Journal of Robotics, Networking and Artificial Life, Vol. 3, No. 2 (September 2016), 111-115

Study on the Technology of MPPT of the Solar Photovoltaic Based on the Model Predictive
Control
Xia Zhao

Schoolof Electrical and Electronic Engineering
Shanghai Institute of Technology, Shanghai, China
Huailin Zhao
Schoolof Electrical and Electronic Engineering
Shanghai Institute of Technology, Shanghai, China
Masanori Sugisaka

Alife Robotics Corporation LTD, Oita, Japan
E-mail:zhao_huailin@yahoo.com
www.sit.edu.cn http://alife-robotics.co.jp/

Abstract
The solar photovoltaic battery is a very important new type of renewable distributed energy. But its output power
is directly affected by the light intensity and temperature. Its voltage-current characteristics have obvious nonlinearfeatures. Therefore, a new MPPT technology based on the model predictive control (MPC) is proposed in thispaper. The simulation results show that the method can quickly track the maximum power point under the practicalenvironmental conditions, and improve the energy conversion efficiency of the system.
Keywords: Photovoltaiccell; Maximum power point tracking; Solar energy; Matlab/Simulink;

1. Introduction
Currently the survival of humanity is inseparablefrom the use of energy. Along with the increasing
depletion of non-renewable energy, development ofrenewable energy has become the theme of today'sworld. Solar energy as a clean and renewable energy
attracts the people's attention. In some way, thatphotovoltaic cells convert solar energy into electricity,
called photovoltaic. Because of its affection ofenvironment and the load, and consideration of the input
and output characteristics of nonlinear, this paper
presents the maximum power point tracking (MPPT)

principles and methods, mentions several MPPT method,and compare the advantages and disadvantages of thealgorithm .
2. Modeling the Solar Cell
Photovoltaic cell is the device that can convert thesun light into electricity using the photovoltaic effect.
The incidence of light on the cell is generates charge
carrier that originate an electric current if the cell isshort-circuited [1]. Basically, the PV phenomenon may bedescribed as the absorption of solar radiation, thegeneration and transport of free carriers at the p–njunction, and the collection of these electric charges at

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the terminals of the photovoltaic device [2]. The
commonly accepted solar cell model is a one diodemodel [3],which is shown in Fig. 1.This Photovoltaic cell
model is a nonlinear device and can be represent as acurrent source model. The I-V characteristics of aphotovoltaic cell is similar to diodes characteristic, andwhich is represent by the following equation:
IRsIpv
IdVRshFig.1. The circuit diagram of the photovoltaic cell qV  (1)
 − 1 aKT  
In each array, cells connected in parallel increase
current and cells connected in series provide greater
output voltages. And if there have parallel connection ofcells in array, the photovoltaic and saturation current canbe expressed as. Also
the characteristic of photovoltaic arrays can bemathematically described as:  q (Vo + IRs )   Vo + IR
(2)
−1 −I = I − I exp
I =I pv,cell − I o,cell  exp pvoaN s KTRshThe equation (2) have a wide application intheoretical analysis of photovoltaic cell. But due to theparameters, K, and are relative to the solar irradiance andthe ambient temperature, and the value of them is hard todetermined. Consider that the value of is very small, but
is very large. So we can approximately see(Vo + I o Rs ) Rsh equal to zero [4]. For the purpose ofefficiency and stability, a maximum power point tracker(MPPT) is a power electronic DC-DC converter inserted
between the photovoltaic array and its load. So it ensure
the photovoltaic array always works at its maximum
power point as the temperature, insolation and load vary.
3. Maximum Power Point Tracking Algorithms
The operation of photovoltaic array are influenced
by solar radiation, temperature and load values. At agiven condition of irradiation and temperature, aphotovoltaic cell can work at difference operation point,
but there is a unique operation point of the photovoltaic
array with maximum output power, that is Maximum
power point (MPP). Obviously, it is necessary to takesome measure to maintain the photovoltaic array work atMPP, and it also can improve the efficiency ofphotovoltaic power system. These measures called
Maximum Power Point Tracking (MPPT)[5]. The
principle of maximum power point tracking is throughadjusting the load impedance to make the photovoltaic
power generation system always work at the near
maximum power point, under different environmental
condition [6].
Many research papers have produced with various
schemes for the MPPT in photovoltaic power generation
system. At now the commonly used method about themaximum power point tracking of photovoltaic theincremental conductance method (INC)[7], theperturbation and observation method (P&O)[8]. Moreover,the fuzzy logic based method could fond in[9] [10]. And
the incremental conductance method (INC) and theperturbation and observation method (P&O) are applied
widely. We will discuss the incremental conductancemethod about MPPT algorithms in detail.
The photovoltaic cell terminal voltage can be
adjusted relative to the maximum power point voltage bymeasuring the incremental () and instantaneousarray conductance () and make use of the mentioned
control strategy. It has better track of any changes either
in load or photocurrent rather than the perturbation andobservation method, but this way of tracking still hassome oscillation which cannot be avoided. Also thesimulation result of the incremental conductancealgorithms will be discussed in next section.
4. Model Predictive Control based Maximum
Power Point Tracking
As mentioned above, conventional methods to track
the maximum power point the result are not as good asexpected, most of them have oscillation and cannot beavoided. And this paper we consider a model predictivecontrol based MPPT technique applied to photovoltaicmodule.
The main characteristic of model predictive control
is predicting the future behavior of the desired control
variables until a predefined horizon in time based on thepresent data of input or output. Also this control variables

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will be optimized by minimizing a cost function to obtaina satisfying control performance of overall system.
This paper we consider a islanded operation
photovoltaic generation system as controlled member,which main consist of a photovoltaic array, a DC-DC
boost converter, and a MPC controller as shown in Fig.2.

TsT
V pv ( k ) − s VC ( k ) + I pv ( k ) (3)
L
L
1
1
(4)
VC ( k=I pv ( k ) −VC ( k ) + VC ( k )+ 1)
CRC… I pv (=k + 1)

V pv (=k + 1)

L
( I pv ( k + 1) − I pv ( k )) + VC ( k )Ts(5)When the switch is closed, the equivalent circuits ofthe boost converter shown as Fig.4.and the equations asfollowing:

Fig.2. Control block diagram of overall islanded
photovoltaic system configuration implementing MPC based
MPPT technique

The photovoltaic array generates electric power
directly from solar radiation. And then the power isdelivered to DC load through a DC-DC boost converter,
whose switch (IGBT) is operated by the MPC controller.
And the states of switch are controlled by the output (S)of MPC controller. When the switch is considered as
open, the equivalent circuits of the boost converter
shown as Fig.3.

Fig.4. Equivalent circuit for boost converter when
the switch is open (S=1)

The discrete model of the system as following:

I pv (=k + 1)

TsV pv ( k ) + I pv ( k )LT VC ( k + 1) = 1 − s  VC ( k ) RC 
L
V pv (=k + 1)
( I pv ( k + 1) − I pv ( k ) )
Ts

(6)
(7)
(8)

Where Ts is sampling frequency, make use of theequation (3), (4), (5) or (6), (7), (8), the behavior of thecontrolled variable
and can be predicted for the
next sampling instant. And we can utilize the predictedvalue of this control variables to distinguish whether thephotovoltaic array work at the maximum power point.
5. Simulation and Result
Fig.3. Equivalent circuits for boost converter when
the switch is open (S=0)

The Euler approximation is then used to obtain thediscrete model of the system:

In the simulation process of Solar photovoltaic cells,
assuming the ambient temperature is maintained at 25degrees, just considering the changes of the solar
illumination and that three time points were given light
700,900

and 1000. Simulate themutations of the light intensity at different moments withthree step signal, Observe and compare the maximum

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power output tracking situation in the current
environment conditions with the use of solar photovoltaic
cells under the control of MPC and INC. The simulation
results are shown in the following figure.

Fig.8. Output power

Fig,5. Light changing after time

The initial value of light was 700, at the second thelight in creases by 200, at the third second the lightchanged into 1000, and the changes of the moments aremutations. Change of the light is shown in Figure 6
Fig.9. Zooming in on the figure of output power

Fig. 6. Current changing after time

Output current is shown in Figure 7,since the output
of photovoltaic solar cells is directly proportional to thelight intensity of the sun, when the sunlight changes, thecurrent of the photovoltaic cell can quickly track changesof the light.

Output voltage and power as respectively shown infigure 8 and figure 9.The MPC control system is noshock, and the tracking speed is significantly faster thanthe INC.
This paper analyzes principle under certain lightintensity and ambient temperature, the output of power
and operating voltage is obviously nonlinear. It isdifficult to operate at the maximum outputting point ofpower. Therefore, in order to improve the conversion rateof solar energy, solar photovoltaic cells designed thepredictive control based on the maximum power point
tracking technology. The simulation shows that thismethod can quickly adjust the solar cell operating voltage
and track the maximum power point fast, at the sametime overcome the shock and other issues brought by theclassic disturbance observer and incremental admittance
MPPT technology.
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Fig.7. Voltage changing after time

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