Modified MPPT with Using Model Predictive

Control for Multilevel Boost Converter

Mostafa Mosal,2, Haitham Abu Rubl, Mahrous E, Ahmed2, Jose Rodriguez3 IDept. of Electrical & machine Engineering, Texas A&M University at Qatar, Doha, Qatar

2Dept. of Electrical & Computer Engineering, Aswan University, Aswan, Egypt 3Dept. of Electrical Engineering, Universidad Tecnica Federico Santa Maria, Valparaiso, Chile

Email: m,mosa@ieee,org, haitham,abu-rub@qatar,tamu,edu, meahmed7@ieee,org

Abstract-This paper proposes a modification in the maximum power point tracking (MPPT) by using model

predictive control (MPC). The modification scheme of the MPPT control is based on the perturb and observe algorithm (P&O). This modified control is implemented on the dc-dc multilevel boost converter (MLBC) to increase the response of the controller to extract the maximum power from the photovoltaic (PV) module and to boost a small dc voltage of it. The total system consisting of a PV model, a MLBC and the modified MPPT has been analyzed and then simulated with changing the solar radiation and the temperature. The proposed control scheme is implemented under program MA TLAB/SIMULINK and the obtained results are validated with real time simulation using dSPACE 1103 ControlDesk. The real time simulation results have been provided for principle validation.

Index Terms-Multilevel Boost Converter (MLBC), Model

predictive control (MPC), Maximum power point tracking

(MPPT), Perturb and Observe algorithm (P&O).

I. INTRODUCTION

Due to its limited reserve oil, the world has given the priority for the energy issue especially in terms of the renewable energies (REs) utilization. One of the main resources of the renewable energy is a Photovoltaic (PV) system. It has been recently become an essential target overall the world [1],[2]. However, most of current PV systems are based on string structure where several modules are connected in series to increase the input voltage that can be boosted for grid connection applications. Unfortunately this configuration of module connection is very sensitive for environmental conditions such as shading phenomena, changing in the temperature [3]-[5]. In case of any partial shading the system generates a lower power, Therefore, it becomes preferable to attach a dc-dc converter into each module using a high voltage gain converter topology to increase the system efficiency,

There are few techniques have been used for boosting the dc voltage with high gain and suitable duty cycle that is far from the saturation point. One of this is the N-stage high step-up converter with switched capacitors as shown in Fig.l [6]. Each switched capacitor cell is composed of a capacitor, a diode and two switches. Each capacitor can be taken as a voltage source, which is switched and recombined by the switches. The current path is provided by the diode when the switches are turned off. High step-up and wide range voltage gain can be realized by in series N switched capacitor cells. But the main problem in this converter is the number of switches is large so the number of gate drive will be large.

Figure 2 illustrates a dc-dc high-voltage converter with a buck converter followed by a push-pull voltage multiplier. It may be extended to high voltage applications with low voltage devices by adding capacitors and diodes without modifying the power stage. However, it requires two stages including three switches and a complex control system; the input current is discontinuous [7]. Moreover, there is a transformer with center tap that is used in this circuit.

The converter in reference [8] shown in Fig. 3 is proposed based on the switched capacitor which charges N capacitors to the input voltage, and connect them in series to feed a boost stage. The switched capacitor stage can operate with high efficiency since it does not regulate the output voltage which is regulated with the boost stage. This converter requires a high number of switches and the output switch is rated to the output voltage.

Source

Source

Figure I. High step·up converter with switched-capacitors.

D5

Inductor

C3

Figure 2. Buck followed by a push-pull voltage multipl ier. 82

C2

D3

Figure 3. Switched capacitor converter with a boost stage.

Load

Lood

Load

978-1-4673-2421-2/12/$31.00 ©2012 IEEE 5080

Multilevel boost converter that was chosen to be used in this paper and is proposed in [9] fades all aforementioned problems in the previous circuits. The main advantages of this converter are the current is continuous, it gives a large conversion dc ratio with low duty cycle and without a transformer, it can be built in a modular way, more levels can be added without changing the main circuit, it provides several self-balanced voltage levels and only one switch is necessary [9].

This paper uses the multilevel boost converter in a PV application. This converter which is connected to a PV should extract maximum power from it. So the control that is applied on the MLBC is a maximum power point tracking control [10]-[13]. This work tries to modify a control based on perturb and observe algorithm (P&O) [14] by using model predictive control (MPC). MPC has emerged as a very powerful method for the control of electrical energy using power converters [15]-[18]. MPC is very intuitive and easy to apply, even in the presence of nonlinearities. In addition, it can avoid the use of linear controllers and modulators. The goal of this modification is reducing the time (increase the response) to achieve the maximum power point (MPP) [19],[20].

This paper is organized in the following way, section II shows the operational principales of the MLBC, section III explains the idea of the modified MPPT control, section IV shows the analyses of the MLBC, section V explain the idea of using bi-directional dc-dc converter in this system, section VI shows the real time simulation results of the modified MPPT control applied on the MLBC, and in the final section VII conclusion is presented.

II. OPERATIONAL PRINCIPLES OF MULTILEVEL BOOST CONVERTER

This section illustrates the operational principles of the MLBC. Figure 4 illustrates the multilevel boost converter which combines the boost converter and the switched capacitor function to provide an output of several capacitors in series with the same voltage and self-balanced voltage. It provides several self-balanced voltage levels and only one switch is necessary. Its output voltage can be increased to any value by increasing the number of levels by using extra capacitors and diodes. To increase additional level to these converter two capacitors and two diodes only will be used without changing in the main circuit. The control of this

03 C2

IL Inductor Load

C1

v�

(a) (b)

topology is simple because there is only one switch in this converter unlike other topologies like switched capacitor converter with a boost stage so there is only one gate drive for this switch.

Assume the number of levels of the MLBC is two, so when the switch is turned on, the inductor is connected to the voltage source. If C3's voltage is smaller than C)'s voltage, C) charges C3 through the diode D2 and the switch as shown in Fig. 4 (a). In the same time the capacitor voltage across C)+C2 discharges in the load. Besides that, when a switch is turned off, the diode D) turns on because the inductor charges the capacitor C) until the voltage on the capacitor C) equal to the summation voltage on the voltage source and the inductor voltage as shown in Fig. 4(b). After that, the diode D3 turns on so the voltage source, the inductor and capacitor C3 charging the capacitor C)+C2 through it as shown in Fig. 4 (C). When the voltage on the C)+C2 is equal to the summation voltage on the voltage source, the voltage on the inductor and the voltage on the capacitor C4, the diode D3 turns off.

III. MODIFIED MAXIMUM POWER POINT TRACKING CONTROL

As known that, the photovoltaic module has a maximum power point. This point is continuously changing with the change of the module temperature and irradiation. The MPPT controller tracks this power point as long as it changes. In this section a maximum power point by using model predictive control (MPC) [19]-[22] will be presented in this section. In general P&O method has a simple feedback structure and fewer measured parameters [23]-[25] like voltage and current sensor. It operates by periodically perturbing (i.e. incrementing or decreasing) the PV module terminal voltage and comparing the PV output power with that of the previous perturbation cycle.

If the perturbation leads to an increase or decrease in module power, the subsequent perturbation is made in the same or opposite direction. In this manner, the peak power tracker continuously seeks the peak power condition. When the steady state is reached, the algorithm oscillates around the peak point. In order to keep the power variation to be small, the perturbation size is kept very small. The algorithm is developed in such a manner that it sets a reference voltage of the module corresponding to the peak voltage of the module.

03 C2

C3 Load

C1

Switch

(C)

Figure 4. Multilevel boost converter (a) when a switch is turned ON, (b) and (C) when a switch is turned OFF.

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Based on the above, the main goal to using the MPC in perturb and observe algorithm (P&O) is to increase the response of the control of MPPT on the PV system when there is abrupt change in a temperature or irradiation because MPC predict the future behavior of the system. As shown in Fig.5 a PV module is connected to a MLBC then to a load like a dc motor. In addition to that, power electronics converter like a bi-directional dc-dc converter [26],[27] with a storage battery is connected in parallel with a dc load to take the surplus power generated from a PV module to charging a storage battery. Moreover, when the power demand from the load is larger than the generated power from a PV, the battery feeds a load with a rest of power (sharing the PV module) throw a bi-directional dc-dc converter. MLBC boosts a small voltage of the PV module to be valid for feeding the load, and in the same time to extract maximum power from a PV module. The controller senses a dc voltage and a dc current of the PV module. Then the predictive model generates the predicted power and the reference power signals. Moreover, the optimized and selector take this signal and then give the pulses to the MLBC. This width of this signal is dependent on MPPT control.

IV. ANAL YSIS OF THE MULTILEVEL BOOST CONVERTER FOR THE IMPLEMENTATION OF THE MPC

The main concept of the MPC is to predict the future value of the PV module output voltage and current (inductor current and capacitor voltage). So in this section a principle of the inductor volt-second balance and capacitor charge balance will be presented. First we consider the electrical diagram in Fig. 4 (a), (b) and (c) that depicts a two-level MLBC. This converter has two capacitors at the output (C1 and C2). For this particular converter the number of levels is equal two. For the first subinterval with the switch is turned on as shown in Fig. 4 (a), the right-hand side of the inductor is connected to the ground.

The inductor voltage and capacitor current for this subinterval are given by:

(1 )

(2)

Where Vpv' I PV is the PV module voltage and current

respectively, I L is the inductor current, C is the value of

the capacitor, L is the value of the inductor and RL is

equivalent series resistance of the inductor (ESR). For the second subinterval with the switch is turned off as

shown in Fig. 4 (b)-(c), the inductor is connected to the output throw a diodes and capacitors. The inductor voltage and capacitors current are then:

dl L-= Vpv(t)-I,R,-VCI(t)-Vd dt (3)

(4)

Where � is the forward voltage diode, Vel is the voltage

of the capacitor.

The discrete time of the aforementioned equations (1)-(4) (the sampling frequency Ts) are:-When a switch is turned ON:

IL(K+1)=IL(K)[1-RLX � ]+Vpv(K)X � (5)

Vpv(K + 1) = Vpv(K) + [Ipv(K) - IL(K)]x �

Also when a switch is turned OFF:

IL(K + 1) = IL(K)[l- RL x Ts]+ Vpv(K)x I: -Vc,(k) L L

Vpv(K + 1) = Vpv(K)+ (Ipv(K)-IL (K))x �

(6)

(7)

(8)

It is note from the previous equations (5)-(8), there are four

inputs IL, Vpv ' Ipv and VCl. So the number of sensors

that should be used will be four and this is undesirable. So these equations can be rearranged and will be modified to decrease the number of sensors by decreasing the number of inputs. The enhancing of equation (6) will present in equation (9). Moreover, equation (7) can be replaced with equation (10).

PV Module Multilevel Boost Converter Load

f---l---+-f-----l

t. Pulses ,

: :----------------------------------------------�-----------, i.lp'.'!. pr

pe

odwiC

ele

rd. Optimized . Predictive L. .. · .. yp.�i· Model R:��:�C" se���tor

l MPPT

Bi-directional dc­dc Converter

Figure 5. Implementation of the MPPT controller scheme through MPC on MLBC.

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Battery

(9)

(10)

The above equations when a switch is turned ON can be expressed in the matrix form as in (11) and when a switch is turned OFF can be expressed in the matrix form as in (12).

[IJk+l)] [1-R xI', 1',] [IL(k)] [0 ] = L L L . + ·�vCk-l) �vCk+l) ° 2 �wCk) -1

[IL(k+l)] [

1 0] [IJk)]

�vCk+ 1) = ° 2 • �)vCk)

(11)

(12)

A possible criterion of predictive control is to minimize a cost function of the control error and the manipulated variable increments during the corresponding prediction horizons [28]. The cost function of this system when a switch is turned OFF is shown in equation (13) then when a switch is turned ON is shown in equation (14).

,-----_�====;;::::;---INO,---( IL(K +1)=fL(K)+Vpv(K)x -t-V,,(K + I) = 2V,,(K)-V(k-l) Pp,,(k + I) = I L(K + I) x Vpv(k + I)

No P(k+l»P(k)

5=0

gs�o = A· lpre/k + 1) - �)v,s�o(k + 1)1 gs�l =A·IP"e/(k+l)- Ppv,s�l(k+l)l

(13) (14)

Where A is the weighting factor of the power errorPlw] . So now after using equation (5) for the predictive inductor

current in the ON state, equation (10) for the OFF state, equation (9) for the predictive PY capacitor voltage for both two states, and equation (11) and (12) for a cost function, a flowchart in Fig.6 will show all the main points of the modified MPPT control by using MPC.

As shown in Fig.6 the voltage of the PY module and the inductor current are measured then the controller observes the state of the switch if it is ON (S=l ) or OFF (S=O). After that, a predicted power can be calculated from the predicted voltage and current according to equations (5), (9) and (10). Moreover, a reference voltage for the maximum power point of the PY module can be generated from comparing two points of the power. One of it is the predicted and another is the current point. If the predicted power is larger than the current power, the controller will check if the predicted voltage is larger than the actual voltage or not. If the

Ye"-------;:======�_-----, IL(K+I)�/L(K) V,,(K + J)=2v"v(K)-V(k-J) P,)k+J) = I, (K +1)' Vp>,k+J)

No P(k+l»P(k) Ye,

'-------------------< gs=o >gs=l yes-------,

Figure 6. Flowchart of the modified MPPT control by using MPC.

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predicted voltage is larger than the existing voltage, the predicted reference voltage will be generated by increasing the current reference voltage by dV. But if the predicted voltage is smaller than the actual voltage, the predicted reference voltage will decrease by dV. On contrary, if the predicted power is not larger than the current power, the controller will check if the predicted voltage is larger than the current voltage or not. If the predicted voltage is larger than the current voltage, the predicted reference voltage will be generated by decreasing the reference voltage by dV. But if the predicted voltage is smaller than the current voltage, the predicted reference voltage will increase by dV. Besides that, a predicted reference power can be calculated from a reference voltage and predicted current. Furthermore, the cost function will be calculated according equation (13) when the switch is turned OFF and equation (14) when the switch is turned ON. If the cost function when the switch is turned ON is larger than the cost function when the switch is turned OFF, the switch is turned OFF to reduce the cost function. But if the cost function when the switch is turned ON is smaller than the cost function when the switch is turned OFF, the controller latch the state of the switch to another sampling time. After that the program is returned again to the first point.

V. BI-DIRECTIONAL DC-DC CONVERTER

The basic non-isolated bi-directional dc-dc converter topology shown in Fig. 6 is the combination of a step-up stage together with a step-down stage connected in antiparallel [26],[27]. The advantages of this topology are high efficiency, small size, weight and lower cost. This converter is connected to a dc-link voltage to adjust the power flow to/from the battery storage system as shown. When the PV module power is larger than the load power, the buck switch (SW2) is activated to charge the battery pack. On contrary, when the PV power is smaller than the load power, the boost switch (SW,) is activated to discharge the battery pack. The MPPT calculation is used to feed the reference signal to the voltage controller of the dc-dc bidirectional converter to adjust the value of the duty cycle to regulate the voltage when charging and discharging the battery pack. The power flow controller determines which switch buck switch (SW2) or boost switch (SW,) should be activated to make the power balance between the PV power and the load power.

Battery

C DC link

Figure 7. Bi-directional dc-dc converter with buck and boost structure

VI. IMPLEMENT A TION RESULTS

The modified control on the MPPT control by using the MPC has been simulated using MATLAB@/SIMULINK@

software and ControlDesk software as a real time simulation to verifY the performance of the modified control system. A three-level MLBC has been chosen and simulated; however the topology can be extended to any number of levels. The model of twenty four photovoltaic modules of KC50T [29] with rated values of 17.4 V 154W has been used. The modified control has been tested by applying a step change in the solar irradiation. The modified control is extracting the maximum power from PV modules. When the irradiation is changed from 900W/m2 to 1000W/m2 and the temperature is 30°C, the maximum power changed from 1007W to 10SOW with a fast response as shown in Fig S. The output current of the PV modules are showed in Fig. 9. In Fig. 9 the PV current is equal to 23.5A when the irradiation is equal to 900W/m2• Moreover, when the irradiation is changed to 1000W/m2, the value of the current is changed to 26A. The value of the PV modules voltage is 42.SV at 900W/m2 and equal to 45.95V at 1000W/m2•

From these two figures, the response time that the system takes it to extract maximum power from the PV modules is less than 10ms. If these results are compared with the results that are mentioned in [30] you will find that the time to extract maximum power from PV modules when there is abrupt change is very small comparing with the results that is mentioned in [30].

1080 1070 1060 1050 1040 1030 1020 1010 1 000 Jt:::==0=.,,====0.,Lg __ - 0-. 3- 0 - --0.-3 1- --:-:0.32

Figure 8. The output power of the PV module when the irradiation is changed from 900W 1m' to 1 OOOW 1m' and the temperature is 30°C.

Figure 9. The output current of the PV module when the irradiation is changed from 900W/m' to IOOOW/m' and the temperature is 30°C.

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VII. CONCLUSION

This paper presents the modified maximum power point tracking control (MPPT) by using model predictive control (MPC). The algorithm that is used in this modification is perturb and observe algorithm (P&O). This modification is applied on the dc-dc multilevel boost converter that is connected to PV modules. This modification improves the response of the system. MLBC extracts the maximum power from PV modules at any level of the irradiation and temperature. The simulation results provided in this paper validate the correctness of the modified MPPT control. Additionally, some experimental results will be provided in the final paper to validate the simulation results.

ACKNOWLEDGMENT

This publication was made possible by NPRP grant [4-077-2-028] from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.

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