by the P&O

algorithm, repositions characteristic I-V of SRC3 until it extracts the

maximum output from the photovoltaic arrangement once again. The

Id current reflects the output extracted from the arrangement. This

control action is ilustrated in figure 15. The tension Vdc is disturbed

in 4V every 50ms. Figure 16 shows the behavior of the exit output of

the photovoltaic arrangement by adjustments in the Vdc tension,

presented in figure 15. The error of relative tracking, R, will almost

reach zero in a permanent regime. This occurs thanks to the

aproximation between characteristic I-V of the entry of the SRC3 and

the MPP of the photovoltaic arrangement.

Figure 13: Characteristic I-V of entry of the SRC3 in nominal

conditions.

Figure 14: Crossing between the characteristics of the CC-CC

converter and the photovoltaic arrangement.

6 EXPERIMENTAL RESULTS

The three-phase CC-CA PWM converter fed in tension, adopted in

this study is the most used converter in the world when it is

necessary to inject energy that comes from a photovoltaic

arrangement in the three-phase electrical grid (Burget et alii, 2008).

Amongst the works that use this converter for these ends, some are

national (Schonardie e Martins, 2007; Cavalcanti et alii, 2006).

There are studies that point to advantages in its substitutions for

other structures like the three-phase CC-CA PWM converter fed in

current (Sahan et alii, 2008) or for multilevel inverters (Selvaraj and

Rahim, 2009). The most varied of current control in the power grid

techniques are employed and of MPPT. The LCL filter on the

interface with the network can make its structure more compact

(Blaabjerg et alii,2004). This is a very productive option for

researchers of this subjetct. The aplication for the three-phase

resonant series CC-CC converter in a two stage inverter is the focus

and the main contribution of this study. Thus, this section is

dedicated to the presentation of experimental results that relate to

the CC-CC stage of the two stage inverter.

Figure 17 presents the 4kW prototype implemented in laboratory.

Figure 15: P&O Algorith: Disturbance in Vdc as the variation

observed in Id.


10/13

The SK20GD065 and SK10GD123 modules were used, both

from Semikron. Each module has six IGBTs of 600V and

1200V respectively. Two SKHI61 command circuits were used,

also from Semikron, take the trigger pulses to these transistors.

The rectifying bridge was implemented with six ultra fast

FFPF05U120S diodes of 1200V and 5. The conditioning board

has two LA 25-NP current sensors and one LV 25-P tension

sensor, both from LEM, so it is possible to monitor the status

variables. In it the synchronism signal is also generated, which

is needed for the controler. The DSP TMS320F2812 responds

by control of the current injected on the grid, by the MPPT and

by the protection of lack of phase, that stops the inverter from

continuing operation when the electrical grid is de-energized.

Simultaneously, the DSP activates the CC-CC stage by using

six PWM ports. Trigger pulses with a frequency of 40kHz are

generated with a duty cicle of 50% and a idle time of 640ns.

Figure 18 presents the resonant currents in nominal operation

conditions. These currents flow by the three-phase transformer,

comprised by three monophasic transformers. The induction

dispersion of each phase are not exactly equal, obviously. This

provokes small differences in the amplitudes of the resonant

currents, which doesnt harm the SRC3s operation and doesnt lead

to a risk of saturation to the transformer. In normal operatingconditions, the continuous tensions that could saturate the

transformer are blocked by the resonant capacitors.

Figures 19 and 20 present the entry and exit currents of the SRC3,

behind their respective filters. These currents have a frequency that

is six times greater than that of the keying and low undulation,

resulting in a continuous flow of output. These are not common

features of the CC-CC converters, especially the monophasic ones.

From these features the atypical value of 680nF for the entry

capacitor, C1.

Figures 20 and 21 favors the visualization of the asymmetry

provoked in the Iin current and in the Vin tension by the differences

in the dispersions inductancies. The use of commercial transformers

would certainly reduce such asymetry.

The ZCS commutation is shown in figure 22. In low outputs this

commutaion becomes dissipative, as shown in figure 23. Theefficiency, shown in figure 24 was around 97,5% in nominal

conditions. Thus, the losses in the SRC3 can be recalculated by (6)

and (2), resulting inRloss= 0,26.

By changing the newRlossvalue in (10), equation derived from (2), it is

possible to obtain the inclination of the I-V entry feature of the SRC3 for

different tension values of the CC bus. Figure 25 confirms this result.

The entry feature of the SRC3 favors the MPPT. This becomes

evident when figure 25 (Vdc = 816) is superimposed over the

characteristic curves of the photovoltaic arrangement for a certain

temperature, resulting in figure 26. For each value of solar radiation

a crossing point between the features of the arrangement and

converter are established. It happens that the inclination defined in

(10) makes these crossings much closer to the MPPs, dispensing the

action of the MPPT in the case of rapid variations of atmospheric

conditions. The temperature varies slowly.

The normal tension of the CC bus corresponds to 816V and its

minimum operation value is around 600V. The inverter needs

tensions above this value to be able to inject current in electric grid.

Figure 16: MPPT performance, analised in the exit terminals

of the photovoltaic arrangement.

Figure 17: The prototype of the modified two stage


11/13

Figure 18: Resonant currents in nominal conditions.

Figure 19: Entry and exit currents of the CC-CC stage and

tension between the collector and emitter of the S1

transistor in nominal conditions.

Figure 20: Entry and exit currents of the CC-CC stage and

tension between the collector and emitter of the S1

transistor for P dc=500W.

Figure 21: Tension in the exit terminals of the photovoltaic

arrangement for P dc = 500W.

Figure 22: Tension and current in the S1 transistor in

nominal conditions.


12/13

7 CONCLUSION

In this study a conceptual change in the topology of the two stage

inverter employed on the processing of photovoltaic solar energy

connected to the power grid was made. Such conceptual change,

that consists in concentrating all of the control structure in the

CC-CA stage gives birth to the modified two stage inverter. In it,

no control action takes place over the CC-CC stage, in other

words, the frequency and ciclical reason are constant by all of the

operating range. Therefore, it was possible to apply the

three-phase inverter in its composition. Between many of the

advantages offered by this converter, the maximum undulation of

1% in exit tension of the arrangement, obtained with a polyester

capacitor of 680nF, whose cost is meaningless, excels.

Commercially, manufacturers adopt undulations of 2% below

10kW in outputs above 100kW and up to 10% for outputs below

10kW. These values usually are reached by capacitative banks that

reach some mili farads.

The low number of sensors that are required by the modified two

stage inverter is even more reduced by the innovative way in which

the D&O algorithm is executed, disturbing the tension on the CC

bus and observing the variation of the direct axis current. These

variables were generated as part of the control of the current

injected on the electric grid. This means that no specific measuring

for the MPPT was made.

Figure 23: Tension and current in the S1 transistor for P

dc=500W.

Figure 24: Efficiency of the SRC3.

Figure 25: I-V characteristic of entry of the CC-CC

converter for different tensions of the CC bus.

Figure 26: Superimposition of the characteristic curves of

the photovoltaic arrangements and of the entry of the

SRC3 for Vdc = 816V.


13/13

The MPPT algorithms tend to become slower as they become

more precise. Rapid changes in the atmospheric conditions

occur frequently. So, abrupt variations in the solar radiation

generally cause important losses. In this inverter, the entry

feature of the three-phase converter compensates almost

entirely the MPPs displacements. Theacting time is limited by

the response time of the CC-CC converter, which is much fasterthan the MPPT grid.

ACKNOWLEDGEMENTS

The authors thank FINEP and the CNPq for the financial

support destined for the development of this study.

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