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Optimised Photovoltaic Solar Charger With Voltage Maximum

Power Point Tracking

Carlos Manuel Ferreira Santos

Electronics and Computers Engineering Department, Instituto Superior Técnico–Uni. Técnica de Lisboa Av. Rovisco Pais, 1049-001 Lisboa

carlos_mfs@hotmail.com

Abstract - This paper describes the use

of solar power to charge Lithium-ion (Li-ion) batteries. Implementation is by a conventional Pulse Width Modulator (PWM) duty cycle ratio control method to design and build a solar battery charger prototype. Maximum power point tracking (MPPT) is used in the photovoltaic (PV) system to maximise the PV output power, irrespective of the temperature and irradiation conditions. It has been implemented a MPPT system, consisting of a buck-type Direct Current (DC)/DC converter managed by a microcontroller unit. The microcontroller is programmed with a simple and reliable MPPT technique: the voltage MPPT (VMPPT). It is presented a model for the Li-Ion battery that is suitable for computer simulation. The used model can be easily modified to fit data from different batteries.

The simulation results achieved by using Pspice and Simulink programs are in good agreement with the experimental results. These results allowed demonstrating the reliability and validity of the proposed MPPT technique. The battery charger prototype was tested and the results obtained allowed to conclude about the conditions of permanent control on the battery charger. Keywords - Solar battery charger, photovoltaic systems, DC/DC converter, maximum power point tracking, duty cycle ratio control, microcontroller.

I. INTRODUCTION

As people are much concerned with the fossil fuel exhaustion and the environmental problems associated with conventional power generation, renewable energy sources, for example photovoltaic panels (PV) and wind-generators are now widely used. Photovoltaic sources are used today in many applications such as battery charging [1], light sources [2], water pumping [3], satellite power systems [4], etc. They have the advantage of being maintenance and pollution free but their main drawbacks are high fabrication cost, low energy conversion efficiency, and nonlinear characteristics. Since PV modules still have relatively low conversion efficiency, the overall system cost can be reduced using high efficiency power trackers which are designed to extract the maximum possible power from the

PV module (maximum power point tracking, MPPT) [5].

This paper describes how solar power may be used to charge lithium-ion batteries (Li-ion). In the literature, many battery charging techniques are investigated and proposed [6]-[7]. These methods use a variety of battery characteristics (voltage and temperature) to achieve a safe and fast charging process. However, in this paper a simple and powerful maximum power point tracking technique, known as Voltage MPPT (VMPPT) [8], is simulated and constructed. The implementation and simulation of the proposed method uses a low-cost, low-power consumption microcontroller, which controls a buck type Direct Current (DC)/DC converter and performs all control functions required by the MPPT process and battery charging.

Due to their high energy densities and long life times, Li-Ion batteries are increasingly used in systems such as portable electronics [9] and electric vehicles [10]. The optimisation design of these batteries has been built [11]-[12] in order to study its internal dynamics. This paper describes a simple dynamic model based on capacitor/resistor networks [13]-[14] in order to predict the charging time and optimise the use of the battery.

This paper is organised as follows: the solar charger system description is presented in Section II; the simulation of the system is analysed in Section III and IV for Pspice and Simulink environment, respectively; Section V presents the design process for the charger and a summary of the achieved results and scope of future work is presented in Section VI.

II. SYSTEM DESCRIPTION The photovoltaic charger system consists of

four subsystems, each with its own function. These four subsystems are connected in accordance with the block diagram presented in Figure 1.

Solar PanelSolar Panel

ControlControl UnitUnit

BatteryBatteryChargerCharger UnitUnit

PWM control signal

OutputVoltage

OutputVoltage

Solar PanelSolar Panel

ControlControl UnitUnit

BatteryBatteryChargerCharger UnitUnit

PWM control signal

OutputVoltage

OutputVoltage

Figure 1- Global Block Diagram – Solar Charger.

2

A. Solar Panel Model The first subsystem (Solar Panel) consists

of one polycrystalline PV module from Solarex. This PV module has a rated power of 1,2Watt and is formed by 18 photovoltaic cells connected in series.

A solar cell is usually represented by an electrical equivalent one-diode model [15] with a series resistance, as shown in Figure 2.

sai

savDi

sR

sI

Figure 2 - Electrical equivalent model – Solar Cell.

Using the equivalent circuit of solar cells it is possible to determine the V-I characteristic of M cells in parallel and N cells in series:

0

ln 1s sasa T s sa

I iv V R i

M Iγ

−= × × + − ×

(1)

Where • m Nγ = × ;

• m is the ideal factor;

• TV is the thermal potential;

• SI is the cell current source;

• sai is the net current;

• 0I is the diode current;

• sR is the series cell resistance.

For the solar panel used for the theoretical and experimental analyses of this paper

1M = , 18N = and it is assumed 1m = . Figure 3 presents the I-V characteristics for

a PV cell and shows the load lines for different load resistances. The slopes of these load lines are given by 1/R. So, lower resistances result in steeper load lines and higher resistances result in flatter load lines. The operating point of the PV connected to these loads is restricted to the intersection of the load line and I-V curve. Therefore for a given irradiance there is only one load resistance that will produce maximum power and if the irradiance changes then the resistance required for operation at MPP also changes. The irradiance is not constant and will change throughout the day therefore maximum power point trackers are needed to match the operating point to the load resistance.

Figure 3-Typical current-voltage I-V curve.

B. Charger Unit

The Charger Unit (second subsystem) includes a DC/DC converter controlled by a Pulse Width Modulation (PWM) signal. The DC/DC converter is formed by two switches and an input and output filter. PWM signal is computed from the Control Unit. The charger unit is a global block that includes the Maximum Power Point Tracking allied to a DC/DC converter with buck topology

On this paper the DC/DC converter is always working in Continuous Conduction Mode (CCM). The DC/DC converter will connect/disconnect conveniently the solar panel from the battery based on PWM signals. Taking in account the idealised buck converter shown in Figure 4 and in order to simplify the results shown bellow, it is assumed that input voltage

sav is ripple free (on Pspice simulation

subsection and in the practical work it was included a capacitor on the left side of the converter in order to minimise the input voltage ripple – less then 3%).

+

-

+

-

+ -sai

sav

LvLi

1L

outi

ci2C

outv

Di

1M

+

-

+

-

+ -sai

sav

LvLi

1L

outi

ci2C

outv

Di

1M

Figure 4 – DC/DC converter (buck topology).

The inductor value, 1L , required to operate

the converter in CCM is calculated such that the peak inductor current at maximum output power does not exceed the power switch current rating

[16]. Thus, 1L is calculated as:

where

• PWMf is the switching frequency;

• outv and outi are the converter output

voltage and current at the maximum input power.

The output capacitor value calculated to give the desired peak-to-peak output voltage ripple is

where sav∆ is the output voltage peak-to-peak

ripple at maximum power.

1 2out

out PWM

vL

i f>

(2)

2 4out

sa PWM

iC

v f=

× ∆ ×

(3)

3

Taking into account that the ripple of the output current must be less than 3% of its mean value, [17], the input capacitor value is calculated to be:

where

• PWMf is the switching frequency;

• sai is the converter output current

at the maximum input power; • sav∆ is the voltage ripple.

It is intended to minimise the voltage

ripple sav , equal to voltage 1Cv , since

voltage outv is supposed to be constant. Figure 5

presents the case where the load is a battery or a resistor-capacitor (R-C) network with ripple free voltage.

outioutiouti

Figure 5-Switch operation – DC/DC converter.

Assuming that all currents and voltages across the circuit are ripple free, when compared to the respective average values and due to the condition of permanent state applied to inductor

1L and capacitor 1C , it is possible to write the

maximum value for voltage outv that allows the

circuit to be in permanent control:

As seen in the I-V curve of typical PV modules (Figure 3) there is a single maximum of power. This means that there is a peak power corresponding to a particular voltage and current.

Instead of finding the maximum via derivative, and employ numerical methods to show a linear dependency between “cell voltages correspond to maximum power” and “cell open circuit voltages” it is assumed that a maximum power point of the used solar PV module lies at about 0,75 times (MV value – voltage factor) the open circuit voltage of the module: the MPPT can be found at 75% of the open circuit voltage, according to (6).

Therefore, by measuring the open circuit

voltage of the solar panel, ocV , a reference

voltage can be generated ( MPV ) and a duty

cycle control scheme can be implemented in order to bring the solar PV module voltage to the point of maximum power.

C. Control Unit The Control Unit (third subsystem) consists

of one Programmable Interface Circuit (PIC) microcontroller, model PIC18F4585 and an Integrated Circuit (IC), SG3524. PIC microcontroller is a high performance 8-bit Reduced Instruction Set Code (RISC) architecture, operates from 2V to 5,5V belonging to 40 pins family [18] and IC is a 16 pin PWM switching regulator circuit.

The microcontroller is used to process measured voltage (from the solar panel output) and to compute the required signal for control of the system (VMPPT algorithm). IC is employed to generate the required PWM command that will control the switch gate of the DC/DC converter. D. Lithium-ion Battery

The fourth subsystem consists of a rechargeable Lithium-ion (Li-ion) battery from Varta. This battery has an output voltage of 3,7V and an energy storage capacity of 1230mAh.

For the theoretical and simulation analyses on this paper it is proposed the model in Figure 6:

0R

Controlled VoltageSource

0R

Controlled VoltageSource

Figure 6–Equivalent Model – Li-Ion Battery.

where,

E = Internal voltage, V;

oE = Constant voltage, V;

K = Polarization voltage, V;

Q = Battery capacity, Ah;

A = Exponential Voltage, V;

B = Exponential Capacity, Ah-1.

1sa

sa PWM

iC

v f≥

∆

(4)

12out in sa PWMv i v L f= × × × ×

(5)

MP V OCV M V= ×

(6)

4

Figure 7–Step-down switching regulator circuit.

III. IMPLEMENTATION IN PSPICE With the help of this simulation program it

was possible to build a basic circuit of a step-down switching regulator with duty cycle ratio control. The circuit is depicted in Figure 7 and allows the modulation of the DC/DC converter. It also allowed predicting the system behavior for different resistive values on the terminal load (estimation for current and voltage values).

An ideal voltage source, 1V in series with a

resistance, PVR was considered in substitution

of the solar panel. This model admits that the solar panel characteristic of Figure 3 can be linearised between points A and S and it is also considered that the working point of the system is setting around point A of maximum power. The Pspice model of the IC SG3524 regulates the PWM pulse width. In turn, the duty cycle

controls the switch gate ( 1M ) allowing the

control of the buck converter and as a consequence, the control of the output voltage and current in the load (represented by

resistance loadR ).

Two schemes were simulated for both

20loadR = Ω and 40loadR = Ω . It is assumed

that the circuit is working on the MPPT point. Figure 8 presents the simulation results for

the system with the load resistance equal

to 20loadR = Ω . In the curves obtained,

3,75refV V= and the circuit is stabilised in the

MPPT. The value of setV (output voltage of the

solar panel) is tending to this operation point which allows predicting that the circuit is being controlled: there is a permanent control of the system (duty cycle ratio control). Another important aspect worth to look at is the ripple

value of the setV voltage (corresponds to the

solar panel output voltage). In Figure 8 the maximum ripple obtained is nearly 3% of the

voltage value, which means that capacitor, 1C

is well dimensioned.

Figure 8- setV and Vref - 20loadR = Ω .

In order to provide the limit to which the system loses control (duty cycle ratio no longer working) some simulations were made and confirmed (5). Firstly, Figure 9 presents the situation where the system is being controlled

( 20loadR = Ω ) contrasting to Figure 10 where

the control is practically inexistent

( 40loadR = Ω ).

Figure 9 presents voltage across

capacitor 1C , PWM signal ( gateV ) and the signal

associated to the PWM from the IC SG3524.

Figure 9- gateV , 3524ramp SGV − and1Cv -

20loadR = Ω .

5

It is possible to see that capacitor is

charging when the switch 1M is OFF and

discharging when 1M is ON. This figure clearly

states the system functioning: when voltage

setV achieves refV switch 1M starts conducting.

Figure 10 presents the system behaviour when in the presence of a resistive load equal to

40loadR = Ω . The duty cycle ratio control has

been lost but capacitor 1C can be in charging

process eventhough the transistor 1M is

conducting.

Figure 10- gateV , 3524ramp SGV − and 1Cv -

40loadR = Ω .

A direct consequence of the lack of control of the system is the higher voltage value across the load (average value near 6V). Figure 11 presents voltage across the

resistance 40loadR = Ω .

Figure 11- V(R_load) - 40loadR = Ω .

The achieved voltage is too high for the conditions stated in this paper and so the system is no longer controlling the ratio power between the input voltage source (simulates the solar panel) and the resistive load. The maximum value given by (7) is overtaken.

IV. IMPLEMENTATION IN SIMULINK Simulink software and its facilities are used

to model the proposed electric models depicted in Figure 12. Library model blocks for a PV module, a VMPPT power tracking and a battery were used. The input and output filter used are similar to those simulated in Pspice program. Saturation and delay functions are introduced to limit the fast response of the “controlled voltage source”, as well as to improve convergence.

Figure 12-Solar Battery Charger.

With Simulink facilities it is possible to characterise the MPPT algorithm (concluding about the voltage factor chosen) and to obtain an estimate charging time for the battery. Figure 13 allows estimating the charging process for the used Li-ion battery (approximately 7 hours). The implementation of the mathematical model of the PV module permits simulation of the nonlinear V-I and P-I characteristic (see Figure 14).

Figure 13-Voltage and SOC-Li-Ion battery.

0.150.10.050

1.75

3.5

5.25

7

10

00.150.10.050

0

0.5

1

1.5

a) V-I Characteristic b) P-I Characteristic

Vsa

[V]

Po

ut[

W]

Isa [A] Isa [A]

(0.15, 7.5)≈ (0.15, 1.3)≈

Figure 14–V-I and P-I Characteristic–PV Block.

_ max 2 0,15 7,5 300 40 5, 2outV k Vµ= × × × × =

(7)

6

vsa

SolarPanel

C1 Diode C2vgate

L1Li-Ion

Battery

Resistive Load

Input Filter Output Filter

Charger Unit

vbat

PWM Output

PIC 18F4585

A/D conversion

IC SG3524vgate

vbat

vsa

Control Unit

Figure 15-Detailed diagram of the proposed solar charger.

V. DESIGN In order to experimentally test the

performance of the proposed solar charger, the solar battery charger prototype of Figure 15 was constructed using one polycrystalline PV module, one Li-Ion battery, a VMPPT buck type tracker (MOSFET power switch), a microcontroller PIC18F4585 and an IC SG3524 (PWM regulator). A. Hardware Design

The hardware that was used was the PICDEM 2 Plus demonstration board from Microchip Technology Incorporated. PICDEM 2 Plus is a simple board that demonstrates the capabilities of PIC18 devices such as PIC18F4585. Connected to this board there is the PV panel and also a breadboard which contains the DC/DC buck converter developed in previous sections and the IC SG3524. Into the output of the buck converter there is the Li-Ion battery connected to. A. Software Design

The flowchart of the control program is shown in Figure 16. Voltage maximum power point tracking program was written in C language, compiled with MPLAB and downloaded to the Microchip embedded development tool ICD2 directly to the PIC.

Program variables

initialisation

Sense Voc

from PV

Calculate VMPPT

VMP=Mv*Voc

(0 < duty cicle < 1)

Activate PWM generator

according to previous result

Delay 1 min

END of charge?

STOP

Calculate Voltage

Maximum Power Tracking

Analog to Digital

conversion here

yes

no

Verify if it is achieved

maximum voltage value 4.2V

Figure 16-VMPPT Flowchart.

The experimental results are divided in two schemes:

• Laboratory tests: solar panel was substituted by an ideal voltage source and the simulation occurs with a resistive load (similar to what was performed in Pspice environment);

• Field tests ran in open space, enabling the use of the solar panel and the Li-Ion battery (similar to the simulations in Simulink).

Figure 17 presents a zoom in of the voltage

refV . According to this plot the achieved mean

voltage value is 3,75V with a delta of 118mV (the voltage ripple is near 3%). Once again the voltage ripple is lower then assumed in the theoretical calculations. The value achieved for

refV means that the system is working at the

MPPT. By comparing Figure 17 with Figure 8 it is possible to observe a very good agreement between the simulation and the practical work.

a) Vref =3,75V – DC value. b) ∆Vref =0,118V – AC value.

xx:1ms/div

yy:2V/div

xx:50µs/div

yy:50mV/div

a) Vref =3,75V – DC value. b) ∆Vref =0,118V – AC value.a) Vref =3,75V – DC value. b) ∆Vref =0,118V – AC value.

xx:1ms/div

yy:2V/div

xx:50µs/div

yy:50mV/div

Figure 17- refV , DC and AC value (laboratory results).

Figure 18 presents the PWM signal ( gateV )

for different load resistances. Regarding the simulations achieved in Pspice environment there is a very good agreement with the following results: for the load resistance equal to

20loadR = Ω the system presents a duty cycle

ratio control (compare with Figure 9) and for

40loadR = Ω the system presents deficient

control (compare with Figure 10). It is practically inexistent.

7

1) xx:10µs/div

yy:5V/div

2) xx:10µs/div

yy:2V/div

1) xx:25µs/div

yy:5V/div

2) xx:25µs/div

yy:2V/div

a) Vgate and VrampRload=20Ω

b) Vgate and Vramp

Rload=40Ω

1) xx:10µs/div

yy:5V/div

2) xx:10µs/div

yy:2V/div

1) xx:25µs/div

yy:5V/div

2) xx:25µs/div

yy:2V/div

1) xx:10µs/div

yy:5V/div

2) xx:10µs/div

yy:2V/div

1) xx:25µs/div

yy:5V/div

2) xx:25µs/div

yy:2V/div

a) Vgate and VrampRload=20Ω

b) Vgate and Vramp

Rload=40Ω

Figure 18-PWM control for different load resistances.

The field test occurred on the 29th July 2008. According to the Portuguese Institute for Meteorology temperatures around 25 to 26 Celsius degrees were expected. The experimental tests occurred in very good conditions at an average power of approximately 0,76W .

Comparing Figure 19 with Figure 14, according to Simulink simulations, it is possible to conclude that the computed results show good agreement with measurements achieved. Again, the value chosen for the voltage factor

VM shows good agreement with the results

obtained.

V-I characteristic

0

2

4

6

8

10

12

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16

Current [A]

Vo

ltag

e [V

]

Figure 19-V-I Characteristic MSX-01.

Figure 20 presents the voltage during the battery charge. The initial State of Charge (SOC) is set to 3,4V in order to accelerate the charging process and to focus in the charging characteristic area that shows utmost importance. The system charges the battery according to a current, which varies between 0,2A to 0,18A, until the battery voltage reaches 4,2V at which the charge mode is disconnected. Under the conditions above the battery takes about seven hours to achieve is maximum capacity. The present results of the battery charging process are also in very good agreement with the simulation results depicted in Figure 13

Li-Ion-charging voltage

3

3,2

3,4

3,6

3,8

4

4,2

4,4

10:3

0

10:4

410

:58

11:1

311

:27

11:4

211

:56

12:1

0

12:2

512

:39

12:5

4

13:0

813

:22

13:3

713

:51

14:0

6

14:2

014

:34

14:4

9

15:0

315

:18

15:3

2

15:4

616

:01

16:1

5

16:3

016

:44

16:5

817

:13

17:2

7

Time [Hours]

Vo

ltag

e [V

]

Figure 20-Li-Ion charging voltage.

VI. CONCLUSIONS

The current paper intends to give a contribution for the solar battery charging process by implementing a MPPT control system that allows a safe and fast charging process using a duty cycle ratio control. By doing this, it is attended to achieve better performance and efficiency for the charging process. The voltage maximum power point tracking (VMPPT) algorithm was used and allowed to simulate the system behaviour for different conditions. For the theoretical analysis, Matlab/Simulink and Pspice facilities are employed and a microcontroller based tracker prototype capable of implementing VMPPT is constructed and used to charge a Li-Ion battery. Based on the results presented before, the following conclusions may be stated.

In Section II, it was made a total description of the system. It were presented electrical models for each of the components namely for the photovoltaic solar cell and for the Li-ion battery. The charger unit (DC/DC converter and the MPPT algorithm) and the control unit (microcontroller PIC18F4585 and IC SG3524) were presented and dimensioned in order to correctly achieve the pre-determined goals for this paper. Throughout this section the MPPT technique implemented is explained and the interconnection of the different elements is set in a clear way.

The simulation of the system in Pspice environment, made in Section III, allowed a better understanding of the system behaviour when in the presence of different resistive loads. The system dynamics is affected for different loads and as a consequence the duty cycle ratio control, that allows the implementation of the VMMPT algorithm, can and as stated will be affected. As evidenced the system control is affected for voltage values above approximately 5,48V that corresponds to a resistive load of 40Ω . Using this simulation tool it was also possible to characterise the system losses during the entire process. As was expected most of the losses presented come from the switch presented in the DC/DC converter.

In Section IV, using Matlab/Simulink tool it was possible to conclude that the theoretical assumptions made, namely the voltage factor

VM used, is a very approximate value of what

can be expected in real time implementation. Other important aspect was the possibility to directly compare the system behaviour: resistive load vs. Li-Ion battery model. The results achieved are in good agreement which is an indicator that the system is properly dimensioned and correctly interconnected. The system is always controlling and seeking for the MPPT. It was also possible to obtain an estimate for the charging process, approximately seven hours for a Li-ion battery fully discharged.

Finally in Section V, it was carried out the practical component of this paper. All the components were interconnected and the solar

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battery charger prototype was tested. The close agreement between simulation and experimental work shows that the electrical models and the sizing of the entire system accurately predict the system behaviour. The experimental work produced a physical implementation of the VMPPT and the functioning of the microcontroller was observed. The battery charger chargied the Li-ion battery and during this process it was possible to see, through measurements in real time, the permanent adjustment in order to achieve always the maximum power transfer from the PV to the battery. The field test occurred on a sunny day and charged the battery in approximately seven hours. Briefly, the main goal for this paper has been achieved. The construction of a solar charger prototype using a microcontroller, which is based on a MPPT algorithm, was implemented and tested in a real life possible usage. The final prototype verified the utility and efficiency of the VMPPT algorithm in order to constantly transfer the maximum power from the PV to the load. Beyond the practical advantage of getting a real solar charger preparing this paper also led to an understanding of the system dynamics and behaviour for different conditions on the load and even environmental issues.

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