Maximum power tracking of a generic photovoltaic system via a fuzzy controller and a two-stage DC-DC converter

T E C H N I C A L P A P E R

Maximum power tracking of a generic photovoltaic system

via a fuzzy controller and a two-stage DC–DC converter

Received: 30 September 2011 / Accepted: 23 April 2012 / Published online: 9 May 2012 Ó Springer-Verlag 2012

Abstract This study presents a new two-stage DC–DC converter for maximum power point tracking (MPPT) and a voltage boost of a generic photovoltaic (PV) system. An intelligent MPPT of PV system based on fuzzy logic control (FLC) is presented to adaptively design the pro-posed fuzzy controlled MPPT controller (FC-MPPTC) while a voltage boost controller (VBC) is used to fix the output voltage to a voltage level that is higher than the required operating voltage to the back-end grid impedance. Modeling and simulation on the PV system and the DC– DC converter circuit are achieved by state-space and the software Powersim. The PV string considered has the rated power around 600 VA under varied partial shadings. The FC-MPPTC and VBC are designed and realized by a DSP module (TMS320F2812) to adjust the duty cycle in the two-stage DC–DC converter. A special FLC algorithm is forged to render an MPPT faster and more accurate than conventional MPPT technique, perturb and observe (P&O). The simulations are intended to validate the performance of the proposed FC-MPPTC. Experiments are conducted and results show that MPPT can be achieved in a fast pace and the efficiency reaches over 90 %, even up to 96 %. It is also found that the optimized tracking speed of the pro-posed FC-MPPTC is in fact more stable and faster than the general P&O method with the boost voltage capable of offering a stable DC output.

1 Introduction

Emission of carbon dioxide is commonly regarded nowa-days as a major obstacle toward a clean world, thus clean energies other than fossil fuel are intensively sought recently by academic societies and industry. Renewable energies have, as one of clean energies, become one viable candidate to replace traditional fossil fuel. Renewable energy comes from natural resources, such as wind power energy, hydro energy, biomass energy, geothermal energy, ocean energy and photovoltaic (PV) energy. Among aforementioned renewable energies, the photovoltaic (PV) energy is expected to be a major clean energy source without pollution and energy waste due to accessibility of solar energy and relative simplicity involved in the man-ufacture, structure and electronics of a PV array.

In a typical PV system, there is usually a DC–DC con-verter (Mohan 1995), which is designed responsible for driving power out of the front-end PV panel. The function of this DC–DC converter is to adjust its impedance seen by the PV panel to be close to the corresponding impedance of the PV panel, thus maximizing the output efficiency. The com-bination of corresponding current and voltage of the PV panel is so-called the maximum power point (MPP) in the characteristic curve-voltage curves. The adjustment of the impedance is made possible via a power switch in the DC– DC converter, the duty cycle of which can actively adjusted by an external controller. A number of past research works have been devoted to design controllers for the on-line tracking of MPP (maximum power point tracking, MPPT), either using a classic or advanced controller (Yuvarajan et al. 2004; Zhong et al. 2008; Xiao et al. 2007). One of most difficult tasks for these controllers is to be adjusted to varied conditions of solar irradiation, shading and external tem-perature that may result in significant changes in the current–

P. C.-P. Chao (&)  W.-D. Chen  C.-K. Chang

Department of Electrical Engineering, National Chiao Tung University, Hsinchu 300, Taiwan

e-mail: pchao@mail.nctu.edu.tw P. C.-P. Chao

National Chiao Tung University, Institute of Imaging and Biomedical Photonics, Tainan 711, Taiwan DOI 10.1007/s00542-012-1518-9

voltage characteristics curves (I–V curves) of a PV array, leading to different locations of MPP. Thus, an on-line tracking scheme for MPP is necessary in order to keep the operation of the PV panel constantly at MPP (Gao2009; Win et al. 2011). Many methods and controllers have been developed to track the MPP like as methods of power feed-back control (Al-Atrash et al.2005), perturb and observe (P&O) (Santos et al. 2006; Hua et al. 1998; Jiang et al. 2005) or incremental conductance (Hussein et al. 1993; Wasynczuk1983). These control schemes suffer different drawbacks during MPPT; for instance, the P&O has oscil-lation problem. Therefore, other intelligent control methods like fuzzy logic or neural network were introduced in (Kottas et al.2006; Chiu2010; Agorreta et al.2009; Bouchafaa et al. 2011; Salah and Ouali2011).

Due to the constant variation in the I–V characteristics curves of a PV panel in realistic operations, the output voltage of the DC–DC converters under MPPT operation may vary in a wide range. It is thus possible that the output voltage is below the required input voltage level to the subsequent inverter and/or grid (e.g. in dark environment), resulting in a great difficulty in power transfer. To remedy the problem, another stage of DC–DC boost converter is add in this study before the inverter and/or grid to perform the power conditioning for providing electric power in high voltage levels. The entire circuit topology becomes a two-stage power conversion circuit.

A fuzzy controlled MPPT (FC-MPPTC) controller for the first stage and a voltage boost controller (VBC) for the second stage are designed in this study for both fast max-imum power tracking and high conversion efficiency. The MPPT controller is used for maximum power transfer, while the VBC is to boost the output voltage above the operable voltages of the back-end electronics (e.g. inverter and/or grid) (SMA Solar Technology2010). Note that the duty-tunings by the two independent controllers in the proposed two-stage converter are able to tackle both fast-changing front-end PV conditions and back-end imped-ance, simultaneously. To design the fuzzy MPPT controller and also determine the duty-tuning schemes for the two stages, a state-space dynamic model in terms of average current is first established, followed by Powersim simula-tion. The performance of the designed fuzzy MPPT and duty-tuning schemes are evaluated by simulations. With satisfactory simulated performance, experiments are next conducted for validation. It is shown that the resulted experimental efficiency is up to 96 %, which is obviously difficult to achieve by a single-stage converter if the I–V characteristics curves vary constantly due to the changes in external conditions, like shading and temperature, etc.

The remainder of this study is organized as follows. Section2analyzes and establishes a state-space model for the PV array, which is followed by determination of

passive components used in the two-stage converter. Sec-tion 3provides the design processes and details of the FC-MPPTC controller. In Sect.4, the performance of designed system is simulated by Powersim to confirm the effec-tiveness of the designed FC-MPPTC controller in enabling a fast and smooth MPPT. Experimental setup and results are also given in this section to validate the controller performance. Finally, Sect. 5 provides brief concluding remarks and intended directions for future research work.

2 System and modeling and design 2.1 System description

A two-stage photovoltaic (PV) system shown in Fig.1 is considered in this study. The system is supposed to consist of a PV array and a two-stage boost converter. The power switches of the system are controlled by the gate drivers programmed via a DSP module. The converter delivers required levels of power output to the rear-end power grid. The impedance of the power grid would be assumed as suitable ones for subsequent analysis in this study. The first and second stages of the two-stage converter are respon-sible for MPPT and voltage regulation, respectively. The equivalent circuit of the considered PV array is shown in Fig.2, where the PV array is modeled by a parallel con-nection of a current source IPH, a diode, an internal parallel

and series resistances, RSH and RS. The relationship

between the current and the voltage of the PV array Vpvcan

be well prescribed by (Kwon et al.2006). Ipv¼ IPH Is exp qðVpvþ IpvRsÞ AKT    1   Vpvþ IpvRs RSH ; ð1Þ where Ipv is the output current of the PV array; Is is the

saturation current; q is the charge of an electron; K is the Boltzmann’s constant; A is the ideality factor of the p–n junction; T is the temperature (deg K) of the PV array. The irradiation and temperature influence the output power in a nonlinear relation at every moment. The characteristics curves for I–V and P–V relations of the PV array (Siemens solar module SP75 is considered) can be simulated by a commercial software Powersim with Eq. (1). Figure3 displays the simulation results for different energy densi-ties and temperatures of a PV array. It is evident from this figure that under the different irradiation and temperature conditions, the maximum power pint (MPP) is changed. It means that the MPP is a time-vary parameter. This makes the maximum power point tracking (MPPT) a difficult task. Various techniques to achieve an on-line, dynamic MPPT have been reported by researchers. The most com-mon one is the Perturb and Observation (P&O) method

(Santos et al.2006; Hua et al.1998; Jiang et al.2005), due to its simplicity and ease to achieve MPPT. The method proposes four simple tuning rules on the duty for different polarity combinations of changes in power and voltage of the PV array. The tuning increment on the duty is however fixed. Therefore, the time span required to reach MPPT is relatively long, not to mention the difficulty for the tracker to stay right on the MPP since each time the perturbation on tuning the voltage is finite. To tackle the aforemen-tioned disadvantage, some intelligent control methods were developed recently (Kottas et al. 2006; Chiu 2010; Agorreta et al. 2009; Bouchafaa et al. 2011; Salah and Ouali2011). In this study, a fuzzy logic controller (FLC) is designed, which make possible a varying increment for the output duty. The increment is determined by the fuzzy mechanism. This aims to realize a fast, smooth and accu-rate MPPT. The designed FLC control algorithm consists mainly of four parts as shown in Fig.4. The input signals experiences fuzzification, interference rules and finally defussification. The interference rules could follow the same deterministic rules adopted by the conventional P&O

method, a flow-chart representation of which is given in Fig.5. The design details of the FC-MPPTC controller is given in Sect.3.

2.2 Modeling on the two-stage DC–DC converter The topology of a two-stage DC–DC converter, as shown in Fig. 6, is adopted in this study for simultaneous MPPT and boosting the output voltage to a required higher level A subsequent DC–AC inverter for converting the power to grid is supposed to be connected to the rear end of the converter. The duty cycle of the switch Q1for the first stage

is adjusted by the designed fuzzy logic control for MPPT, while that of the switch Q2for the second stage is adjusted

for boosting the output voltage to a required DC level for the subsequent inverter and gird.

To model the electrical dynamics of the converter for two stages, two different switching conditions as shown in Fig.7 for the MOSFET Q1and Q2in Fig.6have to be considered.

They results in different sets of governing equations in state-space forms. In case I, the duty cycle of Q1is longer than Q2,

while for case II the duty cycle of Q1is shorter than Q2. The

whole switching period can be divided into three different parts, D1(D01), D2(D02) and 1 - D1- D2(1 - D01- D02). In

the period of D1, Q1and Q2are both on. In the period of D2,

only one of Q1and Q2is on. In the period of (1 - D1 - D2),

Q1and Q2are both off. The time evolutions of all capacitance

currents and inductance voltages for the three periods in case I can be derived by Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL) in the converter topology shown in Fig.6. The derivation results are expressed in terms of state-space form as below,

Fig. 1 The two-stage PV system

_iL1ð Þt _iL2ð Þt _ VC1ð Þt _ VC2ð Þt 2 6 6 4 3 7 7 5 ¼ 0 0 0 0 0 0 D1 L2 0 0 D1 C1 0 0 0 0 0 D1 RLC2 2 6 6 6 4 3 7 7 7 5 iL1ð Þt iL2ð Þt VC1ð Þt VC2ð Þt 2 6 6 4 3 7 7 5 þ D1 L1 0 0 0 2 6 6 4 3 7 7 5VPVð Þ;t ð2Þ _iL1ð Þt _iL2ð Þt _ VC1ð Þt _ VC2ð Þt 2 6 6 4 3 7 7 5 ¼ 0 0 0 0 0 0 D2 L2 D2 L2 0 D2 C1 0 0 0 D2 C2 0 D2 RLC2 2 6 6 6 4 3 7 7 7 5 iL1ð Þt iL2ð Þt VC1ð Þt VC2ð Þt 2 6 6 4 3 7 7 5 þ D2 L1 0 0 0 2 6 6 4 3 7 7 5VPVð Þ;t ð3Þ _iL1ð Þt _iL2ð Þt _ VC1ð Þt _ VC2ð Þt 2 6 6 6 4 3 7 7 7 5 ¼ 0 0 ð1D1D2Þ L1 0 0 0 1D1D2 L2  1Dð 1D2Þ L2 1D1D2 C1  1Dð 1D2Þ C1 0 0 0 1D1D2 C2 0 1D1D2 RLC2 2 6 6 6 6 6 4 3 7 7 7 7 7 5  iL1ð Þt iL2ð Þt VC1ð Þt VC2ð Þt 2 6 6 6 4 3 7 7 7 5þ 1D1D2 L1 0 0 0 2 6 6 6 4 3 7 7 7 5VPVð Þ;t ð4Þ where D1is the duty cycle of part I; D2is the duty cycle of

part II; L1and L2are the inductances of first and second

stage, respectively; iL1and iL2are the currents of L1and L2,

respectively; C1and C2are the capacitances of the first and

second stage, respectively; Vc1and Vc2are the voltage of

C1and C2, respectively; RLis the back-end load; VPVis the

voltage of the PV array, which is also specified and related to iPV, as shown in Eq. (1). iL1is equal to iPVdefined in Eq.

(1). Taking the time averages of state-space variables, the capacitance voltages and inductance currents in Eqs. (2–4), in a single duty-cycle period [i.e., the so-called ‘‘state-space averaging method’’ (Qian 2010)], the governing equations (2–4) can be further simplified as

_iL1ð Þt _iL2ð Þt _ VC1ð Þt _ VC2ð Þt 2 6 6 6 4 3 7 7 7 5¼ 0 0 ð1D1D2Þ L1 0 0 0 1 L2  1Dð 1Þ L2 1D1D2 C1 1 C1 0 0 0 1D1 C2 0 1 RLC2 2 6 6 6 6 6 4 3 7 7 7 7 7 5  iL1ð Þt iL2ð Þt VC1ð Þt VC2ð Þt 2 6 6 6 4 3 7 7 7 5þ 1 L1 0 0 0 2 6 6 6 4 3 7 7 7 5VPVð Þ:t ð5Þ

As for case II, where the duty cycle of Q2is longer than

Q1, the state-space governing equations are also derived

herein. Following the same procedure, the state-space equations in the periods of D01and (1-D01-D02) are in the Fig. 3 aI–V curve and b P–V curve of PV array

same forms as Eqs. (2) and (4), respectively, while the equations for D02can be expressed as

_iL1ð Þt _iL2ð Þt _ VC1ð Þt _ VC2ð Þt 2 6 6 4 3 7 7 5 ¼ 0 0 D 0 2 L1 0 0 0 D02 L2 0 D0 2 C1 D0 2 C1 0 0 0 0 0 D02 RLC2 2 6 6 6 6 6 4 3 7 7 7 7 7 5 iL1ð Þt iL2ð Þt VC1ð Þt VC2ð Þt 2 6 6 4 3 7 7 5 þ D0 2 L1 0 0 0 2 6 6 4 3 7 7 5VPVð Þ;t ð6Þ

which is different from Eq. (3) in some signs of entries in the matrix associated with state variables. Employing the

aforementioned state-space average method on the inductance currents and capacitance voltages prescribed in Eqs. (2,4,6), the governing equations for case II can be further simplified as _iL1ð Þt _iL2ð Þt _ VC1ð Þt _ VC2ð Þt 2 6 6 6 4 3 7 7 7 5¼ 0 0  1D 0 1 ð Þ L1 0 0 0 1 L2  1D0 1D02 ð Þ L2 1D0 1 C1 1 C1 0 0 0 1D01D02 C2 0 1 RLC2 2 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 5  iL1ð Þt iL2ð Þt VC1ð Þt VC2ð Þt 2 6 6 6 4 3 7 7 7 5þ 1 L1 0 0 0 2 6 6 6 4 3 7 7 7 5VPVð Þ:t ð7Þ Start Read VPV, IPV VPV,OLD=VPV, IPV,OLD=IPV

PPV,OLD=VPV,OLD*IPV,OLD

Duty1+

Read VPV, IPV

VPV,NEW=VPV, IPV,NEW=IPV

PPV,NEW=VPV,NEW*IPV,NEW

PPV,NEW>PPV,OLD

VPV,NEW>VPV,OLD VPV,NEW>VPV,OLD

Duty1 -Flag = 0 Duty1 -Flag = 0 Duty1+ Flag = 1 Duty1+ Flag = 1

VPV,OLD=VPV,NEW, IPV,OLD=IPV,NEW, PPV,OLD=PPV,NEW

YES S E Y S E Y NO O N O N

Fig. 5 The computation flow chart of the control algorithm (Zhong et al.2008)

Fig. 6 The two-stage DC–DC converter circuit

With governing Eqs. (2–7) in hands, the system dynamics of each stage in the adopted two-stage converter can be successfully simulated with the controllers designed via aforementioned methods of P&O or FC-MPPTC.

2.3 Determining inductances and capacitances

With electrical dynamics captured by the governing equations derive in the last subsection, effort is dedicated to determine inductances and capacitances of the designed two-stage DC– DC converter. Design of a DC–DC boost converter is basi-cally intended to elevate the original DC input to a steady output DC voltage (Esram and Chapman2007). The desig-nation of passive devices in this converter is carried out by first considering two equivalent circuits as shown in Fig.8, two topologies of which refers to different cases with switch on and off. Following a standard procedure of analysis via the conversion between continuous and discrete representations of the inductance current, as given in (Esram and Chapman 2007), one can obtain the output voltage simply equal to VOUT¼

VIN

1 D; ð8Þ

where D is varied between [0.1, 0.9]. The output voltage is successfully boosted to a higher level. Figure9a shows the waveforms of inductance voltages. The analysis thus far is based on the assumption that the inductance current is continuous. The inductance current in fact varies over a cycle, varying between a minimum value (IL,MAX) and a

maximum value (IL,MIN), which can be expressed in terms

of mean value and change as expressed in equation, that is,

Fig. 8 aThe equivalent circuit with the power switch closed; b The equivalent circuit with the power switch open

Fig. 9 a The waveform of the inductance current in a boost converter; b The inductance current boundary in a boost converter operated in continuous mode

Fig. 7 The duty cycles of the two-stages in the DC–DC converter: acase I, b case II

IL;MAX ¼ ILþDIL

2 ; ð9Þ

and

IL;MIN ¼ ILDIL

2 ; ð10Þ

where DILis the peak-to-peak current of the change value

of inductance. Figure9b shows that the maximum and minimum inductance currents can be obtained, for continuous conduction, as

ILDIL

2 : ð11Þ

At the boundary of continuous and discontinuous conduction,

IL¼DIL

2 : ð12Þ

Another expression for ILis now obtained, i.e.,

IL¼

VIN 1 D

ð Þ2RL; ð13Þ

where RLis the load. Substituting for ILfrom the equation

above and for DiLfrom equation, equation becomes

IL;MAX ¼ VIN 1 D ð Þ2RLþ DTsVIN 2L ; ð14Þ and IL;MIN ¼ VIN 1 D ð Þ2RL DTsVIN 2L ; ð15Þ

where Tsis the sampling period. From Eqs. (14) and (15),

the conditions for continuous conduction is L[DTs

2  1  Dð Þ 2

RL: ð16Þ

Consider L1and L2 as the two inductances in the two

stages of the DC–DC converter adopted in this study. Application of Eq. (16) for L1and L2leads to

L1[ L1B¼D1Ts 2  1  D1ð Þ  VPV IOUT 1B ð17Þ L2[ L2B¼D2Ts 2  1  D2ð Þ 2 VOUT2 IOUT2B ð18Þ

where VPVis the output voltage of the PV array; L1B and

L2B are the critical inductances between CCM and DCM

for the first and second stages, respectively; Iout1Band Iout2B

are the critical output currents between CCM and DCM for the first and second stages, respectively; D1and D2are the

duty cycles for the first stage and second stage, respectively. Utilization of the resulted Eqs. (17) and (18) gives the final designated inductances in the converter circuit adopted in this study. For the PWM design used for

the current study, Ts is equal to 40 ls; Iout1B is equal to

0.5 A and VPV is from 50 to 130 V. Considering the

minimum critical inductance for CCM, VPVis chosen with

130 V, while D1is chosen as 0.5. L1can be then calculated

by Eq. (17) with these parameters as L1[

0:5 40  106_{ ð1  0:5Þ  130}

2 0:5 ¼ 1;300 lm:

ð19Þ Similarly, when the maximum output voltage of second stage (VOUT2,MAX) equals to 300 V, Ts is equal to 40 ls;

Iout2Bis equal to 0.45 A; and D1is chosen as 0.5, L2can be

calculated by Eq. (18) with these parameters as L2[0:5 40  10

6_{ ð1  0:5Þ}2  300

2 0:45 ffi 1;667 lH:

ð20Þ The focus of analysis is now turned to determine two capacitances in each of the two stages in the entire converter circuit. It is known based on fundamental principles that the system output capacitance C2in Fig.6

dictates the level of the peak-to-peak ripple in the output voltage, which are for most cases supposed to be contained. When the switch Q2 is closed, the output voltage is

sustained by the capacitance C2 in Fig.6. During this

period, the capacitance discharges part of its stored energy and it re-acquires this energy when the switch is open. When the switch is open, part of the inductance current charges the capacitance since the inductance current usually remains larger than the current through the load resistor, leading to

ic2ð Þ ¼ C2t dVOUT2ð Þt

dt ; ð21Þ

when the capacitance current ic2 is constant, the voltage

changes linearly with time. Here the period for which the switch is closed is D2Ts, D2Tsis denoted herein by Dt. The

peak-to-peak ripples in the output voltage denoted by DVOUT2(Mohan et al.2003) can then be derived as

DVOUT2¼ic2 D2Tsð Þ C2

¼IOUT2D2Ts C2

; ð22Þ

where IOUT2 is the output current of the second stage.

Similarly, DVOUT1can then be derived as

DVOUT1¼ic1 D1Tsð Þ C1

¼IOUT1D1Ts C1

; ð23Þ

where IOUT1is the output current of the first stage. Based

on Eqs. (22) and (23), the capacitances C1and C2can be

determined by C1¼IOUT1D1Ts

DVOUT1 ¼

IPVð1 D1ÞD1Ts

C2 ¼

IOUT2D2Ts DVOUT2 ¼

IOUT1ð1 D2ÞD2Ts

DVOUT2 ; ð25Þ

where IPVis the output current of solar array; DVOUT1and

DVOUT2are the peak-to-peak ripples in the output voltages

for the first and second stage, respectively. IOUT1 is the

output current of the first stage. Considering that IPV is

equal to 5 A, Ts is equal to 40 ls, D1is equal to 0.5 and

DVOUT1is equal to 0.5 V, Eq. (24) offers the design of C1

as C1 ¼

5 1  0:5ð Þ  0:5  40  106

0:5 ¼ 100 lF: ð26Þ

Considering that IOUT1is equal to 4.5 A, Ts is equal to

40 ls, D2is equal to 0.5 and DVOUT2is equal to 0.5 V, Eq.

(25) offers the design of C2as

C2 ¼4:5 1  0:5ð Þ  0:5  40  10 6

0:5 ¼ 90 lF: ð27Þ

To this point, all the passive components of the design two-stage PV system are successfully determined and listed in Table1. The determined inductances and capacitances would be later used for realizing the two-stage DC–DC converter.

3 Design of fuzzy controller

An MPPT is designed and applied to the switch in the first stage for arbitrary irradiation level and temperature, which is the main objective of the FC-MPPTC proposed in this study. On the other hand, a basic voltage boost controller (VBC) is adopted for the second stage. This VBC employs a fundamental voltage feedback control, as a PI controller. The goal of VBC is to boost the output voltage above the operable voltages of the back-end electronics (SMA sunny boy 4000TL) where the operating voltage rang is required to be from 125 to 440 V. The design of the FC-MPPTC for the first stage is elaborated as follows by the three parts— fuzzification, interference rules and defuzzification.

3.1 Fuzzification

The first phase of computation for a fuzzy controller is fuzzification, which is started with choosing the output voltage (VPV) and power (PPV) of the PV array as the two

input variables of the fuzzy controller to be designed, since the PV voltage is adjusted to reach maximum power during MPPT. The adjustment increment on VPVis tuned based on

the instantaneous value of PPV. In this way, two sets of

membership functions are defined for variations of the output voltage (denoted by DV) and power (denoted by DP) of the PV array, respectively, as shown in Fig.10. On the other hand, the output of the controller is the variation on duty cycle of the switch (denoted byD ^D) for the first stage of the converter. The fuzzification on the aforementioned input and output variables next carried out by five fuzzy sets as NB, NS, ZE, PS, PB in the same triangle membership functions as

Table 1 The designed values of the components of the PV system

L1 1.5 mH RP-PV1 22 KX L2 2 mH RP-PV2 150 KX C1 220 lF RP-PV3 22 KX C2 220 lF RP-PV4 150 KX ROUT2.1 50 KX RPV1 470 KX ROUT2.2 470 X RPV2 10 KX RG1 150 X RPV3 50 KX RG2 1.5 KX RPV4 1 KX RG3 150 X RL 10 X

RG4 1.5 KX RHY 1 KX Fig. 10 The membership functions of a voltage variation; b power

shown in Fig.10. The range for input DV is chosen from -4 to 4. The range for input DP is defined from -8 to 8. The range for output D ^D is defined from -0.04 to 0.04.

3.2 Fuzzy rule base and fuzzy inference

With memberships defined, linguistic rules for the fuzzy controller are determined based on the rules in fact equiva-lent to those described in Fig.5for the aforementioned P&O method. This would lead the operating point of the PV array to approach the maximum power point. Even with the same linguistic rules, the FC-MPPTC controller proposed herein is considered more advanced than the conventional P&O method due to its capability to continuously tune the level of duty increment via the mechanism of fuzzification, inter-ference and defuzzification. The IF–THEN rules of fuzzy control for the four conditions following the flow chart of control algorithm in Fig.5could be expressed as

IFDP\0 and DV\0; THEN D ^D\0; ð28Þ

IFDP\0 and DV[ 0; THEN D ^D[ 0; ð29Þ IFDP[ 0 and DV\0; THEN D ^D[ 0; ð30Þ IFDP[ 0 and DV[ 0; THEN D ^D\0: ð31Þ The associated rule table is shown in Table2, which enables a continuous, smooth adjustment on the duty increment D ^D.

3.3 Defuzzification

Having forged fuzzy interference scheme, linguistic output variables need to be converted into numerical values. The subsequent defuzzification is carried, which is in fact an inverse transformation of fuzzification. It maps the output from the fuzzy domain back into the numerical domain. The center average method is used herein for defuzzifica-tion, which could be expressed as

D ^D¼ P4 i¼1Wi DD P4 i¼1Wi ; ð32Þ

where W is the height of fuzzy set and DD is the center of area of fuzzy set.

4 Simulation and experiments

With system models established and controllers deigned, simulations and experiments are conducted to tune controller parameters and validate the expected performances of simultaneous MPPT by the first stage and boosting the output voltage to a required higher level by the second stage. 4.1 Simulation results

The dynamics of the state-space equations (5) and (7) is simulated by a MATLAB program. The results are com-pared with those by Powersim. The system description for the circuit simulation carried out by Powersim is shown in Fig.11. The input voltage is 21 V, L1 is 1.5 mH, L2 is

2 mH, C1 and C2are both 220 lF, RLis 10 X. Note that

these passive components are chosen satisfying design criteria distilled by Eqs. (19–20) and (26–27). The com-parison between the results of state-space and Powersim simulation are shown in Table3, where two conditions are considered: (1) the duty of the first stage is longer than second one and (2) duty of the first stage is shorter than second one. It is seen form the results given in this table that the state-space equations render results very close to those by Powersim. This verifies the correctness of the established state-space equations.

The afore-mentioned P&O and designed FLC algorithms are realized and embedded into the block DLL in this figure by C language. Comparison is made between the methods of P&O and FLC in term of performance in MPPT. Figure12 presents varied simulation results by governing equations or Powersim for MPPT, where the Siemens solar module SP75 is considered. The corresponding MPP is at 74.8 Watt with VMPPin 17 V and IMPPin 4.4 A. Note that since the resulted

simulation results by state-space equations and Powersim are distinguishable if presented in the figure, only the results from Powersim are plotted as the representative simulation results. It is seen from this figure that MPP is reached within a short period of 0.02 s. Also, much more oscillation occurs for the case with the P&O method employed, not only in tran-sient but also in the steady state period. On the contrary, the designed FLC could track the MPP in a faster pace with high precision. In a short conclusion, the simulation results show that the proposed FC-MPPTC with the designed two-stage converter and the PV system could track the MPP efficiently and effectively.

4.2 Experimental validation 4.2.1 Experimental setup

An experiment system as shown in Fig.13 is established for validating the expected performance of controllers and

Table 2 Fuzzy rule table

dP dV NB NS ZE PS PB NB NB NB NB PB PB NS NS ZE ZE ZE PS ZE NS ZE ZE ZE PS PS PS ZE ZE ZE NS PB PB PB PB NB NB

the two-stage DC–DC converter. It includes a 32-bit microprocessor of DSP (TI TMS320F2812), an optical coupler circuit and a current sensor (HY-10P). The afore-mentioned DSP chip (TMS320F2812) is a stand-alone module which features a 150 MHz clock, a high-perfor-mance 32-Bit processor, and 12-bit ADC output. The optical coupler is an isolating device consisting of a transmitter and a receiver, through which the electrical signal is converted to a light beam, transferred, then con-verted back to an electrical signal. In this way, electro-magnetic interference and undesired electrical pulsations could be isolated to the DSP module. Note that an optical

isolator is usually regarded as a single integrated package, but the opto-isolation can also be achieved by using sep-arate devices. Digital opto-isolators modify the state of their outputs when the input state changes. Analog isolators produce an analog signal which reproduces the input. Figure14 shows the circuit insight of the isolated gate driver. In addition, the diode (1N5819) improves the falling time with the optical coupler, which accelerates the charge into ground. Finally, the hall current sensor (HY-10P) is used to sense the electrical current from the photovoltaic panels. Figure15 shows the schematic of the hall sensor that connects the resistance from the output of HY-10P into ground and in a parallel fashion with a zener diode to limit the output voltage under 3 V. This avoids the breakdown of the analog to digital channel (ADC) of DSP (TMS320F2812). Table4lists the currents converted to the voltage for ADC sensing.

The voltage and current of the PV module are sensed by an optical coupler circuit and a current sensor, respectively. The sensed signals of voltage and current are used as the inputs to the FC-MPPTC. One particular realistic design of the circuit is that if the voltage of the PV array is higher than the back-end operation of the inverter voltage, the voltage of PV array would be passed via switch QP-PV1to

drive the back-end inverter. The corresponding by-pass loop is also shown in Fig. 13 on the top portion of the entire circuit. On the other hand, the switch QP-PV1is off, Fig. 11 The circuit model established by Powersim

Fig. 12 Simulation results of the output power of the PV array with P&O method and FLC

Table 3 Simulation result based on state space and Powersim model

Condition (1) Condition (1)

The duty of the first stage is longer than second one The duty of the first stage is shorter than second one

D1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

D2 0.2 0.4 0.6 0.8 0.4 0.2 0.3 0.5

Vout(State space) 29.17 43.74 74.98 174.7 70 65.61 99.96 209.6

when the voltage of the PV array needs to be boosted to the operating voltage of inverter.

Figure16gives a photo showing the implementation of the designed circuit for the two-stage DC–DC converter.

Figure17shows the entire testing system, where a photo-voltaic (PV) panel is replaced by the Agilent Solar Array Simulator (E4362A), which is a 600 W PV simulator, and a direct-current power module that simulates the output characteristics of a photovoltaic (PV) string. This E4362A is in fact a current source with a low output capacitance that offers current–voltage curve changes to allow users to accurately simulate the output of different PV strings under various environmental conditions. Four key operational parameters (VOC, ISC, VMP, IMP) are needed for the PV

simulator to create a characteristic curve of a PV string. VOC, ISC, VMPand IMP are open-circuit voltage,

short-cir-cuit current, voltage at MPP and current at MPP, respectively.

4.2.2 Experiment results

Figure18shows the experiment results by setting the open circuit voltage Voc of the PV-string simulator E4362A at

130 V, short circuit current Isc 3 A, maximum power

voltage VMP 110 V and the maximum power current IMP

2A. Figure18a is the interface of the Agilent web control, which is provided by the simulator E4362A, where is seen for this case an I–V curve of a PV panel. The red point is the instantaneous operating point of the PV array in terms of current and voltage. With the designed FC-MPPTC controller implemented by the DSP module and in opera-tion, the operating point (red dot) is successfully stabilized

L1 RL HY10 -P + 15V RHY -1 5V RPV3 RPV4 DZV TLP250 +1 5V DG1

TMS320F2812

Fig. 13 The designed two-stage photovoltaic and converter system

Fig. 14 The schematic of the isolated gate driver circuit

Fig. 15 The schematic of the hall current sensing circuit

Table 4 Measurements by the hall current sensor

IPV(A) 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

after some period of time to the MPP. The stabilization evolution is shown in Fig.18b. It is seen from this sub-figure that with the DSP module power on (the controller on), the output power is maximized to approximate 220 W in a time period around 13 s, when the current and voltage of the PV panel reaches 2 A and 110 V, respectively, actually corresponding to the location of the red dot in Fig.18a. Note that the 13 s is much longer that the stabi-lizing time period of 0.02 s simulated by governing equa-tions or Powersim, as previously shown in Fig.12, since in experiments the MPPT is activated intermittently with 1 s rest each time between two successive duty adjustment. For this case of MPPT, only 13 times of adjustments are needed to reach MPPT. Except the rest time, the actual operation period needed for MPPT is less than 1 s, showing a fast MPPT achieved by the designed FC-MPPTC controller.

Note also that noises are observed in various signals which are possibly resulted from ADC and/or environment.

Fig. 16 The implemented designed circuit

Fig. 17 Experimental Setup

Fig. 18 Experimental results by the PV simulator (VOC= 130 V,

ISC= 3 A, VMP= 110 V, IMP= 2 A); a Agilent web control; b

Wave-forms (VPV, IPV, PPV); c Output voltage waveforms in the second

stage; d The duties of two-stage converter

Fig. 19 Experimental results by the PV simulator (VOC= 120 V,

ISC= 3 A, VMP= 100 V, IMP= 2 A); a Agilent web control; b

Wave-forms (VPV, IPV, PPV); c Output voltage waveforms in the second

stage; d The duties of two-stage converter

Fig. 20 Experimental results by the PV simulator (VOC= 110 V,

ISC= 3 A, VMP= 90 V, IMP= 2 A); a Agilent web control; b

Wave-forms (VPV, IPV, PPV); c Output voltage waveforms in the second

Figure18c shows the output voltage waveforms of the second stage in the adopted DC-C converter, where the value of the output voltage is stabilized at 199 V, showing the capability of the designed controller and circuit topol-ogy to provide a constant output and maximum power output from the PV panel. The waveforms of the duties in the two stages are shown in Fig.18d. The duty cycle of first stage and second stages are approximately equal to 32.3 and 23.5 %, respectively, at MPP. The required time for stabilizing at MPP is approximately equal to 11 s to reach the maximum power point.

The performance of the designed FC-MPPTC controller and the two-stage converter topology are also tested for different I–V characteristics of the PV module. Their simulation results similar to the previous case are shown in Figs.19 and20, where Vocof the PV-string set lower as

120 and 110 V, respectively. With the designed FC-MPPTC controller in operation, both PV panels are stabi-lized at their MPPs successfully within 13 s. The voltages at MPPs VMP’s are 100 and 90 V, respectively, for the two

cases. The final duties in the two stages in Fig.19d for the case with Voc= 120 V equal to approximately 23.5 and

38.2 %, respectively, the final duties in the two stages in Fig.19d for the case with Voc= 110 V approximately

equal to 20.5 and 41.1 %, respectively. Therefore, when VMPbecomes low, the duty for the second stage is tuned to

a higher level, while the first one to a lower level. It is obvious that the tunings on the duties for the two different stages in the DC–DC converter while the maximum power tracking is in action by the designed FC-MPPTC controller are actually heading toward opposite direction.

Much effort is next paid to collect experimental data on the powers at different stages, which is intended to com-pute the conversion power efficiencies of the designed circuit. Varied trails of MPPT for different I–V charac-teristics of the PV panel are carried out. The results are summarized in Table5. In this table, POUT1is the realistic

power output of the PV simulator measured at the output of the first-stage, which is supposed to be ideally equal to PMP

at steady state while MPPT is effective. The difference between shown in this table reflects inevitable power los-ses, like switching and conduction losses. VOUT2and POUT2

are the output voltage and power of the second stage in the adopted two-stage DC–DC converter. Two efficiencies are defined to further evaluate the performance of the designed FC-MPPTC controller and DC–DC converter. They are defined by g_2ndstage¼POUT2 POUT1; ð33Þ gsystem¼ POUT2 PMP : ð34Þ

The above-defined two efficiencies g2ndstage and gsystem in fact refers to those of the 2nd-stage converter and the entire system. It is seen from Table5 that the system conversion efficiency varies from 90 to 96.302 %, which all above 90 %, showing satisfactory energy conversion results of the designed FC-MPPTC controller and DC–DC converter. The best efficiency is obtained for the case with VOCand ISCbeing 130 V and 3 A, respectively, for the I–V

characteristics of the PV panel.

5 Conclusion

A new two-stage DC–DC converter equipped fuzzy tracker for maximum power point tracking (MPPT) and simulta-neous voltage boost of a generic PV system is proposed in this study. Modeling and simulation on the PV system and the DC–DC converter circuit are carried out by the state-space technique and the software Powersim. The simula-tions are intended to validate the performance of the pro-posed FC-MPPTC. It is shown that the tracking process for the maximum power point is as fast as within 0.02 s, which is also proven in a much faster pace and stable with designed FC-MPPTC as compared to conventional P&O method. Experiments are also carried out to validate the expected performance of the designed FC-MPPTC

Table 5 Measured powers for tuning duties of the two switches in the two stages

Voc(V) Isc(A) VMP(V) IMP(A) PMP(W) Pout1(W) Vout2(V) Pout2(W) g2nd-stage(%) gsystem(%)

130 3 120 2 240 234.611 215 231.125 98.514 96.302 130 3 110 2 220 218.289 199 198.005 90.708 90.002 130 3 100 2 200 198.167 195 190.125 95.942 95.063 120 3 110 2 220 219.243 200 200.000 91.223 90.909 120 3 100 2 200 198.831 193 186.245 93.670 93.123 120 3 90 2 180 178.751 183 167.445 93.675 93.025 110 3 100 2 200 199.702 194 188.180 94.230 94.090 110 3 90 2 180 178.596 180 162.000 90.707 90.000

controller and the two-stage DC–DC converter. It is shown that a fast MPPT is achieved within less than 1 s, while the efficiency could reach more than 90 %, even up to 96.302 %, with varied conditions on the I–V characteristics of the PV cell considered. In short, the designed two-stage PV system with proposed FC-MPPTC and VBC is proven working effectively in extracting power from a generic photovoltaic system.

Acknowledgments The authors are greatly indebted to AU Op-tronics Corp. (AUO) for the supporting research. The authors also appreciate the support from National Science Council of R.O.C under the grant no. NSC 101-2623-E-009-006-D and 100-2221-E-009-091-. This work was also supported in part by the UST-UCSD International Center of Excellence in Advanced Bio-Engineering sponsored by the Taiwan National Science Council I-RiCE Program under Grant NSC-100-2911-I-009-101.

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