Electrical Power and Energy Systems 64 (2015) 792–803

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Electrical Power and Energy Systems

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Design and real-time implementation of a new auto-tuned adaptiveMPPT control for a photovoltaic system

http://dx.doi.org/10.1016/j.ijepes.2014.07.0800142-0615/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.

Raseswari Pradhan, Bidyadhar Subudhi ⇑Department of Electrical Engineering, Centre of Excellence on Renewable Energy System, National Institute of Technology Rourkela, Odisha 769008, India

a r t i c l e i n f o

Article history:Received 1 July 2013Received in revised form 10 July 2014Accepted 26 July 2014

Keywords:Polynomial PV modelRLS methodMPPTAuto-tuned PID controller

a b s t r a c t

This paper presents design of an auto-tuning based adaptive maximum power point tracker (ATAMPPT)for a photovoltaic (PV) system. The maximum power point (MPP) of a PV system varies continuously inaccordance with changing weather conditions. To cope up with fast varying weather conditions, there is anecessity of an adaptive MPPT system in which MPP of the PV system needs to be quickly estimated andtracked. The proposed ATAMPPT comprises of a DC/DC boost converter equipped with an adaptive MPPTalgorithm. This ATAMPPT is incorporated between the PV system and load. In this new MPPT system, apolynomial curve-fitting approach is employed to model the PV system whose parameters are identifiedon-line using a Recursive-Least-Square (RLS) algorithm. Further, the real-time performance of the pro-posed MPPT system is validated by using a prototype PV control system set-up developed in our labora-tory. The performances of the proposed ATAMPPT have been compared with that of three existing MPPTsnamely Perturb and Observe (P&O) and an adaptive P&O MPPT. From the obtained results it is observedthat the overall approach of the proposed ATAMPPT control is simple, user-friendly and it exhibits accu-rate MPP tracking.

� 2014 Elsevier Ltd. All rights reserved.

Introduction

A PV system can harvest maximum possible power if it is oper-ated at its MPP. In view of achieving this maximum PV power, aMPPT is employed between the PV panel and load. MPPT is a veryimportant component of a PV system which consists of a MPPTalgorithm, a controller, PWM generator, comparator and a DC/DCboost converter. The MPPT algorithm calculates the reference oper-ating point of the PV system that aligns with the MPP. A DC/DCboost converter forces the PV system to operate at MPP ascalculated by the MPPT algorithm. A PWM generator generatesgate-pulses according to the signal received from the controller.Designing a suitable MPPT algorithm and a controller are veryimportant tasks in achieving maximum power harvest in a PVsystem [1].

A good number of MPPT algorithms and their implementationsare reported in [2] for constant and fast changing weather condi-tions and also for partial shedding mismatched conditions. Incre-mental Conductance (INC) and Perturb and Observe (P&O)methods are more popular MPPTs because of their simplicity andease in implementations [3]. Also, INC and P&O MPPTs have beenmodified to improve the PV power harvesting efficiency and MPP

tracking accuracy [4–8]. An adaptive P&O (APO) proposed in [5]is a low cost MPPT that involves a simple adaptive MPP trackingalgorithm, a PI-controller and a sensor. But, the main concern inall these MPPTs is the dependency of MPP tracking response onthe perturbation size. Also, the tracking signal oscillates aroundits reference point even at the steady-state [9–10]. On the otherhand, Newton–Raphson method (NRM) is found to be an appropri-ate technique for determination of MPP because it does not dependon empirical formula and trial and error [11]. Although NRM algo-rithm deals with double integral term of the tracking signal, butthe estimated MPPs using NRM are not oscillatory like P&O andINC MPPTs. Also, the NRM technique is a very convenient tech-nique to calculate MPPs on-line by considering linearized mathe-matical model of the PV panel and DC/DC boost converter [12].

The main concern in maximum PV power harvesting is todesign and implement a controller in the situation of fast changingweather conditions because the MPP of a PV panel is dependent onthe weather conditions [13]. PI and PID-controllers are commer-cially accepted controllers owing to ease in their implementation.But opportunities exist in modifying these controllers to achieveadaptive control actions [14–17]. A fixed gain PID-controller can-not handle fast variations in weather conditions for a wide operat-ing range [15,16]. Although adaptive controllers such as the modelreference adaptive controller (MRAC) and self-tuning regulator(STR) have been successfully applied to PID-controlled DC/DC

R. Pradhan, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 792–803 793

converters but the parameter tuning algorithms of these adaptivecontrollers are very complex and dependent on plant parameters[18]. For control action involving high frequency switching, thetuning algorithm should be simple and should have fast conver-gence [19]. The main challenge involved in designing an adaptivecontroller for the current problem is the development of a param-eter tuning algorithm that ensures stability and convergence ofcontroller parameters [18]. For DC/DC power converter control,auto-tuning control has been successful in providing adaptive con-trol action on-line [18]. It is also found that an auto-tuner is basedon a simple and robust algorithm. It does not affect converter oper-ation under normal condition [19]. The auto-tuners presented in[18,19] work efficiently for normal load regulation problem butmay not handle MPPT control because MPPT controller has to workin a situation of fast changing reference signals. Adaptive algo-rithms should involve tuning of controller parameters efficientlyand quickly for a PV system which has uncertain actual dynamics.Hence, the auto-tuner proposed in this paper is equipped with atuning algorithm that is based on linearized models of PV paneland DC/DC boost converter. By considering linear models of thePV panel and DC/DC boost converter, it also becomes easier todesign and implement the adaptive algorithm successfully.Although on-line MPPT operation is possible using an ideal PVpanel model, but its accuracy is affected by the neglect of shuntand series-resistances [20]. Hence, instead of neglecting anyparameters, a polynomial curve-fitting mathematical model [11]can be used where recursive parameterization is possible. Thispolynomial model is constructed from real-time data of PV panelvoltage, current and power, hence is independent of manufac-turer’s data-sheet. For construction of a polynomial model, a math-ematical function is generated that approximately fits the data. Thecontributions of our proposed ATAMPPT algorithm are as followssuch as (a) the proposed MPPT uses Newton–Raphson method tosolve for dp/dv as this method is one of the fastest convergingmethods, (b) proposed ATMPPT is a digital one and (c) ATAMPPT

IpvId Ish

R s ipv

R shDvpv

+

-

(a)

(c

PV Panel

MPPT

vpv

vpv

ipv

Vref

e- +

Fig. 1. (a) Equivalent circuit model of a PV system, (b) MPPs of PV system at different

is an adaptive MPPT technique that can deal with wide range vari-ations in the weather conditions.

The paper is organized as follows. The maximum power pointestimation problem is formulated in Section ‘Problem Formula-tion’. The proposed auto-tuner based adaptive MPPT controller ispresented in Section ‘Proposed Auto-tuning based Adaptive MPPT’.Section ‘Results and Discussion’ describes both simulation andexperimental results with discussions. Section ‘Conclusions’ con-cludes the paper.

Problem formulation

The equivalent circuit of a PV system is shown in Fig. 1(a).When solar radiation G falls on the PV system, current Ipv is gener-ated. At the output terminal of the PV system voltage vpv andcurrent ipv are available. Applying Kirchhoff’s current law, the cur-rent–voltage (I–V) characteristics can be expressed as

ipv ¼ Ipv � I0 expvpv þ ipvRs

NsVt

� �� 1

� �� vpv þ ipvRs

Rshð1Þ

where I0 is the dark-saturation current, Ns, Rs and Rsh are number ofseries cells in the PV panel, series resistance and shunt resistancerespectively. Vt is the thermal voltage of the PV system given by

Vt ¼akbT

eð2Þ

where a is diode-ideality factor, kb is Boltzmann’s constant, T isjunction temperature and e is the charge of an electron.

The output power of the PV system is given by

ppv ¼ vpv � ipv ð3Þ

There exists a single point called maximum power point (MPP) atany solar irradiance at which output power of the PV system isthe maximum as shown in Fig. 1(b). Hence,

(b)

)

BoostConverter

PWM

ATAMPPT

LOAD

Gate pulse

u

vo

MPPT

vpv

ppv

MPP1

MPP2

voc1voc2

ppv2

ppv1

solar irradiances, and (c) structure of PV system with an on-line MPPT controller.

ZOH

ADC

vref (k)

+e(k)

Auto-tuner

DPIDController

ω

u(k)

vpvipv

i (k)

Ku, Tu

MPPCalculation

y(k)

DPWMv(k)

v(k)

PV Panel

u(k)

voEstimation of

( )G S

ReferenceDC/DCBoost Converter model

v

i

vo

Ʃ-

Fig. 2. Topology of proposed Auto-tuning based adaptive MPPT controller for MPPT operation of PV panel.

Fig. 3. Flow-chart for selection of lowest possible polynomial order of curve-fitting-polynomial PV panel model.

794 R. Pradhan, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 792–803

@ppv

@vpv¼ 0 ð4Þ

Voltage at MPP (vref) can be calculated by solving Eq. (4) using aMPPT algorithm. Then using a DC/DC boost converter as shown inFig. 1(c), the operating point of the PV system can be adjusted tothis calculated vref. The MPPT problem is concerned with estimationof the MPP using MPPT algorithm. Then the PV system is forced tooperate at that estimated MPP by providing an appropriate duty-signal to the DC/DC converter. The MPPT algorithm and the control-ler both need to be efficient because their performances are directlyrelated to the power conversion efficiency of the entire PV system.

Proposed auto-tuning based adaptive MPPT

A PV system with the proposed MPPT controller is shown inFig. 2. PV panel voltage vpv and current ipv are sensed and sampledby an Analog-to-Digital Converter (ADC) to v(k) and i(k). Thesesampled v(k) and i(k) are supplied to the MPPT algorithm to gener-ate vref(k). This vref(k) is the voltage at which operating point of PVsystem coincides with MPP of PV panel. Then, vref(k) is comparedwith v(k) to generate an error signal e(k) as follows.

eðkÞ ¼ v ref ðkÞ � vðkÞ ð5Þ

Here, the objective of the controller is to minimize this error e(k).The error signal e(k) is used as the input to discrete PID-controller(DPID) to generate control signal u(k). The auto-tuner tunes theparameters of DPID in response to receiving a signal y(k) andparameter x from a linearized model of boost converter wherey(k) is the boost converter output and x is the un-damped naturalfrequency component of the linearized model of boost converter.The signal u(k) is sent to a PWM generator so that it generatesthe required gate-pulse for the boost converter. Thus, the controloperation is to be accomplished in the following five distinct steps.

(a) Selection of the accurate polynomial model of PV panel.(b) Estimation of PV panel parameter (h).(c) Calculation of MPP voltage vref using the MPPT algorithm.

(d) Linearization of the boost converter.(e) Tuning the DPID controller parameters using an auto-tuner.

Selection of PV panel model order

To design an adaptive MPPT controller, identification of PV sys-tem model is first required. In this work, a polynomial curve-fittingmodel for the PV system is considered. Typically system identifica-tion involves two distinct steps namely polynomial order determi-nation and parameter estimation (estimating coefficients ofpolynomial describing PV system dynamics). The order of the poly-nomial curve-fitting model is selected as follows. Usually, the PV

R. Pradhan, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 792–803 795

panel dynamics is identified by its I–V or P–V characteristics. TheMPPs are more distinct in P–V curves than that of I–V curves. Hence,the P–V curve is chosen for curve-fitting [11]. Then, taking PV panelvoltage sample v(k) and power sample p(k) as input and outputrespectively, the order of the polynomial model is determined.Here, p(k) is calculated by multiplying v(k) and i(k). At first, annth-order polynomial model is considered. The nth-order polyno-mial describing the P–V characteristics of the PV-panel is given as

pðkÞ ¼ b0ðkÞ þ b1ðkÞvðkÞ þ b2ðkÞv2ðkÞ þ :::þ bnðkÞvnðkÞ ð6Þ

Where k is the sample number. The order of the linearized polyno-mial model of PV panel represented by (6) can be selected followingthe steps shown in Fig. 3.

In this selection process, at first, order n is selected for the lin-earized polynomial model. Then the fitness of the polynomial canbe evaluated using the following formula [13].

Fitnessð% ageÞ ¼ 1� pðkÞ � pðkÞpðkÞ

��������

� �� 100 ð7Þ

where pðkÞ is the estimated power sample by an nth order polyno-mial model and pðkÞ is the power sample of the standard PV model.

(a

RLSv (k)

i (k)

vref Calc

( ) ( )0 ,..., nb k b kΛ Λ

Input v(kInitiali

Is e(

Calculate a

Calculate p

k

update v(k) and i(k)

Ca

(b

(c

Fig. 4. (a) Complete MPPT algorithm to calculate vref, (b) NRM Algorithm for MPP estim

Then, the (n�1)th order is considered and its fitness is tested. Theprocess is continued up the fitness becomes P set lower limit. Itis to be noted that the lowest limit is set in such a manner thatthe lowest possible ordered polynomial model of the PV panel canbe considered to avoid complexity and unnecessary extra mathe-matical calculations during on-line system identification process.This above process is carried out at standard testing condition(STC) that is at 1000 W/m2 and 25 �C. Then, the polynomial modelis cross-validated at other weather conditions.

Estimation of PV panel parameters

Eq. (6) can be rewritten in regressor form as

pðkÞ ¼ /TðkÞhðkÞ ð8Þ

where the regressor vector / and parameter vector h are given by

/ðkÞ ¼ 1 vðkÞ � � � vnðkÞ½ �hðkÞ ¼ b0ðkÞ b1ðkÞ � � � bnðkÞ½ �T

ð9Þ

A recursive least square (RLS) algorithm (Fig. 4(a)) can be employedfor the PV parameters extraction. The kth sampled panel voltage

)

( ) , ( )f k f kCalculation

NRM vref (k)

ulation

) and i(k); k=1ze e(k) = 1

k) <= 10-3 Sample v ref = v(k)

nd using eq

(k) using eq(8)

= k + 1

lculate

)

)

ation, and (c) Relationship between dpdv and v for the studied SSI-M6-205 PV panel.

L D

C2Sw vo

ipv

vpv

io

ic2

DC-DC Boost Converter

Gate signal

C1

ic1

RL

iL

(a)

L

D

C2 vo

ipv

vpv

io

ic2

DC-DC Boost Converter

vL

Sw RLC1

ic1

iL

(b)

L

C2 RL

iL

vpv

io

DC-DC Boost Converter

vL

Sw voC1

ic1 ic2

ipv

(c)

Fig. 5. (a) Equivalent circuit of boost converter, (b) circuit when Sw is open, and (c)circuit when Sw is closed.

796 R. Pradhan, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 792–803

v(k) and power p(k) are selected as input and output of the RLSblock. Signal p(k) is the product of v(k) and current i(k). The PVpanel model in Eq. (8) is already in regressive form. Hence RLS algo-rithm can be applied directly to estimate h as follows.

hðkÞ ¼ hðk� 1Þ þ KðkÞ pðkÞ �uTðkÞhðk� 1Þh i

ð10Þ

KðkÞ ¼ Cðk� 1ÞuTðkÞkþuTðkÞCðk� 1ÞuðkÞ ð11Þ

CðkÞ ¼I � KðkÞuTðkÞ� �

Cðk� 1Þk

ð12Þ

where p(k), K(k), k and C(k) are the measured power, the Kalman-gain matrix, the forgetting factor such that 0 < k < 1 and the covari-ance-matrix respectively at kth sample.

Determination of vref

The procedure for calculation of vref(k) is shown in Fig. 4(a). TheP–V characteristics of a PV panel at different solar radiations whichindicates that with variations in solar radiation, the peak powerpoint and corresponding voltage point change. That voltage pointcan be estimated as follows.

Let, the derivative of actual PV power with respect to actual PVvoltage is represented as f(v) such as

f ðvÞ ¼ dpdv ð13Þ

Referring Eq. (4), at MPP,

f ðvÞ ¼ 0 ð14Þ

Then, voltage at MPP can be determined by solving Eq. (14). Thiscan be solved by using the Newton–Raphson method (NRM). Flow-chart for NRM for finding MPP is shown in Fig. 4(b).

Using NRM, the first-derivative (dp/dv) and second-derivative(d2p/dv2) of the nth-order polynomial of PV panel can be written as

f ðvÞ ¼ dpdv ¼ b

K

1ðkÞ þ 2bK

2ðkÞvðkÞ þ 3bK

3ðkÞv2ðkÞ þ :::þ nbK

nðkÞvn�1ðkÞ

_f ðvÞ ¼ d2p

dv2 ¼ 2bK

2ðkÞ þ 6bK

3ðkÞvðkÞ þ 12bK

4ðkÞv2ðkÞ

þ . . .þ nðn� 1ÞbK

nðkÞvn�2ðkÞð15Þ

where bK

i are the estimated parameters of the PV system. AlthoughNRM is one of the fastest methods of root finding, but it does nothave the guarantee of convergence unless v(0) is properly chosen.This problem is clear from the relationship between f(m) and v asshown in Fig. 4(c). In this figure, point ‘1’ and ‘4’ are the open-circuitand short-circuit points respectively. In between ‘1’ and ‘4’, trueMPP lies at ‘3’. But, there exists a local minimum at point ‘2’ whereis _f ðvÞ zero and division of zero occurs during the calculation ofMPP. If v is initialized from ‘1’, then it will suffer from the unwanteddivision of zero problems in between the estimation procedure.Hence, it is advisable to choose initial point of v between ‘5’ and‘4’ to avoid the divergence problem.

Linearization of DC/DC boost converter model

A DC/DC converter is required to force the operating voltage ofPV panel to the MPP voltage. In this work, a non-isolated boosttype converter is used because this converter is widely used asPV system interface due to its simplicity and efficiency [21]. ADC/DC boost converter has been used in this paper for MPPT oper-ation. The circuit of a boost converter is shown in Fig. 5(a) and theirequivalent circuits for different switching operations are shown in

Fig. 5(b) and (c). vpv and ipv are voltage and current of the PV panel,iL is the current through inductor L, the voltage and current of loadRL are vo and io, the current through capacitor C2 is ic2.

The model is described as follows. The switching signal u(k)with the required duty-ratio d(k) is generated by the proposedauto-tuning based MPPT controller. In this paper, the assignedobjective of the controller is to generate a switching signal so thatit does the MPPT operation.

When the switch is OFF, then switching control signal (Fig. 5(b))

ipv ¼ ic1 þ iL ) �vpv

rpv¼ C1

dvpv

dtþ iL )

dvpv

dt

¼ � 1rpvC1

vpv �1C1

iL ð16Þ

and

vpv ¼ LdiL

dtþ vo )

diL

dt¼ vpv

L� vo

Lð17Þ

where rpv is the dynamic resistance of the PV panel and is calculatedas follows.

rpv ¼ �dvpv

dipvð18Þ

Table 1Data of SSI-M6-205 PV system with MPPT.

Parameters Values

Parameter Values of SSI-M6-205 PV System at STCOpen-circuit voltage, Voc (V) 35.55Short-circuit current, Isc (A) 7.91MPP voltage, vref (V) 28.04MPP current, Iref (A) 7.1Number of series cells, Nse 60Number of shunt cells, Nsh 1Short-circuit temperature coefficient of current, KI (% per �C) 0.06No. of series PV panel in the PV array 5

Parameter values of MPPT systemInductance, L (mH) 5Capacitance, C1 (lF) 180Capacitance, C2 (lF) 330Sampling time, Ts (ls) 1Switching frequency of DC/DC Boost converter (kHz) 10MPPT refresh time 5 sPower rating 1 kW

Fig. 6. Comparison of different order of polynomial of PV panel models with that ofthe actual model at STC.

R. Pradhan, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 792–803 797

The value of rpv is usually negative near MPP [11]. When the switchis ON (Fig. 5(c)), then

ipv ¼ ic1 þ iL )dvpv

dt¼ � 1

rpvC1vpv �

1C1

iL ð19Þ

and

vpv ¼ LdiL

dtð20Þ

Let d is the duty-ratio of the switching signal u, then Eqs. (16)–(19)are combined as

dvpv

dt¼ � 1

rpvC1vpv �

1C1

iL

diL

dt¼ 1

Lvpv �

vo

L�d

y ¼ vpv

ð21Þ

Here, L and C1 are kept fixed for a given DC/DC boost converter andonly rpv varies. Laplace transforming Eq. (21), we get

Table 2Estimated PV panel parameters with variation in solar radiations.

G (W/m2) T (�C) b0 b1 b2 b3 b4

500 9.3598 51.1171 �6.1516 0.2617 �0.0037600 11.4216 49.1796 �5.9143 0.2557 �0.0036700 25 12.7764 44.9902 �5.4154 0.24 �0.0035800 13.1865 39.294 �4.7357 0.2174 �0.0033900 12.4703 32.7069 �3.9409 0.1903 �0.003

1000 10.5023 25.7226 �3.0837 0.1606 �0.0027

sVpvðsÞ ¼ �1

rpvC1VpvðsÞ �

1C1

ILðsÞ

sILðsÞ ¼1L

VpvðsÞ �Vo

L�DðsÞ

YðsÞ ¼ VpvðsÞ

ð22Þ

Eq. (22) can be rewritten in transfer function form as

GðsÞ ¼ VpvðsÞ�DðsÞ

¼VoðsÞLC1

s2 þ 1rpv C1

sþ 1

LC1

ð23Þ

The general form of a 2nd-order system is given by

GðsÞ ¼ K0

s2 þ 2fxsþx2 ð24Þ

where K0 and f are the system-gain and damping-ratio of the step-response of the DC/DC boost converter. Comparing Eqs. (23) and(24),

K0 ¼VoðkÞLC1

x ¼

ffiffiffiffiffiffiffiffi1

LC1

s

f ¼ 12rpvLC1x

ð25Þ

Here, the magnitudes of L1, C1 and x are fixed. The value of dynamicresistance of PV panel varies with changing weather conditions.

Auto-tuning procedure of controller parameters

A discrete time PID-controller (DPID) has been chosen for theproposed ATAMPPT because it is easy to implement in digital com-puting platform. The kth-samples witching signal to the boost con-verter with discrete DPID controller during MPPT operation isgiven as

uðkÞ ¼ Kc eðkÞ þ Tc

Ti

Xk

n¼0

eðnÞ þ TdeðkÞ � eðk� 1Þ

Tc

" #ð26Þ

where Kc, Ti, Td and Tc are the proportional-gain, integral-time,derivative-time and sampling period respectively of the controller.However, conventional DPID based MPPT controllers generally donot work well for actual systems, higher order systems, time-delayed linear systems, on-line operation and complex systemswithout precise mathematical models. To overcome these difficul-ties, the DPID controller has to provide necessary duty-ratio ofswitching signal u(k) so as to obtain actual v close to vref both in

Fig. 7. Variations in PV panel parameters with solar radiations.

Table 3Comparison of Estimated voltage and power of a PV panel at MPP (vref and Pmax respectively) using NRM with that of simulated voltage and power with variation in solarradiations.

G (W/m2) Actual vref Estimated vref evmpp Actual Pmax Estimated Pmax epmax(%) gMPPT (%)

500 27.61 26.24 4.962 100.5941 104.3101 3.694 96.306600 27.78 26.44 4.8236 121.6577 124.7192 2.5165 97.4835700 27.89 26.59 4.6612 142.6554 145.1007 1.7142 98.2858800 27.96 26.71 4.4707 163.5504 165.4192 1.1426 98.8574900 28 26.81 4.25 184.3157 185.6459 0.7217 99.27831000 28.04 26.88 4.0685 204.9302 205.7572 0.4035 99.5965

Table 4Estimated PID controller parameters using the proposed auto-tuning method withvariation in solar radiations.

G (W/m2) T(�C)

Ku x Tu Kc Ti Td

500 0.0593 55.1021 0.114 0.0236 0.0536 0.0134600 0.0591 68.0324 0.092 0.0235 0.0509 0.0121700 25 0.0589 80.0153 0.0787 0.0233 0.0376 0.0094800 0.0586 90.3110 0.067 0.0231 0.0308 0.0086900 0.0584 98.4446 0.064 0.0229 0.0296 0.00791000 0.0582 106.7915 0.058 0.0228 0.0283 0.0071

798 R. Pradhan, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 792–803

fixed and variable weather conditions in accordance with changingin environmental conditions. For varying weather conditions,parameters of DPID controller such as Kc, Ti and Td are to beadjusted. The tuning procedure of these parameters is describedas follows.

The tuning of the DPID controller is based on experiment per-formed in closed loop. This tuning method is simple as values ofx and GðsÞjs¼jx is only required for the tuning of DPID-controllerparameters. Taking x as input, the new auto-tuner evaluates thetuning-parameters such as tuning-gain (Ku) and tuning-time-con-stant (Tu) as follows.

Ku ¼1

jGðjxÞj

Tu ¼2px

ð27Þ

where

argðGðjxÞÞ ¼ �p ð28Þ

In the new Auto-tuner, the PID parameters Kc, Ti and Td are usuallycalculated using predefined empirical relations as follows [18,19].

Kc ¼ 0:6Ku

Tc ¼ 0:5Tu

Td ¼ 0:125Tu

8><>: ð29Þ

GM

PM

Fig. 8. Frequency response of PV system with the proposed ATAMPPT technique atSTC.

The effectiveness and accuracy of the proposed ATAMPPT can beestimated by observing its (i) percentage of absolute error in MPPtacking and (ii) MPPT efficiency. The percentage of absolute errorin MPP tacking and MPPT efficiency at STC can be estimated as

evmpp ¼vmpp actual � vmpp estimated

vmpp actual

��������� 100

epmax¼ pmax actual � pmax estimated

pmax actual

��������� 100

gMPPT ¼ 1� epmax

ð30Þ

Fig. 9. MPP voltage tracking performances of PV system with five PV panelsconnected in series with (a) P&O-MPPT, (b) APO-MPPT [5] and (c) proposedATAMPPT-MPPTs at STC.

Fig. 10. MPP voltage tracking performances of PV system with one PV panel using proposed ATAMPPT-MPPTs.

(a)

(b)

(c)

PVPanel

DC-DCBoost

Converter

FPGABoard

PersonalComputer

1-ϕInverter

SignalConditioner

LoadLCFilter

RCFilter

v1 i1 v2 i2 i3v3

pulse Pulse

Conditioned signals

Data and Command

Load

SPARTAN 3AFPGA board

DAQ

Voltagesensor

DC/DC Boost converter

DSO

Temperature Display

Fig. 11. (a) PV modules, (b) photograph of PV system prototype, and (c) complete block diagram of the above PV system prototype.

R. Pradhan, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 792–803 799

800 R. Pradhan, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 792–803

Results and discussion

In order to validate the efficacy of the proposed Auto-tunerbased MPPT controller, we first obtain the P–V characteristics atdifferent weather conditions (Fig. 1(b)) of SSI-M6-205 PV system[13] whose manufacturer’s data-sheet is shown in Table 1.

Simulation results

We present here the procedure of fixing up the order of thepolynomial in selection of the PV panel prior toon-line evaluationof MPPs. For this order selection, fitness of the PV model polyno-mial with some selected order like 8th, 6th and 4th is checkedusing Eq. (7). P–V characteristics of PV model with 8th, 6th and

Fig. 12. Spartan-3A DSP Trainer Kit with following components such as (1)SPARTAN-3A DSP Processor, (2) PLL Clock Setting, (3) JTAG Connector, (4) RS232Serial Port, (5) Parallel Port, (6) LCD Display, (7) PWM Connector, (8) SDA BusConnector, (9) Power Supply and (10) USB.

ADC

FIRFilter

MPPTControl

Algorithm

v1, i1

v1,i1

v1, i1, v2, i2,v2set

v3, i3,v3set

FromADC

Device

VPE SPARTAN 3A

Fig. 13. System architecture

Fig. 14. Simulation results from

4th ordered polynomials are shown in Fig. 6 with their absolutepercentage of fitness.

Referring to Fig. 6, it is observed that P–V characteristic in caseof 8th order polynomial model of PV panel has as high as 99.9399%of percentage fitness at STC with respect to the reference P–V char-acteristic. Meanwhile, P–V characteristics in case of the 6th and the4th order polynomial models have 99.827% and 96.6227% of fitnessrespectively. To reduce the calculation complexities, the order ofthe polynomial model should be as low as possible. The fitness ofthe 4th order polynomial model is having the simplest structureamong 8th, 6th and 4th order polynomials of PV panel and alsohaving more than 95% of fitness. Hence, 4th order polynomialmodel for PV panel is considered in this paper. After selection ofthe model, the next step is extraction of model parameters of thePV system. A 4th order polynomial of a PV system is given as

pðkÞ ¼ b0ðkÞ þ b1ðkÞvðkÞ þ b2ðkÞv2ðkÞ þ b3ðkÞv3ðkÞþ b4ðkÞv4ðkÞ ð31Þ

where the regressor / vector and the parameter vector h are given by

/ ¼ 1 vðkÞ v2ðkÞ v3ðkÞ v4ðkÞ� �

;

h ¼ b0ðkÞ b1ðkÞ b2ðkÞ b3ðkÞ b4ðkÞ½ �Tð32Þ

The proposed Auto-tuner based MPPT algorithm was implementedas follows. Auxiliary load is varied with a fixed number of steps anddata of v and p are acquired and temporarily stored in the data base.Using those data of v and p in Eqs. (10)–(12), h is estimated asshown in Table 2 and Fig. 7.

Table 2 and Fig. 7 show the estimated PV panel parameter vec-tor h such as b0–b4 with variation in solar radiation. From, Fig. 7, itcan be observed that with every change in solar radiation, h is alsovarying distinctly that leads to the variation in the operating pointof DC/DC boost converter such as the voltage and current at MPP.

Varying v with very small step-size of 0.5 mV, p was evaluatedusing Eq. (31). The evaluated data of v and p were used in NRM

DACInterface

InverterControl

ConverterControl

Pulse1Vref

Pulse6

ToDAC

Device

DSP Trainer Kit

of PV system controller.

VPE SPARTAN 3A FPGA.

Table 5Device Utilization Summary.

Name of Block Available Used Utilization(%)

Number of Slice Flip flops 33,280 2678 8Number of 4 input Look-up Tables

(LUTs)33,280 4309 12

Number of occupied Slices for logic 16,640 4262 25Total number of 4 input LUTs 33,280 5666 17Number of bonded Input/Output Blocks

(IOBs)519 36 6

Number of BUFGMUXs 24 2 8Number of DSP48As 84 13 15Total 1,17,107 16,966 14.5

R. Pradhan, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 792–803 801

block. Using NRM, voltage at MPP was evaluated as shown inTable 3 and used as the reference voltage point vref for DC/DC boostconverter. Referring to Table 3, the percentage absolute error inestimated power at STC is only 0.4035%. Lowering the radiationthis epmax increases but still it is less than 4% at 500 W/m2.

For a given DC/DC boost converter, the tuning of PID-controllerparameter was accomplished by using the new auto-tuningmethod during MPP tracking process. In this procedure, theDPID-controller parameters vary with dynamic resistance of PVpanel (rpv) which again varies with solar radiation. Then, rpv wascalculated at v = 20 volts. Using value of rpv in Eq. (28), parametersof linear DC/DC boost converter model are estimated as shown inTable 4.

The frequency of the PV system with the proposed ATAMPPT isshown in Fig. 8. In this figure, it can be seen that in this casexgm > xpm and both GM and PM are positive. From the above resultsit is verified that that PV system with this new MPPT is stable.

A comparative analysis of MPP tracking performances of PV sys-tem with the proposed ATAMPPT and some of the existingrenowned MPPTs such as P&O [2] and an adaptive P&O (APO) [5]can be seen in Fig. 9(a)–(c). Referring Fig. 9(c), it can be observedthat the settling time of PV system with the proposed ATAMPPTis <0.05 s whereas the settling times in case of P&O and APO basedMPPTs are 0.3 s (Fig. 9(a)) and 0.17 s respectively (Fig. 9(b)). It canalso be observed that there are voltage oscillations present in caseof P&O and APO. Fig.10 shows the MPP tracking performances ofthe PV system with proposed ATAMPPT in case of one PV panelfor step change in solar irradiance 250-500-1000 watts/m2.

(a)

(b)

vinDat

Data samp

T = 5

TOFF =

Fig. 15. Simulation results from

Experimental results

The PV system is a stand-alone type. It consists of PV array,DC/DC boost converter, inverter, SPARTAN 3A FPGA board, signalconditioners (voltage and current sensors), personal computerand a board with analog filtering circuits. Fig. 11(a) shows thePV array where five PV modules are connected in series.Fig. 11(b) shows the photograph of the prototype experimentalset-up of the PV system and Fig. 11(c) demonstrates the blockdiagram of the above system. In this PV system experimentalset-up, the Spartan-3A FPGA (Fig. 12) has been used for controlimplementations.

a packet

ling �me (0.2μs)

P1

Converter gate pulse(Duty-ra�o = 58%)

P12

P11

P13P14

Inverter gate pulse

20 ns

Clock pulseTime-period = 30 ps

150 ps

VPE SPARTAN 3A FPGA.

(a) (b)

PV V

olta

ge(v

olts

)D

uty-

ratio

(%)

Time, t (s)Time, t (s)

Fig. 16. (a) Simulated PV voltage and (b) experimental PV voltage and converter gate pulse for temperature of 35 �C and solar irradiance of 958 W/m2.

802 R. Pradhan, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 792–803

System architecture

For FPGA implementation, the system architecture of the con-trol structure of the given PV system prototype is shown in Fig. 13.

FPGA simulation results

The project status for implementation of the proposed control-ler in FPGA is shown in Fig. 14. FPGA simulation results of the givenPV system prototype are shown Fig. 15. From Fig. 15(a), it can beseen that time period (T) and OFF period (TOFF) of the convertergate pulse are 5 ls and 2.1 ls respectively. Hence, the duty-ratioof this pulse is T�TOFF

T

� � 100 ¼ 5�2:1

5

� � 100 ¼ 58%. Fig. 15(b)

shows the data sampling time (0.2 ls) and flow of the PV panelvoltage vpv data packets.

System architecture synthesis

After modeling all blocks of the system architecture of PV sys-tem shown in Fig. 12, the blocks are required to be synthesized.

(a)

(b)Time [s]

PV V

olta

ge [V

] 0.9s

A

B

4V

Fig. 17. MPP tracking results of prototype PV system showing (a) simulated PVvoltage and (b) experimentally obtained PV voltage varied from open-circuitvoltage to MPP voltage with APO-MPPT (scales: x-axis 0.5 s/div and y-axis 10 V/div).

Functional performance of each of these blocks can be representedby their respective number of lines of VHDL codes, number of logicelements used and percentage utilization of the FPGA device toconstruct these blocks. System architecture synthesis perfor-mances of all the above blocks for the proposed ADAMPPT areshown in Table 5. The SPARTAN 3A FPGA used in this work con-tains 16,640 logic elements. Out of which only 4262 logic elementshas been used for implementation of ADAMPPT. Hence, the deviceutilization is only 25%. In this table, the component BUFGMUX isusually used in Spartan-3, Spartan-3E and Spartan-3A devices. Itrepresents a multiplexed global clock buffer that can be selectedbetween two input clocks say I0 and I1. When the selected input(S) is Low, the signal on I0 is selected for output (O) whilst whenthe selected input (S) is High, the signal on I1 is selected for output(O) (Source: XACT Libraries Guide, Xilinx Corporation, 2001).

Fig. 16 shows comparison between the experimentally obtainedand the simulated MPP tracking performances of the prototype PVsystem with proposed ATAMPPT. From Fig. 16 shows the simulatedand experimental gate pulse of the converter for same environ-mental condition. It can be seen that the duty-ratio of the

(a)

(b)

PV V

olta

ge [V

]Tim

e

0.6s

A

B

Time [s]

2V

Fig. 18. MPP tracking results of prototype PV system showing (a) simulated PVvoltage and (b) experimentally obtained PV voltage varied from open-circuitvoltage to MPP voltage with ATAMPPT (scales: x-axis 0.5 s/div and y-axis 10 V/div).

R. Pradhan, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 792–803 803

gate-pulse is 58% for both simulation and experiment. It can alsobe observed that the gate-pulse is exactly matching with that ofthe FPGA simulated result as shown in Fig. 15(a).

MPP tracking results PV system with APO-MPPT [5] and ATA-MPPT are shown in Figs. 17 and 18. Fig. 17(a) shows simulatedMPP tracking results such as PV voltage and PV current of PV sys-tem with APO-MPPT [5]. It can be seen in this figure that PV cur-rent is changing from 0 A to 2.2 A taking around 0.7 ms and thenoscillates around 2.2 A. During that period PV voltage changes from109 V to 91 V and oscillates around that 91 V. Fig. 17(b) showsexperimental result displaying the tracking voltage of PV systemwith APO-MPPT [5]. In this figure, ‘A’ denotes the point when MPPTis made ON and MPP tracking was started. Time between A and Bwas the MPP tracking period. After B, voltage of PV system settledat MPP voltage. It is found that tracking periods is 0.9 s and voltagefluctuation at steady-state is 4 V in case of APO-MPPT. But, trackingperiod and voltage fluctuation at steady-state in case of proposedATAMPPT are 0.6 s and 2 V respectively as shown in Fig. 18(a)and (b). Therefore, performance of PV system with ATAMPPT isbetter than that of APO in terms of tracking period and voltagefluctuation at steady-state.

Conclusions

A new adaptive MPPT based on an auto-tuning technique calledATAMPPT is proposed in this paper for PV systems and its effective-ness are verified. The proposed MPPT tracking method can esti-mate the MPPs of a PV system on-line using a RLS based systemidentifier and a NRM technique. The ATAMPPT is compared withthree existing MPPTs such as P&O and APO. Both simulation inMATLAB/SIMULINK and experimental results are presented to val-idate the efficacy of this proposed approach. This auto-tuning takesplace on-line and uses the on-line estimated MPPs of the PV panel.The simulation and experimental results clearly demonstrate thatthe ATAMPPT provides effective tracking of MPP so that maximumpower can be extracted from the PV panel at changing weatherconditions.

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