FPGA-based real time incremental conductance maximum power point tracking controller for photovoltaic systems

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1&

Published in IET Power ElectronicsReceived on 17th February 2013Revised on 3rd October 2013Accepted on 28th October 2013doi: 10.1049/iet-pel.2013.0603

294The Institution of Engineering and Technology 2014

ISSN 1755-4535

FPGA-based real time incremental conductancemaximum power point tracking controller forphotovoltaic systemsRasoul Faraji, Amin Rouholamini, Hamid Reza Naji, Roohollah Fadaeinedjad,

Mohammad Reza Chavoshian

Department of Electrical and Computer Engineering, Graduate University of Advanced Technology, Iran

E-mail: [email protected]

Abstract:Maximum power point tracking (MPPT) is an important issue in photovoltaic (PV) systems. Hence, we need to designan efficient and cost-effective system which is able to transfer the maximum power received from PV cell to the load. This studydescribes the hardware implementation of a real time incremental conductance (INC) MPPT algorithm for a PV module.According to the PV dynamic model, a criterion is presented that by modifying the original algorithm, an adaptive variablestep size INC algorithm is realised and efficiently is implemented on XILINX XC3S400 field programmable gate array(FPGA). At first, the PV model characteristics and the proposed algorithm with the mathematical equations are modelled andsimulated using ‘MATLAB/Simulink-system generator’ environment; then the system performance is examined. It is worththat some solutions are proposed to simplify the system based on the design constraints for hardware implementation ofdigital controller on FPGA. The optimised design of hardware architecture and the high processing speed of FPGA haveenhanced the performance of digital controller in designed MPPT system. The experimental results show the proposedmethod provides a good tracking speed and also mitigation of fluctuation output power.

1 Introduction

In recent years, the installation of renewable energygeneration systems is rapidly growing because of concernabout environmental issues and the decline in the fossil fuelresources. Among all kinds of renewable energytechnologies, photovoltaic (PV) technology is one of themost common systems because it has some advantages suchas cleanness, low maintenance cost, availability andnoiselessness.Research on PV systems consists of different subjects

including PV modelling, maximum power point tracking(MPPT) algorithms, power converter configuration and gridconnection issues. Different models were proposed for PVcells in the literature. Single diode model is the simplestand most widely used model for PV cells as it offers agood compromise between simplicity and accuracy [1].Double diode model provides a more accurate P−Vcharacteristic of PV cell whereas the equations of thismodel are more complex [2]. Many different dynamic PVmodels were presented in literature [3–5]. These modelsshould be implemented in real time applications byconsidering their complexity.PV cells rarely work in maximum power point (MPP)

because the maximum output power of PV cells depends onvarious variables (temperature and irradiation). Considering

the non-linear properties of PV cells we need to track themaximum power by means of controllers to improve powerconversion efficiency of PV cells.Different MPPT algorithms have been proposed to increase

the efficiency of PV systems [6–12]. These methods vary inconvergence speed, oscillations around the MPP,complexity, cost and electronic equipment requirements[13]. In recent years, various MPPT algorithms have beenimplemented on the FPGA as the platform for its controller.Some of the most useful algorithms are Perturb & Observe[14, 15], constant voltage [16, 17], incremental conductance[18] and artificial intelligence methods [9, 19, 20] whichare widely used in PV applications. P&O method is themost widely used algorithm because of its simplicity ofimplementation. This method is based on perturbation inthe operation voltage, thus the major drawback of thismethod is oscillation around MPP and the amount of powerloss in this point. Constant voltage method is based onapproximately constant ratio between Vmpp andopen-circuit voltage. Although this method is quite simple,but it is difficult to determine the optimum value ofconstant ratio between Vmpp and Voc, and even moreimportant requirement of sudden interruption of PV powerto measure open-circuit voltage [8]. The artificialintelligence methods such as fuzzy logic [21] and neuralnetwork [22] provide more rapid and accurate solutions for

IET Power Electron., 2014, Vol. 7, Iss. 5, pp. 1294–1304doi: 10.1049/iet-pel.2013.0603

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the MPPT problem but are generally more complicated inimplementation which limits their use in real-timeapplications.Incremental conductance method is based on the fact that
the power–voltage curve of PV generator at constant solarirradiance and cell temperature levels has normally only oneMPP [23]. In this work, a criterion is presented based ondynamic model of PV cells to improve the performance ofincremental conductance (INC) method. It is based on usingLambert W-function [24], which has been fruitfully usedfor expressing the current–voltage characteristic of a solararray [5, 25]. Based on this criterion, a modified adaptiveINC method with a variable perturbation step size isintroduced to improve tracking speed and power fluctuationaround MPP. In the following, the modelling and thehardware implementation of the MPPT system as well asconsiderations in practical implementation are investigated.In this paper: Section 2 presents a dynamic model of PV

cell. In Section 3, dynamic behaviour of buck converter isexplained and Section 4 describes the proposed MPPTalgorithm. The simulation results are presented in Section5. Hardware implementation of the MPPT system andexperimental results are discussed in Sections 6 and 7,respectively. Finally, conclusion is presented in Section 8.

Table 1 Parameters and electrical specifications of theLORENTEZ LC80-12M solar array at 25°C, 1000 W/m2

Parameter Description

IMP 4.6 AVMP 17.2 VPMAX 80 WISC 5 AVOC 21.6 VKV −0.0756 V/KKI 0.0045 A/KNS 36Rs 0.248 ΩRp 234.96 ΩCp 40 nF/cm2

2 PV cell modelling

To evaluate the performance of PV and MPPT systems, it isnecessary to model the current–voltage characteristics of thePV cell in different operating conditions. Fig. 1a shows thedynamic model of PV cell that it is used in this research.As shown in this figure, the proposed dynamic modelincludes a current source that its current is directlyproportional to irradiation. Rs resistance represents theequivalent series resistance of the PV array, where theequivalent parallel resistance is considered as Rp. Cp is anembed transition and diffusion capacitance [26].In this work, to verify the performance of the proposed

modified variable step size INC MPPT algorithm, aMATLAB-Simulink model of PV system is initiallydeveloped. The parameters of a commercial solar cellLORENTEZ LC80-12M model are extracted and used forthe PV array model in simulation and the experimentalresults. The related parameters and the electricalspecifications of PV module are listed in Table 1.Some parameters in Table 1 are inserted according to data

sheet of LORENTEZ LC80-12M solar array, for example IMP,VMP, PMAX, ISC, VOC, KV, KI and NS.

Fig. 1 Dynamic model of PV cell

a In forward zoneb In reverse zone


Rp and RS are calculated based on this fact that there is onlya pair (Rp, Rs) that warranties Pmax, m = Pmax, e = VmpImp at the(Vmp, Imp) point of the I–V curve, that is, the maximum powercalculated by the I–V model for basic equation of PV cell(Pmax,m) is equal to the maximum experimental power fromthe datasheet (Pmax, e) at the MPP [27]

Pmax,m = Vmp IPh − I0 expVmp + RsImp

VTa

( )− 1

( )[

−Vmp + RsImp

Rp

]= Pmax , e

(1)

Rp = Vmp Vmp + ImpRs

( )/ VmpIph − VmpI0

[

× expVmp + ImpRs

( )Nsa

q

kT

⎛⎝

⎞⎠+ VmpI0 − Pmax , e

⎤⎦ (2)

Above equation means that for any value of Rs there will be avalue of Rp that makes the mathematical I–V curve cross theexperimental (Vmp, Imp) point. Finally using the iterativeprocess Rs and Rp are calculated (Fig. 2).Capacitance is estimated exploiting the splitting of the

output characteristic because of the charge and dischargeeffect. The phenomenon appears to be relevant when thediode in Fig. 1a is reverse biased. For this purpose theanalysis is referred to the model in reverse zone, shown inFig. 1b. In this zone, the static parameters are given by thesum between the series and parallel resistance. Generallythe Rs is orders of magnitude smaller than the Rp; therefore

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Fig. 2 Simplified flowchart of the iterative process to calculate theRs and Rp

Fig. 4 DC/DC buck converter with variable input

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for this analysis it is neglected. For a given climatic condition,the output characteristic can be expressed as [28]

i1 = Iph −V

Rp− c

∂V

∂t

( )1

(3)

i2 = Iph −V

Rp− c

∂V

∂t

( )2

(4)

c = i1 − i2∂V/∂t( )

2− ∂V/∂t( )

1

(5)

The current–voltage relationship describes the outputcharacteristic of the dynamic model of the PV cell that it isgiven as

I = IPh − I0 expV + RsI

VTa

( )− 1

[ ]

− V + RsI

Rp− C

∂ V + RsI( )

∂t

(6)

VT = NSKT

q(7)

where IPh and I0 are PV and saturation currents of the PV cell

Fig. 3 Characteristic curves of the PV cell

a I−V curve of the PV cell in different conditionsb PV array power curve and different resistive load power curves


respectively. The VT is the thermal voltage with NS cellsconnected in series, k is the Boltzmann constant(1.3806503 × 10−23 J/K), q is the electron charge(1.60217646 × 10−19 C), a is the diode ideality constant andT is the temperature of the PV cell. The above-mentionedequations describe the variations of the I–V characteristicsof the PV cell considering temperature and irradiation, asshown in Fig. 3a.As illustrated, under different irradiations and temperatures

the curves are changing. Hence, it is necessary to track theMPP of PV cells using a controller.

3 DC/DC converter

A DC/DC buck converter is utilised to implementMPPT scheme for PV system in this research. Accordingto the power–voltage characteristic of PV cell, only inone point the maximum power can be achieved. Now,when the PV cell is directly connected to load, onlyif the load size is equal to voltage divided by currentin MPP, then the maximum power can be received from PVcell.Fig. 3b shows a P−V curve of PV cell and resistive load

power curves. For this case, the MPP will be achievedwhen the load resistance is equal to 3.45 Ω. On the otherhand, the MPP varies with the temperature of PV cell andsolar irradiation. Considering these variations, the loadresistance should be changed to maximise thecorresponding PV generated power. Therefore an interfacethat forces the PV cell to operate at MPP is required. In thispaper, as shown in Fig. 4, the buck converter with avariable input is used. A MPP controller changes the dutycycle ratio of MOSFET in the buck converter.


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4 Description of the proposed MPPTalgorithm
In this section, the proposed algorithm is described based onthe INC method. This algorithm controls the duty cycle ratioof MOSFET and redound a fast and accurate response ofMPPT problem. The INC is one of the MPPT methods thatit has different convergence speeds and oscillations aroundMPP depending on the step size of the duty cycle ratio [29,30]. In other words, reducing the step size of duty cycle,the convergence speed and also the oscillations around theMPP are decreased and vice versa. In simple INC, a fastresponse and small oscillations cannot exist simultaneously.In the proposed algorithm, the step size of the duty cycleratio is not considered as a constant. The higher step size isused when the system operates far from MPP, whereas thestep size is decreased for the area around MPP. Also werequire a criterion to determine how a system operatesclosely to the MPP.In literature, several analytical models have been proposed

to describe the behaviour of solar cells under differentenvironmental conditions [5, 25, 30, 31]. Here, we analysethe proposed model. According to (6) and disregard ofseries and parallel resistors and capacitances, the outputpower of PV cell is calculated by the following equation

PPV = VPVIPV − VPVI0 expV

VTa

( )− 1

[ ](8)

at MPP the value of ∂p/∂v should be zero, now we have thefollowing equation

∂P

∂V= − IPV

I0+ 1

( )+ V

VTa+ 1

( )exp

V

VTa

( )= 0 (9)

With multiplying the expression e in (9) and based onthe relation XeX = Z = > X =W(Z ) we have [5, 25]

V

VTa+ 1

( )exp

V

VTa+ 1

( )= IPV

I0+ 1

( )(10)

VOP1 = WIPVI0

+ 1

( )e

[ ]− 1

{ }VTa (11)

Fig. 5 INC algorithm

a Improved INC algorithm block diagramb Presentation of INC algorithm operation at I−V and P−V curves of the cell


The accuracy of VOP1 can be increased by considering thedrop voltage of series resistance

VOP = VOP1

− IPV + VOP1

Rp− I0 exp

V

VTa

( )− 1

( )[ ]Rs (12)

where VOP is a suitable criterion that specifies the best MPP,which W(x) denotes the Lambert function that it is theinverse of Z = XeX. Note that the use of the LambertW-function allows the apparently explicit calculation ofthe array current as a non-linear function of the terminalvoltage [5]. This function has a very complicatedstructure, where R[z]≥ 1. To realise a simple calculation,the principal branch of W is analytic at 0. This followsfrom the Lagrange inversion theorem, which gives theseries expansion of (13) [24]. This expansion of thediscrete series is used to simplify the computations ofLambert function for processing in the ALU of digitalcontroller

W (x) =∑1n−1

(− n)n−1

n!zn (13)

Vop estimates the value of optimum voltage at MPP.Therefore the amount of difference between outputvoltages of the cell with Vop can be as a criterion (ξ) fordetermining the location of cell’s operating point based onMPP. Using this method, we can set the step size ofPWM signal such that it shows two functionalities basedon the situation of operating point of the cell.The algorithm of improved INC is shown in Fig. 5a. This

algorithm represents that, by considering the ξ value, the stepsize of duty cycle ratio is equal to ΔD1 when the margin of theoutput voltage and VOP are very small, whereas the step sizeof duty cycle ratio is equal to ΔD2 when the output voltage isfar from the VOP. Performance of other parts of the proposedalgorithm is such as the conventional INC method. Thereforeat MPP, dI/dV is equal to −I/V. Moreover, the left side ofMPP is dI/dV >−I/V, thus a reduction in converter’s duty


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cycle ratio is necessary to achieve MPP. Similarly, the rightside of MPP is dI/dV < − I/V, thus an increase inconverter’s duty cycle ratio is essential to achieve MPP(Fig. 5b).
5 Evaluation of simulation results

In order to verify the performance of the proposed variablestep size method, a PV system shown in Fig. 6a issimulated by SIMULINK. This system contains the PVarray, MPP controller, buck converter and resistive load.Testing the system before its practical implementation

reduces design time and costs. The resources of the FPGAsused for preliminary testing can be sufficient for thecomplete system modelling [32].The proposed MPPT controller is modelled and simulated

using system generator (Fig. 6b) based on the INC algorithmshown in Fig. 5a. This controller consists of three parts; INCalgorithm, the duty cycle step size adjustment and PWMsignal generator. Duty cycle (ΔD) step size adjustmentblock and also the INC block are designed based onobtained mathematical models. The presented model isformulated in Mcode block based on (12). In this block aseries expansion is used to simplify the calculation ofcomplex functions such as exponential and Lambertfunctions. By measuring PV cell current and voltage values,ΔD adjusting block calculates Vop value based onmathematical model and by considering this value it selectsthe duty cycle step size value of pulse width modulation(PWM) signal. Then duty cycle adjustment block is appliedthe obtained value into PWM generator.As mentioned before, the design in this environment is

based on the basic blocks including Register, Add/sub,multiplexer etc., as well as optimised complex mathematicalblocks which are directly implementable on FPGA.

Fig. 6 System modelling

a System modelling in Simulinkb Proposed MPPT model created with system generator


Implementing the controller of MPPT system byconsidering design constraints based on FPGA in systemgenerator, leads to the simulation results similar toexperimental ones. In the following, the validity of modelbased on the proposed method and its advantage over theconventional INC method is investigated.The proposed model is simulated based on the following

conditions: the first irradiation level is 500 W/m2; at t = 0.5s, the irradiation level suddenly changes to 900 W/m2. Thetemperature is constant at 25°C. These variations are shownin Fig. 7a.To compare the performance of the proposed algorithm and

fixed step size conventional INC method, simulations areconfigured under exactly the same conditions. The PVvoltage, current and power of conventional INC MPPTmethod with fixed step size of 0.1 and 0.0001 underirradiation step-change condition are shown in Figs. 7b–d,respectively.As we can see, increasing step size (ΔD = 0.1) system at a

fraction of a second reaches to MPP and also shows betterdynamic response per quick irradiation changes, butfluctuations around MPP is increased. For the small stepsize (ΔD = 0.0001), the speed of tracking MPP is greatlyincreased but the fluctuations around the MPP in steadystate is decreased.The dynamic response of the proposed variable step size

method is shown in Figs. 7e–h. The variation in the stepsize follows the proposed design aspects: when thetracking system operates far away from the MPP, the stepsize is equal to 0.1. In addition, when the operating pointis close to the MPP, the step size is equal to 0.0001, toachieve good dynamic response and small oscillationsaround MPP. In addition, the irradiation level is changedat 0.5 s, and the proposed method ensures fastconvergence and robust performance. Therefore the


Fig. 7 Simulation results

Performance of step size INC algorithm of ΔD = 0.1 and ΔD = 0.0001a Variation of irradiation for the studied casesb Voltage wave form of fixed step size INC algorithm (ΔD = 0.1 and ΔD = 0.0001)c Current wave form of fixed step size INC algorithm (ΔD = 0.1 and ΔD = 0.0001)d Power wave form of fixed step size INC algorithm (ΔD = 0.1 and ΔD = 0.0001)e Voltage wave form of variable step size of the proposed INC algorithmf Current wave form of variable step size of the proposed INC algorithmg Power wave form of variable step size of the proposed INC algorithmh Output power of PV cell under variation of load at 1000 W/m2 and 25°C

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proposed method can solve the drawback in fixed step-sizeconventional INC method and improve the efficiency of thePV cell.Also, the output power of PV cell is shown in Fig. 7h for

various resistive loads. A load fed by the buck converter is


equal to 1 Ω; at t = 0.5 s, the load changes to 2 Ω. TheMPPT controller causes division of voltage and current ofbuck converter which are being equal to load. Therefore themaximum power of PV cell is extracted under variousenvironmental conditions and load changes.


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6 Hardware implementation of the MPPTsystem
In this section, the hardware implementation of proposedalgorithm on FPGA and the circuitry are described in details.

6.1 MPPT controller

The main problem in hardware implementation of theproposed method is implementing its complex functionsbased on specific constraints of FPGA. These functionsincrease the execution time and the area overhead.Although the software-like use of FPGAs is simple, but theuser should not forget that the compiler has to deal withthese strong constraints [33].There are some practical approaches to approximate these

functions with simple FPGA designs. In [4, 34], somemodels are presented in which PV cell equations have beensimplified so that, it is suitable for FPGA implementation.These methods have tried to simplify the equations withhigh approximation. In [35], functions such as exponentialfunctions have been implemented in an optimised wayusing CORDIC algorithm. The next method is usingFPGA’s look-up tables. MPP relationships of a PV systemare calculated beforehand using FPGA’s look-up tables foreach probable environment condition and stored in thememory of MPPT’s control system. During the operation,the corresponding MPP for a particular condition is selectedform that memory and is implemented [6]. Anotherapproach is utilising optimised IP cores like the multiplier,divider and adders that are optimised with XILIXNsynthesis tools, which are adequate to implement thecomplicate PV models [22].IP core is a circuit function module which is a

pre-designed, easy to transplant, with independentintellectual property rights and certain features [36]. IPcore-based design is utilised in designing many complexsystems and this reduces design time and improvesperformance of designed systems because the IP cores areusually designed for specific operations and are optimisedin terms of speed, area, power consumption and efficiency.Therefore the IP cores are used in an ALU in our design.The calculation of (12) is done in ALU section of digitalcontroller (Fig. 8). By receiving input data, ALUimplements the equations using aforementioned IP coresand series expansion. Then it selects the step size of PWMsignal and applies it to INC MPPT block. To reduce theexecution time, operators are implemented in pipelinearchitecture.According to bibliographic research on implementation of

different types of numeric applications in VLSI technology, it

Fig. 8 Block diagram of the digital control system on FPGA


can be noted that fixed point representation is used morebecause it is much easier for implementation thanfloating-point. Most digital platforms support only this typeof representation [37]. In this work, a representation infixed-point with 18 bits is chosen (9 bits for integer partand 9 bits for real part), because the operators that utilisedin ALU structure is 18 bits which facilitates the realisationof the ALU.To obtain the optimal frequency of the system clock, the

ALU is synthesised separately and 52 MHZ clockfrequency is achieved for this block. In this work, PWMsignal frequency is set to 100 kHz and accuracy of eachduty cycle step size is 1/256 bits (28 = 256) so the operatingfrequency of INC block will be 25.6 MHz. Forclock distribution a digital clock manager and forimproving accuracy of generated clock frequency twocounters are used.In this system, considering that the clock speed of ALU

block is much more than clock speed of INC block, ALUblock calculates the required values and applies ΔD valuesto INC block before the new PWM signal cycle isproduced. The block diagram of the implemented digitalcontrol system is shown in Fig. 8.

6.2 Analogue-to-digital converter (ADC)

Considering that the FPGAs has a high-speed data processingand also the maximum delay in digital control loops isoccurred through the ADC, so we should select an ADCwhich can synchronise itself with FPGA. In this circuit, an8-bit ADC (TDA8703) is used which can sample the inputsignal with rate of 4.43 MHz. In experimental circuits forsetting clock frequency of A/D converter many issues areconsidered such as A/D sampling rate (Nyquist rate), PWMfrequency (switching frequency), duty cycle ratio, FPGAclock frequency and also values of inductors and capacitorsused in buck converter circuit and their steady-statecharacteristics. In this circuit, the Hall-effect sensor modelACS712-05B is used for sampling the current of PV cell.Unlike the simple old method in which currentmeasurement is done by measuring the voltage of a seriesresistor, current sensors determine the current value morecarefully and prevent the negative effect of adding anadditional resistor.

6.3 DC/DC converter

In our design, a buck converter is used which converts the celloutput voltage into load voltage range. The power driver IC(IR2113) is used to drive the power Mosfet (IRF540). Thecalculated values for different compounds of the DC/DCbuck converter are: L = 35 µH, Cin = 10 µF, Cout = 470 µFand switching frequency is 100 kHz.Important parameters to specify the inductor size are

switching frequency, inductor–current ratio andsaturation-current ratio that must be considered incalculations. The inductor size directly affects theconverter efficiency, load-transient response, ripple currentand converter peak current. Also the size of outputcapacitance must be calculated such that minimises thevoltage overshoot and ripple present at the output of astep-down converter. In [38, 39], the considerations andprinciples to design the buck converter have been wellstudied.Selecting the proper input capacitor size in buck converter

is very effective to reduce fluctuations caused by switching in


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the output of the solar cell. The small values for this capacitorcause intense fluctuations in the cell output. The large valuesincrease the system response time; thus under variable climateconditions, the operation at the MPP cannot be achievedappropriately. Therefore according to input capacitor valuea well-understood trade-off between fluctuations andresponse time must be provided. In this design, to show theimpact of the proposed method in reducing the fluctuationsas well as the response time, a capacitor with Cin = 10 µF isused. The schematic of buck converter circuit is shown inFig. 4.
Fig. 9 Experimental results

a Tracked power from conventional INC method (fixed ΔD at 1/256)b Tracked power from conventional INC method (fixed ΔD at 8/256)c Proposed variable step-size INC method waveformsd Tracked power from the proposed MPPT in steady statee Evaluation of proposed system under dynamic environment [different solar irradf Evaluation of proposed system under dynamic environment [different load value


7 Experimental results

For performance evaluation, the adaptive MPPT software isdeveloped using VHDL for Xilinx XC3S400 FPGA. In thissection, first some existing variable step size INC methodsare reviewed; then the performance of proposed INCmethod is compared with fixed and variable step size INCmethods.Menniti et al. [40] introduced an INC method that sets ΔD

to a variable quantity which is proportional to the sum of theconductance and the incremental conductance. It is focused

iation values (500 and 900 W/m2)]s (2 and 1 Ω)]


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on how to determine the minimum and maximum values ofthe variable step size. In this study, ΔDmin and ΔDmax mustbe determined based on the presumptions and pre-computeddata, therefore the obtained optimal results may be validonly for a given system and operating conditions. In [41],ΔD value is defined based on the dP/dV slope (ΔD =N*dP/dV ). If the dP/dV value is higher than previous dP/dV, thenthe scaling factor N is increased and vice versa. After ΔD isset, its value is applied in an INC algorithm to detect theMPP. According to this method, one time the value of dP/dV is calculated and the other time the value of dI/dV. Theproblem with this method is that when the maximum powerobtained from the cell is exactly equal to MPP, ΔD isreduced while ΔD needs to be reduced near the MPP to notallow the operating point go far from the MPP. Using thedP/dV slope to determine ΔD causes fluctuations in thevalue of ΔD around the MPP. By Applying a rule, Liuet al. [42] have improved the method provided in [41]. It isknown that dP/dV is almost at its lowest value around theMPP. To ensure convergence, the variable step size shouldobey the following rule
N × dP

dV, DDmax (14)

If the above equation is satisfied, ΔD will be increased; and ifnot, ΔD will remain in the previous mode. This approach canreduce the fluctuations around the MPP.The number of system clocks to determine the appropriate

ΔD as well as the occurred errors in system for detecting thesuitable ΔD be increased Using simple MPPT methods.Consequently, the delay time to reach the MPP is increased.The proposed method uses mathematical equations to detectproperly the operating point to determine ΔD, and the MPPwith minimum possible clocks is tracked.In [43], a dynamic mathematical model to describe

non-linear characteristics is provided. A fractional-ordersystem described by a fractional differential-integral

Table 2 Review of existing works on hardware implementation of MP

Work,publication year

Converter type Switchingfrequency

Cellpower

[44] (2013) flyback converter 40 kHz 250 W

[41] (2013) buck converter – 50 W[45] (2012) buck converter – 150 W FLC[46] (2012) boost converter 5 kHz 80 W[47] (2011) boost converter 50 kHz 110 W[48] (2006) DC/AC inverter 15 kHz 2 kW[42] (2008) push–pull

converter20 kHz 120 W

[49] (2013) boost converter 50–100 kHz 1.5 kW[10] (2011) buck converter – 87 W

a[15] (2006) boost converter 100 kHz 10 W[50] (2011) buck converter 100 kHz 20 W lo

[51] (2012) DC/AC inverter 100 kHz 80 W[52] (2012) boost converter – 55 W n[53] (2006) boost converter 500 kHz 85 W e[54] (2012) two stage DC/DC

converter– 220 W

[55] (2013) boost converter 50 kHz 200 W[56] (2012) boost converter 300 kHz 100 W e[43] (2011) boost converter – 87 Wproposed buck converter 100 kHz 80 W

(‘–’: unknown)


equation is applied to the INC algorithm to adjust the PVarray voltage toward the MPP. Owing to heavymathematical computations, this system uses the ‘PCPentium-IV 2.4 GHz and Matlab’ software. As of complexmathematical calculations, these algorithms either are notimplementable in a single chip or an embedded system, orthey consume too much time because of floating-pointcomputations. Hsieh et al. [44] presented a two-phasetracking that forms a PV power-increment-aided INC(PI-INC) MPPT to improve the tracking behaviour of theconventional INC MPPT. The PI-INC MPPT is carried outby a two-phase approach identified by specific thresholdzone on PPV−VPV and IPV−VPV curves. According to thethreshold zones, the range of changes in ΔD is determinedso that the speed of reaching to MPP is increased. In thismethod, because of constraints defined for running thealgorithm using a microcontroller, the MPP tracking time isgreatly increased. This time depending on some conditiontakes about 5–13 s.In the proposed MPPT system design, the contributions are

made in several aspects of whole system, including systemsimulation, FPGA-based controller programing, converterdesign and experimental setup. According to these features,the proposed MPPT system shows a proper tracking speedwith high efficiency. Now, the performance of proposedsystem is examined based on experimental results.The control system starts to increase the duty cycle ratio

from 0%. In each system clock, A/D converter samples thevoltage and current values of PV cell and applies them innumerical format to the implemented controller on theFPGA. Then the controller sets the ΔD perturbationsaccording to control algorithm. Buck converter sets theoutput power of cell by changing duty cycle ratio such thatit reaches its maximum value.Figs. 9a and b show the power tracking results obtained

from the INC method with the fixed step size of 1/256 and8/256, (solar irradiance level is 600 W/m2 and temperatureis 38°C). As illustrated, the tracking time is 7 ms when ΔD

PT algorithms

MPPT Hardware platform Trackingspeed

INC Embedded controllerdsPIC33FJ06GS202

5 s

INC Microcontroller PIC18F4520 2 s-based P&O MPPT DSP TMS320F28335 1.5 s

P&O FPGA Quartus II 564 msINR Microcontroller C515C 500 msINC Microcontroller Intel 87196 500 msINC DSP TMS320LF2407 250 ms

P&O FPGA XC4VLX60 100 msvoltage

pproximation lineAnalogue circuitry 88 ms

P&O FPGA XC2C384 85 msad current-based

MPPTDSP TMSF28335 80 ms

distributed MPPT Analogue circuitry 70 mseuro-fuzzy (NFC) FPGA Virtex II 30 msxtremum-seeking Analogue circuitry 20 ms

FLC DSP TMS320F2812 20 ms

P&O-based PI DSP TMS320F240 20 msxtremum-seeking Analogue circuitry 20 ms

INC PC Pentium-IV 2.4 GHz 16 msINC FPGA XC3S400 2.5 ms


Fig. 10 Prototype of proposed PV system

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= 1/256 whereas it takes only 2.3 n ms when ΔD = 8/256.Larger ΔD gives larger fluctuations in output voltage asshow in Fig. 9b. Fig. 9c shows the results obtained fromthe proposed variable step-size INC algorithm. As we cansee that the tracking time is 2.5 ms, and the voltage andcurrent waveforms fluctuations are decreased around MPP.Fig. 9d shows the MPP steady-state waveforms in details.According to the measured values, cell voltage with an

average of 16.6 V and its current with average of 3.2 A arereached to steady state at D = 62%. The proposed method isimproved tracking time by 64% compared with fixed stepsize of ΔD = 1/256 and has shown 22% fewer oscillationsaround the MPP compared with fixed step size of ΔD = 8/256. According to the experimental results and thecharacteristic curves of the PV cell (Fig. 3a), the controllerhas well tracked the MPP and the efficiency of theproposed method is about 98.8%.To evaluate the functionality of proposed MPPT system

under dynamic environment, it has been tested in practicalconditions. As it is shown in Fig. 9e, the amount ofirradiation is changed between 500 and 900 W/m2. Theproposed system is tracking the MPP at least possible timefor sudden change in solar irradiation and reaches to steadystate at optimum power. The MPP system should keep theoutput power of the cell in a constant amount as load ischanging. Fig. 9f shows the functionality of system as loadis changing from 2 to 1 Ω. As we can see in this figure, themultiplication of output voltage in output current of the cellis the same as load is changing.The functionality of proposed MPP controller based on

FPGA is compared with some recent works in Table 2which shows the proposed algorithm has the best timingperformance for MPP tracking with high speed performanceof FPGA. One of the most important features of FPGA is

Table 3 Device utilisation summary

Utilisation Details

1283 (18%) number of slices flip flops1813 (26%) total number of 4input LUTs7 (43%) number of MULT 18 × 18 s309 312 total memory usage, kB52 maximum frequency, MHz81.9 power consumption, mw


implementing circuits by hardware description which givesit the highest timing performance in compare to DSPs,microcontrollers and even analogue circuits counterparts.The proposed system could track the MPP in just 2.5 msusing low cost components.The designed prototype is shown in Fig. 10 and some

details of implemented hardware resources are presented inTable 3.

8 Conclusion

In this paper, a criterion is set based on comparison betweenthe operating point of cell and its MPP to determine the dutycycle ratio perturbations of the PWM control signal using thedynamic model of PV cells. By this method, the responsetime and fluctuations in the steady state are improved. Thepresented model is simulated based on hardware descriptionand implemented on XC3S400 FPGA. A dynamic model isimplemented based on optimised IP cores in ALUcontroller. Also a clock frequency of 52 MHz is achievedfor its processing. Based on the experimental results, withhigh processing speed of FPGA and also using high speedA/D converter, the proposed algorithm transferred receivedpower from PV to the load in 2.5 ms with lowest fluctuations.

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FPGA-based real time incremental conductance maximum power point tracking controller for photovoltaic systems