Energy Conversion and Management 93 (2015) 249258Contents lists available at ScienceDirect

Energy Conversion and Management

journal homepage: www.elsevier .com/ locate /enconmanMaximum power point tracking for PV systems under partial shadingconditions using current sweepinghttp://dx.doi.org/10.1016/j.enconman.2015.01.0290196-8904/Crown Copyright 2015 Published by Elsevier Ltd. All rights reserved.

Corresponding author. Fax: +852 23301544.E-mail address: steve.tsang@polyu.edu.hk (K.M. Tsang).K.M. Tsang, W.L. Chan Department of Electrical Engineering, The Hong Kong Polytechnic University, Kowloon, Hung Hom, Hong Kong

a r t i c l e i n f oArticle history:Received 18 November 2014Accepted 10 January 2015

Keywords:Photovoltaic systemMaximum power point trackingPartial shading conditionsa b s t r a c t

Partial shading on photovoltaic (PV) arrays causes multiple peaks on the output powervoltagecharacteristic curve and local searching technique such as perturb and observe (P&O) method couldeasily fail in searching for the global maximum. Moreover, existing global searching techniques are stillnot very satisfactory in terms of speed and implementation complexity. In this paper, a fast globalmaximum power point (MPPT) tracking method which is using current sweeping for photovoltaic arraysunder partial shading conditions is proposed. Unlike conventional approach, the proposed method iscurrent based rather than voltage based. The initial maximum power point will be derived based on acurrent sweeping test and the maximum power point can be enhanced by a finer local search. The speedof the global search is mainly governed by the apparent time constant of the PV array and the generationof a fast current sweeping test. The fast current sweeping test can easily be realized by a DC/DC boostconverter with a very fast current control loop. Experimental results are included to demonstrate theeffectiveness of the proposed global searching scheme.

Crown Copyright 2015 Published by Elsevier Ltd. All rights reserved.1. Introduction

The conversion efficiencies for various PV arrays are still verylow. Consequently, different MPPT algorithms [17] have beendeveloped so that power can be extracted as much as possible fromthe PV system. However, the output powervoltage characteristiccurve of a PV array is highly affected by solar irradiation. If the irra-diation is not uniform, multiple peaks could easily occur on thepowervoltage characteristic curve and all local searching algo-rithms [17] may be trapped in a local maximum which indirectlyintroduce a power loss. Recently, there are many MPPT algorithms[814] proposed to address the partial shading problems and theseglobal searching techniques are based on the extension of perturband observe method, particle swarm optimization (PSO), fuzzylogic and artificial neural networks (ANN). The problems withthese algorithms are that they may introduce large power oscilla-tions and are complicated to implement, especially for those artifi-cial intelligent based MPPT algorithms.

In general, DC/DC converters are usually attached to the outputterminals of PV arrays and served as power extraction device. Inorder to achieve the maximum power point tracking, most of MPPTalgorithms rely on adjusting the operating duty ratio of the DC/DCconverter which indirectly adjusting the PV output voltage. Thedynamics of the DC/DC converter is usually not considered in thedesign of tracking algorithm. However, a change in the duty ratiowill affect both of the PV output voltage and current. For aDC/DC boost converter, it is a non-minimum phase process andthis may easily cause power oscillation if the perturbation on theduty ratio does not have sufficient time to settle down. In thispaper, a new global searching algorithm which is based on currentsweeping is proposed. The search on the maximum power point isbased on a search on the PV output current rather than the PVoutput voltage. By taking into account of the DC/DC converterdynamics, a fast current controller is developed for the DC/DC con-verter such that a tight control on the PV output current isachieved. A very quick current sweeping signal can then be synthe-sized for the DC/DC converter and the global maximum powerpoint can be identified in a very short duration of time. A finer localsearching routine can be employed to refine the searchingalgorithm. Simulation and experimental results are included todemonstrate the effectiveness of the proposed searchingtechnique.2. PV model and its response to current excitation

A simplified equivalent circuit for a PV array is shown in Fig. 1awhere rs is the series resistance and voc is the open circuit voltagefor the PV array respectively. The relationship between the outputvoltage and the output current is given by

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250 K.M. Tsang, W.L. Chan / Energy Conversion and Management 93 (2015) 249258vpt voc iptrs 1

If the output current ip(t) can be controlled so that it could rampup from 0 to voc/rs during the time interval NT, the output currentbecomes

ipt voctNTrs

; 0 6 t 6 NT 2

The instantaneous power from the PV array is given by

Pt vptipt v2octNTrs

v2oct

2

N2T2rs; 0 6 t 6 NT 3

The maximum power point can be obtained by differentiating(3) with respect to time t and the maximum power point isachieved at time tmax = NT/2 with a current

imax voc2rs

4

and the corresponding maximum power output is given by

Pmax v2oc4rs

5

If a very quick current sweeping from 0 to voc/rs can be carriedout, the maximum power point can easily be identified by locatingthe required current for the output power to achieve maximum.The simplified model, which is shown in Fig. 1a, has not taken intoaccount the inherent capacitance of the PV array. The capacitancewill introduce dynamics to the output response of the PV array andthis will cause a phase shift between the PV output power and theoutput current. The output current obtained when the PV outputpower is at maximum is no longer the PV output current relatingto the maximum power point. If the inherent capacitance is mod-eled as cp and is connected in parallel with the PV array as shownin Fig. 1b, the PV array dynamics is governed by

cp _vpt ipt ictvpt voc iptrs

6rs

voc

ip

vp+-

(a) Simplified model

rs

voc

i p

vp+- cp

ic

(b) Simplified model with capacitance

Fig. 1. Equivalent circuit for PV array.The steady-state response of (6) is exactly the same as (1) andthe maximum power points for the two systems are the same atthe steady state. If the output current ic(t) is a ramp function whichis given by

ict voctNTrs

; 0 6 t 6 NT 7

and the initial output voltage vp (0) = voc, the output voltagebecomes

vpt voc 1tNT

1N1 et=T

; 0 6 t 6 NT 8

where T = rscp is the approximate time constant for the PV array.The instantaneous output power can be obtained by multiplying(7) and (8) to give

Pt vptict v2ocNTrs

t t2

NT tN1 et=T

; 0 6 t 6 NT 9

Moreover, the maximum power point can be obtained by differ-entiating (9) with respect to t and set the result to zero

dPtdt

v2oc

NTrs1 2t

NT 1N1 et=T t

Net=T

0; 0 6 t 6 NT

10

Assume N is very large and the dynamics et/T can be approxi-mated by zero. The maximum power point can be achieved at

tf N 1T

211

and the corresponding output current

if N 1voc

2Nrs12

If N is very large, (12) will be very close to the true maximum powerpoint (4). In actual practice, N cannot be too large in order to speedup the searching mechanism. If N is small, the difference between(4) and (12) becomes significant. To counteract the difference, anegative current ramp can be applied to the PV array. Considerthe negative ramp from voc/rs to 0 during the time interval NTwhichis given by

ict vocrs

voctNTrs

; 0 6 t 6 NT 13

and the initial output voltage vp (0) = 0, the output voltage becomes

vpt voctNT

1N 1Net=T

; 0 6 t 6 NT 14

The instantaneous output power can be obtained by multiply-ing (13) and (14) to give

Pt v2oc

rs

tNT

1N 1Net=T t

2

N2T2 tN2T

tN2T

et=T

0; 0 6 t 6 NT 15

The maximum power point for the negative ramp can beobtained by differentiating (15) with respect to t and set the resultto zero

dPtdt

v2oc

rs

N 1N2T

2tN2T2

1NT

1N2T

tN2T2

et=T

; 0

6 t 6 NT 16

Assume N is very large and et/T can be approximated by zero.The maximum power point can be achieved at

tb N 1T

217

KPs+KIs

1LsU+ +-

+icr icd

vp-U

Fig. 3. Block diagram for the PV current control loop.

K.M. Tsang, W.L. Chan / Energy Conversion and Management 93 (2015) 249258 251and the corresponding output current

ib vocrs

N 1voc2Nrs

18

If both of the forward and backward current sweeping tests arecarried out, an approximate maximum power point can beobtained from (12) and (18) as

imax if ib2

voc2rs

19

which is the same as (4). As (19) is independent of N, a fast currentsweeping test can easily be carried out. Notice that the currentsweeping test result is equally valid for series and parallel con-nected PV arrays. The average power obtained from (9) and (15)based on tf and tb is given by

Pm v2oc4rs

N2 1 2eN1=2

N2

!20

For large N, the average power obtained in (20) is close to thetrue maximum power.

3. PV array output current control

The search for the maximum power point as shown in (19)demands for a tight control of the PV array output current. Fig. 2shows a PV array which is coupled with a DC/DC boost converterand connected to a rechargeable battery. When the power switchS is on, the PV output current is governed by

vpt L_ict 21

where L is the inductance of the boost converter. When the switch Sis off, the current is governed by

vpt vbt L_ict 22

where vb(t) is the voltage of the rechargeable battery. If the switchis driven by pulse width modulation (PWM) signal, the state aver-aging dynamics for the PV output current is governed by

vpt 1 dtvbt L_ict 23

where d(t) is the duty ratio of the PWM signal. Assume the changein the battery voltage vb(t) is small and it can be approximated by U,(23) can be written as

vpt U Udt L_ict 24

Consider a PI controller of the form

GPIs KP KIs

25vp

ic

vb

L

SPV panel +

-

Fig. 2. A schematic diagram for the PV system.where KP and KI are constants, it is connected to the boost converterto form a closed loop system as shown in Fig. 3. If the current con-trol loop is very fast, the disturbances caused by vp(t) and vb(t) canbe eliminated by the integral action. The closed loop characteristicequation for the current control loop can be approximated as

Ds 1 KPs KIULs2

0 26

The undamped natural frequency of the control loop is given by

xi ffiffiffiffiffiffiffiffiffiKIUL

r27

and the damping ratio of the control loop is given by

fi KPU2xiL

28

The bandwidth and damping ratio of the current control loopcan easily be set by KP and KI based on (27) and (28). The requiredduty ratio for the switch S can be obtained as

dt KPicrt ict KIZ

icrt ictdt 29

where icr(t) is the required output current from the PV array.

4. Implementation of the maximum power point controller

To test the performance of the proposed maximum power pointcontroller, five (330 W, 40 V) PV panels were connected in series toserve as the renewable energy source. The open-circuit voltage andshort-circuit current for the PV panels were 48.58 V and 9.02 A,respectively. To protect the PV panels from the hot-spot problem,by-pass diodes are connected in parallel with different PV panelsas shown in Fig. 4. For the DC/DC boost converter, power MOSFET,SiHP22N60S, is employed to realize the switch S and the induc-tance of the boost inductor is 10 mH. A LiFePO4 battery pack(10 A h, 320 V) is used as the energy storage because the character-istics of Lithium ion batteries [15] are better. Instead of using bat-teries, it is also possible to connect to the utility grid [16] with asuitable inverter. The switching frequency for the PWM signal is60 kHz. An industrial PC is used to sample all required variablesand to implement the control loop. The sampling frequency is10 kHz. For the current control loop, the bandwidth is 500 Hzand the damping ratio is 1. From (27) and (28), the required PIcontroller

GPIs 0:1963308:4

s30

To test the tracking performance of the current control and theeffectiveness of current sweeping in maximum power point track-ing, the converter input current is commanded to follow a 0.5 Hztriangular signal which increases from 0 to 9.02 A and thendecreases from 9.02 A back to 0. At 25 C, two cases have beentested and their short-circuit currents are listed in Table 1. Regard-ing off-line tests for the PV panel, the voltage to current and power

vp

Fig. 4. Configuration of the PV array.

Table 1Short-circuit currents for different PV panels.

Panel 1 Panel 2 Panel 3 Panel 4 Panel 5

Case 1 7A 7A 7A 7A 7ACase 2 7A 7A 5A 5A 5A

252 K.M. Tsang, W.L. Chan / Energy Conversion and Management 93 (2015) 249258to current characteristic curves for the two cases are shown inFig. 5. For case 1, there is only one peak in the power curve. Forcase 2, there are multiple peaks. The maximum power points forthe case 1 and case 2 are at 6.3 A and 4.7 A respectively. Fig. 6shows the output current, output voltage and output power fromthe PV array for case 1 during the current sweeping test. The PVoutput current tracks the reference signal very well up to the limitof the PV panel. There is a small overshoot of the PV output currentat the end of the ramping up action. This is due to the inherentcapacitance of the PV panel. Once it has been discharged, the out-put current quickly falls back to its limiting value. As shown inFig. 6, the two maximum power points during the ramping upand down are if = 6.71 A and ib = 5.62 A respectively. The estimatedmaximum power point from (19) is 6.165 A which is very close tothe actual maximum power point of 6.3 A. A finer local searchcould quickly locate the true maximum power point. Fig. 7 showsthe test results for case 2 for the same current sweeping test. Againthe PV output current tracks the reference current very well. FromFig. 7, the two maximum power points during the ramping up anddown are if = 5.31 A and ib = 3.75 A respectively. The estimatedmaximum power point using (19) is 4.53 A. Again it is very closeto the true maximum power point of 4.7 A. It should be noted thatthe local maximum power point searching mechanism failed totrack the new maximum power point for case 2 if the initial stateof the PV panels is case 1. The local searching mechanism mighteasily trap around the local maximum which is around 6.3 A.5. MPPT algorithm

The full current sweeping test cannot be carried out all the time.Otherwise the total power that can be extracted from the PV arraywill be very limited. The full current sweeping test will be carriedout when the change in the extracted power is more than a certainthreshold. The threshold cannot be too small or too big. If thethreshold is too small, full current sweeping will be carried outmost of the time. If the threshold is too big, full current sweepingwill rarely be carried out. The threshold should be set to around 510% of the rated maximum power of the PV system. For the rest ofthe time, a smaller scale current sweeping test is carried out. Aflowchart for the proposed MPPT algorithm is shown in Fig. 8.The procedures for carrying out the global and local MPPT can besummarized as follows:

(a) Set the sampling frequency for the control system as Fs, theperiod of the sweeping test as 2NT, the amplitude of triangu-lar signal for full test as IM/2 and the amplitude of triangularsignal for fine tuning test as DIM, where IM is the maximumcurrent that could be delivered by the PV panel and DIM isthe amplitude of the small perturbation. Initially set ic = 0,Pm = Pf = Pb = 0.

(b) Apply low-pass filtering on vp(t) and ic(t) to remove effectscaused by high frequency switching and sample the filteredsignals vp(k) and ic(k) from the PV array at time step k. Thecutoff frequency of the low-pass filters is set to a valuewhich should be higher than the bandwidth of the currentcontrol loop but lower than the sampling frequency Fs ofthe control system and the switching frequency of theconverter.

(c) Record the current maximum power point ic and set themaximum power P = Pm. Initially set if = ib = ic, Pf = 0 andPb = 0.

(d) Set the small scale current sweeping test signal as

Forward sweepingir(k) = ic + 2(k 1)DIM/NT, k = 1, 2, . . ., NTFs/2 + 1.Backward sweepingir(k) = ic + DIM 2(k NTFs/2 1)DIM/NT, k = NTFs/2 + 2,NTFs/2 + 3, . . ., 3NTFs/2 + 1.Forward sweepingir(k) = ic DIM + 2(k 3NTFs/2 1)DIM/NT, k = 3NTFs/2 + 2,3NTFs/2 + 3, . . ., 2NTFs + 1.

(e) Set k = 1.(f) Compute the running average of the extracted power asPek aPek 1 1 aPk 1

where 0 < a < 1 is a constant.

0 2 4 6 80

50

100

150

200

250

300

Current (A)

Vol

tage

(V

)

0 2 4 6 80

500

1000

1500

Current (A)

Pow

er (

W)

(a) Case 1

0 2 4 6 80

50

100

150

200

250

300

Current (A)

Vol

tage

(V

)

0 2 4 6 80

500

1000

1500

Current (A)

Pow

er (

W)

(b) Case 2

Fig. 5. Current to voltage and current to power characteristics for the two tested cases.

K.M. Tsang, W.L. Chan / Energy Conversion and Management 93 (2015) 249258 253(g) Sample vp(k) and ic(k). Calculate the instantaneous powerP(k) = vp(k)ic(k).

(h) For forward sweeping, if P(k) > Pf, set if = ic(k) and Pf = P(k).

For backward sweeping, if P(k) > Pb, set ib = ic(k) and Pb = P(k).

(i) If jPekPkjP > e, go to step (m) and start a full currentmaxsweeping test to identify the global maximum point. Pmaxis the ideal maximum power of the PV panels.

(j) Set k = k + 1 and go to step (f) until k = 2NTFs + 1.(k) Calculate ic and Pm based on (19) and (20) asic if ib2

Pm Pf Pb

2

(l) Go to step (c).(m) Initially set ic = 0, Pm = Pf = Pb = 0. Set the full current sweep-

ing test signal as

Forward sweepingir(k) = ic + 2(k 1)IM/NT, k = 1, 2, . . ., (2IM ic)NTFs/2IM + 1.Backward sweepingir(k) = ic + 2IM 2(k (2IM ic)NTFs/2IM 1)IM/NT,k = (2IM ic)NTFs/2IM + 2, (2IM ic) NTFs/2IM + 3, . . .,(2IM ic)NTFs/2IM + NTFs + 1.Forward sweepingir(k) = ic + 2(k (2IM ic)NTFs/2IM + NTFs 1)IM/NT,k = (2IM ic)NTFs/2IM + NTFs + 2, (2IM ic)NTFs/2IM + NTFs +3, . . ., 2NTFs + 1.

(n) Set k = 1.(o) Calculate the instantaneous power P(k) = vp(k)ic(k).(p) For forward sweeping, if P(k) > Pf, set if = ic(k) and Pf = P(k).For backward sweeping, if P(k) > Pb, set ib = ic(k) and Pb = -P(k).

(q) Set k = k + 1 and go to step (o) until k = 2NTFs + 1.

(r) Calculate ic and Pm based on (19) and (20) asic if ib2

Pm Pf Pb

2

(s) Reset running average power to Pe(0) = Pm.(t) Go to step (c).

6. Experimental results

To test the tracking performance of the proposed MPPT algo-rithm, the operation of the PV panel is switching between case 1and case 2. The period for the sweeping test is 0.8 s in order tospeed up the tracking process. The magnitude for DIM is set to0.09 A which is about 1% of IM. Initially, the full-scale currentsweeping is disabled and only local searching mechanism basedon the small scale current sweeping test is employed to identifythe maximum power point. Fig. 9 shows the tracking performanceof the small scale current sweeping test when the PV output cur-rent is initially 0 A. The PV panel operates initially at case 1 andswitched to case 2 after 62 s. Under case 1 situation, the maximumpower point is tracked in about 50 s and the PV output currentstays around the maximum power point onwards. When thecondition switched to case 2 after 62 s, the small scale currentsweeping test failed to track the new maximum power point andthe PV output current is trapped at the local maximum powerpoint which is around 6.4 A.

(a) Maximum power point during ramping up for case 1 Channel 1 PV output voltageChannel 2 PV output current Channel 3 PV output power

vp ic

vp

ic

(b) Maximum power point during ramping down for case 1Channel 1 PV output voltageChannel 2 PV output currentChannel 3 PV output power

vp

ic

vp ic

Fig. 6. Output voltage, output current and output power for case 1.

254 K.M. Tsang, W.L. Chan / Energy Conversion and Management 93 (2015) 249258When the full-scale current sweeping test is enabled, the over-all tracking speed has been improved. The condition for the full-scale sweeping test to carry out is governed by e and it is set to0.1 during the test. a is set to 0.9. Fig. 10 shows the tracking perfor-mance when the full-scale sweeping test is enabled. Again initialPV output current is set to zero and the PV panel operates initially

(a) Maximum power point during ramping up for case 2 Channel 1 PV output voltageChannel 2 PV output currentChannel 3 PV output power

vp ic

vp

ic

(b) Maximum power point during ramping down for case 2Channel 1 PV output voltageChannel 2 PV output currentChannel 3 PV output power

vp ic

ic

vp

Fig. 7. Output voltage, output current and output power for case 2.

K.M. Tsang, W.L. Chan / Energy Conversion and Management 93 (2015) 249258 255at case 1 and switched to case 2 after 42 s. Under case 1 situation,the full-scale current sweeping test is activated and the maximumpower point is tracked in about 12 s. The PV output current staysaround the maximum power point onwards. When the conditionswitched to case 2 after 42 s, the full-scale sweeping tests are acti-vated again and the new maximum power point is tracked in less

Initialize Im, Im, ic*, Pmax. Set up the full current sweeping signal.

Set Pf=Pb=0, Pe(0)=Pm. Record ic*. Set up small scale current sweeping signal.

k=1

Sample vp(k) and ic(k). Calculate P(k) and Pe(k).

Is reference current ramping up?

Is P(k) > Pf ?

Pf = P(k)

Is P(k) > Pb ?

Pb = P(k)

Is change of power < ?

k = k + 1

Has completed 1 cycle ?

Yes

Yes

Yes

Yes

No

No No

Calculate ic* and Pm.

Yes

k = 1

No

Change reference signal to full scale. Set ic* = 0, Pf = Pb = 0.No

Is reference current ramping up?

Is P(k) > Pf ?

Pf = P(k)

Is P(k) > Pb ?

Pb = P(k)

Yes

Yes Yes

No

No No

Sample vp(k) and ic(k). Calculate P(k) and Pe(k).

k = k + 1

Has completed 1 cycle ?

Calculate ic* and Pm.

Yes

No

Fig. 8. Flowchart for the MPPT algorithm.

256 K.M. Tsang, W.L. Chan / Energy Conversion and Management 93 (2015) 249258than 5 s. The PV output current converged to around 4.8 A. The out-put power delivered by the PV panels is very much higher than thecase when only local searching mechanism is used. Unlike otherlocal searching schemes, the proposed searching mechanism couldescape from the local maximum and search for the global maxi-mum power point efficiently.

Channel 1 PV output voltageChannel 2 PV output current Channel 3 PV output power

vp ic

ic

vp

Fig. 9. Output voltage, output current and output power using small scale current sweeping.

Channel 1 PV output voltageChannel 2 PV output current Channel 3 PV output power

vp ic

ic

vp

Fig. 10. Output voltage, output current and output power using full-scale and small current sweeping.

K.M. Tsang, W.L. Chan / Energy Conversion and Management 93 (2015) 249258 257

258 K.M. Tsang, W.L. Chan / Energy Conversion and Management 93 (2015) 2492587. Conclusions

Maximum power point tracking based on current sweeping hasbeen successfully implemented. The average value of the maxi-mum power points during forward and backward sweeping pro-vides a good estimate of the actual maximum power point. Thesearching mechanism performs well under partial shading condi-tions and global maximum power point can easily be tracked bythe proposed searching scheme. Experimental results demonstratethe effectiveness of the searching mechanism in identifying themaximum power points under normal and partial shadingconditions.

Acknowledgment

The authors gratefully acknowledge the support of the HongKong Polytechnic University.

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Maximum power point tracking for PV systems under partial shading conditions using current sweeping1 Introduction2 PV model and its response to current excitation3 PV array output current control4 Implementation of the maximum power point controller5 MPPT algorithm6 Experimental results7 ConclusionsAcknowledgmentReferences