Photovoltaic Water Pumping System Controlled by Cascade Sliding Mode

This study presents a new maximum power point tracking algorithm applied to a photovoltaic water pumping system in order to optimize the photovoltaic power generation. This system is driven by an induction motor controlled by a cascade sliding mode control in order to track a set of reference trajectories such as currents, rotor flux and speed. By using the MATLAB-SIMULINK software, modeling and simulation studies are investigated to highlight the utility of the proposed system.


INTRODUCTION
In order to cover the energy requirement, researches are being made for renewable energy.Privately, Photovoltaic (PV) energy is produced by direct transformation of solar illumination to electrical energy.One of the world wide applications is the water pumping system driven by induction motor as it has been presented in Abid et al. (2007) and Mezouar et al. (2007).
In this study, the PV water pumping system is constituted by a PV generator, a condenser, a Pulse Width Modulation PWM inverter, an induction motor and a centrifugal pump.
In order to force the PV generator to operate at its maximum power point under different solar illumination values, we develop a maximum power point tracking algorithm MPPT which calculates the reference speed of the induction motor versus the solar illumination as in Abid et al. (2007), Arrouf and Bouguechal (2003) and Barazane et al. (2003).The induction motor is distinguished by its rigidness, reliability and relatively low cost.However, the difficulty to control the induction motor is related to the fact that its mathematical model in Park configuration is nonlinear and highly coupled as demonstrated in Arrouf and Ghabrour (2007), Mahmoudi et al. (1999), Marouani andBacha (2009) andTarik Duru (2007).Due to the development of power electronics and microprocessors, the induction motor control is possible by applying field oriented techniques as presented in Abid et al. (2007) and Mahmoudi et al. (1999).
These techniques provide the decoupling stator and rotor machine frames that allow obtaining a dynamical model similar to that of the direct current machine.
Nevertheless, a discontinuous behavior is imposed by the switching devices of the inverter supplying the induction machine.Therefore, it is suitable to look for some techniques which are appropriate to discontinuous operation of the switching devices.The Sliding Mode is an All or Nothing (AoN) control low which is the most appropriated to the control of the switchers of the power converters of the PV water pumping system.So, in this study, we will demonstrate that the Sliding Mode Control allows a high performance in controlling of the induction motor.Robustness of this control low will be highlighted versus changing parameters and external disturbances as it has been presented in Arrouf and Ghabrour (2007), Mimouni et al. (2004), Utkin (1993) and Weslati et al. (2008).

MODELING OF THE PHOTOVOLTAIC WATER PUMPING SYSTEM
The photovoltaic water pumping system includes a PV generator, a DC bus, an inverter, an induction motor and a centrifugal pump.Following sections present models of these subsystems.
The PVG model: The mathematic model of the PVG with N s series connected solar cells and N P parallel connected panels is given by (1), (Abid et al., 2007;Arrouf and Bouguechal, 2003): The DC bus model: To avoid the submission of the PVG to the over-voltages coming from the inverter, we insert a condenser C between them.The DC bus current Ic is given by (2): The inverter model: The three-phase inverter consists of three independent arms.Each one includes two switches which are complementary and controlled by the Pulse Width Modulation PWM as in Abid et al. (2007), Arrouf and Bouguechal (2003) and Arrouf and Ghabrour (2007).The stator voltages (v sa , v sb , v sc ) are expressed in terms of the upper switches as follows: s 1 , s 2 and s 3 are the controller signals applied to the switches.
The induction motor model: By considering the stator voltages (v ds , v qs ) as control inputs, the stator currents (i ds , i qs ), the rotor flux (Φ dr , Φ qr ) and the speed (Ω) as state variables, the electrical model of the induction motor in the d-q referential axis linked to rotating field is given by (7), as in Abid et al. (2007), Arrouf and Ghabrour (2007), Mahmoudi et al. (1999), Marouani and Bacha (2009) and Mezouar et al. (2007): where, The mechanical modeling part of the system is given by: where, J = The total inertia of the machine f = The coefficient of friction C r = The load torque Ω = The mechanical speed of the machine The electromagnetic torque is given by: ( ) where, p is the number of pole pairs.The hydrodynamic load torque of the centrifugal pump is given by (9) as in Abid et al. (2007): where, A p = The torque constant (A p = P n /ω rn 3 ) P n = The nominal power of the induction-motor ω rn = The rotor nominal speed The centrifugal pump model: The centrifugal pump is described by the lows of similarity which are given by ( 12) as in Marouani and Bacha (2009): where, Q' and Q are, respectively the flow and the nominal flow of the pump, H' and H are, respectively his height and total height; N' and N are respectively his speed and nominal speed.

THE CASCADE SLIDING MODE CONTROL
The rotor flux field oriented control: By using the electrical model of the induction machine given by ( 6), one can remark the interaction of both inputs, which makes the control design more difficult.So, the first step of our work is to obtain a decoupled system in order to control the electromagnetic torque via the The rotor flux Φ r and its position θ s are estimated by means of stator current and speed and are given as follows: ( / (1 .)). where, s is the differential operator (s = d/dt).
Then, the stator equations on d, q-axis become, (Barazane et al., 2003) Sliding mode control: In this study, the sliding mode control theory is applied to the rotor field oriented induction motor in such away to obtain simple surfaces.The proposed control scheme is a cascade structure as shown in Fig. 1, in which two surfaces for each axis are required.The internal loops allow to control the stator current components (i ds , i qs ); whereas the external loops provide the speed and the rotor flux (Ω, Φ r ) regulations as in Arrouf and Ghabrour (2007) and Mimouni et al. (2004).
The sliding surfaces for each axis are chosen as follows: ( ) ( ) ( ) ( ) The (i ds ) ref and (i ds ) ref references are determined by the outer loops and take, respectively the values of (i ds ) c and (i qs ) c. Using ( 13) and ( 14), it follows: • On d-axis: for the rotor flux regulation, we have: Thus, the controller is: ( ) ( ) ( ) The controller on d-axis is given by: ( ) ( ) ( ) In the same way: • On q-axis: for the speed regulation: And the controller is given by: ( ) ( ) ( ) To satisfy the stability condition of the system, all of the following gains (k d , k q , k Φ , k Ω ) should be chosen positive.
High performances must be obtained by choosing appropriate gains as in Arrouf and Ghabrour (2007).k d and k q take the admissible values of transient stator voltage in direct and quadrature axis, then k d = (v ds ) max and k q = (v qs ) max .k Φ takes the value of (i ds ) max = (Φ r ) ref /M.k Ω takes two times of stator quadrature current value (i qs ) max admissible by the machine.
Using Park transformation, the reference voltages in the (a, b, c) coordinates are given by ( 27) as in Abid et al. (2007):

Calculation of the reference variables:
The reference flux value is (Φ r ) ref = 1wb.The reference speed Ω ref is calculated by the MPPT algorithm analyzed in above section.
Maximum power point tracking algorithm: By neglecting frictions and losses, we can express the power of the induction motor as follows as in Abid et al. (2007): So, the reference speed Ω ref can be expressed as: Table 1 presents the reference speed and the optimal PV power for different values of the solar illumination.
We can determinate the relation between illumination E and the approximated reference speed Ω * app by using the curve fitting technique as in Abid et al. (2007), Arrouf and Bouguechal (2003) and Barazane et al. (2003).The approximated reference speed is given by ( 30 Architecture of the photovoltaic water pumping system: The architecture of the photovoltaic water pumping system is described by Fig. 2. The subsystems of the proposed configuration are a PV generator, a condenser, a PWM inverter, an induction-motor and a centrifugal pump. The main components of the sliding mode control block are the four sliding surfaces S (Φ r ), S (Ω), S (i ds ) and S (i qs ).In order to calculate the reference speed, we use a sensor to measure the illumination value and a calculator to deduce the reference speed via the MPPT.

RESULTS AND DISCUSSION
In order to demonstrate the effectiveness of the proposed control technique applied to the photovoltaic water pumping system, some simulations have been carried out.So, the proposed design scheme which is described by Fig. 2 is implemented in MATLAB/SIMULINK software using parameters given in Table 2.

Variation of the solar illumination value E:
In a first step, we choose to vary the solar illumination value E as it is shown in Fig. 3 and to see its impact on the performances of the photovoltaic water pumping.Figure 5a illustrates the waveform of the mechanical speed of the induction motor which is closed to its optimal value.
The same remark is given to the electromagnetic torque shown by Fig. 5b.
It is clearly shown that the induction motor is operating at its optimal conditions.Figure 5c represents the waveform of the centrifugal pump flow which is closed to its optimal value for each value of E.
Then, we can conclude the important role of the sliding mode control and the proposed MPPT to make the photovoltaic water pumping system operating at its optimal conditions.Study of the robustness of the system: In a second step, we choose to vary the rotor time constant T r at 20% of its initial value at it is shown in Fig. 6, in order to prove the robustness of the system at the disturbances and the drifts of the motor driven pump parameters.
Figure 7a to c show, respectively the waveform of the motor speed, the electromagnetic torque and the pump flow.
So, a rapid response is obtained.The different variables are lightly affected by the T r change at a short and then, they return to their optimal values.The same remark is given to the centrifugal pump flow which proves that the water pumping system operating at its optimal conditions.Then, the robustness of the controlled system is highlighted by the appropriate type controller which is a sliding mode control and the cascade structure used.

CONCLUSION
We have proved the utility of the developed algorithm MPPT in resolution of the problem of degradation of the performances of the PV generator following the variation of the power according to climatic factors and its role to minimize the total cost since it replaces electronic devices like converter used for tracking of the maximum power point.
Furthermore, the sliding mode control applied to the field oriented induction motor pump has succeeded in the regulation of the motor speed and then in optimization of the performances of the system.Such a control scheme provides protection of the connected inverter and machine with regards to stator current since these latter are controlled.Besides, the robustness quality of the proposed controllers appears clearly in the test results by changing machine parameters.Finally, this installation provides the minimization of the total cost since we choose to stock the water and not the energy which requires the use of electrical batteries.
1) where, I pv , V pv and P pv = The Photovoltaic (PV) current, voltage and power I ph = The light-generated current I s = The reverse saturation current R s and R sh = The PV array series and shunt resistances A

=
R r = The stator and rotor resistances L s and L r = The stator and rotor inductances T r = The rotor time constant (T r = L r /R r ) The total leakage coefficient (σ = 1 -M²/L s L r )

Fig. 5 :
Fig. 5: Simulation results for the SMC under illumination variation corresponding to the new value of E after a short transient.So, we can note the utility of the MPPT algorithm in optimization of the PVG performances.Figure5aillustrates the waveform of the mechanical speed of the induction motor which is closed to its optimal value.The same remark is given to the electromagnetic torque shown by Fig.5b.It is clearly shown that the induction motor is operating at its optimal conditions.Figure5crepresents the waveform of the centrifugal pump flow which is closed to its optimal value for each value of E.Then, we can conclude the important role of the sliding mode control and the proposed MPPT to make the photovoltaic water pumping system operating at its optimal conditions.

Table 1 :
Reference speed and PV power versus the illumination value