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Solar Energy 86 (2012) 2383–2396

Analysis and implementation of an adaptative PV based batteryfloating charger

Nabil Karami a,⇑, Nazih Moubayed b, Rachid Outbib a

a Laboratory of Sciences in Information and Systems (LSIS), Aix-Marseille University, Marseille, Franceb Department of Electrical and Electronics, Faculty of Engineering 1, Lebanese University, Tripoli, Lebanon

Received 3 August 2011; received in revised form 9 March 2012; accepted 7 May 2012Available online 6 June 2012

Communicated by: Associate Editor Elias Stefanakos

Abstract

In a system composed of a photovoltaic (PV) cell, a converter and a resistive load, the Maximum Power Point Tracking (MPPT)techniques are applied at the output of the PV panel and not at the level of the load. In this study, the considered load is a batteryat different States Of Charge (SOC) that is charged by the PV panel. The power consumed by the battery is related to its SOC. Conse-quently, an empty battery consumes more current than a charged one. At full state of charge, the battery does not call for more energyand thus it is not rewarding to extract more power from the PV panel.

Besides, in a stand-alone photovoltaic system, the size of the PV panel and the battery should be respected. Thus, the PV current atdifferent irradiances should be compatible with the charging current required to charge the battery at different SOC. A critical situationoccurs at high irradiance when the PV panel delivers a high current at Maximum Power Point (MPP) that exceeds the tolerated chargingcurrent. The current reaches the top limit when the battery is totally empty, caused by the big difference in potential between the con-verter output and the battery voltages. In this case, the battery starts to gas when attempts are made to charge it faster than it can absorbthe energy. On the other hand, in a fully charged battery, the difference in potential between the converter and the battery is zero. In thiscase, there is no need to track the MPP.

In this study, we will focus on the load type and suggest new methods to reach the MPP depending on the load state. In the proposeddesigns, the components of the stand-alone system are protected even if they are not well sized. In addition, we will focus on the devel-opment of the PV array mathematical model. The results achieved with the system, as well as the experimental results of a laboratoryprototype, will be given.� 2012 Elsevier Ltd. All rights reserved.

Keywords: Renewable energy; Solar panel; Photovoltaic cell; Battery; DC/DC converter; MPPT

1. Introduction

Photovoltaic energy has become one of the most prom-ising sources of energy as it is a free and sustainable energy.A PV array under constant uniform irradiance has a cur-rent–voltage characteristic (I–V curve), as shown inFig. 1. There is a unique point on the curve, called the max-

0038-092X/$ - see front matter � 2012 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.solener.2012.05.009

⇑ Corresponding author.E-mail addresses: [email protected] (N. Karami), nmoubayed@

ieee.org (N. Moubayed), [email protected] (R. Outbib).

imum power point, at which the array operates with max-imum efficiency and produces maximum output power(Tan et al., 1991; Hohm and Ropp, 2000). When a PVarray is directly connected to a load – ‘direct-coupled sys-tem’ (Fig. 2a), the system operating point is at the intersec-tion of the I–V curve of the PV array and the load line. Ingeneral, this operating point is not at the PV array’s MPP,which is clearly seen in Fig. 1. That is, the MPP of the PVgenerator is reached only in some moments throughout theyear. Thus, it is possible to talk about lost PV generatorutilization, therefore, in a direct-coupled system, the PV


mailto:[email protected]

mailto:nmoubayed@ ieee.org

mailto:nmoubayed@ ieee.org

mailto:[email protected]


0 0.5 1 1.5 2 2.5 3 3.50

1

2

3

4

5

6

7

8

Vmp

Imp

Voc

IscMPP

DC load line

Operating point

Voltage (V)

Cur

rent

(A)

Current vs. Voltage curve

Fig. 1. Maximum power point location on the current versus voltagecurve.

Fig. 2. PV coupling methods: (a) direct coupled method and (b) couplingwith MPP tracker.

2384 N. Karami et al. / Solar Energy 86 (2012) 2383–2396

array should be oversized to ensure that the load powerrequirements are complied with. This leads to an intolera-bly expensive system (Salas et al., 2005).

To overcome this problem, a switch-mode power con-verter, called a maximum power point tracker, is used tomaintain the PV array’s operating point at the MPP(Fig. 2b). The MPPT does this by controlling the PV arrayvoltage (or current) independently of that of the load.

The MPPT of photovoltaic cells has been a researchtopic over the past few years, with the aim of reachingthe maximum power point in minimal time and error(Moubayed et al., 2008; Esram and Chapman, 2007). Sev-eral algorithms for control of the switching convertersachieve MPP (Jain and Agarwal, 2007). Some of the widelyused schemes are the hill climbing methods (Bose et al.,1985), the incremental conductance method (Husseinet al., 1995), the ripple based method (Calais et al., 1998)and the constant voltage method (Salameh et al., 1991).These techniques differ in many aspects including simplic-

ity, convergence speed, hardware implementation, sensorsrequired, cost range of effectiveness and needs for parame-terization. All these techniques focus on the maximum PVpower extraction regardless of the load types and natures.

This paper is organized as follows. The different types oftrackers are described in Section 2. The mathematicalmodel of a PV cell and the maximum power point trackerare reviewed in Sections 3 and 4, respectively. An open anda closed control loop for DC/DC buck converter designsare available in Sections 5 and 6, respectively. Section 7proposes a design using a microcontroller with three differ-ent circuits and algorithms that manage the current and thevoltage depending on the battery SOC. The final design iscalled a PV based battery floating charger, which protectsthe PV panels and increases the battery lifetime by control-ling the converter output voltage with respect to the con-sumed current, the available PV current and theconverter Mosfet tolerated current.

2. Type of trackers

2.1. Motorized solar cell tracking

Motorized tracking consists in implementing PV panelson a mechanical rotating board with different control strat-egies depending on the country and the day of the year.There are two types of mechanical tracker: single-axistrackers and dual-axis trackers.

� Single-axis solar tracker: a mechanical design allows thePV panel to move along the X axis and thus able to fol-low the sun from dawn to nightfall.� Dual-axis solar tracker: This tracker is an electrome-

chanical device that has the photovoltaic modules fixedto its upper frame and which achieves maximum irradi-ance on top of them. The entire structure moves fromEast to West (azimuth tracking) and moves along a sec-ond axis with a tilt over the horizontal plate position.The panels are positioned in such a way that they arealways directed towards the sun, consequently improv-ing their performance.

There are many algorithms used to control the trackingmotion of the PV panels whose benefits vary depending onthe cost or the complexity of the system. In fact, some con-trollers are time based and move the PV panel periodicallyin the same direction of the sun. Other controllers imple-ment the sun map location inside the tracker controllermemory. This technique is more precise but there areenergy losses due to the process of supplying the panelmotors on a cloudy day when searching for sun is worth-less. Another method used to solve the problem of energyloss in the panel motors is to use a small pilot cell to trackthe sun and send the best position for the main panel. Alight sensor technique is also used to detect the sun irradi-ance on the corners of the PV panel and then it is driven tothe position where the sensors detect a uniform irradiance.

Fig. 3. PV electrical model.

N. Karami et al. / Solar Energy 86 (2012) 2383–2396 2385

2.2. Electrical maximum power point tracking

A maximum power point tracker is an electronic systemthat operates the photovoltaic modules in a manner thatallows the modules to produce all the power they are capa-ble of. MPPT is not a mechanical tracking system that“physically moves” the modules to be oriented directly tothe sun, but it is a fully electronic system called power con-ditioning converter (switching converter), which varies theelectrical operating point of the modules, so that they areable to deliver the maximum available power. The problemconsidered by MPPT techniques is to find automaticallythe voltage VMPP and the current IMPP at which the PVarray should operate to obtain the maximum power outputPMPP for a given temperature and irradiance (Fig. 1).

An MPP tracker consists of two basic components(Fig. 2b); a switch-mode converter and a controller withtracking capability. The switch-mode converter is the coreof the entire supply. The converter allows energy at onepotential to be drawn, stored as magnetic energy in aninductor, and then released at a different potential. Thegoal of a switch-mode power supply is to provide a con-stant output voltage or current.

When it is properly applied, a maximum power pointtracking control can prevent the collapse of the PV arrayvoltage under excessive load demand, particularly whensupplying a constant-power type of load. The control pro-cess feedback signals, such as the array current and voltage,determine a proper direction in which to move the operat-ing point. These continuously updated set points fluctuatearound the voltage corresponding to the array peak powerpoint. By adjusting the operating point of the array to thepoint Vmp shown in Fig. 1, the array output power is max-imized, and the most efficient use of the solar array isrealized.

The Perturb-and-Observe (P&O) algorithm is by far themost commonly used in commercial MPP trackers.Although, there is as yet no consensus on which algorithmis the ‘best’. In this algorithm, perturbations are periodi-cally introduced into the control signal of the switchingconverter, and the resulting effects are observed on thePV output power. The P&O method is described in detailsin Section 4.

3. Solar array mathematical model

The photovoltaic cell is represented as an equivalent cir-cuit containing a current generator (modeling the conver-sion of solar radiation to electric energy), a diode(accounting for the physical properties of the semiconduc-tor cells) and two resistors, a shunt resistor and a seriesresistor (Fig. 3). The four variables involved in this modelare the two input variables, solar radiation EG (W/m2) andambient temperature Ta (�C), and the two output terminalvariables, PV cell current I (A) and voltage V (V).

The characteristic equation of the PV cell model isobtained by applying Kirchoff’s current law to the equiva-

lent circuit shown in Fig. 3, where I and V are respectivelythe terminal current and voltage of the model. The currentI is obtained by:

I ¼ IPh � Id � Ish ð1Þwhere Iph is the Photo current; Id is the Diode current; Ish isthe Shunt current.

The mathematical equation expressing the output cur-rent of a single cell is the Shockely equation for an illumi-nated pn junction and is given as (Al-Amoudi and Zhang,2000; Premrudeepreechacham and Patanapirom, 2003):

I ¼ Iph � I0 eðqðVþIRs

AKT Þ � 1� �

� ðV � IRsÞRsh

ð2Þ

where Iph is the Photo current; I0 is the Leakage or reversesaturation current; q is the Electron charge =1.602 � 10�19 C; V is the Solar cell voltage; A is the Idealityfactor �1.5 � 3; k is the Boltzman constant =1.3806 � 10�23 JK�1; Rs is the Series cell resistance; Rsh isthe Shunt cell resistance.

I0 can be expressed in another form which depends onthe temperature of the solar cell as:

I0 ¼ I0rTT r

� �3

eqEGkA ð

1T r�1

TÞ ð3Þ

where I0r is the I0 at reference temperature Tr; EG is theBand gap energy; Tr is the Reference tempera-ture = 301.18 K; T is the Cell temperature.

Iph of Eq. (1) is a function of incident solar radiation andcell temperature and is given as:

Iph ¼ ½Isrc þ kiðT � T rÞ�S

100ð4Þ

where Iscr is the Short circuit current at Tr; ki is the Shortcircuit current temperature coefficient; S is the Global solarradiation in mW/cm2.

The mathematical equation expressing the output cur-rent of np cells is given as:

I 1þ Rs

Rsh

� �¼ npIph � npI0 ek0ðVns

þIRsÞ � 1� �

� V =ns

Rshð5Þ

where np is the Number of parallel cells; ns is the Number ofseries cells; K0 is the q/AkT.

The following equation can be applied to simulate thecharacteristics of a solar array, where the given parameterssuch as np, ns, Rs, Rsh and Iscr are known.

S=200W/m2

S=400W/m2

S=600W/m2

S=800W/m2

S=1000W/m2

0 oC10 oC20 oC30 oC40 oC50 oC

0 oC10

oC20 oC30

oC40 oC50

oCS=200W/m2

S=400W/m2

S=600W/m2

S=800W/m2

S=1000W/m2(a) (b)

(c) (d)

PV power at different irradiance

PV power at different temperaturePV current at different temperature

PV current at different irradiance

Voltage (V)Voltage (V)

Voltage (V)Voltage (V)

Cur

rent

(A)

Cur

rent

(A)

Pow

er (W

)Po

wer

(W)

Fig. 4. Variation of current and power at different irradiances and temperatures. (a) Array current increases with irradiance. (b) Array power increaseswith irradiance. (c) Array voltage decreases as temperature increases. (d) Array power decreases as temperature increases.


P ¼ npIphV � npI0V eK0ðVnsþIRsÞ � 1

� �� V

Rsh

Vnsþ IRs

� �ð6Þ

The temperature of a solar cell is expressed by:

T ¼ 3:12þ 0:25S þ 0:899T a � 1:3ws þ 273 ð7Þ

where Ta is the Ambient temperature; ws is the Wind speed,S is the Solar radiation.

Considering a constant wind speed, Fig. 4 shows thevariation of power and current at different irradiancesand temperatures. The current flowing from the array isdirectly related to the irradiance for which the array volt-age remains almost constant. Voltage increases as paneltemperature decreases. Maximum power is extracted athigher irradiance and lowest temperature.

Fig. 5. PV system with MPPT.

4. Perturb and observe method

The P&O algorithm operates by periodically perturbing(i.e. incrementing or decrementing) the array terminal volt-age or current and comparing the PV output power withthat of the previous perturbed cycle. When the PV arrayoperating voltage changes and the power increases (dP/dVPV > 0), the control system moves the PV array operat-ing point in one direction, and vice versa. This scenario isrepeated in the next perturbation cycle (Esram and Chap-man, 2007; Wong, 2008).

4.1. P&O algorithm

A common problem in P&O algorithms is that the arrayterminal voltage is perturbed every MPPT cycle; therefore,when the MPP is reached, the output power oscillatesaround the maximum point, resulting in power losses inthe PV system. This is especially true in constant or slowly-varying atmospheric conditions. The change in voltage isdone using a DC/DC converter (shown in Fig. 5), whichcan be either a boost, a Buck or a Buck-Boost converter.There are four different possible scenarios, shown as follow:

Case 1: V present > V previous ) P present > P previous


DV > 0) DP > 0

Case 2: V present < V previous ) P present < P previous

DV < 0) DP < 0

Case 3: V present > V previous ) P present < P previous

DV > 0) DP < 0

Case 4: V present < V previous ) P present > P previous

DV < 0) DP > 0

At first, the P&O algorithm of Fig. 6 starts by calculat-ing the power value at 0 V. Then, the voltage is slightlyincreased and a new power value is calculated. In fact,

Fig. 6. P&O a

the first voltage increment provides a power escalationsince the first assumption is at 0 V.

The infinite loop of the tracker algorithm starts by com-paring the new value of P with the previous one. The fourcases described above have to be considered in order todecide on which direction the new voltage value will be.The voltage step change is considered small (around0.1 V) for a modest power variation. The right voltage stepvalue can be determined experimentally regarding the timeresponse and the power overshoot.

4.2. Perturb and Observe simulation results

The simulation results illustrated in Figs. 7–9 show thegrowing voltage value as well as the current and powervariations. Voltage (in dashed blue) starts from zero andincreases by 0.1 V on every perturbation cycle. Current

lgorithm.

Fig. 7. Voltage and current variations searching for MPP.

Fig. 8. Power value swings around MPP.

Fig. 9. A zoom-in on the power oscillation around the MPP.


(in solid green1) starts from ISC and decreases until thepower reaches the maximum. The implemented algorithmshould start inversely from the open circuit voltage Voc

value to prevent the PV short circuit ISC on every startup.Power ripples shown in Fig. 9 are the results of the ±0.1perturbation voltage.

In a direct coupled PV/battery mode (Fig. 10a), theoperating point is determined by the battery’s potential.Typically, this operating point is not the ideal operatingvoltage at which a module is able to produce its maximumavailable power. In addition, the P&O experimental stepsof the MPPT are not applicable when the load is a batterythat has to be charged by the PV panel. Given that the PVpanel voltage should be fixed to 2.23–2.3 V per cell (Wong,2008; Genesis Series Batteries Application Manual, 2005;Yuasa All NP Series Batteries User Manual, 1999), thatis, 13.8 V for a battery of 12 V. Moreover, the internalresistance of the battery is related to its state of charge.Therefore, using Ohm’s law, the current needed to chargethe battery is fixed by the battery itself and cannot be chan-ged. For instance, if the battery is empty, it behaves like aresistor with low impedance and absorbs significant cur-rent. Vice versa, when the battery is fully charged, itbehaves like a resistor with high impedance, and consumesmodest current. Therefore, using the MPPT is not alwaysrewarding as the load may not be able to absorb all thegenerated power and there is no need to locate the maxi-mum power point in similar kinds of PV couplings.

Many systems described in Pernia et al. (2009), Eakbur-anawat (2006), Muhida (2003), Eftichios et al. (2003) usethe MPPT by assuming a fixed battery voltage for simplifi-cation. If the input and the output powers of a DC/DCconverter are given equal (case of 100% converter effi-ciency), the relation can be described as:

PowerPV ¼ Powerbat ð8Þ

Therefore,

V PV IPV ¼ V batIbat ð9Þ

Assuming a fixed battery voltage, Vbat is replaced by aconstant EB, and the above equation will be:

V PV IPV ¼ EBIbat ð10Þ

Therefore, from Eq. (10), the PV power Ppv dependsonly on the battery current Ibat. The PV power reachesits maximum, Ppv,max, only when battery current reachesits maximum Ibat,max.

In a step-down DC/DC converter, there is only one con-trol parameter, namely the duty cycle D, of the power elec-tronics switch. The duty cycle D of a DC/DC converter canbe expressed as (Muhida, 2003):

1 For interpretation of color in Figs. 1–10, 12, 14, 15 and 17–22, thereader is referred to the web version of this article.

Fig. 10. Different PV/battery connection modes. (a) Direct PV/battery connection. (b) A controlled DC/DC converter is used to fix the charging voltagebased on Vref. (c) A PID controller is used to control the PWM signal based on the difference between Vref and the battery voltage Vbat. (d) Smartcontroller design where voltage and current are controlled based on Vref and Iref.

Table 1Electrical characteristics of the PV panel with an irradiance level of 1 kW/m2.

Symbol Quantity Value

PMMP Maximum power 135 WVMMP Voltage at PMMP 17.7 VIMMP Current at IMMP 7.63 AISC Short-circuit current 8.37 AVOV Open-circuit voltage 22.1 VTSC Temperature coefficient of ISC 0.00502 A/�CTOC Temperature coefficient of VOC �0.081 V/�C


D ¼ V bat

V PV¼ IPV

Ibat;with 0 < D < 1 ð11Þ

From Eq. (11), we can conclude that by maximizing thebattery current at the converter output, we can trackthe maximum power point of the PV panel by controllingthe duty factor of the DC–DC converter. The drawbackof this method lies in the assumption that the battery volt-age remains relatively constant, which is not the genuinesituation at different states of charge.

This study takes into consideration variable batteryvoltages at different states of charge. The new designapplies a feedback system totally different from the tradi-tional MPPT that reads the PV cell output and not the loadinput. The system is treated by means of two methods; thefirst one is based on a PID controller and the second one isbased on a microcontroller with current protection algo-rithm. These two methods use the DC/DC converter toreach the desired output voltage.

5. Direct coupling with a buck converter

This study considers coupling a PV panel with a batteryvia a DC/DC converter, as shown in Fig. 10b. The PVpanel used is KD135GH-2PU from Kyocera, where VMMP

and IMPP are respectively 17.7 V and 7.63 A at 1000 W/m2

Am

plitu

de (V

olt)

Time (sec)

Fig. 12. Voltage time response of the buck converter.


irradiance. The PV module main specifications are shownin Table 1.

The load is made of 6 OPzV series batteries, 2 V each. Abuck converter is used to step down the PV potential to thebattery limit. The buck converter, shown in Fig. 11, is com-posed of a switching component (a Mosfet or an IGBTtransistor) and a low pass filter made of a coil and a capac-itor (Salas et al., 2002; Anthony et al., 1994).

The expression of the buck average output voltage isobtained as follows:

V 0;avg ¼ DE ð12Þ

When the switch is ON, the voltage across the inductorL is expressed by:

vLðtÞ ¼ LdiL

dt¼ E � v0 ð13Þ

When the output voltage V0 remains steady at V0,avg, theinductor current iL increases linearly during the ON periodof the switch. Then:

DI ¼ E � V 0;avg

L� DT ¼ DðE � V 0;avgÞ

fLð14Þ

where f is the frequency (Hz), T the period (S), and L theinductance (H).

During the ON period, the inductor current rises fromiL,min to iL,max , where:

iL;min ¼ iLð0Þ ¼ iLðT Þ ¼V 0;avg

R� DI

2ð15Þ

and

iL;max ¼ iLðDT Þ ¼ V 0;avg

Rþ DI

2ð16Þ

R represents the internal resistor of the connected batteries.The capacitor current iC is expressed as follows:

iCðtÞ ¼ iLðtÞ � iRðtÞ ¼ iLðtÞ �V 0;avg

Rð17Þ

iCð0Þ ¼ iCðT Þ ¼ �DI2

ð18Þ

iCðDT Þ ¼ DI2

ð19Þ

Fig. 11. Buck converter design.

Since the current through the capacitor varies linearly,the average charging current is going to be half of its peakvalue of the triangular waveform. This peak is shown to beDI/2. Hence:

IC;avg ¼DI4

ð20Þ

Based on the average charging current, the change inoutput voltage DV becomes:

DV ¼ IC;avg � ðT=2ÞC

¼ DI � T8� C

¼ DI8� f � C

ð21Þ

The duty cycle of a DC buck converter that convertsfrom the PV panel voltage of 22.1 V to the series batteriesvoltage of 13.8 V is given by output/input ratio which is62%. For a 1 Amp peak-to-peak current output and at25 kHz switching frequency, the inductor value is 328 lH.A capacitor of 500 lF produces a 10 mV peak-to-peak out-put ripple voltage.

The buck open loop transfer function is given by:

GðsÞ ¼1

LC

S2 þ SRC þ 1

LC

¼ x2n

S2 þ 2nxnS þ x2n

ð22Þ

where the natural frequency xn ¼ 1=ffiffiffiffiffiffiffiLCp

and the dampingratio n ¼ ð1=2RÞ �

ffiffiffiffiffiffiffiffiffiL=C

p.

The open loop step response illustrated in Fig. 12 showsa 13.8 V steady output, a 48% overshoot and 7 ms settlingtime, which are not acceptable in a real application, espe-cially for loads with sensitive electrical characteristics.Therefore, the system should be controlled by an externalcontroller like a PID controller in order to reach an accept-able overshoot (usually 5%) and a smaller settling time.

6. Direct coupled systems with PID output potential control

In a typical closed loop design criteria, the toleratedovershoot is 5% and the settling time depends on the effi-ciency and the cost of the components implemented in


the design. For an efficient buck controller design, it isdecided to get the settling time for 5 ms. Fig. 10c showsthe block diagram of the charger system using a PIDcontroller.

The transfer function of the PID controller looks likethe following:

GcðSÞ ¼ KdS2 þ KpS þ KiS

ð23Þ

Kp is the proportional gain, Ki the integral gain, and Kd thederivative gain.

The transfer function of the buck design (plant) is:

GðSÞ ¼ 6:09� 106

S2 þ 1111S þ 6:09� 106ð24Þ

The closed loop of the block diagram shown in Fig. 13is:

T ðSÞ ¼ Gc� G1þ Gc� G

ð25Þ

In order to get the right overshoot and settling time, thedesired time domain equation requires that the maximumovershoot be 5% and the settling time 5 ms. Therefore:

n ¼ 0:6901 and xn ¼ 1449 rad=s

Thus, the desired closed loop transfer function becomes:

GclðSÞ ¼ 2:1� 106

S2 þ 2000S þ 2:1� 106ð26Þ

Comparing the denominator of T(S) and Gcl(S) yields:

Fig. 13. Closed loop PID controller.

Time (sec)

Am

plitu

de (V

olt)

Fig. 14. Open loop, desired, and closed loop response.

Ki ¼ 1721;Kp ¼ 0:9841 and Kd ¼ 0:00096:

The output response of the system is shown in Fig. 14where the design criteria are respected.

In the case of a battery load, the overshoot and the set-tling time are not critical elements of the circuit since thebattery charging dynamic response behaves like a chargingcapacitor and reduces the effect of fast overshoots. Also,the time response of the controller is not critical if it isbetween 5 ms and 5 s. Therefore, the implementation of aPID controller in the circuit is not rewarding and it willnot bring any benefits to the complete system.

7. Microcontroller based smart direct coupled system

In general, a battery can be represented as a resistiveload with different values depending on the state of charge.Here a question may be asked: what happens when the bat-tery is fully discharged? In this case, the battery behaveslike a very small resistance, and requires a big amount ofcurrent. Based on the study of Calais et al. (2008), Quin-tana et al. (2002), Goss et al. (2011), Yang (2006), Kawak-ita et al. (2002), over-current can cause the heating of cellsand interconnections and indirectly affects the degradationof the PV module. On the other hand, when the battery isfully charged, the consumed current becomes zero. Thus,there is no need to find the MPP unless the battery is cou-pled with another load, and this is not the case in thisstudy. In the case of a partially discharged battery, themaximum power delivered by the PV panel may not becompatible to the battery capacity and therefore the excessof energy is turned into heat, which then causes the electro-lyte to boil and evaporate.

In order to avoid the above mentioned problems, a spe-cial controller is designed. The proposed system is able tocontrol the floating voltage difference between the PVand the battery in order to moderate the consumed current.Moreover, it protects the global system (PV, converter andbattery) from the PV over-current and from the batteryovercharge. Therefore, the system can be considered anadaptive PV based battery floating charger.

7.1. Controller design

Using an ascending voltage technique, the proposedcontroller can charge the battery until it reaches 13.8 V.Note that the current value depends on the difference inpotential between the source and the load. This techniqueis called floating charging (Wong, 2008; Niu, 2004) and itis used to supply the battery with a proportional amountof current and voltage depending on its state of charge.

Fig. 10d and Fig. 15 represent the block diagram of thesystem. The desired voltage and the maximum allowed cur-rent are supposed to be determined. The primary proposedsystem reads the actual current and voltage and comparesthem to the desired ones based on the algorithm proposedin Fig. 16.

Fig. 15. The Microcontroller compares the preset voltage and current values with the actual ones and drives the buck converter.

Fig. 16. Microcontroller program algorithm.


In fact, the role of the microcontroller is to read theactual battery current and compare it to the maximumallowed one (“Max current” in Fig. 15). If the differenceeI is negative in the case of high battery consumption cur-rent, the duty cycle of the PWM signal decreases. If not, thebattery voltage is read and compared to the reference volt-age (“Desired voltage” in Fig. 15). The desired voltage islimited to 13.8 V in our experimental case. If the batteryvoltage is less than the desired one, the duty cycle isincreased providing a voltage raise across the battery.When the actual battery voltage exceeds the desired limit,the PWM duty cycle decreases. Besides, an equality match-

ing between the desired and the actual voltages maintainsthe error eV to zero. Therefore, the duty cycle maintainsits old value. Having an adjustable desired voltage and cur-rent, the system becomes a universal charger for all batterysizes. The algorithm used is illustrated in Fig. 16.

As shown on the algorithm in Fig. 16, the microcontrollerincreases and decreases the value of the duty cycle by one.Thus, if the PWM signal generator is based on an 8-bit divi-sion, the microcontroller needs 256 cycles to change the dutycycle from zero (0%) to its maximum (100%). Therefore, 256loops of the proposed algorithm are needed to get the max-imum value when starting from 0. In a well structured

Fig. 19. Controller board design.


microcontroller program code, the loop can take about50 ls for a controller running at 1 ls per instruction; conse-quently, the response time for 256 loops is 13 ms, which isgood enough to supply battery loads.

7.2. Determination of the maximum allowed current

The weakness of the above design lies in its inability toaccommodate the PV current which is a function of irradi-ance. PV panels are able to deliver extra current at higherirradiance and the maximum tolerated current proposedin Fig. 15 should be function of that irradiance in orderto grab as much PV power as possible. Therefore, threeenhanced designs are proposed. The first one uses a pilotPV cell, the second one takes around 90% of the PV cellshort circuit current and the third one uses a shunt currentsensor.

7.2.1. First method: Pilot cell

This method consists in placing a pilot cell next to themain PV cell to measure the irradiance value and feedthe microcontroller with the appropriate value in order todetermine the Imax (Fig. 17). The relation between the realIpv and the Ipilot can be experimentally extracted and savedin a lookup table inside the microcontroller memory ormodeled as a formula.

Fig. 17. Design enhancme

Fig. 18. Design enhencement using

7.2.2. Second method: PV short circuit

This method consists in disconnecting the PV cell fromthe buck converter and shorting it in order to get the Isc

using a current sensor. The Imax can be between 78% and92% of the Isc, as described in Esram and Chapman(2007), Hart et al. (1984), Masoum et al. (2002). Thismethod causes the destruction of the PV cell by heatingup the internal bus-bar and wires connecting the seriesand parallel cells.

nt using pilot PV cell.

on-board current measurement.


7.2.3. Third method: PV resistor shunt

This method is similar to the previous one, except that asmall resistor is placed in series with the PV cell. The resis-tor can be chosen so that the PV maximum current is at90% of the PV short circuit current (Fig. 18). This methodis unworthy and needs a resistor and a relay to switchbetween the buck and the resistor circuits. In addition,

Fig. 20. Buck converter design.

Fig. 21. Visual Basic p

the inconvenience of this method appears in the periodicpower disconnection at every current sample reading.

7.3. Pilot cell design description

7.3.1. Pilot cell design implementationThe design in Fig. 17 is implemented on two Printed Cir-

cuit Boards (PCB’s). The first one is the controller board(Fig. 19) and the second one is the buck converter(Fig. 20). The controller board is based on the microcon-troller PIC16f874A from Microchip�, in which the algo-rithm described in Fig. 15 is implemented. Thismicrocontroller has eight analog inputs, two built-inPWM signal generators and a Universal SynchronousAsynchronous Receiver Transmitter “USART” module.Four analog inputs are used to read the desired and theactual voltage and current. The buck converter is drivenby the PWM signal delivered based on the proposed algo-rithm. On every program cycle, data are sent serially to aVisual Basic program designed to plot the input and outputvoltages and currents.

The buck converter is based on the IRFP064 HEXFETPower Mosfet having a 0.009 X RDS(on) resistance, a 60 VVDSS voltage, and 70 A ID current. The Mosfet is drivenby the IR2110chip from International Rectifier�.

rogram interface.

Fig. 22. Experimental charging result.


The visual basic interface shown in Fig. 21 is designed toread the PIC microcontroller data, plot them, and exportthem to an excel sheet file.

7.3.2. Experimental results obtained on a pilot cell

The system is connected to a low state of charge batteryand is charged at two different irradiance levels. The irradi-ance is sensed by a pilot PV cell on which the microcontrol-ler can determine the maximum allowed battery current.The reference voltage is fixed to 13.8 V. At startup, thePIC generates a PWM signal with 0% duty cycle and incre-ments it until the battery voltage and current are under thevoltage and current criteria. The graph in Fig. 22 showsthat the battery voltage is 10 V and it increases with theduty cycle. At point “A” the battery current reachesthe upper limit and the microcontroller holds the value ofthe duty cycle to protect the PV panel from current surge.It is obvious that the charging voltage is not reaching thereference 13.8 V at this point. At point B the irradiance isincreased and a new current limit is proposed by the micro-controller based on a lookup table implemented inside itsmemory. The duty cycle is therefore increased and is heldwhen the battery voltage reaches 13.8 V. Between points“B” and “C”, the battery current and the PWM graphshow a slight decrease because the current needed for thebattery decreases while charging. After a full charge, thecurrent decreases to around zero amperes while the voltageremains fluctuating around 13.8 V.

7.3.3. Effect of temperature and irradiance on the battery

charger

As mentioned before, the output voltage of the PV panelused is 22 V which is higher than the battery voltage by10 V. From the specifications of the PV panel listed inTable 1, an increase of 1�C removes 0.08 V from the PVpanel terminal. At 50 �C, the PV panel output voltagedecreases by 2 V to around 20 V, which is also greater thanthe proposed charging voltage. Therefore, the system is not

affected by the temperature as far as the PV provided volt-age is greater than 13.8 V (assuming a 100% DC/DC con-verter efficiency).

Moreover, the battery charging time depends mainly onthe charging current applied to it, and so to the irradianceapplied to the PV panel. The charging time is longer at lowirradiance without PV voltage collapse and is shorter athigh irradiance without surging over current.

The proposed design can be adapted to all PV and bat-tery sizes, provided only that the open circuit PV voltage isgreater than the connected battery potential.

8. Conclusion

This study shows the difference between the direct-cou-pled and the indirect-coupled applications of a PV panel.Also, it focuses on two closed loop techniques to supplya fixed voltage load. The maximum power point trackingconsiders only the maximum benefits of the solar cell andis almost used to cross the output with the power lines sothat this power can be sold.

The second technique focuses on the load nature andrespects its potential and current regardless of the PV powerand losses. The PID controller of the buck output voltageshows a complicated study especially for various load nat-ure and parameters. For example, a buck supplying a resis-tive load is modeled in a different way than if it is supplyinga battery load. Batteries are modeled as resistive and capac-itive load arranged in a complicated circuit and thereforethe pole placement of the PID depends on these values, con-sequently on the state of charge of the battery.

The microcontroller based control technique computesonly the difference between the desired and the actual loadvoltage and tracks like a proportional controller with afixed up/down value. There is no need to enhance the set-tling time and the response time in a non-sensitive load likebatteries. Finally, the implemented system shows great andfaultless results and assures an adaptive floating battery


charger independently of the irradiance and temperaturefactors.

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