Modelling and Simulation of MPP Tracker Using ...

MODELLING AND SIMULATION OF MPP TRACKER USING PSPICE ANALOG BEHAVIOR MODELLING L. Hassaine 1, A. Chouder 1, M. Haddadi 2 and A. Malek 1 1

PV Laboratory, Centre de Développement des Energies Renouvelables, BP 62, Route de l'Observatoire, Bouzaréah, Algiers, Algeria 2 Electronic Laboratory, Ecole Nationale Polytechnique, Rue Hassen Badi, Algiers, Algeria

ABSTRACT Photovoltaic power use a maximum power point tracking (MPPT) in order to deliver the highest power to the load when changes in insolation and temperature occur. It overcomes the problem of mismatch between the solar cells and the given load. This paper presents a circuit-based model of PV generator using Analog Behavior Modelling (ABM) of Pspice. The insolation and temperature are introduced as parameters in this model. The use of DC/DC converter as a maximum power point tracker is of great interest, it is continuously matches the output characteristics of PV generator to the load. The DC/DC converter is first modelled by the so-called "State Space Averaging Method" to derive the transfer function between control variable an PV voltage terminals. The PV generator is taken as a current source in this paper. A PI controller is used to ensure the stability for the whole system.. The obtained simulation results show the powerfulness of Pspice in helping the design process and in investigating a real way in order to achieve a better maximum power tracking. INTRODUCTION In designing a photovoltaic (PV) generator, one must, because of economic and sizing reasons, obtain the maximum amount of energy converted to meet the load requirements. A photovoltaic array can operate over a wide range of output voltage and output current. The I-V characteristics of the PV array is affected by the levels of insolation and temperature, which causes the maximum power point to fluctuate. The use of DC/DC converter as a maximum power point tracker is of great interest, it is continuously matches the output characteristics of PV generator to the load. The control loop design of the DC/DC converter is of prime interest in tracking the maximum power point and in keeping with a fixed operation condition. In order to supervise the design of complex systems, a number of powerful component-based electronics simulation systems, such as Pspice, have been made available over the last few years. They do not, in their basic form, provide a circuit model of a solar cell, which is difficult to integrate with current electronics simulation technology used in the generic modelling at circuit levels. CELL MODEL A mathematical description of the current-voltage (I-V) terminal characteristic for PV cells has been available for some time The solar array is a non-linear device and can be represented as a current source model as shown in Figure 1. One of mathematical model which reflect the behaviour of such cells, especially those constructed from monocristallin silicon is a model of simple exponential given by the following equation [1,2].

   q (V + R s I )  V + Rs I  − 1 − I = I ph − I0 exp  R sh  A kB T    World Renewable Energy Congress VII (WREC 2002)

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(1)

Editor: A.A.M. Sayigh

Figure 1: Cell Model

The principal parameters used in this mathematical model show that the characteristic of a the PV Cell is a function of insolation and temperature which causes the maximum power point to fluctuate and profoundly influences the design of the converter and control system. These parameters are given by the following equations [1]: I ph

=

{I cc

. φn + I t (Ta − Tr )} n p

(2)

I = I ph − I D

(3)

ID

  q VL / n s  = I 0 exp  − 1  n p  A K Tc  

(4)

I0

T = I 0r  c  Tr

3  q Eg  1 1     − Tc   B K  Tr

(5)

Tc

= 276 + φ 4 + 0,9 Ta

(6)

PSPICE MODEL OF PV GENERATOR

In order to investigate the influence of insolation and temperature individually, we use ABM of Pspice features [3] for the design process of MPPT tracker. This approach is illustrated in Figure 2. φ (parameter)

ns (parameter) np (parameter)

Pspice Model of PV generator

I-V (characteristic)

T (parameter) Figure 2: Approach illustrated Pspice model of PV generator

The Pspice model of PV generator is represented in Figure 3. Equations 1-6 [1]were used in this simulation to obtain the characteristic curves of a solar array as show in Figure 4. Each curve has a maximum power point Pmax, which is the optimal operation point. Results of simulations introduced the parameters variation The simulation of the PV model allowed as to plot the different curves by introducing the variables parameters. Influence of insolation and temperature on the characteristic P-V Figure 4 shows the array output power for a range of insolation levels at temperature 27 °C and output power for a range of temperature levels at insolation : 1000 W/m2 and a resistive load which was varied from 0 to ∞. MODEL AND CONTROL SYSTEM

To design the control system of a converter, it is necessary to model the converter dynamic behavior, it is of interest to determine how variations in the power input voltage , the load current, and the duty cycle d(t) affect the output voltage. The circuit of PV generator with a boost converter has higher energy for PV systems including an MPPT [7], it is represented in Figure 5. The PV generator is taken as a current source and this equivalent circuit model operate in Continuous - Current Mode (CCM) under PWM control.

World Renewable Energy Congress VII (WREC 2002)

Copyright 2002. Published by Elsevier Science Ltd.

Editor: A.A.M. Sayigh

Figure 3: Pspice model of PV generator

Figure 4: Influence of insolation and temperature on array output power

Figure 5: Equivalent circuit of PV generator with a boost converter

The DC/DC converter is first modelled by the so-called "State Space Averaging Method" to derive the transfer function between control variable an PV voltage terminals. The state averaged model of this system is formed by tacking a weighted average of the Eqn. 7-9 and may expressed as [4] :

x&= Ax + Bu

(7)

A = D A on + (1 − D) A off

(8)

B = D Bon + (1 − D) Boff The global matrix of the system can be represented in following :  dv pv   − 1 − 1  0      c   v pv  +  − (1 − D )  V  didt  =  rs c   B − rl   i L     L   1  L  dt   L L 

(9)

(10)

The state space averaging approach is widely used to derive expressions and analysis for small signal characteristics of pulse-with-modulation (PWM) controlled DC/DC converters [4]. ~ x d~ = A~ x (t) + B ~ u ( t ) + [(A1 − A 2 ). X + (B1 − B 2 ). U ]. d ( t ) (11) dt

World Renewable Energy Congress VII (WREC 2002)

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vpv  d ~  −1  dt    ~  =  rs C  d iL   1   dt  L  

−1  ~ 0 0 C  .  v pv  +  − 1 v +  1  V . ~  ~ B B d − rL   iL   L   L  L 

(12)

The charging voltage usually rises slowly, therfore, the voltage is assumed constant as seen from the battery ~ side. The disturbance of the voltage is represented by a voltage perturbation VB . The PV generator is taken as a current source, thus, the PV generator terminal voltage has to be adjusted to deliver the maximum power. The effect of a small perturbation of PV array terminal voltage to system stability has to be considered carefully. The small signal model of the control to input transfer function is expressed as [5,6] : v TP (S) = ~PV d

(13)

vB = 0

So, after simplifing, the transfer function becomes : Vpv − rs (1 − D)(rs + rL )  s 2  s  ω2 + 2 ξ ω + 1 n  n  L + rL rs C 1 − 2 ξ2 , ξ = 2 (1 − D )

v pv ~ = d Where ω2n =

1 − rL rs L C

ωr = ωn

(14)

Frequency analysis Pspice model in Figure 6 show the ABM circuit simulation of the small signal model described by Eqn. 14.

Figure 6: ABM circuit simulation of the small signal model

Elaplace =

(0.41 10

− 21.4 −6

)

s 2 + 0.44 10 − 3 s + 1

(15)

Results of simultation The frequency analysis gives the gain curve and the phase curve were represented in Figure 8. The Bode digram shows that the phase margin is very poor as shown in Figure 7. A Proportional-Integral (PI) compensator is introduced to make the system stable. A phase margin is 10°, thus, the additional phase lead necessary to satisfy the relative stability requirement is 55°. In order to achieve a phase margin of 65° as shown in Figure 8. MPPT PROCESS

The perturbation and observation method [8] witch moves the operating point by periodically increasing or decreasing the array voltage is used to determine Vref. Figure 9 shows the diagram of the proposed scheme. It consists of two loops, maximum power point tracker. The maximum power point tracking loop is used to set a corresponding Vref to the comparator, the voltage loop is used to regulate the solar array output voltage according to the Vref which is set in the MPPT loop. The function in the two loops are illustrated in by the following Figure 9. And Figure 10 schows the simulated results of MPPT with PI compensator[4,5,6].

World Renewable Energy Congress VII (WREC 2002)

Copyright 2002. Published by Elsevier Science Ltd.

Editor: A.A.M. Sayigh

Figure 7: Bode diagram of gain and phase curves without PI compensator

Figure 8: Bode diagram of gain and phase curves with PI compensator

Figure 9: MPPT process with PI compensator

Figure 10: Simulated results of MPPT

CONCLUSION

The obtained simulation results show the powerfulness of Pspice in helping the design process and in investigating a real way in order to achieve a better maximum power tracking. and show how averaging and linéarisation technique may be used to obtain linear transfer functions for DC-DC converters In order to supervise the design of complex systems. The perturbation and observation method makes the system able to follow the rapid changes of insolation and achieve the maximum power tracking. NOMENCLATURE

Where np , ns : Cells in parallel and in series, VL : Load voltage, IL : Load current, Iph : Light generated current,, ISC : Short circuit current (2.83A at SC), φ : Solar insolation in W/m2, φn : Normalised solar insolation, It : Short circuit current temperature coefficient (2.3×10-4 A/K), TC : Cell operating temperature in K, Tr : Cell reference temperature, Ta : Ambient temperature in °C, ID : Diode current, I0: Inverse saturation current of diode, I0r : Inverse saturation current of diode at reference temperature (2.210-5A), k/q : Boltman’s constant/electronic charge- (8.62 10-5), a, b : Cell constants (2.36, 3.15) and Eg : Bandgap of semiconductor. Ipv: Current of PV generator, rL: Series resistance of the inductor L, rs: Equivalent resistance of the solar array. REFERENCES

1. 2. 3. 4. 5. 6. 7. 8.

Lawrance, W.B. and Troster, R. (1992), Renewable Energy, 6, pp. 591-596. Gow, J.A. and Manning, C.D. (1999), IEE Proc. Electr. Power, 146, pp. 193-200. Cotorogea, M. (1998), IEEE, Transactions on Industrial Electronics, pp. 17-21. Forsyth, A.J. and Mollov, S.V. (1998), Power Engineering Journal, pp. 229-236. Hua, C. and Lin, J.R. (1996), IECON, Proc. of IEEE, 3, pp. 1705-1710. Hua, C., Lin, J.R. and Shen, C. (1998), IEEE, Transactions on Industrial Electronics, pp. 97-107. Glasner, I. and Appelbaum, J. (1996), IEEE, Transaction on Energy Conversion, pp.355-358. Van der Merwe, L. and Van der Merwe, G.J. (1998),IEEE, Trans. on Energy Conversion, pp. 214-217.

World Renewable Energy Congress VII (WREC 2002)

Copyright 2002. Published by Elsevier Science Ltd.

Editor: A.A.M. Sayigh