Optimization of Photovoltaic Energy System:

A case study of Hanoi city

X.L. Dang1, E. Hoang1, H. Ben Ahmed2, M. Petit3, H.T. Pham4 1SATIE, ENS CACHAN, CNRS, UNIVERSUD, 61, av President Wilson F-94230-Cachan, France.

2SATIE-Brittany Branch, ENS de Cachan-Ker Lann Campus, 35170 BRUZ, France. 3Department of Energy, Supélec, Campus de Gif sur Yvette, 91192 GIF SUR YVETTE, France.

4Department of Power System, Hanoi University of Technology, Hanoi, Vietnam.

E-mail: xdang@satie.ens-cachan.fr

Abstract – Optimizing the output power from Photovoltaic system

(PV system) is one of the most essential issues in using efficiency

renewable energy sources. The purpose of this paper is to

investigate a method to optimize the output power from the

system. And the system is applied to calculate energy in year 2009

in Hanoi city. In order to do that, a hybrid system is built and

simulated in MATLAB/Simulink. In this system, the use of

equivalent switching boost converter is performed with the

objective of calculating the produced power from the PV system

and estimating the losses in the components of the converter

during a given time. Also, there is a comparison between the using

of boost converter circuit with Pulse Width Modulator (PWM)

generator which controls the on and off of MOSFET in the

converter and its equivalent. The comparison proved that it could

be applied to compute losses for a long period with the equivalent

circuit.

I. INTRODUCTION

The development of renewable energy and the improvement

of efficiency the hybrid system are considered to be the most

important issues for the sustainable environment. Among

various types of renewable energy sources, solar energy has

been promoted dramatically worldwide for the dispersed

generation in recent years. Moreover, photovoltaic (PV)

systems produce electricity without CO2 in comparison with the

fossil fuels and solar energy is an energy limitless source.

These properties have led to many governments interested in

increasing the deployment of the system. PV system could be

applied in charging battery, the hybrid vehicles, water pumping

and connecting into Distributed Energy Resources (DER)

systems. The solar cell has nonlinear V – I and P – V characteristics

which depend on the irradiance and the operating temperature

[1]. It is interesting to note that in most recent studies [3]-[5],

the DC/DC boost converter in the PV system usually applies to

control the maximum output power point of the solar cell.

However, very little was found in the literature on tracking the

maximum power value at the output of the converter.

Therefore, this paper has been working on tracking this maximum power. For the sake of doing that, a PV system is

designed as shown in Fig. 1. It is assumed that the voltage over

the battery, , which is also output voltage of the converter,

, is constant during the calculation period. So in order to

track the maximum output power from the system, it is

necessary to track the maximum current passing through the

diode of the converter.

Fig. 1. Overview of PV system.

However, this current is not the stable current [2] which

depends on so much the modulation of duty ratio of the DC/DC boost converter. Hence the average current value through the

diode is considered as the main parameter to optimize the

output power.

Once the output voltage of the converter is fixed, the

converter receives variables input voltage, , which is also the

output voltage of PV arrays, . Normally, the input voltage of

the converter is changed in accordance with a certain duty

cycle. And duty cycle is varied with the using a pulse width

modulation (PWM) technique. With the aim of changing duty

cycle, a model of converter is built in MATLAB/Simulink with

the application of PWM technique. This model is connected

with PV array model and an ideal battery as shown in Fig. 1,

which is expressed by a voltage source in MATLAB/Simulink.

However, the time for calculation in the PV system model is

very long. Because of the value of carrier frequency in PWM

generator in range of 1 kHz to 1 MHz [2], it is affected

significantly to set the time sample in MATLAB/Simulink and

to impact the calculation time. So it is suggested to apply the

equivalent the DC/DC boost converter as mentioned in [2].

In this paper, the PV system is detailed in Section II within

the boost converter with PWM and the equivalent converter

model; and the comparison between two models in term of

output power during one day. In section III, the impact of duty

cycle on maximizing output power from PV system is

presented with different atmospheric conditions in a given time.

In section IV, studying the system based on the database from

Hanoi city in year 2009. Finally, some conclusions are given

about the optimized method and the potential applications.

II. SIMULATION OF PV SYSTEM MODEL

A. Construction of the model

A photovoltaic system which consists of PV array model, a

DC/DC boost converter and an ideal battery, is built in

MATLAB/Simulink as shown in Fig. 2.

Fig. 3. DC/DC boost converter with PWM model.

In this system, two models of the boost converter that are

taking account to losses in the components, have been

introduced to calculate output power from PV array. The basic

idea is the replacement of pulse-width-modulated (PWM)

switch model in Fig. 3 by the equivalent boost converter model

as shown in Fig. 4. Because the main advantage of the

equivalent model is enabled to reduce calculation time in

MATLAB/Simulink. Besides, the major sources of power loss

are the inductor copper loss and conduction losses due to

semiconductor device forward voltage drops. And it is assumed

to ignore the small switching losses; and model has only the

important dc component of the waveforms [2].

For the estimation of the losses in DC/DC boost converter,

the inductor copper loss is placed by a resistor, RL, in series

with the inductor. The actual inductor then consists of an ideal

inductor, L, in series with the copper loss resistor. Next to the

conduction loss in semiconductor device, the forward voltage

of a MOSFET or BJT can be modeled with reasonable accuracy

as an on-resistance Ron. In the case of a diode, IGBT or

thyristor, a voltage source plus an on-resistance yields a model

of good accuracy [2]. The DC/DC boost converter in this study

is designed to operate in the continuous conduction mode

(CCM) which means that the inductor current is always higher

than zero.

The inductance value is chosen to be higher the minimum

inductance Lmin for operation in CCM is given by [2]

(1)

Where f is the switching frequency to control opening and

closing in the terminal gate of the MOSFET and is

the changing current maximum in inductor.

The capacitance is designed to keep the voltage output ripple

within the desired boundary. The minimum capacitance Cmin

required for certain output ripple is given by

(2)

Where is the changing voltage maximum over

capacitor and R is the resistor load.

These parameters of the components in the boost converter

and PV array are given in Table I .

Fig. 2. Simulation of PV system.

Fig. 4. The equivalent DC/DC boost converter model.

TABLE I

SELECTED PARAMETERS OF COMPONENTS IN THE PV SYSTEM

Item Symbol Parameter Value Unit

MOSFET

VDSS Drain-to-Source voltage 100 V

RDS(on) Static Drain-to-Source

on-resistance 0.185 Ω

ID Continuous drain current 10 A

Diode

IFAV Average forward

rectified current 10 A

VRRM Repetitive peak

reverse voltage 100 V

VF Forward voltage 0.66 V

Inductor L Ferrite inductor 30 mH

Capacitor C Power capacitor 2.5 mF

Panel solar

Pp Typical peak power 60 W

Vpp Voltage at peak power 17.1 V

Ipp Current at peak power 3.5 A

ISC Short-circuit current 3.8 A

VOC Open-circuit voltage 21.1 V

KI Temperature coefficient

of short-circuit current 3 mA/

0C

A Ideal factor

(Si-poly technology) 1.3

L×W Dimensions 0.5173 m2

B. Comparison between two converter models in PV system

With the aim of comparing between the two models, the

boost converter model with PWM in Fig. 3 is connected to the

PV array and the battery as shown in Fig. 2. Then it is replaced

by the equivalent ones without PWM in Fig. 4. The average

current passing through diode and the output voltage of PV

array are used as the terms of comparison between two

converter models. Because there is a relation between input and

output voltages of the boost converter and also between input

and output current passing through the converter. After that,

using the PV system within two converter models calculates the

output power during one day in order to consider the

calculation time between them.

The conversion ratio between input and output voltages of

the boost converter varies with the duty cycle, D, of the switch,

according to the following equation:

. (3)

With:

(4)

The mathematical equation to express the relation between

the average current passing through the diode, , and duty

cycle in the converter as given in [8]

(5)

With:

(6)

Here, is the lighted-generated current or photocurrent,

is photovoltaic output current, is the cell saturation of

dark current, is series-parallel number of cells of PV array,

is series number of cells of PV array, is electron charge

( ), is the Boltzmann’s constant ( ), is the cell’s working temperature, is

an ideal factor and is the series resistance.

The photocurrent mainly depends on the solar radiation and

cell’s working temperature [...] which is defined as:

(7)

Here, is the cell’s short-circuit current at a 250C and 1

kW/m2, is the cell’s reference temperature and is the solar

radiation in kW/m2.

Besides, the cell’s saturation current varies with the cell

temperature, which is described as

(8)

Here, is the cell’s reverse saturation current at reference

temperature and a solar radiation, is the band-gap energy of

the semiconductor is used in the cell and A is the ideal factor

which is depends on PV technology. Given the PV open-circuit

voltage, , at reference temperature and ignoring the shunt-

leakage current, the reserve saturation current is given by

(9)

It is necessary to build a general PV model that is to verify

the nonlinear I-V and P-V output characteristics. PV model is

built by using MATLAB/Simulink to illustrate these

characteristics as mentioned in (5)-(9).

Some methods have been proposed in [6]-[7] for tracking the

maximum output power from the PV array. In order to do that,

it is obviously required to measure output voltage and current

of PV array. However, once PV array connects to the converter

and the battery which is maintained stably, output power from

PV system simply depends on current passing through the

diode in the converter. And it is therefore likely that only

current sensor is should be used. With the purpose of doing

that, the MAC method [8] is applied in this paper.

Fig. 5. Comparison between converter model with PWM and the equivalent ones.

Considering (kW/m2) and 0C are the chosen

input parameters in PV model. And it can be seen from Fig. 5

that the first two seconds is the time to change the value of duty

cycle from 0 to 1. The objective of doing that is to track the

maximum value of the average current passing through diode

and the optimal duty cycle at the maximum current. Next, the

last fifteen minutes is a range of time to maintain the maximum

value of the average current by keeping the optimal duty cycle.

There is no significant difference between two converter

models in term of the average current passing through diode

and the output voltage of PV array due to eliminate of

switching losses in two models. Thus, the use of equivalent

converter model is a physical approach in analyzing the

converter circuit.

In addition, the PV system within the two converter models

is applied to calculate the output power during one day. The

solar radiation and temperature during one day are shown in

Fig. (15) and (16). Fig. 6 shows that the equivalent model

provides very similar the power output to the ones with PWM.

Moreover, the simulation time of the PV system with the

former model was 145 seconds in comparison to 995 seconds

with the ones latter model. So the equivalent converter model

without PWM could be applied to calculate the PV system in a

long term such as one year due to simulation time reduction.

III. IMPACT OF DUTY CYCLE ON MAXIMIZING

OUTPUT POWER FROM PV SYSTEM.

With particular atmospheric condition, it is always allowed to

track the maximum output power from PV system by using

MAC method and to calculate this power during a given time

by applying the equivalent DC/DC boost converter. The value

of duty cycle at the maximum output power, which is named

optimal duty cycle, is also changed in accordance with

particular atmospheric condition. With the aim of finding the

relation between the optimal duty cycle and atmospheric

condition, three possible scenarios are made. And there is a

comparison output power from PV system by using constant

duty cycle (each value varies from 0.1 to 0.9) and optimal duty

cycle in each scenario.

A. Scenario 1 (S1): and from 50C to 600C

In the first scenario (S1), a value of solar radiation λ = 0.9

kW/m2 is chosen and assumed constant during the calculation

time. And temperatures change from 50C to 600C. It can be

seen from Fig. 7 that optimal duty cycle ( ) increases

with the rising of the temperature. Based on voltage-power

output characteristic of PV array with different temperatures in

[7], the voltages at maximum output powers of PV array

decrease once the temperature increases, and duty cycle

increases in case of reducing output voltage from (3).

Fig. 8 shows that the output power by using optimal duty

cycle is always higher than the other constant duty cycle.

Besides, it is also observed that once the temperature changes

from 150C to 200C or 300C to 350C, respectively, it could be

chosen a particular value duty cycle D = 0.2 or 0.3 to operate

MOSFET. Therefore, it is suggest applying optimal duty cycle

in case the variation of temperature is above 100C.

Fig. 7. Optimal duty cycle in S1.

Fig. 8. Output power from PV system in S1.

Fig. 6. Comparison output power from PV system in one day.

B. Scenario 2 (S2): from 0 to 1 kW/m2 and .

In the second scenario (S2), a value of temperature TC = 250C

is selected and assumed constant during the calculation time.

And solar radiations vary from 0 to 1 kW/m2.

It can be observed from Fig. 9 that optimal duty cycle curve

is not linear in case of changing the solar radiation. Because the

output voltages at maximum output powers of PV array change

non-linearly with the maximum powers in case the temperature

is constant as mentioned in [7].

As shown in Fig. 10, the output power by applying optimal

duty cycle with different solar radiations is always higher than

the other constant duty cycle. Also, the curve at the value of

duty cycle at D = 0.3 is approached to the optimal duty cycle

ones due to the overlap of the optimal duty cycle curve with the

curve of D = 0.3 at 250C as shown in Fig. 8. Hence, it could be

applied the constant duty cycle in order to simplify the control

of MOSFET in case of .

Fig. 9. Optimal duty cycle in S2.

Fig. 10. Output power from PV system in S2.

C. Scenario 3 (S3): and . In the third scenario (S3), solar radiation and temperature of

one real day are chosen as shown in Fig. (15) and Fig. (16). Fig.

11 shows the variation of optimal duty cycle following the

changing of the temperature and solar radiation in one day.

In addition, it can be observed from Fig. 12 that the optimal

duty cycle curve indicates the highest output power value

overall curves with different value of duty cycle. Concerning

the time from 8h to 10h, the temperature changes from 240C to

350C during this time, it could be seen the curve Dopt overlaps

the curve D = 0.3 due to within the range of temperature Dopt =

0.3 as shown in Fig. 7. And from 10h to 11h, the curve Dopt

overlaps the curve D = 0.4 due to the changing of temperature

from 350C to 420C. So the optimal duty cycle could be applied

at the city which has the variation of temperature significantly

in order to optimize the output power from PV system.

Fig. 11. Optimal duty cycle in S3.

Fig. 12. Output power from PV system in S3.

Fig. 13. Efficiency of boost converter in one day.

D. Estimation of the efficiency of the converter.

The efficiency of the converter, η, is given [2]by :

(14)

Where Pout is the output power from the PV system and Pin is

the input power from converter. And Fig. 13 shows the

efficiency of the boost converter during one day.

IV. CASE STUDY OF HANOI CITY

In order to determine the efficiency of the using optimal duty

cycle in the PV system, the database of solar radiation and

temperature of Hanoi city in year 2009 is chosen to calculate

annual energy production from the system.

It can be seen from Fig. (14), using the optimal duty could

achieve more production energy from the PV system than the

other duty cycle.

V. CONCLUSION

The importance application of equivalent DC/DC boost

converter model is proved in this paper, especially in

calculating the output power from the PV system in year. The

model is also taking account into losses in components of the

converter.

And also, it is possible to estimate the efficiency of the whole

PV system. Moreover, the impact of the changing duty cycle in

optimizing energy production from PV systems is considered to

the variation of solar radiation and temperature in one year.

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Fig. 15. Solar radiation in one day.

Fig. 14. Temperatures in one day.

Fig. 14. Annual production energy with different duty cycles.