Tracking Power Photovoltaic System with Sliding Mode Control Strategy

Energy Procedia 36 ( 2013 ) 219 – 230

1876-6102 © 2013 The Authors. Published by Elsevier Ltd.

Selection and/or peer-review under responsibility of the TerraGreen Academy

doi: 10.1016/j.egypro.2013.07.025

Terragreen13 International Conference

Tracking power photovoltaic system with sliding mode

control strategy

D. Rekioua , A.Y.Achour, T. Rekioua

a

Laboratory LTII, Department of Electrical Engineering, University of Bejaia, Algeria

Abstract

The output power induced in the photovoltaic modules depends on solar radiation and temperature of the solar cells. To maximize the efficiency of the system, it is necessary to track the maximum power point of the PV array. In this paper an application of sliding mode control strategy is applied to track maximum power of photovoltaic cells. In this control system, it is necessary to measure the PV array output power and to change the duty cycle of the DC/DC converter control signal. This method is simple and robust to irradiance and temperature variations. To test the robustness of this control, we compared the results with those obtained using the Perturb & Observ. method. Obtained results are presented and show the performances of sliding mode control strategy under the parameter variation environments.

Keywords:Photovoltaic, DC/DC converter, Sliding mode control, Maximum power point tracking, Cells. 1.Introduction

Over the years, several MPPT algorithms have been developed and widely adapted to determine the maximum power point [1-7]. The control technique the most used consist to act on the duty cycle automatically to place the generator at its optimal value whatever the variations of the metrological conditions or sudden changes in loads which can occur at any time.

Many methods have been developed to determine the maximum power point (MPP). In Ref.[8], to track MPP, a look-up table on a microcomputer is employed. It is based on the use of a database that includes parameters and data such as typical curves of the PV generator for different irradiances and temperatures. In Ref.[9], curve-fitting method is used, where the nonlinear characteristic of PV generator is modelled using mathematical equations or numerical approximations. These two algorithms have as disadvantage that they may require a large memory capacity, for calculation of the mathematical formulations and for storage of the data. Open-circuit voltage photovoltaic generator method is employed in Ref.[10], it approximates linearly the voltage of PV generator at the MPP to its open-circuit voltage and a linear dependency between the current at the MPP and the short-circuit current for the short-circuit photovoltaic generator method presented in Ref.[11]. These methods are apparently simple and economical, but they are not able to adapt to changeable environmental conditions. Ref.[12] presents perturb. and observe (P&O) method which is based on iterative algorithms to track continuously the MPP through the current and voltage measurement of the PV module. Most control schemes use the P&O technique because it is easy to implement [13-16] but the oscillation problem is unavoidable.

*Corresponding author. Tel/Fax: +21334215006/+21334215005 E-mail address: dja_rekioua@yahoo.fr.

ScienceDirect

Conductance incremental method presented in Ref. [16] requires complex control circuit. The two last strategies have some disadvantages such as high cost, difficulty, complexity and instability.

Intelligent based control schemes MPPT have been introduced (fuzzy logic, neural network) [16-25]. The fuzzy logic controllers (FLC) are used very successfully in the implementation for MPP searching. The fuzzy controller improves control robustness, it does not need exact mathematical models, it can handle non-linearity and this control gives robust performance under parameters and load variation.

In this paper, a sliding mode control is applied to track maximum power of photovoltaic system. The advantages of this control are various and important: high precision, good stability, simplicity, invariance, robustness etc.... This allows it to be particularly suitable for systems with imprecise model. Oftenff it is better to specify the system dynamics during the convergence mode. In this case, the controller structure has two parts, one represents the dynamics during the sliding mode and the other represents the discontinuous system dynamics during the convergence mode.

We present firstly in this paper the studied system with the proposed MPPT. Then the modelisation of the overall system is developed. Finally obtained simulation results and some experimental ones are presented to show the performances of sliding mode control comparing to P&O method.

2. Proposed description system:

The configuration of the studied system is shown in Fig.1.It consists of a PV array, input capacitor, an MPPT power stage and a sliding controller

Fig1.Proposed system.

3. Modeling of the proposed system

3.1 Model of PV Array

In literature, there are several mathematical models that describe the operation and behavior of the photovoltaic generator [4]. These models differ in the calculation procedure, accuracy and the number of parameters involved in the calculation of the current-voltage characteristic. In this paper we use the one diode model. Its equivalent circuit consists of a single diode for the phenomena of cell polarization and two resistors (series and shunt) for the losses (Fig. 2). This model is used by manufacturers by giving the technical characteristics of their solar cells (data sheets).

Fig.2. Simplified equivalent circuit of solar cell G, Tj T Iph Ipv Id IRsh Rsh Rs Vpv Duty cycle D Irradiance Temperature MPPT power stage Sliding MPPT Controller IL Vpv V0 Load Cpv 0 5 10 15 20 25 30 35 40 45 50 0 0.5 1 1.5 2 2.5 3 3.5 4 Vpv (V) I p v (A )

Ipv(Vpv) characteristic of this model is given by the following equation [5]: Rsh d ph pv I I I I (1) sh pv s pv j s R I V q ph pv _R I R V kT AN I I I s pv pv . 1 exp . . 0 » » ¼ º « « ¬ ª ¸ ¸ ¹ · ¨ ¨ © § (2)

The simulation is based on the datasheet of Siemens SM110-24 photovoltaic module. The parameters of this solar module are given in Table 1. The module is made of 72 solar cells connected in series to give a maximum power output of 110 Wc.

Table .1

Parameter of the PV panel SIEMENS SM 110-24

PPV 110W Impp 3.15A Vmpp 35V Isc 3.45A Voc 43.5V αsc 1.4mA/°C βoc -152mV/°C Pmpp 110W

Fig.3 Comparison of experimental results with simulation ones(I-V and P-V)

3.2. MPPT Control strategy

3.2.1. Perturb & Observ control

This is the most widely used method [2], [6], [12], [15], [26]. A feedback loop and few measures are needed. The bloc diagram of the P&O method is given in Fig.4. The panel voltage is deliberately perturbed (increased or decreased) then the power is compared to the power obtained before to disturbance. Specifically, if the power panel is increased due to the disturbance, the following disturbance will be made in the same direction. And if the power decreases, the new perturbation is made in the opposite direction. The advantages of this method can be summarized as follows: knowledge of the characteristics of the photovoltaic generator is not required, it is relatively simple. Nevertheless, in steady state, the operating point oscillates around the MPP, which causes energy losses. The MPPT is necessary to draw the maximum amount of power from the PV module.

Fig. 4 Bloc diagram of Perturb & Observe method

Perturb & Observe Technique Vpv

V Vopt

Fig.5 Evaluation of the PPM in terms of rapid increase and decrease of insolation

Fig.6 Evaluation of the MPC in terms of rapid increase and decrease of the temperature

We note that the algorithm P&O follows fast enough movement from the point of maximum power imposed by the change of insolation. The power generated by the photovoltaic generator is proportional to the insolation but with strong oscillations in steady state.

3.2.2.Sliding mode control

The advantages of sliding mode control are various and important: high precision, good stability, simplicity, invariance, robustness etc....

The design of the control can be obtained in three important steps and each step is dependent on another one:

x The choice of surface.

For a system defined by the following equation, the vector of surface has the same dimension as the vector control (u).

u

t

x

B

x

t

x

A

x

x

,

˜

,

˜

(3)

We find in literature different forms of the sliding surface and each surface has better performance for a given application. In general, we choose a non-linear surface. The nonlinear form is a function of the error on the controlled variable (x), it is given by:

x e t ) x ( S 1 r x¸ ˜ ¹ · ¨ © § _O w w (4)

whereex is the difference between the controlled variable and its referenceex xxx

x

O is a positive constant.

r

is the number of times to derive the surface to obtain the control. x is the controlled variable

The purpose of the control is to maintain the surface to zero. This one is a linear differential equation with a unique solution ex 0for a suitable choice of parameter Ox with respect to the convergence

condition.

x The establishment of the invariance conditions

The conditions of invariance and convergence criteria have different dynamics that allow the system to converge to the sliding surface and stay there regardless of the disturbance: There are two considerations to ensure the convergence mode.

¾ The discrete function switching

This is the first convergence condition. We have to give to the surface a dynamic converging to zero. It is given by: °¯ ° ® ­ ² ¢ ¢ ² x x 0 x S si 0 x S 0 x S si 0 x S ₍₅₎

It can be written as:

x Sx 0

Sx ˜ ¢ (6)

¾ Lyapunov function:

The Lyapunov function is a positive scalar function for the state variables of the system. The idea is to choose a scalar function to ensure the attraction of the variable to be controlled to its reference value. We define the Lyapunov function as follows:

x S 2 1 x V _˜ 2 ₍₇₎

The derivative of this function is:

x Sx Sx

Vx ˜x (8)

x Determination of the control law.

The structure of a sliding mode controller consists of two parts. The first one concerns the exact linearization ueq and the second one concerns the stabilization un

.

n eq u

u

u

(9)

Whereu_eqcorresponds to the control. It serves to maintain the variable control on the sliding surface.

n

u is the discrete control determined to check the convergence condition (Eq.6.).

We consider a system defined in state space by Eq.3 and we have to find analogical expression of the control (u). t x x S t S x S w w ˜ w w w w x

(10) Substituting Eq.3 and Eq.9 in Eq.10., we obtain:

eq

Bx,t un x S u t , x B t , x A t S x S ˜ ˜ w w ˜ ˜ w w x (4.24) We deduce the expression of the equivalent control:

t , x A t S t , x B t S u 1 eq _w ˜ w ˜ ¸¸ ¹ · ¨¨ © § ˜ w w

(11)

For the equivalent control can take a finite value, it must:

0 t , x B x S_{˜ z} w w

(12) In the convergence mode and replacing the equivalent command by its expression in Eq.11, we find the new expression of the surface derivative:

n u t , x B t S t , x S ˜ ˜ w w x

(13)

And the condition expressed by Eq.6. becomes:

0 u t , x B t S t , x S ˜ ˜ _n¢ w w ˜

(14)

The simplest form that can take the discrete control is as follows:

S

x

t

sign

ks

u

_n

˜

,

(15)

Where the sign of ks must be different from that of Bx,t x S_˜ w w

4. Application of Sliding mode control to Track Photovoltaic System

In sliding mode controller, the control circuit adjusts the duty cycle of the switch control waveform for maximum power point tracking as a function of the evolution of the power input at the DC/DC converter. In this control system, it is necessary to measure the PV array output power and to change the duty cycle of the DC/DC converter control signal [27-31]

The system can be written in two sets of state equation depends on the position of switch S.

>

V V (1 S)

@

L 1 dt di C dc L (17)

>

L load

@

C _{i (1 S) i} C 1 dt dV ₍₁₈₎

We introduce the concept of the approaching control [30]. We select the sliding surface as:

0 dV dP pv pv (19) Fig. 7. DC-DC converter VC C E iL Iload RLoad L S=1 Vdc Cdc S=0

0 dV ) I. R ( d dV dP pv 2 pv pv pv pv (20) 0 dI dR I R . I. 2 dV ) I. R ( d dV dP pv pv 2 pv pv pv pv 2 pv pv pv pv (21) 0 ) dI dR I R . 2 ( I dV dP pv pv pv pv pv pv pv ₍₂₂₎ where pv pv pv I V

R is the equivalent load connect to the PV. with Ipv IL

The non-trivial solution of Eq.22 is:

0 ) dI dR I R . 2 ( pv pv pv pv ₍₂₃₎

The sliding surface is given as:

) dI dR I R . 2 ( L pv L pv ' V ₍₂₄₎

We have to observe the duty cycleD. Its control can be chosen as:

D ' D D if V²0 D ' D D if V¢0

Eqs.17 and 18 can be written in general form of the non linear time invariant system. D g(X). ) X ( f X. (25)

The equivalent control is determined from the following condition [30]:

0 X . dx d T . . »¼ º «¬ ª V V (26)

f(X) g(X).

0 dx d eq T . D »¼ º «¬ ª V V (27)

We obtain the equivalent controlDeq:

C pv T T eq _V V 1 ) X ( g . dX d ) X ( f. dX d »¼ º «¬ ª V »¼ º «¬ ª V D ₍₂₈₎

The equivalent duty cycle must lies in0¢Deq¢1

The real control signal D _{is proposed as [30]:}

1

V

D

D

_eq

kc

if

0

¢

D

_eq

kc

V

¢

1

0

D if

D

_eq

kc

V

d

0

where the control saturate if

D

_eq

kc

V

is out of range, kc is a positive scaling constant.

Fig. 8.Operating point according to the sign

D

5. Numerical simulation

To test the robustness of sliding mode, we compared the results with those obtained using the Perturb & Observ method.

Fig.9. Electrical characteristics of the two controllers in the case of insolation variation Ppvma Vpvmax Ppv(A) Vpv(V) MPP

D

_decrease

D

increase

0

¢

V

V

¢

0

Fig.10. Electrical caracteristics of the two controllers in the case of temperature variation 0 10 20 30 40 1 1.5 2 2.5 3 3.5 Vpv[v] Ip v[ A] 0 10 20 30 40 0 20 40 60 80 100 120 Vpv[v] Pp v [w ]

Fig.11. Electrical characteristics of the two controllers in the case of temperature and insolation variation.

Obtained results show a Good Stability in steady state and a better efficiency compared to that of the control P&O.

5. Conclusion

In the method the sliding mode, regardless of the ranges of variation of meteorological parameters, the responses are more stable, more accurate and robust. Tests conducted by the variation of insolation and temperature, clearly show that the system is insensitive to the first test and are very insensitive with the simultaneous action of the two parameters. The sliding mode control (CMG) has good static and dynamic performance (stability and accuracy), that is to say a tolerable response time without overshoot. In addition, it also gives better tracking and a near total rejection of the disturbance. In this paper, we can concluded that the correct choice of the surface of the slide, allows the sliding mode control, to make improvements over linear MPPT controls (such as P & O).

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