Maximum Power Point Tracking using Model Predictive Control of a Flyback Converter for

Photovoltaic Applications Mohammad Shadmand1, Student Member, IEEE, Robert S. Balog2, Senior Member, IEEE, and Haitham Abu Rub3, Senior

Member, IEEE Renewable Energy & Advanced Power Electronics Research Laboratory1&2

Dept of Electrical & Computer Engineering, Texas A&M University, College Station, USA1&2 Dept of Electrical & Computer Engineering, Texas A&M University at Qatar, Doha, Qatar3

mohamadshadmand@gmail.com1, robert.balog@ieee.org2, haitham.abu-rub@qatar.tamu.edu3

Abstract —Due to the variable, stochastic behavior of the solar energy resource, Maximum Power Point Tracking (MPPT) of photovoltaic (PV) is required to ensure continuous operation at the maximum power point to generate the most electrical energy. This paper presents a Model Predictive Control (MPC) MPPT technique. Extracting the maximum power from PV systems has been widely investigated within the literature; the main contribution of this paper is improvement of the Perturb and Observe (P&O) method through a fixed step predictive control under measured fast solar radiation variation. The proposed predictive control to achieve Maximum Power Point (MPP) speeds up the control loop since it predicts error before the switching signal is applied to the flyback DC/DC converter. Comparing the developed technique to the conventional P&O method indicates significant improvement in PV system performance. The proposed MPC-MPPT technique for a flyback converter is implemented using the dSpace CP 1103.

I. INTRODUCTION The reduction in the cost of photovoltaic cells has further

increased interest in renewable energy source, which continues to gain popularity with 60% annual growth in the installed capacity of photovoltaic (PV) systems from 2004 to 2009, and 80% in 2011 [1]. However the low conversion efficiency of PV cells is a significant obstacle to their wide spread use [2]. Therefore Maximum Power Point Tracking (MPPT) is required to ensure the maximum available solar energy is harnessed from the solar panel [3-8]. The PV array can feed power to the system through a DC/DC converter boosting the output voltage [7, 9-11]. A maximum power point tracking (MPPT) control technique is required for the PV system to operate at the maximum power point [12].

Many MPPT methods have been suggested over the past few decades; the relative merits of these various approaches are discussed in [13]. The critical operating regime is low insolation. Capturing all of the available solar power during low insolation periods can substantially improve system performance. An effective MPPT controller and converter can use available energy to significantly reduce the amount of installed PV.

Considering the MPPT methods discussed in [13], candidate techniques considered include Incremental Conductance (INC)

[14], Perturb-and-Observe (P&O) [15], fractional Open-Circuit Voltage (Voc) [16], and Best Fixed Voltage (BFV) [17]. Each approach has certain advantages and disadvantages for the present application. INC is a well-known technique with relatively good performance; however, INC method cannot always converge to the true maximum power point.

P&O is a well-known technique with relatively good performance; however, P&O method cannot always converge to the true maximum power point. Also, P&O is relatively slow, which limits its ability to track transient insolation conditions. The main contribution of this paper is to improve the P&O method performance by predicting the error one step

PV M

odul

e

LoadVc

+

-

1:n

Vpv

+

-

Switch

C

Snubber Circuit

Snubber Circuit

Transformer

Lm

IsIPV

Model Predictive

ControlP&O

Vpv

Ipv

Switching Signal

Fig. 1: Flyback converter with snubber circuit for PV application.

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210

100020003000400050006000

4998 W

Daily Energy 17.4 kWh

Po

wer

[W

]

Hour Fig. 2: Output power of one the PV arrays during a partially cloudy day.

978-1-4799-4881-9/14/$31.00 ©2014 IEEE

ahead in horizon through model predictive control technique. The proposed method has faster response than conventional P&O under rapidly changing atmospheric conditions.

II. PRINCIPLE OF MODEL PREDICTIVE CONTROL Early applications of the ideas of Model Predictive Control

(MPC) in power electronics can be found from the 1980’s considering high-power systems with low switching frequency [18]. The use of higher switching frequencies was not possible at that time due to the large calculation time required for the control algorithm. However, with the development of fast and powerful microprocessors, interest in the application of MPC in power electronics has increased considerably over the last decade [19-23].

The main characteristic of MPC is predicting the future behavior of the desired control variables [19] until a predefined step ahead in horizon of time. The predicted variables will be used to obtain the optimal switching state by minimizing a cost function. The model used for prediction is a discrete-time model which can be presented as state space model [24]. The MPC for power electronics converters can be designed using the following steps [19]:

• Modeling of the power converter identifying all possible switching states and its relation to the input or output voltages or currents.

• Defining a cost function that represents the desired behavior of the system.

• Obtaining discrete-time models that allow one to predict the future behavior of the variables to be controlled.

The designed controller should consider the following tasks:

• Predict the behavior of the controlled variables for all possible switching states.

• Evaluate the cost function for each prediction. • Select the switching state that minimizes the cost

function.

The general scheme of MPC for power electronics converters is illustrated in Fig. 3 [19]. In this scheme measured variables, )(KX , are used in the model to calculate

predictions, )1(~

+KX , of the controlled variables for each one of the n possible actuations, that is, switching states, voltages, or currents. Then these predictions are evaluated using a cost function which considers the reference values, )1(* +KX , design constraints, and the optimal actuation, S, is selected and applied in the converter. The general form of the cost function, g, subject to minimization can be formulated as

( ) ( ) ( ) ( )

( ) ( )⎥⎦⎤

⎢⎣⎡ +−+++

⎥⎦⎤

⎢⎣⎡ +−++⎥⎦

⎤⎢⎣⎡ +−+=

11

1111

*~

*22

~

1*11

~

KXKX

KXKXKXKXg

nnnλ

λ

…

(1)

where λ is the weighting factor for each objective. To select the switching state which minimizes the cost function g, all

possible states are evaluated and the optimal value is stored to be applied next.

The power converter can be from any topology and number of phases, while the generic load shown in Fig. 3 can represent an electrical machine, the grid, or any other active or passive load. In this paper the flyback topology with snubber circuit illustrated in Fig. 1 has been selected for the proposed MPPT technique.

III. MAXIMUM POWER POINT TRACKING USING MODEL PREDICTIVE CONTROL

The low conversion efficiency of PV systems is a significant obstacle to their growth [2], therefore Maximum Power Point Tracking (MPPT) is required to ensure the maximum available solar energy is harnessed from the solar panel [3-5].

Many MPPT methods have been suggested over the past few decades; the relative merits of these various approaches are discussed in [13]. The critical operating regime is low insolation. Capturing all of the available solar power during low insolation periods can substantially improve system performance. An effective MPPT controller and converter can use available energy to significantly reduce the amount of installed PV.

Considering the MPPT techniques listed in [13], candidate techniques include Incremental Conductance (INC) [14], Perturb-and-Observe (P&O) [15], fractional Open-Circuit Voltage (Voc) [16], and Best Fixed Voltage (BFV) [17]. Each approach has certain advantages and disadvantages for the present application.

P&O is a well-known technique with relatively good performance; however, P&O method cannot always converge to the true maximum power point. Also, P&O is relatively slow, which limits its ability to track transient insolation conditions. The main contribution of this section is to improve the P&O method performance by predicting the error one step ahead in horizon through model predictive control technique.

( )KX

( )KX

( )1* +KX

( )1~

1 +KX

( )1~

2 +KX

( )1~

+KXn

Fig. 3. MPC general schematic for power electronics converters.

The proposed method has faster response than conventional P&O under rapidly changing atmospheric conditions.

A flyback converter is chosen as a DC/DC converter. P&O determines the reference current for the MPC which determines the next switching state. This technique predicts the error of the next sampling time and based on optimization of the cost function g, illustrated in Fig. 5, the switching state will be determined. The inputs to the predictive controller are the PV system current and voltage, and the reference current.

By deriving the discrete time set of equations, the behavior of control variable can be predicted at next sampling time k. The proposed methodology is based on the fact that the slope of the PV array power curve is zero at the predicted MPP, positive on the left and negative on the right of the predicted MPP.

The discrete time set of equations of the flyback converter shown in Fig. 1 is given by (2) and (3) when switch is “ON” and (4) and (5) when switch is “OFF” [25]:

)()()1( kikvL

Tki PVPVS

PV +=+ (2)

)(1)1( kvRCTkv C

SC ⎟

⎠⎞

⎜⎝⎛ −=+ (3)

)()()1( kvLnTkiki C

SPVPV −=+ (4)

)(1)()1( kvRCTki

nCTkv C

SPV

SC ⎟

⎠⎞

⎜⎝⎛ −+=+ (5)

Now after determination of the reference current using the procedure shown in Fig. 4, the cost function can be obtained as following

refPVS ikig

S−+=

== )1(1,01,0

(6)

The objective is to minimize the cost function g. The final switching state for MPPT can be determined using procedure illustrated in Fig. 5.

However in this paper the MPC-MPPT is done for one step ahead in horizon, but the discrete time equation can be extended to n-step in horizon as following

)()1()()()1( nkvLnTSkv

LTSnkinki C

SPV

SPVPV +−+−+=++ (7)

)()1()(1)1( nkiCnTSkv

RCTSnkv PV

SC

SC +−+⎟

⎠⎞

⎜⎝⎛ −=++ (8)

)1()( −−=Δ kvkvv PVPV

)1()( −−=Δ kikii PVPV

0=Δi

0=Δv

)(kii PVref =

)()(

kikv

iv

PV

PV−=ΔΔ

)()(

kikv

iv

PV

PV−>ΔΔ

α−= )(kii PVref

0>Δv

α+= )(kii PVref

Fig. 4. MPC procedure to determine reference current using P&O

),(kvPV )(kiPV , refi

)1(1,0, += ki sPV

refsPVs ikig −+= == )1(1,0,1,0

0=s

1=s

10 == < ss gg

Fig. 5. MPC-MPPT procedure

0 10 20 30 40 50 60 70

0

5

10

1 kW/m2

Cu

rren

t (A

)

Voltage (V)

0.75 kW/m2

0.5 kW/m2

0.25 kW/m2

0 10 20 30 40 50 60 700

200

400

600 1 kW/m2

Po

wer

(W

)

Voltage (V)

0.75 kW/m2

0.5 kW/m2

0.25 kW/m2

Fig. 6. I-V and P-V characteristics of the array.

where S is the switching state and Ts is the sampling time. By increasing the number of steps to two or three, the computation time will be increased but better control performance expected to be achieved.

The I-V and P-V characteristic of the PV systems used in this paper for different irradiance levels are illustrated in Fig. 6. In this paper the model predictive control for MPPT is compared to the commonly used perturb and observed method. Fig. 7 illustrates the simulation results of the proposed MPC and conventional P&O method. The system is tested under three irradiance level changes. As shown in Fig. 7 the performance of the MPC method is better than the conventional P&O method. More specifically by applying a

1.4 1.45 1.5 1.55 1.6 1.65 1.70

2

4

6

8

10

Time(s)

Ipv(

A)

Ipv MPC MPPT

1.4 1.45 1.5 1.55 1.6 1.65 1.70

2

4

6

8

10

Time(s)

Ipv(

A)

Ipv P&O MPPT

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

2

4

6

8

10

Time(s)

Ipv(

A)

Ipv MPC MPPT

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

2

4

6

8

10

Time(s)

Ipv(

A)

Ipv P&O MPPT

0.1 0.2 0.3 0.4 0.50

2

4

6

8

10

Time(s)

Ipv MPC MPPT

0.1 0.2 0.3 0.4 0.50

2

4

6

8

10

Time(s)

Ipv(

A)

Ipv P&O MPPT

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.840

45

50

55

60

65

Time(s)

Vpv

(V)

Vpv P&O MPPT

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.840

45

50

55

60

65

Time(s)

Vpv

(V)

Vpv MPC MPPT

1.4 1.45 1.5 1.55 1.6 1.65 1.740

45

50

55

60

65

Time(s)

Vp

v(V

)

Vpv P&O MPPT

1.4 1.45 1.5 1.55 1.6 1.65 1.740

45

50

55

60

65

Time(s)

Vp

v(V

)

Vpv MPC MPPT

Fig. 7. Comparison of proposed MPC MPPT to conventional P&O MPPT

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80.4

0.5

0.6

0.7

0.8

0.9

Time (s)

Du

ty C

ycle

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8400

500

600

700

800

Time (s)

Irra

dia

nce

lev

el (

W/m

2 )

Fig. 8. Solar irradiance level of the case study and the duty cycle.

Fig. 9. PV current, voltage, and power of MPC-MPPT.

Fig. 10. PV current, voltage, and power response to step change in the irradiance from 500 W/m2 to 750 W/m2.

step change in the irradiance at time 1.5 s, when using the proposed MPC method the MPP is tracked at time 1.52 s, but when using the P&O method the MPP is tracked at time 1.60 s. The detail descriptive plots are illustrated in Fig. 7. Matlab/Simulink and dSPACE CP1103 is used for the experimental results. The real time implementation of the MPC-MPPT is illustrated in Figs. 9 and 10. It confirms the simulation results as shown.

IV. CONCLUSION This paper presents an improved MPPT technique by

predicting the error at next sampling time before applying the switching signal using MPC. The proposed predictive MPPT technique is compared to commonly used P&O method to show the benefits and improvements in the speed and efficiency of the MPPT. The results show that the MPP is tracked much faster by using the MPC technique than P&O method. The dSpace CP1103 is used for implementing the control technique experimentally.

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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