Hybrid Modeling and Simulation for the Boost Converter in Photovoltaic System

Youjie Ma, Deshu Cheng, Xuesong Zhou Tianjin University of Technology

Tianjin 300384, China e-mail: chengdeshu@126.com

Abstract—Photovoltaic (PV) system is composed of several elements as solar cells, boost converter, inverter and load. 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. Based on finite state machine (FSM), the hybrid modeling of boost converter is presented. Finally, provides a simulation environment for such combination between continuous time system and finite automata, which employs the simulink and stateflow from Matlab.

Keywords-boost converter; hybrid systems; automata; finite state machine ; photovoltaic; solar cells; modeling ;simulation

I. INTRODUCTION Photovoltaic (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 PV 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 used in regulated switch mode DC power supplies. From the control point of view, power electronics 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 several operating modes and the transition from one mode to another is governed by the evolution of internal or external variables or events. Such system is composed of a family of different dynamic modes such that the switching pattern gives continuous. A hybrid automaton has been successfully employed in emerging applications on the border between computer science and control theory. The converter is modeled as a hybrid system which can operate in two distinct modes and the switching between these modes is decided by a controller. The switching among these modes is governed by finite state machine (FSM),

which generates control signal according to receiving external signal and state information. Most modern electronic systems have both intricate control requirements and concurrency. Thus, combining FSM with concurrent models of computation is an attractive and increasingly popular approach to design. FSM has long been used to describe and analyze intricate control sequences, and be in wide use for modeling the behavior of computing systems. Since Harel introduced that State charts model [3] in 1987, a number of variations have been explored [4]. The hybrid converter modeling comprises a FSM embedded in the continuous time scheme.

II. PHOTOVOLTAIC SOLAR CELLS According to physical structure and output characteristic

of solar cells, we have easy access to mathematical model. Solar cell is actually a P-N junction, which characteristic is similar to diodes. It’s equivalent circuit is composed of photoproduction current source and a series of resistance (see Fig. 1) [5].

Figure 1. Equivalent ciruit for photovoltaic solar cells

In terms of equivalent circuit, we can know

ph d shI I I I= − − (1)

D sU V IR= + (2) Where I and U are the terminal current and current respectively of the PV, Iph is the photoproduction current，Id is current through diode, Rs and Rp are series resistance and parallel resistance. According to V I− output characteristic of solar cells,

( )( ) ( ){ }0 0exp / 1 exp / 1d D T SI 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 electric charge, I0 is diode’s reverse saturation current.

2009 Second International Conference on Information and Computing Science

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DOI 10.1109/ICIC.2009.330

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Iph is proportional to the sunlight strength, and also relates with temperature, so

1 ( ) /ph ref c ref refI I ht T T S S⎡ ⎤= + −⎣ ⎦ (4)

ISCref is short-circuit current under the reference sunlight and temperature, ht is cells module temperature coefficient, TCref

and Sref are reference temperature and sunlight strength. Resistance value of Rp is so large than Rs that it is not

considered important in a fixed parameter range.

Based on the formula (1) ～ (4), we can receive

mathematical model of solar cells.

(5)

III. HYBRID SYSTEMS AND HYBRID MODELS

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 [6]. 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 [7]. Owing to the existence of DC-DC converter and inverter, photovoltaic system is a hybrid system. There are several modes of operation towards the power electronic converters. Circuits are consistently changing based 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 several 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 accurately describe the dynamic behavior of such hybrid systems. Only in this way it be possible to develop designs that fully take into consideration the relations and interaction of the continuous and discrete parts of the system [6]. There are some of common hybrid models, such as automaton model, hybrid petri net, hiberarchy model, and MLD. Automaton model is very beneficial for power electronic system. Based on computer science and control theory, tools are now evolving for analyzing and designing hybrid systems within the hybrid automaton framework.

IV. BOOST CONVERTER 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 increase the voltage by using a boost converter.

A. Topology A boost converter using a power MOSFET is shown in

Fig 2. The dc-dc boost converter circuit is modeled in two modes of operations. These modes depend on the switch position and conduction of the diode. The state variables are the inductor current iL and the capacitor voltage uc . Vin is output voltage of solar cells.

CM1

VinRG

DmL

Figure 2. Equivalent ciruit for Boost converter

Mode 1: when switch is ON, the inductor acquires and stores the energy from solar cells. The current rises through L and the switch during ton. The full-supply voltage is applied across the inductor L.

s L

cc

dV L idt

u dC uR 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

cL c

dV L i udt

udi C udt R

= +

= + (7)

B. Hybrid Model The converter is modeled as a hybrid system, which can

operate in two distinct modes. The switching between these modes is decided by FSM. The control scheme proposed in this work uses FSM to decide choice which state equation. The FSM outputs state-dependent Boolean variables that decide execution paths by selecting state equation. The hybrid mode switching scheme is expressed by a hybrid automaton show in Fig.3 [8]. Virtually, finite state machine is a hybrid automaton.

Figure 3. Hybrid automaton of the switching scheme

( ){ }01 ( ) / exp / 1ref c ref ref sI I ht T T S S I q V IR AKT⎡ ⎤= + − − + −⎡ ⎤⎣ ⎦⎣ ⎦

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The rectangular blocks represent the modes. Each arc represents a transition from one state to the next state. The transition condition is given besides the arrow. If the states reach these transition conditions, the system will be switched into the next mode.

V. SIMULATION OF HYBRID SYSTEM FSM are in wide use for modeling the behavior of

computing 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. 4 depicts a run in Matlab with L=250μH, C=1mF, Vin=20V and R=1Ω.

Figure 4. Simulation of boost converter based on FSM

Figure 5. Stateflow structure of “boost FSM”

Figure 6. Simulation results of boost converter in photovoltaic system

VI. CONCLUSION 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 used in regulated switch mode DC power supplies. Hybrid automaton can develop models that accurately describe the dynamic behavior of such hybrid system. 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.

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[3] D. Harel, “Statecharts: A visual formalism for complex systems,” Sci. Comput. Program, vol. 8, pp. 231–274, 1987.

[4] M. von der Beeck, “A comparison of statecharts variants,” in Proc. Formal Techniques in Real Time and Fault Tolerant Systems, LNCS 863.

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