Abstract--Photovoltaic (PV) system is compod of veral elements as solar array, boost converter, inverter and load. The solar array should be integrated with a dc-dc converter and a control algorithm to perform a arch to track the maximum power continuously. We adopt perturbation and obrvation method to implement Maximum Power Point Tracking (MPPT) for solar cells. Owing to the existence of converters, photovoltaic system is a hybrid system contains continuous dynamic and discrete dynamic. Traditionally, the power electronic converter is difficult to model. This paper illustrates the modeling method of hybrid system, especially finite automata model. Bad on Finite State Machine (FSM), the hybrid modeling of boost converter is prented. Finally, provides a simulation environment for such combination between continuous time system and finite automata, which employs the simulink and stateflow from Matlab.
Index Terms—boost converter, finite state machine (FSM), hybrid model, Photovoltaic, simulation
I. I NTRODUCTION
HOTOVOLTAIC (PV) systems have been extensively employed for large power generation around the whole world in recent decades [1],[2]. The conversion of solar energy into electric energy is performed by means of photovoltaic cells. A boost converter is employed to step up the output DC voltage of the P
V cells to a higher fixed voltage level in order to supply a required voltage for the load. The boost converter is also derived in detail to examine the dynamic behavior of the studied PV system.
Due to rapid growth in the power electronic techniques, PV energy is of increasing interest in electrical power applications. The converters are widely ud in regulated switch mode DC power supplies. From the control point of view, power electronic circuits and systems constitute excellent examples of hybrid systems, since the discrete switch positions are associated with different continuous time dynamics. Hybrid models characterize systems governed by continuous differential and difference equations and discrete variables. Such systems are described by veral operating This work was supported by the National Natural Science Foundation of China (Grant No.50877053).
The authors are the State laboratory of Power Systems, Tianjin University of Technology, Tianjin 300384, China (e-mail: ; ; ; ). modes and the transition from one mode to another is governed by the evolution of internal or external variables or events. Such system is compod of a family of different dynamic modes such that the switching pattern gives continuous. A hybrid automata [3] has been successfully employed in emerging applications on the border between computer science and contro
l theory.
Becau of existence of switching component, boost in the PV system is a hybrid dynamic system. A hybrid system is a hierarchical rule-driven interconnection of discrete-level and continuous-level sub-systems. Turn on and off of switching component are discrete events. State variable’s changes show continuous state over time in a group of topology of boost converter. The application of discrete event systems supervis continuous state systems. Finite State Machine (FSM) theory is important tool for the modeling in hybrid system [4]. Nonlinear effects exist in the power electronic converters, such as bifurcation, chaos. Traditionally, power electronic converters have been difficult to model and simulate becau of the discontinuous nature of their underlying differential equations. Hybrid systems are typically modeled as reactive discrete elements that are driven by active continuous elements. This work suggests a modeling and simulation framework for a boost converter that employs a Matlab/Simulink bad on FSM in the context of hybrid system theory.
The power electronic converter topologies for Maximum Power Point Tracking (MPPT) [5] and voltage conversion are studied in this paper. The maximum power point of photovoltaic array is a variation per hour, so a arch algorithm is given according to the current-voltage (I-V) and power-voltage (P-V) characteristic of solar cell. By using Perturbation and Obrvation method, do impedan
ce matching between boost converter and photovoltaic array in order to realize MPPT faction. Bad on the boost’s FSM model, results of simulation by MATLAB/Simulink and stateflow verified favorable tracking performance of this system.
II. S OLAR A RRAYS
A. Solar Array Model
According to physical structure and output characteristic of solar cell, we have easy access to mathematical model. Solar cell is actually a p-n junction, which characteristic is similar to
MPPT Control of Photovoltaic System
Bad on Hybrid Modeling and its
Simulation
Ma Youjie, Cheng Deshu , Zhou Xuesong and Guo Runrui
P
ret是什么意思diodes. The various parameters of the solar cell are modeled as follows (e Fig. 1) [6]. The current source generates the photocurrent I ph
, which is proportional to the solar irradiation.
Fig. 1. Equivalent circuit of a solar cell
In terms of equivalent circuit, we can know
I=I ph d sh I I −−
提高课堂教学效率(1) D
s U V IR =+
(2)
Where I and V are the terminal current and voltage respectively of the solar cell, I ph is the light generated current ，I d is current through diode, R s and R p are ries resistance and parallel resistance of the cell.
zizima
According to I-V output characteristic of solar cell,
()(){}
00exp /1exp /1d D T s I I V V I q V IR AKT =−=+−⎡⎤⎣⎦ (3) Where A is the ideality factor of p-n junction, K is Boltzmann constant (1.38 ×10- 23 J/K), T is the temperature, q is the electronic charge, I 0 is diode’s rever saturated current. I ph is proportional to the sunlight strength, and also relates with temperature, so
1()/ph ref c ref ref I I ht T T S S ⎡⎤=+−⎣⎦ (4)
I ref is short-circuit current under the reference sunlight and
temperature, ht is cell module temperature coefficient, T ref and S ref are reference temperature an
d sunlight strength. Resistance value of R p is so large than R s that it is not considered important in a fixed parameter range.
Bad on the formula (1) ～ (4), we can receive mathematical model of solar cell.
()01()/exp 1s ref c ref ref q V IR I I ht T T S S I AKT ⎧⎫+⎡⎤⎪
⎪⎡⎤=+−−−⎨⎬⎢⎥⎣
⎦⎪⎪⎣⎦⎩⎭ (5) B. Output Characteristics of Solar Cell
The output characteristics are dramatically affected by the irradiation, temperature. Equ.5 shows that the solar cell has non-linear output characteristics. The I-V characteristics are shown in Fig.2. When output voltage of solar array is smaller, the change of output current is extremely small and solar array is considered as a constant current source. However, the current decreas quickly as soon as the voltage exceeds a critical value, and solar array is considered as a constant voltage source.
The P-V characteristics are also shown in Fig.2. The output power first incread and then decread. During this process,
there exists a maximum power point.
)
Fig. 2. I-V and P-V characteristics of solar cell
III. M PPT C ONTROL A LGORITHM
A. Maximum Power Point Tracking
The characteristic of solar cell is dependent upon the insolation, temperature and array voltage, it is necessary to implement Maximum Power Point Tracking in order to move the solar cell operating vol
tage clo to the maximum power point under changing atmospheric conditions. The solar panel shall be integrated with a dc-dc converter and a control algorithm, performed by the microcontroller, to perform a arch to track the maximum power continuously. Maximum power point tracking is also ud to provide a constant voltage to the required load. There are a ries of control algorithms, such as perturbation and obrvation method, incremental conductance method, optimum gradient method, fuzzy logic control method. The techniques are generally bad on voltage reference to adjust to achieve maximum power point. B. Perturbation and Obrvation Method
The most common method in this filed is the perturbation and obrvation method [7]. It involves periodically increasing or decreasing the solar cell’s voltage. If a given perturbation results in an increa in the array’s power then the subquent perturbation is made in the same direction. If the result is a decrea in power, the disturbance is made in the opposite direction. In this it continuously eks the maximum power point.
We adopt variable step method to arch the maximum power point. Expecting the target: when the maximum power point is far away, step length is bigger and increa the optimal speed; when near maximum power point, step length is lesr, the system steadily works in point. The ratio between variation of power (P) and voltage (V) are considered to be the step length of duty ratio D, which is a
ctually the slope of each operating point under the condition of very short sampling time.
To regard battery as the load, we can adjust to output voltage of solar array by changing duty ratio D of boost converter. Owing to D=U0/Ui and invariable voltage of battery, we adjust D in the opposite direction to implement power’s rai. when operating point is on the left of maximum power point, △V*△P>0，near the maximum power point by reducing the duty ratio to increa output voltage. when operating point is on the right of maximum power point, △V*
△P<0，near the maximum power point by increasing the
duty ratio to decrea output voltage(e Fig. 3).
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Fig. 3. Schematic diagram of MPPT
IV. H YBRID S YSTEMS AND H YBRID M ODELS
A. Hybrid Systems The hybrid systems of interest contain two distinct types of components: subsystems with continuous dynamics and subsystems with discrete dynamics that interact with each other [8]. The continuous dynamic is generally given by
differential-algebraic equations. The discrete dynamic is generally modeled by automata or input-output transition systems with a countable number of states [9]. Owing to the
existence of dc-dc converter and inverter, PV system is a
hybrid system. There are veral modes of operation towards the power electronic converters. Circuits are consistently changing bad on the different modes and various external conditions. Turning on and off of the switch is the discrete dynamic; while the continuous dynamic is state variable’s changing in the different mode during the continuous time. B. Hybrid Models Hybrid models characterize systems governed by
continuous differential and difference equations and discrete variables. Such systems are described by veral operating modes and the transition from one mode to another is
governed by the evolution of internal or external variables or
events [2]. When the continuous and discrete dynamics coexist
and interact each other, it is important to develop models that
graveyardaccurately describe the dynamic behavior of such hybrid
systems. Only in this way can it be possible to develop designs
that fully take into consideration the relations and interaction
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of the continuous and discrete parts of the system [8]. There
are some of common hybrid models, such as automaton
hammer headmodel, hybrid petri-net, hiberarchy model, and MLD [10]. Automaton model is very beneficial for power electronic system. Bad on computer science and control theory, tools are now evolving for analyzing and designing hybrid systems within the hybrid automaton framework.
V. B OOST C ONVERTER
The boost converter is asked to operate in the condition for continuous inductor current. So it needs relative large inductor.
Due to lower output voltage of solar cells, so it is necessary to
increa the voltage by using a boost converter. A. Topology
A boost converter using a power MOSFET is shown in Fig. 4. The dc-dc boost converter circuit is modeled in two modes of operations. The modes depend on the switch position and conduction of the diode. The state variables are the inductor current i L and the capacitor voltage u c . V in is output voltage of
solar cells.
Fig. 4. Equivalent circuit for Boost converter
Mode 1: when switch is on, the inductor acquires and stores the energy from solar cells. The current ris through L and the switch during t on . The full-supply voltage is applied across the inductor L. The state equations are as follows,
s L
c c
d V L i dt u d
C u R dt == (6)
Mode 2: when switch is off, the inductor current flows through the load, and the stored energy of inductor as well as source is transferred to the capacitor and the load.
s L c
c
L c d V L i u dt u d i C u dt R =+=+
(7)
B. Hybrid Model for Converter The converter is modeled as a hybrid system, which can
麦克杰克逊的歌operate in two distinct modes. The switching between the
modes is decided by FSM. The control scheme propod in
拼箱this work us FSM to decide choice which state equation.
The FSM outputs state-dependent Boolean variables that
decide execution paths by lecting state equation. The hybrid
mode switching scheme is expresd by a hybrid automaton
show in Fig. 5 [11]. Virtually, finite state machine is a hybrid
automaton.
Fig. 5. Hybrid automaton of the switching scheme
The rectangular blocks reprent the modes. Each arc reprents a transition from one state to the next state. The transition condition is given besides the arrow. If the states reach the transition conditions, the system will be switched into the next mode.
interaction
VI. S IMULATION OF H YBRID S YSTEM FSM is in wide u for modeling the behavior of computi
ng systems. Matlab’s stateflow and simulink, provides a simulation environment for boost converter. A two-bit output (sa, sb) is sufficient to describe all possible states, and make a choice for the differential equations from different operation mode. In Fig. 6 depicts a run in Matlab with L=250μH,
C=1mF , V in =20V and R=1Ω.
Fig. 6. Simulation of boost converter bad on FSM
Fig. 7. Stateflow structure of “boost FSM”
Fig. 8. Simulation results of boost converter in photovoltaic system
VII. C ONCLUSION
Photovoltaic system is now recognized to be most widely accepted as renewable energy sources to benefit communities, especially in developing countries and remote areas. The converters are widely ud in regulated switch mode DC power supplies. Hybrid automaton can develop models that accurately describe the dynamic behavior of such power
electronic circuit. Hybrid models characterize systems
governed by continuous differential and difference equations and discrete variables. FSM model for boost converter is correct and controllable. The results are comparable in the light of minor differences in the simulation environment. The approach can be extended to other converter easily. Boost converter can effectively get through MPPT, which is
favorable for improving efficiency of solar array. Using the perturbation and obrvation method can quickly and accurately track the maximum power output for solar array.
VIII. R EFERENCES
[1] M. Garozzo, C. Messana, A. Previ, and R. Vigotti, "The Italian PV
program: Accompishments and future goals," Proceedings of the Biennial Congress of the International Solar Energy Society, Denver, Colarado, USA, pp. 331–336, 1991.
[2] R.H. Annan and L.O. Herwig, "Photovoltaic industry and electric utility
roles in the U.S. photovoltaic program," Proceedings of the Biennial Congress of the International Solar Energy Society, Denver, Colarado, USA, pp. 315–320, 1991.
[3] K. Kobayashi, J. Imura, "Minimal Reprentation of Finite Automata
for Hybrid Systems Control," in Proc. 2006 45th IEEE Decision and Control Conf , pp.930–935.
[4] R.O. Ocaya, B. Wigdorowitz, "Application of finite state machines in
hybrid simulation of dc-dc converters," 2007 IEEE, pp.1–4, 1997.
[5] J.H.R. Enslin, M.S. Wolf, D.B. Snyman, W. Swiegers, "Integrated
photovoltaic maximum power point tracking converter," IEEE Trans.Industrial Electronics , vol. 44, pp. 769-773, Dec. 1997.
[6] J. Merten, J. M. Ansi, C. Voz, A. V. Shah, R. Platz, and J. Andreu, "
Improved Equivalent Circuit and Analytical Model for Amorphous Silicon Solar Cells and Modules," IEEE Trans. Electron Devices , vol. 45, pp. 423–429, 1998.
[7] Youngok Jung, Junghun So, Gwonjong Yu, Jaeho Choi, "Improved
perturbation and obrvation method (IP&O) of MPPT control for photovoltaic power systems," in Proc.2005 IEEE Photovoltaic Specialists Conf , pp.1788–1791.
[8] P.J. Antsaklis, "Special issue on hybrid systems: theory and applications
a brief introduction to the theory and applications of hybrid systems," Proceedings of the IEEE , vol. 88, pp. 879–887, 2000.
[9] A.T. Sava and H. Alla, "Combining hybrid Petri nets and hybrid
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[10] Y. Yin, S.Hosoe , "Tracking control of the continuous and discrete
大学英语四级准考证打印
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[11] A. van der Schaft and M. Schumacher, "Introduction to Hybrid
Dynamical Systems," New York: Springer–Verlag, 2000.
IX. B IOGRAPHIES
Ma You-jie was born in Tianjin, China, on Oct 26, 1964. She received M.S.E.E and D.S.E.E degrees from Tsinghua University, Beijing, China, in 1990 and 1993, respectively.
She is Master tutor and Professor in Tianjin University of Technology. Her current rearch interests include power electronics control, non-linear excitation control, renewable generation power system design and hybrid system theoretical
Rearch.
Cheng De-shu was born in Tianjin, China, on June 17, 1984. He received B.S.E.E degree from the Tianjin University of Technology, Tianjin, China, in 2007, and studied at this school continuously for the master degree.
His current rearch interests include power electronics control, grid-connected photovoltaic systems, and wind generation systems.
Zhou Xue-song was born in Jiangxi, China, on June 23, 1964. He received the B.S.E.E degree in south China University of Technology, Guangzhou, China, in 1984, respectively, and the M.S.E.E and D.S.E.E degrees from Tsinghua University, Beijing, China, in 1990 and 1993.
He is tutor of a Ph.D. student and Master tutor in Tianjin University and Tianjin University of Technology, respectively. His current rearch
interests include mechanical parking system, wind generation systems, grid-connected photovoltaic systems and power electronics control.
Guo Run-rui was born in Jilin, China, on Dec 29, 1982. He received B.S.E.E degrees from Jilin University, Jilin, China, in 2006, and graduated from the Jilin University, and studied at Tianjin University of Technology.
His current rearch interests include power electronics control, grid-connected photovoltaic systems, and wind generation systems.
