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Sensors and Materials, Vol. 33, No. 11 (2021) 3991–4001
MYU Tokyo
S & M 2740

Simulation and Analysis of Power-point Tracking
via Photovoltaic Sensors
Fujian Zhang,1 Weidong Ye,1* Guoping Lei,2
Yingying Liu,1 Xian Wang,1 and Chao He3**
1College of International Vocational Education, Shanghai Polytechnic University, Shanghai 201209, China
2School of Electronics and Information Engineering, Chongqing Three Gorges University,

Chongqing 404130, China

3School of Communication and Information Engineering,

Chongqing University of Posts and Telecommunications, Chongqing 400065, China(Received July 1, 2021; accepted October 4, 2021)

Keywords: PV cells, radiation intensity, output characteristics, maximum power point tracking, output
power

The photovoltaic (PV) cell is the basic component of a solar power system as it converts lightenergy into electricity by the PV effect. To increase the efficiency of conversion, the maximum
power point (MPP) of the battery must be tracked in real time. We have established a systemmodel based on the main characteristics of the PV power generation system and PV cells thatconsiders the nonlinearity of the PV cell output. The mathematical model of a PV array isestablished by MATLAB/Simulink and combined with the common equivalent circuit of a PV
cell and the mathematical model of PV power generation. This model enables the maximum
power point tracking (MPPT) control of the PV cell through the simulation of its current-voltage(I–V) characteristic curve, which shows the cell’s operation within its electrical circuit. We
propose a MPPT control algorithm based on this model as an improved perturbation observation
method. This algorithm controls the working current of the inverter of the PV cell using a PV
sensor. Changes in light intensity or working temperature do not affect the ability of the tracking
system to reliably track the MPP. This method does not need complex analysis and the control isbased on a simple principle. Simulation results show that the algorithm has good dynamic
performance in a steady state. The proposed method can track the MPP and improve the PV
power generation efficiency by reflecting changes in illumination intensity with time.

1.

Introduction

The progress of science and technology and the improvement of people’s living standards
require more energy than before, which can no longer be satisfied with traditional fossil fuelpower generation. Therefore, the large-scale development and utilization of new forms of energy
are necessary to protect the environment and achieve sustainable development. The depletionand environmental problems of fossil fuels have led to the development of renewable energy
sources. Among the sources, photovoltaic (PV) power (solar power) generation has attracted*Corresponding author: e-mail: wdye@sspu.edu.cn**Corresponding author: e-mail: d170101004@stu.cqupt.edu.cn

https://doi.org/10.18494/SAM.2021.3520

ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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much research interest as it is easier to install solar power plants and obtain energy with much
fewer geographical limitations on the plants than for other renewable energy sources. Therefore,
large-scale PV power plants have been developed rapidly and have become increasingly popular.
This has contributed to the rapid development of PV cells as the essential component of thesesystems. However, the output of PV power generation systems is significantly affected by lightintensity and temperature, which does not allow stable power generation.
To solve this problem by improving the efficiency of systems, the maximum power point
tracking (MPPT) method has been proposed. The principle of MPPT is to maximize the energy
transfer from PV cells, which depends on the incidence angle of sunlight, the temperature of the
PV cell, and the electrical properties of the system, by using various sensing technologies. To
collect the maximum power from a PV power generation system using MPPT, several
components, such as a sliding mode controller (SMC), a voltage source inverter (VSI) and griddesign, and a PV generator (PVG) are required.(1) These are integrated into the system to display
its motion trajectory with the inverter topology that is used in an algorithm to optimize themaximum power point (MPP).
The module for motion trajectory includes a calendar chip that calculates the current positionand height of the sun using the current time and local latitude and longitude. The microcontroller
drives motors to move the PV panels to receive the maximum incidence of sunlight.(2) The PV
array and inverter are important for improving the power conversion rate in MPPT because
decreasing the number of electronic devices and having a compact structure will enable simple
control, low power consumption, and, accordingly, high conversion efficiency.(3) This is related
to the algorithm that controls the system efficiently. Previous research on algorithms for MPPT
mainly adopted the MATLAB/Simulink platform.(4) The hill-climbing algorithm was proposed
for boosting circuit operation and achieving effective MPPT,(5) which is regarded as simple andeffective. This method combines simplified particle swarm optimization and the step-size
perturbation observation method to ensure a fast, simple, and efficient process with limited
hardware resources.
In this study, we propose a new design of a view-based motion trajectory system and amathematical model for improving the efficiency of the PV automatic tracking system. The
system replaces the traditional trajectory system with the view-based system. The new model
provides optimal and stable PV arrays and an accurate simulation of the PV power generation
system that improves the power generation and decreases the current loss due to the transmission
between components of the PV power generation system.

2.

Methods

2.1

Basic principle of MPPT

MPPT is a dynamic and self-optimizing process that matches the internal resistance of the
PV battery. Its function is the real-time detection of the voltage of the power generated by the PV
panel to monitor the peak voltage and current of the PV power generation system. The highvoltage allows the high efficiency of the battery pack, which is the purpose of using MPPT.(6,7)

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The factory-set peak voltage (Vpp) and ambient reference temperature of a solar panel are about
17 V and 25 °C in general, respectively. Under ideal conditions, the charge and discharge
efficiencies of the solar controller increase by about 50% with MPPT.(8) Recent MPPT algorithms
adopt various methods such as fixed voltage, disturbance observation, incremental conductivity,and fuzzy logic control methods.(9) Figure 1 shows a schematic diagram of an MPPT system that
includes a PV module, a DC-DC converter circuit, and a pulse-width modulation control circuit.
2.2

Control algorithm

The disturbance observation method is often applied to the control of MPPT to improve thesystem power oscillation near the MPP of a PV battery by reducing the perturbation step size.(10)This method is not efficient in maintaining a balance between tracking speed and obtained
power so it has limited applications. When the step size is large, the tracking speed increases,
and operating points vary greatly near the MPP, which results in a large loss of output power but
accurate tracking.(11) If the step size is small, the range of operating points decreases near the
MPP, resulting in a small power loss and an increased number of disturbances. This increases
the tracking time,(12) and the power–voltage (P–U) characteristic curve satisfies ΔP/ΔU = 0 near
the MPP. To simplify the calculation, ΔP/ΔU is replaced with a certain voltage increment.(13)When the duty cycle decreases, U increases by ΔU to U1 (U1 = U + ΔU).
(1) When Pk > Pk−1, the operation mode is located on the left side of the MPP and the disturbancedirection remains unchanged.
(2) When Pk < Pk−1, the operation mode is located on the right side of the MPP and the
disturbance direction changes.
When the duty cycle increases, U decreases by ΔU to U1 (U1 = U − ΔU).
(1) When Pk > Pk−1, the operation mode is located on the right side of the MPP and the
disturbance direction remains unchanged.
(2) When Pk < Pk−1, the operation mode is located on the left side of the MPP and the disturbancedirection changes.

Fig. 1.

(Color) Schematic diagram of MPPT system.

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Sensors and Materials, Vol. 33, No. 11 (2021)

Mathematical model

A solar PV power generation system transforms solar energy into electric energy through thePV effect of solar cells and stores the energy in the battery. Since the battery is connected to theload at both ends, current flows through the load to produce output power as shown in Fig. 2.
Figure 3 shows a circuit of the battery of the PV power generation system. According toKirchhoff’s current law and Kirchhoff’s voltage law, the mathematical model of current andvoltage is defined as(5)IL = Iph − ID − Ish.

(1)

When Rs is small and Rsh is large, they have a negligible effect on the output of the battery.
Therefore, in the analysis of the actual circuit, Rs or Rsh can be ignored.(5) When Rsh of theequivalent circuit in Fig. 3 reaches several thousand ohms, its effect on the circuit can also be
neglected. Thereby, the circuit model is simplified to that shown in Fig. 4, and the output
characteristic is expressed as q (VOC + I L RS )  IL =I ph − I D exp  − 1 .

AKT
 


(2)

According to Eq. (2), the output voltage and current for the battery are affected by lightintensity and temperature, which have a linear relationship with Iph.(5) The relationship between
light intensity and temperature is defined as

Fig. 2.

Fig. 3.

(Color) Schematic diagram of a PV cell.

(Color) Circuit model of the battery of the PV power generation system.

Sensors and Materials, Vol. 33, No. 11 (2021)

Fig. 4.

3995(Color online) Simplified circuit model of the battery of the PV power generation system.

U OC
=


AKT  I phln + 1 ,
q
 ID


(3)

where AKT is the temperature coefficient of the open-circuit voltage and UOC is the open-circuit
voltage for the benchmark test (light intensity G = 1000 W/m2 and temperature = 25 °C).(14)3.

Results and Discussion

3.1

Parameters of simulation

A MATLAB/Simulink simulation of the battery of the PV power generation system based on
the above equations was established. The parameters of the battery are shown in Table 1.
The output characteristics of the voltage and current of the battery are determined by ambient
temperature (T) and light intensity (G). The model of the battery was simulated by using
different values of G and T, whose standard values were 1000 W/m2 and 25 °C, respectively. By
setting G = 1000 W/m2, T values of 5, 15, 25, 30, and 40 °C were used to obtain the simulated
values of the parameters. The obtained results are shown in Table 2.
The simulated values of the parameters were calculated with T = 25 °C and G = 200, 400,
600, 800, and 1000 W/m2. The obtained results are shown in Table 3.

Table 1
Parameters of battery of PV power generat ion
system used in simulation.
ParameterValue
21.6 V
VOC
17.2 VVm
3.41 A
I SC
3.19 A
Im
0.015
α
−0.07
β
R
2Ω

Table 2
Simulated values of parameters obtained by modelwith G fixed at 1000 W/m 2 .
T (°C)VOC (V) Vm (V) I SC (A)I m (A)
5
35.6
31.2
3.11
2.89
15
28.6
24.2
3.26
3.04
25
21.6
17.2
3.41
3.19
30
18.1
13.7
3.335
3.265
40
11.1
6.7
3.185
3.415

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Sensors and Materials, Vol. 33, No. 11 (2021)

Table 3
Simulated values of parameters obtained by model with T fixed at 25 °C.
G (W/m 2)
VOC (V)Vm (V)I SC (A)I m (A)
200
21.6
17.2
0.638
0.682
400
21.6
17.2
1.364
1.276
600
21.6
17.2
2.046
1.914
800
21.6
17.2
2.728
2.552
1000
21.6
17.2
3.41
3.19

3.2

Simulation results

3.2.1 V–I and P–U relationships
The simulated results were plotted as V–I and P–U curves for different values of sunlightintensity and temperature. Figures 5 and 6 show the simulation results of I–V and P–U curves at
T = 25 °C with G values of 200, 400, 600, 800, and 1000 W/m2.(15) With the solar radiation
intensity (G) fixed at 1000 W/m2, the ambient temperature was lowered from 40 to 5 °C. It was

(a)

(b)

Fig. 5.

I–V and P–U curves of simulated PV power regulation system at T = 25 ℃ and different light intensities.

Fig. 6.

V–I and P–V curves of simulated PV power regulation system at G = 1000 W/m 2 and different temperatures.

(a)

(b)

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found that the maximum power and optimal working voltage of the system gradually increased
with decreasing temperature. Also, with the ambient temperature (T) fixed at 25 °C, the solar
radiation intensity was reduced from 1000 to 200 W/m2.
The optimal working voltage remained unchanged, but the maximum power gradually
decreased. As the PV array is highly susceptible to external factors, the operating voltage andthat of the system have a nonlinear relationship. Therefore, it is important to make the systemhave one MPP with varying light intensity or temperature, which maximizes the efficiency of
the PV power generation system.
3.2.2 Simulation results
The simulation model of the disturbance observation method was established by MATLAB/
Simulink by using the parameters in Table 2. In addition to the parameters, a sampling time of 5× 10−5 s, a switching frequency of 2 × 103, a disturbance compensation length of 0.001 mm, andan initial duty cycle of 0.5 were input to the simulation model. The simulated results are shownin Figs. 7 and 8.

Fig. 7. (Color online) P–V curve when G = 1000 W/m 2 and T = 25 °C. (a) MPP, (b) Im, and (c) Vm tracking
diagrams.

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Fig. 8. (Color online) P–V curve when G = 800 W/m 2 and T = 15 °C (until 0.1 s), and G = 1000 W/m 2 and T = 25 °C(up to 0.2 s). (a) MPP, (b) Im, and (c) Vm tracking diagrams.

Figure 7 shows that the system reached the MPP in less than 0.01 s for G = 1000 W/m 2 and T= 25 °C. The maximum power achieved by the disturbance observation method was 55.1 W witha fluctuation of 1.8 W, which we regard as ideal for the MPP tracking system. The power firstreached a peak and fluctuated until a stable MPP value of 55 W was maintained after 4 ms.
For G = 800 W/m2 and T = 15 °C, the power fluctuated considerably and reached a stablevalue of 42 W. Then, G and T were changed to 1000 W/m2 and 25 °C, respectively, which
contributed to the sudden increase in power to 55 W from 0.1 s (Fig. 8).
Figure 9 shows that the power fluctuated and reached a stable value of 30 W at 0.1 s for
G = 600 W/m2 and T = 30 °C. The power suddenly dropped to less than 10 W, then increased to
20 W when G and T were changed to 600 W/m2 and 30 °C, respectively.
Both step-change modes can track the MPP and the output voltage and current of the PVbattery within about 0.01 s. The parameters (light intensity G and temperature T) of the systemchange at 0.1 s, which occurs in about 1 ms. Once again, by tracking the MPP and reaching a
steady state, the dynamic characteristics and stability of the system can reflect changes in lightintensity in a timely and smooth manner, and the system can quickly trace the maximum power
output of the PV battery.(16)Sensors and Materials, Vol. 33, No. 11 (2021)

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Fig. 9. (Color online) (a) Simulation comparison of the MPPT in different step sizes. (b) Simulation comparison of
the Convention P&O and Proposed MPPT.

4.

Conclusions

To determine the characteristics of the MPP of a PV power generation system, we establishedand simulated a model using MATLAB/Simulink. The MPPT of a PV battery was obtained by
an improved disturbance observation method. Simulation results revealed that the system model
found the MPP efficiently, which effectively improved the output efficiency of the PV system.
This method requires only a small part of the PV cell body to be used as the PV sensor tomonitor its electrical and temperature characteristics and to ensure the maximum efficiency of
power generation. The simulation results of the I–V and P–V characteristic curves of the PV cells
show the linear characteristics of the cells’ operation, which reduces the instability andcomplexity of the PV system. Once the working point of the circuit is adjusted to the MPP, thePV cell always operates at the MPP owing to the strict linear relationship between the PV celland the PV sensor. Similarly to other tracking algorithms, it realizes the automatic tracking of
the PV cells to obtain the MPP for enhancing the efficiency of PV cells.

Acknowledgments
This work was supported by the National Key Research and Development Program of China(No. 2017YFC0804704) and Shanghai Polytechnic University Foundation (No. EGD21QD20).

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About the Authors
Fujian Zhang received his B.S. degree in electrical engineering andautomation from China University of Mining and Technology and his M.S.
degree in mechanical design and theory from Shanghai Branch of General
Coal Research Institute in 2004 and 2007, respectively. Now he is working in
the College of International Vocational Education, Shanghai Polytechnic
University. His research interest lies in the key technologies of electric vehicles
and vehicle network communication. (fjzhang@sspu.edu.cn)
Weidong Ye received his B.S. degree in mechatronics from Shanghai
Polytechnic University and his M.S. degree in software engineering from
Fudan University. Now he works in Shanghai Polytechnic University. His
research direction is in the key technology of industrial engineering andsatellite power ground data acquisition and control. (wdye@sspu.edu.cn)

Guoping Lei received his B.S. degree in School of Electronic and Information
Engineering from Chongqing Three Gorges University and his M.S. degree in
School of Communication and Information Engineering from Chongqing
University of Posts and Telecommunications in 2006 and 2009, respectively.
Now he is working in Chongqing Three Gorges University, where he iscurrently a professor. His research interest lies in wireless communication.
(187044145@qq.com)

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Yingying Liu graduated from Shanghai Dianji University with a major inelectrical engineering and from Northeast Petroleum University with abachelor's degree in electronic information engineering. Now she works at
Shanghai Polytechnic University. Her research direction is battery capacity
research. (yyliu@sspu.edu.cn)

Xian Wang received her B.S. and M.S. degrees from East China University of
Science and Technology in 2008 and 2011 in China, respectively. Now she
works as a laboratory technician at Shanghai Polytechnic University. Her
research areas are about the channel estimation of communication systems andsignal processing. (wangxian@sspu.edu.cn)

Chao He received his B.S. and M.S. degrees from Chongqing Three Gorges
University in China in 2014 and 2017, respectively. Now, he is currently
pursuing his Ph.D. degree from School of Communication and Information
Engineering, Chongqing University of Posts and Telecommunications. His
research interests include MEC, VNE, and FiWi broadband access network.
(d170101004@stu.cqupt.edu.cn)