Ingeniare. Revista chilena de ingeniería, vol. 21 N° 3, 2013, pp. 380-393

Methodology for the design of a stand-alone photovoltaic power supply

Metodología para el diseño de un sistema fotovoltaico autónomode suministro de energía

Julio López Seguel' Seleme Isaac Seleme Junior^ Pedro F. Donoso-Garcia^Lenin Martins Ferreira Moráis^ Porfirio Cabaleiro Cortizo^ Marcos A. Severo Mendes^

Recibido 27 de marzo de 2012, aceptado 24 de abril de 2013Reeeived: March 27, 2012 Accepted: April 24, 2013

RESUMEN

Este trabajo presenta una completa metodología para el diseño de un sistema fotovoltaico autónomoque maximiza el uso de la energía solar. El método propuesto prioriza la mejor opción en términos deeficiencia en cada etapa del proyecto. Para asegurar el correcto funcionamiento y extender la vida útil dela batería se propone una estrategia de control para el proceso de carga. Resultados experimentales sonproporcionados para un sistema fotovoltaico autónomo de baja potencia eléctrica destinado principalmentepara la iluminación y electrodomésticos básicos de hogares de bajos ingresos.

Palabras clave: Sistemas de energía fotovoltaica, convertidores de potencia DC-DC, almacenamiento deenergía, electrónica de potencia, buck.

ABSTRACT

This paper presents a complete methodology for the design of an autonomous photovoltaic system tomaximize the use ofsoiar energy. It is a method that prioritizes the best cost-effective choice at everystep of the project. In order to ensure the proper use and extended battery life time, a control strategyfor charging the batteries is proposed. Experimental results are provided for a stand-alone photovoltaicsystem with low electrical power, intended primarily for the illumination and basic appliances of low-income households.

Keywords: Photovoltaic power systems, DC-DC power converters, energy storage, power electronics, buck.

INTRODUCTION and an inverter, in case there are loads operatingwith AC voltage.

Autonomous photovoltaic systems are characterizedby having only the energy generated by photovoltaic A stand-alone photovoltaic system requirespanels as their source. Thus, one needs an energy maximizing the use of solar energy and the energystorage device, usually a battery bank, to ensure power storage in reserve, to achieve economic and technicalsupply at night or in periods of low solar incidence. sustainability. The low conversion efficiency ofIn general a single photovoltaic power system is commercial solar modules between 6 and 16% [1] andbasically composed of an array of photovoltaic the high cost of installafion are the major obstaclesmodules, a charge controller, one or more batteries of this type of generation. In order to increase the

Facultad de Ingeniería y Arquitectura. Universidad Arturo Prat. Av. Arturo Prat N° 2120. Iquique, Chile.E-mail: julio.lopez.seguel@unap.clDepartamento de Engenharia Eletrônica. Universidade Federal de Minas Gérais. Av. Antonio Carlos N° 6627. Belo Horizonte,Brasil. E-mail: seleme@cpdee.ufmg.br; pedro@cpdee.ufmg.br; lenin@cpdee.ufmg.br; porririo@cpdee.ufmg.br

López Seguel, Isaac S., Donoso-Garcia, Ferreira M., Cabaleiro C. y Severo M.: Methodology for the design of a stand-alone

efficiency of the system and, thus, reduce the costof the energy generated, it is necessary to ensurethat the system operates as long as possible on thepoint of maximum power of the panels. However,due to the characteristics of photovoltaic panelsthis point is variable and highly dependent onweather conditions and the system load. To ensurethe operation of photovoltaic modules at the pointof maximum power, even with weather variationsand variations in load, the use of a technique thatcontinuously seeks the point of maximum powermust be used. These control algorithms are knownas MPPT (maximum power point tracking) andcan increase the energy produced between 15 and30% [2].

One of the main factors for the successful use ofa photovoltaic system isolated from the grid is thecorrect sizing of its components. The basic parametersto consider are: the amount of energy to be producedin terms of the amount of energy being consumed.The design should aim to obtain a compromisebetween the photovoltaic energy available and theexpected energy demand. In order to maximize theautonomy of the system, we consider it necessaryto use high efficiency illumination of the LED orfluorescent lights which use an electronic ballastto manage the energy consumed in lighting. Theseelectronic ballasts can be fed through a DC bus. Wealso consider the need for AC voltage bus to theappliances which use this kind of voltage. Anotherimportant factor is the reliability of the system, whichbasically depends on the autonomy of the systemface to prolonged periods without sunshine. Somesimilar studies have been published in the literaturefor different applications and context [3-4].

This paper presents a methodology for sizing of themain components of an autonomous photovoltaicsystem in series connection. In a series system(Figure 1), the battery bank is placed in serieswith the flow of energy. The battery charger hastwo purposes, flrst to ensure the added batterylifetime via an appropriate voltage control of theloading process, and second to ensure by means ofsome MPPT technique to maximize the capture ofsolar energy provided by the PV array. The MPPTacts on the duty cycle to achieve maximum powervoltage (Vmax) of the panels. Furthermore, thevoltage control uses as reference for the batteriesthe optimum battery charge voltage (Vch) in order

to regulate the duty cycle, since Vmax and Vchusually do not coincide. The MPPT and the voltagecontrol must be independent, therefore, one needsa proper strategy to discern which of the controlswill be in operation.

An example will be presented where the conditions ofsolar energy available in the region are defined, andthe expected energy consumption of the residenceand the autonomy of the system is provided. Fromthe definitions above mentioned the sizing of thePV array, the battery bank and the battery chai-geris made. A strategy for the control of the powerconverter is also proposed. It should be noted that thesizing of the inverter is not addressed in this work.

DC Bus AC Bu.s

Inverter

Photovoltaicarray

BatteryCharge/MPPT

Figure 1. Block diagram of a stand-alone seriesphotovoltaic power supply.

SOLAR ENERGY CONSUMPTIONEXPECTED AND AVAILABLE

Determination of energy consumption of theresidenceThe expected daily power consumption was definedconsidering a stand-alone photovoltaic system withlow electrical power, intended primarily for theillumination and basic appliances of low-incomehouseholds. High efficiency lamps, low consumptiondomestic appliances and standard times of useprovided by [5] were considered. Table 1 showsthe installed load for residence under study, 98(W), and the daily energy consumpfion (DEC),approximately 326 (Wh/day).

Levels of solar radiation of the ioealityBelo Horizonte in Minas Gerais, Brazil was thelocation chosen for the installation of the system.Meteorological information was obtained through thedatabase of solar potential from CEPEL (referencecenter for solar and wind power - Brazil) [6]. Theaverage rates of solar radiation of Araxá, the closestcity to Belo Horizonte where records are available,were considered. The database from CEPEL gives

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Ingeniare. Revista chilena de ingeniería, vol. 21 N° 3, 2013

Table 1. Energy consumption expected in thehousehold.

Loads

Livingroom lamp

Bedroom 1 lamp

Bedroom 2 lamp

Bathroom lamp

Kitchen lamp

Satélite receptor

Color TV 14"

Stereo system

Total

Power(W)

11

8888

10

369

98

Use(h/day)

43313442

Energy(Wh/day)

442424

82440

144

18326

the rate of solar radiation to the angle that providesthe highest monthly minimum. Table 2 shows thevalues of radiation for the plane inclined at 13 degreesfrom the horizontal and pointed toward geographicnorth, which maximizes the average of the month.As the photovoltaic system must guarantee theenergy supply during all months of the year, thelowest incidence rate, which corresponds to themonth of June, with a daily rate of 4.90 kWh/m-,must be consider for the design.

Table 2. Monthly average daily radiation (kWh /m ) in Araxa for the installation angle ofthe modules which provides the highestmonthly minimum ( 13 ° to the geographicNorth).

MonthJanuary

FebruaryMarch

April

MayJune

July

AugustSeptember

October

NovemberDecember

Average

Radiation5.10

5.14

5.305.01

5.08

4.905.41

5.635.10

5.38

5.114,92

5.17

PV ARRAY AND BATTERY BANK

Sizing the PV arrayTo make a correct sizing of the panels and othercomponents of the system, it is important to know,besides the radiation conditions of the locality

in which the system will be deployed, and thecharacteristics of the load, other parameters whichare also important: the voltage levels that the systemwill operate are and, moreover, what the estimatedlosses of system components photovoltaic are.

Regarding the operating voltage of the system,it was fixed at 24 volts, to reduce the dc current,and consequently reduce the gauge of cables usedin photovoltaic system installations. The fact ofreducing the cuiTent tlowing through the systemhas a positive impact on its efficiency, because thelosses in the electronic components of the dc/dcconverter are significantly reduced [3]. Anotherbenefit of using a voltage of 24 volts is the widerange of commercially available devices that workwith this inverter input voltage.

As for the estimation of losses in the wiring, inthe battery stack, in the dc/dc converter and inthe inverter, default values suggested in [6] wereused. These values are presented in Table 3. It isimportant to mention that to calculate the systemlosses, estimate losses for a commercial drive werealso included. Even though it is not our objectiveto study the dc/ac conversion stage, it is necessaryto consider it for the correct sizing of the system.

The calculation of the minimum capacity ofgeneration of the photovoltaic modules is determinedby the solar energy accumulated (SEA) duringthe day in the location where the system will beinstalled. A convenient parameter to express thecumulative value of this energy is the number ofhours of full sun, i.e., the number of hours that thesolar radiation must remain constant and equal to1 kW/m- incident light power in "standard testcondition" (STC), as defined by IEC 61215 [7].

Table 3. Parameters for sizing the PV system.

Installed loadDaily energy consumption (DEC)

Monthly average daily radiation

Operating voltage of the DC (VQC)

AC output voltage (VAC)

Wiring efficiency* (ri, )

Battery bank efficiency* (rihaii)

Inverter efficiency* (ri¡^)

DC converter efficiency* (riDc)

98 W

326 Wh/day

4.9 w/m~

24 VllOV

98%

95%

85%

90%

* Default value suggested in (61.

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López Seguel, tsaac S., Donoso-Garcia, Ferreira M., Cabaleiro C. y Severo M.: Methodology for the design of a stand-alone...

For the city of Belo Horizonte, the number of hoursof full sun (FS) is:

SEA 4.9kWh/m' ^ ^ .FS = = — = 4.9 h

STC lkW/m-

One can say that the value of 4.9 kWh/m^ of dailyradiation is produced by 4.9 hours of constant incidentpower at 1000 W/m^. Thus, the parameters adoptedfor calculating the array of photovoltaic panels andother system components are presented in Table 3.

The specifications of the necessary minimum powerthe PV generator must be:

DEC 326 Wh"min = = = 66.53 W

FS 4.9 h

Considering the efficiency of the components ir\f),the minimum power must be corrected (P,„|„ Q^^ )using equation (3):

'^minCorr

where: TIT =

(0.98 0.95 0.85 0.9)

• ilbatt

= 93.41 W

Because weather conditions vary, it is necessaryto store enough energy not only for a night time,but for longer intervals with below-average solarradiation. It was determined that the system shouldhave an autonomy of 2 days (according to regulatoryresolution N" 83, September 20,2004 ANEEL [8],the Brazilian Agency for Electric Energy, whichdetermines this minimum value for low consumptionsystems) and that, upon returning from a conditionof maximum discharge, it fully recharges in 3 daysof normal sunlight (FRD).

The calculation of the power to maintain the autonomyof the system (Paut)> i-e., the power that the batterybank must supply to the loads can be calculated byequation (4). Therefore, the minimum power for 2cloudy days shall be:

Pau, = ' + = 93.4 1 { 1 + j ] = 155.68W

where NCD corresponds to the number of cloudydays.

For the case studied, two photovoltaic panels of80 W nominal power were chosen, connected inseries to provide a nominal voltage of 24 volts, thusa nominal installed power of 160 W. Two Isofotonpanels model 1-80 NP were used.

Sizing of the battery bankFor the sizing of the battery stack two importantparameters should also be considered: the autonomyof the system and the depth of discharge for batteriesaccepted. The autonomy of the system correspondsto the number of days in which the energy storedin the battery stack is sufficient to meet demandwithout any spare energy by the photovoltaic panels.This parameter representing the reliability of thePV; however the increase in the number of days ofautonomy of the system leads to a direct increasein the cost of the battery stack and consequentlythe cost of the system.

The depth of discharge of a battery is directly relatedto its lifetime. As can it be seen in Figure 2, the useof a high depth of dischaige impacts significantlythe battery lifetime.

S 40

a.

\

100% C

30» C

— ^

ischarge Depth

ischarge Depth

ischarge Depth

\

400 600 301 1000

Number of Cycles

Figure 2. Charge retention capacity with charge-discharge cycles for three maximumdepths of discharge in lead acid batteries[9].

The daily energy consumption of the PV system,considering the losses, is:

E =DEC 326 Wh

(0.98-0.95 0.85 0.9)• = 457.72 Wh (5)

The capacity (C) of the battery bank can be calculatedfrom the total energy to be stored (equivalent tothree days of operation - NDO) and the nominalvoltage

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C =NDO E 3-457.72 Wh

24 V= 57.21

The capacity value calculated in (6) implies thaton average the batteries will be subjected to dailycycles with depth of discharge at around 33%. Inorder to guarantee a minimum period of operation ofthe storage system of three years, one can determinethat 57.21 Ah is equivalent to 80% of total capacity.It can also be observed from Figure 2 that, for adepth of discharge 30%, the number of guaranteedcycles is approximately 1100. Thus, the minimumcapacity of the batteries (Cj-orr) is:

^

ö^57.21 Ah

0 8.,, ^, . ,

= 71.51 Ah (7)

Two batteries were chosen: brand Newmax FNC,model 12800, 80 Ah capacity and nominal voltageof 12 volts each. The batteries are connected inseries in order to provide the required voltage of24 volts DC bus.

Photovoltaic panel modelsIn order to obtain a straightforward way of describingthe electronic behavior of a photovoltaic cell it isuseful to create an equivalent electric model. Thesimplest equivalent circuit of an ideal cell is thatof a current source in parallel with a diode, havinga series resistance, Rg which describes the voltagedrop, the losses of the semiconductor material,the metallic contacts and their junctions. Anotherresistance in parallel Rp describes the losses of theelectrical perturbations and perturbations in the PNtransidon zones. Figure 3 shows the photovoltaicmodel where IpH represents the generated currentfor a given radiation, the diode D represents the PNjunction, I, is the current produced by the cell tothe external circuit, V is the voltage at the output

-AAA/ ' ^

D

terminals and Rp and Rs are the equivalent paralleland series resistances [10].

The Isofoton 1-80 NP photovoltaic panel modeledbased on the curves given by the manufacturer. Themathematical equations describing the panel are:

nk-T _ J

/ =/. .fiT.J^íi'^)]" r..

1000

(8)

(9)

(10)

with the parameters in Table 4, where V is the outputvoltage, I the output current, Ipi, the photocurrent,Ir the reverse saturation current, n ideality factor ofthe junction, T the environment temperature, q theelectron charge, k the Boltzmann constant, Ijc theshort circuit current, a the short circuit temperaturecoefficient of the cell, T the reference temperature,Pjuf, the incident radiation, I . the reverse saturationcurrent at T and EQ the silicon band-gap energy.

Table 4. Parameters for the 1-80 NP photovoltaicpanel.

Parameter

IscVQC

Tr

Irr

a«

Rp

RsEG

k

q

Value6.3 A21.6V

298.15 K1.7787 e-8 A

1.18 mA/K

1.20.46 n7 mi)

1.1 eV1.38e-23 J/K

1.6e-19C

The obtained model matches very well the curvesgiven by the manufacturer, as can be seen inFigure 4. Details on the procedure of model fittingare presented in [11] where the authors describe aprocedure to fit the model behavior to that obtainedwith commercial modules.

Figure 3. Photovoltaic Panel Model.

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López Seguel, Isaac S., Donoso-Garcia, Ferreira M., Cabaleiro C. y Severo M.: Methodology for the design of a stand-alone...

Obtained modelO Dataotlsoíotonl-SO

Voltags

Figure 4. Matching between the model and themanufacturer curve with radiationPsun=1000W/m2 and temperature

POWER CONVERTER

Choice of converter topology DC-DCGiven the configuration of the PV array (two panelsI Isofoton NP-80 connected in series), and therange of the operation voltage of the battery stack(between 21-28.8V), the topologies best suited forthe battery charger would be the Buck topologyand Buck-Boost topology (acting only as a voltagestep-down), since the maximum power voltage ofthe PV array is the larger than the operating voltageover a wide range of incident radiation (Figure 5).

Voltage (V)

Figure 5. Operating range of the charge controllerobtained from the simulation of the PVarray.

From the standpoint of ease of implementation, theBuck converter would be more appropriate, since theBuck-Boost converter inverts output voltage, whichcould lead to a more complex wiring diagram toanalyze and implement [11]. Nevertheless it is nota conclusive argument. Thus, given the applicationfor which the converters are designed, it is assumed

that an analysis on the relation of powersPx) is the most appropriate. In this analysis, PQrepresents the power output of the converter andPx the power used by the switching elements.For the analysis described one assumes that: a)the current ripple is neglected, i.e., the converteroperates only in continuous conduction mode, b)the output voltage ripple is negligible, c) the inputvoltage can vary, implying that the duty cycle mustbe controlled to maintain constant output voltage.With these assumptions, it is possible to calculatethe peak voltage and current in the switch, allowingthe calculation of Px. By knowing this value it ispossible to draw the curves that relate the switchloss power with the output power for the cycle.These curves are shown in Figure 6 for variousDC/DC converters [10].

' Duty Cycle

Figure 6. Energy use in several DC/DC converters.

It can be seen from Figure 6 that the use of theswitching elements in Buck converters is quitegood, since the output voltage and input are of thesame order of magnitude. Rather, the Buck-Boostconverter switches have a lower rate of use fromthe point of view of energy efficiency, peaking at25% with a duty cycle of 0.5, i.e., for situationswhere the input voltage is equal to the output.Thus, since energy efficiency is very importantfor photovoltaic applications, the choice of a Buckconverter is considered, for the case studied, the mostappropriate. Figure 7 shows the typical topologyof a Buck converter.

Selection of the inductorA Buck converter operating in continuous conductionmode presents the following relationship betweenthe average input voltage Vj, and output voltage,VQ in steady state: V(,=DVi. When considering theboundary condition of maximum power available, an

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Ingeniare. Revista chilena de ingeniería, vol. 21 N° 3, 2013

Vi — 4= Load Vo

Figure 7. Buck converter topology.

incident radiation of 1000 W/m^ and the temperatureof the modules as equal to 15 °C, one can obtain bysimulation, the operation of the arrangement. As itcan be seen form Figure 8, the open circuit voltageX)c = 44.6 V, the maximum power voltage V^ x -35.74 V, the maximum power current, I. ^ = 4.88A, and the maximum power being P^^^ = 174.57 W.

7457180

120

., 100

; 60

40

20

/

/

/

/

/

/

\

0 « 20 3674

Voltage (V)

G 10 aD 35.74 440

Voilage (V)

Figure 8. Simulation curves for the PV airay givenas a radiation boundary condition of 1000W/m^ and panel temperature of 15 ° C.

Since the module power depends on the voltage atits terminals and consequently on the duty cycle, andthat in the ideal power converter, input and outputpowers are equal, the output current should followthe power variation. The maximum average cunent,lomax' in the output occurs for the maximum powercondition of PV array (174.57 W) and a minimumvoltage at the battery stack (21V). So, the maximumaverage current, Io ax = 174.57 W / 21 V = 8.31 A.

Considering an ideal Buck and neglecting the outputvoltage ripple, the inductor current ripple in outputcan be given by the following relationship [11]:

0 ( 1 - 0 )f L (11)

when D is minimum and the converter input voltageis maximum. However, the minimum value of Ddepends on V according to:

i max(12)

So the maximum current ripple in the inductor fora given operating condition can be represented as:

f-L(13)

From equation (13) it is clear that the maximumripple current in the inductor is when D^j,/!- D in)is maximum. Figure 9 shows the curve of Dn,i„(l-Dn,¡n) as a function of the battery bank voltage. Herewe see that for a voltage of 22.3 V in the batterybank (duty cycle D = 0.5, considering V = 44.6)one has the highest value for ^^xxk 1 " O| j„) = 0.25and as a result the highest inductor current ripple.Defining a switching frequency of 24 kHz for theproject, and accepting a current ripple of 10% ofthe maximum average output current Iomax» oneobtains the value of the inductance for the inductorfrom equation (13).

L =44.5-0.25

24000-0.1-8.31= 558 I

22.3 23 24 25 26 27 28

Voltage iti the bank of batteries (V)

Figure 9. Simulation curve Dmin(l-Dfnin) as afunction of the voltage at the batterybank for Vi,,,ax = 44.6 V.

Where f is the switching frequency and L is theinductance of the output filter, D is the duty cycle ofthe converter and Vo is the average voltage output.Thus, for a given V , the maximum ripple occurs

Selection of the output capacitorThe alternating component of the inductor currentcirculates in the output capacitor C of Buck converter,while the dc component circulates in the battery

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López Seguel, Isaac S., Donoso-Garcia, Ferreira M., Cahaieiro C. y Severo M.: Methodology for the design of a stand-aione..

bank. The current in the capacitor causes both avariation of the charge in the capacitor as well as avoltage drop across the parasitic series resistance.Below are given the expressions of the capacitorvoltage ripple caused by the load variation (AVßcap)(14) and the voltage ripple (AVQ.RSE) caused by theequivalent series resistance (RSE), respectively

^c f(14)

(15)

A maximum ripple voltage caused by load variationof 1 % of the minimum value of the average outputvoltage is acceptable. Thus, by manipulating equation(14), one determines the minimum capacitance ofthe output capacitor:

Ai, 0.1-8.31

0.01-21-8-24000= 19.85 |iF

For the voltage ripple caused by the parasitic seriesresistance, one chooses also a maximum value of 1 %of the minimum value of the average output voltage.Thus with (15) one calculates the maximum parasiticresistance admissible for selecting the capacitor:

RSE = 0.01-21

0.1-8.31= 252.7

Selection of the MosfetFor the choice of Mosfet, its losses were calculated.These losses, when a Mosfet is used in a staticconverter, are analogous to the losses of a bipolartransistor, i.e., a portion is associated with theconduction losses and the other with the switchinglosses. The total losses in the Mosfet as a functionof the duty cycle can be estimated as [12]:

In which rds(on) corresponds to the drain-sourceresistance when conducting, IQ is the average switchcurrent, D is the duty cycle, Vj is the drain-sourcevoltage applied to the Mosfet, f the switchingfrequency, t the rise time of current and tf is the

fall time of the current in Mosfet, while C¿^ is itsdrain-source capacitance.

After testing several models, the one with the smallestlosses, the IRF540Z International Rectifier Mosfetwas chosen. Table 5 presents the most relevantparameters required for this Mosfet loss calculation.Figure 10 shows the simulation of the total losses asa function of the duty cycle for the Mosfet chosen.The highest loss occurs for a duty cycle D = 0.605and corresponds to 1.407 W.

Table 5. Electrical characteristics of MosfetIRF540Z.

Parameter

VDSS

^dsion)

tr

^D(max)

tf

Value

lOOVdc26.5 mfi

51 ns36Adc

39 ns80 pF

0.605 0.7

Duty Cycle

Figure 10. Simulation of the total losses in theMosfet chosen as function of the dutycycle D, for Vo=2 IV.

Selection of the DiodeJust as in the case of the Mosfet, the diode presentsconduction and switching losses. Because of using aSchottky diode in this project, the switching losseswere ignored. Therefore, only the conduction losseswere considered, which are given as a function ofduty cycle for the Buck converter, as [10]:

In which rx is the direct conduction resistance ofthe diode. Ig the average current through the diode,Irms the effective current through the diode, D theduty cycle and Vf the voltage drop on the diode in

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Ingeniare. Revista chilena de ingenieria, vol. 21 N° 3, 2013

conduction. The maximum average current thatthe diode must withstand is 8.31 A, which is thecondition of maximum power delivered by the PVarray used in the design of the Buck converter. Themaximum blocking voltage of the diode will be 44.6V, which is the open circuit voltage of the set for thisweather. Another important parameter in the choiceof the diode is related to losses: it is important thatthe diode has a low conductance resistance. Afterreviewing several models, we have chosen theMBR20100CT of International Rectifier, becauseit complies with project specifications and it wasthe one with the lowest losses of the diodes tested.

Table 6 presents the most relevant electricalparameters for the chosen diode, from its datasheet.Figure 11 shows the simulation for the calculation oflosses for the Schottky diode as a function of dutycycle, D. The highest loss occurs for a duty cycleD - 0.558 and corresponds to 3.866 W.

Table 6. Electrical characteristics of the diodeMBR20100CT.

Parameter

IF(AV)

VR

Vr

fr

Value20 A100 A

0.95 V15.8 mW

Duty Cycle

Figure 11. Simulation of the total losses in the diodeSchottky as a function of duty cycle D,forVo=21V.

CHARGER CONTROL STRATEGY

The lead-acid batteries need a strategy to control theirprocesses of loading and unloading to prevent earlydegradation of its acdve material and consequentreduction of its estimated lifetime. Thus, during

the charging process the charger should match theflow of energy delivered from the battery to ensurea full charge within the limits of voltage, currentand battery temperature. Also, during the processof discharging the driver should avoid the batteryof discharging beyond its limit of energy supply.

A fast, safe and complete charging cycle of a Lead-acid battery, according to some manufacturers, isto divide the process into three regions, which are:(1) charging the battery when deeply discharged(bulk charge); (2) overcharge region, which is anintermediate region and (3) float charge, when thebattery is practically charged. Figure 12 describes thevoltage-current characteristics of these three stages.

Region 1 ,

- ^

Region 2 Region 3

c:::zi:.

f^

g V.

Time (sec)

Figure 12. Battery charging region.

In order to provide a complete charge for the batteryan elaborated control strategy must be applied,such that the battery would be charged as fast aspossible, within its operation limits, given that thedaily generation period for the photovoltaic panelsis limited.

In the first region, corresponding to fully dischargedbattery it is important that the arrangement ofphotovoltaic modules operate at the maximum powerto apply the largest admissible current to the batteriesin order to charge them in the shortest time intervalpossible. That is when the MPPT technique is used.The algorithm implemented was the IncrementalConductance MPPT [13].

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López Seguel, Isaac S., Donoso-Garcia, Ferreira M., Cabaleiro C. y Severo M.: Methodology for the design of a stand-alone..

For the second region, corresponding to partiallycharged battery, it has been proposed a strategyof constant charging voltage with current dmit.According to the manufacturers of batteries, thismethod is most suitable for lead-acid batteries, sinceit protects the battery against overload during thefinal stage of load fiuctuation [14]. The strategy ofconstant voltage with current limit was implementedwith two cascaded control loops, an inner loop tolimit the recharging current and an outer loop tomaintain constant reference voltage. This outerloop is regulated at the equalizadon voltage, i.e.,28.8 V [14].

For the third region, which is when the battery isalmost fully charged, the same strategy as for thesecond region remains, only with a different voltagereference of 27 V. To avoid a deep discharge, beyondwhat is admitted by the manufacturer, the controllerwill have to perform the disconnection of the loadevery dme the voltage at the bank terminals reachesits minimum allowed value of 21 V.

Voltage controlFigure 13 shows the proposed strategy for thecontrol voltage, where Gv(s) corresponds to thetransfer function of the compensator loop voltage,Gi(s) to the transfer function of the compensatorcurrent loop, Hi(s) to the transfer funcdon of thecurrent sensor, Hv(s) to the transfer function of thevoltage sensor and KM(S) corresponds to the transferfunction of the PWM modulator. For the linearmodel of the buck converter, Gi(j(s) correspondsto the transfer funcdon relating the work cycle dwith the inductor current /" , Goi(s) correspondsto the transfer function reladng ¡^ with the outputvoltage ^° . Blocks Gipv(s) and Gip(s) represent the

perturbations ofsmall signal input voltageload current ip respectively, over /" .

and

Modeling the BuckThe transfer functions of the Buck linear modelwere obtained averaging the variables in state spacewhich is valid for small variations around the pointof operadon at steady state. Detail of the approachis shown in [12]. The transfer funcdons obtainedare shown below:

ÍL(S) __ 0.0009544 J-I-0.8294

Vpy(s) 6.443x 10"' .s- + 0.000859 .s + 5.04

¡i(s) 0.04027-.?+ 35

d(s) 6.443x10"' -.s- +0.000859-5 + 5.04

¿L(.Î) -0.000253-.i--5

jQj (S) — —i

6.443x10"'•

0.000253-.S'-H5

i_(s) 0.001151-.5

(18)

(19)

(20)

(21)

Aiming to prove the validity of the average modelobtained for the Buck, its behavior was comparedwith the switched circuit, using the Power Systemstoolbox of Matlab. Figure 14 shows the dynamicsof the output voltage of the converter in responseto a voltage step of 10% of provided voltage bythe PV array. The result shows that the averagemodel behaves satisfactorily. Several tests weremade showing that for every small variadon in theinputs of the converter resulted in accurate averagevoltage dynamics.

33

S

31

30

28.8

26

_

switched circuitaveraged model

L ...t

, X\ ^ .A X>

001 0.015 0.02 0.025 003 0 Q35 D04Time (SBC)

Figure 14. Comparison of the switched circuit andthe average model behavior.

Analogical compensatorsIn order to obtain the digital compensators theindirect method was chosen. In other words, trom the

Figure 13. Block diagram of the voltage control. development of an analogical controller one obtains

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Ingeniare. Revista chilena de ingeniería, vol. 21 N° 3, 2013

a discrete controller with similar performance forany given discretization technique. In this study weopted for the methodology proposed in [15] for thedevelopment of analogical compensators, the startingpoint being the frequency response of the converter,modeled with the average value of the variables.

Figure 15 shows the structure of the controllers usedfor both the loop voltage as for the current loop,which according to the methodology proposed in [ 15]has been suggested when the phase lead required isless than 90°. Its transfer function is shown in (22):

Figure 15. Structure of compensator used.

(22)

The current controller was adjusted to have a phasemargin of 60° and a cutoff frequency of 1/5 of theswitching frequency, which is 4800 Hz. Equation(23) shows the transfer function obtained. Thevoltage controller was set to have a phase margin of60° and a cutoff frequency of 1/25 of the switchingfrequency, which is 960 Hz. Equation (24) showsthat the transfer function designed for this controller.

G, (s) =1-h 0.00012-.v

2.297 10"" •5^+2.506-10" -5

1 + 0.0003448-5

'2.205 10"^-5^+0.0002766 s

(23)

(24)

Figure 16 shows the Bode plots for the designedcurrent compensator, for the system withoutcompensation and for the compensated system. Theanalysis of the diagram shows that all establishedspecifications are met: cutoff frequency of 4.8kHz and phase margin of 60°. Figure 17 shows theBode plots for the designed voltage compensator,for the system without compensation and for thecompensated system. The analysis of the diagramallows checking that the specifications imposed forthe voltage loop control were also met: bandwidthof 960 Hz and phase margin of 60°. In order to

observe the performance of the controllers, theclosed-loop system was simulated. Figure 18 shows

SodeDlagr»nGm = hf dB (at hf Hz). Pm = 60 deg (at 4.8e*aO3 m)

uneompensated system

controller

compensated system

10 10 10

Frequency (Hz)

Figure 16. Bode diagram for the current loop.

Bode DiagramGm» 23 dB (al 6.568+003 Hz). Pm - 60 deg (at 960 Hz)

•100

o

uneompensated system

controller

compensated system

— —

Freciuency (Hz)

Figure 17. Bode diagram for the voltage loop.

jmmmmmmmmmmm

0.028 0.0285 0.029 0.0295 0.03 0.0305 0.031 0.0315 0.032 0.0325 0.033

0028 0.0285 0029 0.0295 0.03 00305 0031 0.0315 0.032 0.032S 0.033Time (sec)

Figure 18. Waveforms for the output voltage andinductor current response to a step inputvoltage of 20%.

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López Seguel, Isaac S., Donoso-Garcia, Ferreira M., Cabaleiro C. y Severo M.: Methodology for the design of a stand-alone.

the dynamical behavior of the load voltage and theinductor current to a variation in the load currentof 20%. According to the results obtained, controlperformance is satisfactory given the quick transientresponse to disturbances considered.

Discrete time compensatorsThe criterion used for selecting the discretizationmethod was based on the best preserved frequencyresponse. Using the discretization tools of MatlabBode gain and phase curves were obtained forvarious methods. For the current compensator case,the technique that best preserves the properties offrequency response is the Bilinear Transformationwhich maintained the properties of gain and phaseof the analogical current compensator at least asfar as the cutoff frequency (4800 Hz) as it can beseen in Figure 19. As for the analogical voltagecompensator, the Linear Interpolation technique

Î :— -i-i-

rKT

-Hrl----

m

1—•n—1

" /

1

--; GiW

10- 10'Frequency (Hz)

Figure 19. Bode diagrams for the analogical anddiscrete current compensator.

Frequency (Hz)

Figure 20. Bode diagrams for the analogical anddiscrete voltage compensator.

has been chosen; the compensator preserved theproperties of phase and gain as far as, at least, thecutoff frequency (960 Hz), as shown in Figure 20.Equation (25) presents the driver discrete currentloop transfer function, and (26) the discrete gridvoltage controller:

G,iz) =39.02-z^-HI.55-z-27.47

2^-0.611-2-0.389

0.2872-2^-0.003165-2-0.2227

2^-1.593-2 + 0.5929

(25)

(26)

Figure 21 shows the response of the output voltageof the average model and its discrete time equivalentsubject to an input reference step from 28.8 V to27 V. It can be observed an increase in overshootfrom 13% in the continuous model to 20% of thediscretized one. Yet, it can be considered acceptablefor the purposes of this study.

Discrete systemcontimxus system

I •

Time (sec) x io

Figure 21. Response to a reference step for thecontinuous and discrete system.

The detailed modeling of the buck converter bymeans of the average switching technique, themethodology used for the design of the controllersand the discretization process of the analogicalcontrollers, fall outside the scope of this study andare not presented, however they can be found indetail in [16].

The control system was implemented using aTMS320F2812 digital signal processor from TexasInstruments. Figure 22 shows the flowchart of thestrategy developed and Figure 23 shows proposedthe control scheme.

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Ingeniare. Revista chilena de ingeniería, vol. 21 N° 3, 2013

Activate relaydisconnection

load

Figure 22. Flowchart of control strategy proposedfor the battery charger.

Figure 23. Control scheme proposed for the batterycharger.

EXPERIMENTAL RESULTS

A battery charger was developed using a Buckconverter. The prototype is divided into three maincircuits, a measuring board, a signal conditioningboard and control, and a driving card (Figure 24).

Several tests were made to validate the operationof the charger. Figure 25 shows the test performedin a clear day without clouds throughout the wholetest. The batteries were at 15% of their full charge,approximately, at the beginning of the test. Threerelevant variables were measured: the power issuedby the panels, the recharging current and the voltageat terminals of the battery stack at intervals of 30seconds, between 10:00 A. M. and 5:00 P. M.

Figure 24. Prototype for the battery charger.

10:00 11:00 12:00 13:00 14:00 1S:00 16:00

0 00 n o o 12:00 13:00 14:00 15:00 16:00 17:00

. Bulk charge

^ . - - - - - • ^

MPPT

' Overcharge

Voltage control

1 1 1

Float charqe-

10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

Time (Hours)

Figure 25. Curves obtained in the test for chargingthe battery bank.

CONCLUSIONS

This paper presents a complete methodology for thedesign and construction of a stand-alone photovoltaicpower supply. AH stages of development are carefullystudied and the most efficient solution is adopted.On the other hand, the method sought to preventthe battery from malfunction in its operation thatcould compromise its durability. Therefore, a controlstrategy for the battery charge is also proposed. Thiscontrol strategy is also in charge of maximizing theproduction of photovoltaic energy by incorporatingan MPPT technique. The proposed methodology canalso be replicable to other photovoltaic systems ofgreater electric energy consumption. Finally, thiswork is intended to be very practicing engineerorientated with useful guidelines on dimensioningand choosing the most appropriate converter andelectronic components. A practical example with

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López Seguel, Isaac S., Donoso-Garcia. Ferreira M., Cabaleiro C. y Severo M.: Methodology for the design of a stand-alone...

experimental data for the battery charging processhas been given,

ACKNOWLEDGMENTS

This work was sponsored by Programa demejoramiento de la calidad de la educación superior(MECESUP-Chile) and Fundaçào do Amparo àPesquisa de Minas Gérais (FAPEMIG-Brasil).

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[13] S.J. López, S.I. Seleme Jr., P.F. Donoso-Garcia, L.F. Moráis, PC. Cortizo and M.A.S.Mendes. "Comparison of MPPT approachesin autonomous photovoltaic energy supplysystem using DSP". Industrial Technology(ICIT), 2010 IEEE international conferenceon. pp. 1149-1154. March, 2010. ISBN:978-1-4244-5695-6.

[14] Newmax. "Manual Técnico Série 12 volts".Fecha de visita: June 17,2009. URL: http://www.newmax.com.br/baterias/br/pages/downloads, asp

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