-
Direct Duty Ratio Controlled MPPT Algorithm forBoost Converter
in Continuous and Discontinuous
Modes of OperationPallavi Bharadwaj, Vinod John
Department Electrical Engineering, Indian Institute of Science
Bangalore
Abstract—Demand of increased lifetime, compact size andreduced
cost of PV systems has led to the incorporation of LCLfilters in
the boost converter of a grid connected PV system.Additional
filtering offered at the input by LCL filter reduces theinductance
of boost converter. This calls for an algorithm whichcan track the
maximum power in both discontinuous (DCM)and continuous conduction
modes (CCM) of boost converteroperation accurately. Direct duty
ratio based perturb and observealgorithm for MPPT has been
implemented in real time usingVHDL based FPGA. The sensitivity of
the algorithm to DCMand CCM operation of converter is analysed. It
is shown thatthe duty ratio increment used in the MPPT algorithm
needs toevaluate. The direct duty ratio based approach is found to
workwell with both modes of operation, even with mode
transitions.
Index Terms—Solar, photovoltaic, maximum powerpoint tracking
(MPPT), boost DC-DC converter,continuous/discontinuous conduction
mode, perturb andobserve (P & O).
I. INTRODUCTION
Power converters are normally connected at the output ofPV
panels as an interface between panel and load. Use of DC-DC
converters such as buck, boost and cuk converter have beenreported
in literature. Buck converter as used in [11], may notbe suitable
for low voltage PV systems, specially when gridconnection is
involved. Cuk converter as used in [10], requiresan additional set
of LC filter as compared to buck and boostconverters. In this work
boost converter has been used as thePV system has an MPP voltage of
15V and DC bus voltageneeds to be higher for grid connection
through an inverter. AnLCL filter has been included at the input of
the boost converterwhich reduces the inductance of boost, which can
further leadto design of an optimised converter having low cost,
low sizeand high efficiency. But low inductance also leads to
DCMoperation, therefore need arises for a robust MPPT
algorithmwhich has tracking ability with mode transitions
involved.
Maximum power point tracking (MPPT) is a method ofobtaining the
maximum possible power out of static solarpanels for given
irradiation and temperature conditions. Someof the commonly used
MPPT techniques include perturband observe (P & O) algorithm,
incremental conductancealgorithm, open circuit voltage and short
circuit current basedmethods [7]. P & O is widely used in PV
MPPT applications
This work is supported by Department of Information Technology,
Govt ofIndia under NaMPET Phase 2 under Project on Mini Full
Spectrum Simulator.
PVmodule
L D
Cdc
R0
Cf
Ls Rs
Sw
Req
Inverter
grid
Fig. 1. Circuit diagram of grid connected PV system.
because it is relatively simple and has real time tracking
abilityof MPP [7]. P & O algorithm has several variations
basedon control parameter involved. First is the voltage based
P& O which is the most common [8], [10]–[12]. Second
oneinvolves current perturbation instead of voltage [9]. In
boththese methods duty ratio is commonly used as an
indirectvariable to actually change the voltage or current [11].
Thirdkind of P & O is called as direct duty ratio control
[8],[13], wherein duty ratio is the direct control variable and
itundergoes step changes in order to achieve MPPT.
Currentperturbation method is not commonly used as it involves
shortcircuit current measurement, which poses difficulty in
practicalimplementation. Out of voltage based and direct duty
ratiobased P & O methods latter one is preferred for this
workas direct duty ratio control offers better energy utilisation
andimproved system stability than reference voltage control
[8].
The main focus of this work is the detailed study of directduty
ratio based algorithm, to study its behaviour for differentmodes of
converter operation namely - continuous conductionmode (CCM) and
discontinuous conduction mode (DCM). Ithas been shown that duty
ratio based algorithm is effective forboth modes of operation for
boost converter.
II. DUTY RATIO BASED MPPT ALGORITHMA. Theoretical background
Fig. 1 shows a grid connected PV system wherein a PVpanel feeds
a boost converter with input LCL filter, whichfurther feeds the
grid via inverter. The input LCL filter consistsof stray inductance
Ls and resistance Rs of cables connectingpanel on roof, to the
converter located in laboratory. Addi-tional capacitor Cf and boost
inductor L together form LCL
-
0 5 10 150
10
20
30
V(V)
P(W
)
0 5 10 150
2
4
V(V)
I(A) d decd inc
- - load line--- panel characteristic
Fig. 2. Determination of operating point of a solar PV panel
dependson irradiation, temperature and terminal load resistance.
The projection ofoperating point is taken on panel’s Power-Voltage
curve, shown for threeloading conditions obtained by operating at 3
different duty cycles.
filter. This combined LCL filter acts as an attenuator to
highfrequency boost inductor current ripple and effectively onlyDC
current flows from the PV source thereby enhancing itsefficiency.
Due to the incorporation of LCL filter in the circuitboost inductor
value can be reduced for same ripple current.This gives reduced
cost and size benefits. However reductionin L value may cause
discontinuous mode of operation ofboost converter. So the MPPT
algorithm needs to have MPPtracking ability in both DCM/CCM. For
this the working ofdirect duty ratio MPPT algorithm is analysed in
continuousand discontinuous modes of operations of boost
converter.
The basic principle behind any MPPT algorithm is digitalcontrol
of converter in such a manner that the load seenby PV panel
corresponds to the maximum possible poweroutput for any given load.
Consider the current-voltage andcorresponding power-voltage
characteristic of a PV panel,as shown in Fig. 2. The operating
point is obtained by theintersection of solar panel’s
current-voltage (I-V) curve andload line which is dependent on load
connected. The solarpanel terminal equation [1] is written as
I = IL − Is(eV +IRsmnsVt − 1) − V + IRs
Rsh(1)
And the equation of load line for a load resistance ‘R’ can
bewritten as
I = V/R (2)
The intersection of the two above mentioned equations isshown in
Fig. 2 for three different cases of load resistance. Thecurrent
gain, voltage gain and equivalent resistance reflectedat the source
terminals depends on the mode of operation ofthe boost converter,
as given in Table I. Symbols shown inTable I are:- k = 2LRoTs , Ro
=output resistance, Ts =switchingperiod, L = boost inductance, d =
duty ratio of switch Sw =
TonToff+Ton
. To visualise the effect of duty ratio on equivalentresistance
(Req) it is plotted in Fig. 3 for CCM mode andDCM mode. In DCM the
equivalent resistance is dependenton ‘k’, therefore it is shown for
two different values of ‘k’.
TABLE ICOMPARISON OF GAINS AND EQUIVALENT RESISTANCE FOR CCM
AND
DCM OPERATION FOR A BOOST CONVERTER.
Equivalent Resistance CCM DCM
Current Gain (1− d)
(k +√k2 + 4kd2
2d
)(d+k +√k2 + 4kd2
2d
)Voltage Gain
1
(1− d)
(d+k +√k2 + 4kd2
2d
)(k +√k2 + 4kd2
2d
)Equivalent Resistance Ro(1− d)2 Ro
(k +√k2 + 4kd2
2d
)2(d+k +√k2 + 4kd2
2d
)2TABLE II
CIRCUIT PARAMETERS FOR THREE DIFFERENT BOOST
CONVERTERCONFIGURATIONS
Case k Ro L TsA 0.024 160Ω 100µH 50µsB 0.14 200Ω 700µH 50µsC
0.16 300Ω 1200µH 50µs
0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
1
Duty Ratio (d)
R eq/
R oCCMDCM, k = 0.024DCM, k = 0.140
Fig. 3. Variation of equivalent resistance with duty ratio in
CCM mode andDCM mode.
For values of ‘k’ higher than 0.15 converter operates in
CCMalways and equivalent resistance in CCM mode is independentof
‘k’. In this paper analysis is done for 3 cases of boostconverter
configurations corresponding to the three differentcombinations of
Ro, L and Ts values. These are listed in TableII.
As discussed before, operating point of a PV panel de-pends on
the panel’s current-voltage characteristic (for giventemperature
and irradiation condition) and the load line. Theslope of the load
line is inverse of equivalent resistance asseen by the PV panel.
From Table I it can be observed thatReq is a function of duty
ratio. By changing the duty ratio ofthe boost converter, operating
point for the PV panel can becontrolled. For a particular set of
load resistance, inductanceand switching frequency of the boost
converter, there willbe a range of duty ratio for which converter
will operate in
-
0.2 0.4 0.6 0.8 1
0.020.040.060.080.1
0.120.140.16
DutyCRatio(d)
d×(1
-d)2
d(1-d)2 vsCd
LC=C700µ
H,CRCo=C200ΩLC=C100
µH,CRCo=C160
ΩLC=C1200µH,CRCo=C300Ω
kC=C0.14
kC=C0.16
kC=C0.024
CCM
CCM DCM CCM
DCM DCM DCM CCMCCM
Fig. 4. DCM-CCM boundary is given by the intersection of d(1−d)2
= k =2L
RoTsfor boost converter. Here duty ratio range for CCM/DCM
operation
are shown for three different sets of Ro, L values, with Ts
fixed at 50µs.
CCM and in DCM for remaining range. CCM-DCM boundarycan be
observed in Fig. 4, wherein three cases are showncorresponding to
the ones listed in Table II.The parameter ‘k’ is directly
proportional to inductance andswitching frequency. The value of ‘k’
falls for small inductancevalue as well as lower switching
frequency. Lower inductancevalue leads to lower size as well as
lower cost of converter.Also, the filtering objective can be met
with a smaller inductorL, and this can also lead to higher
efficiency. However if ‘k’value is small then range of DCM
operation is large. If MPPcan be tracked effectively in DCM then
the converter cost andsize can be minimised and higher efficiency
can be achieved.
From Fig. 4 it is clear that for a given duty ratio,
theoperation of converter in CCM or DCM mode is determinedby Ro, L,
Ts values. Whether MPP falls within the rangespanned by ‘d’
variation in CCM region or DCM region,solely depends on Ro, L, Ts
values. Also it can be observedfrom Table I and Fig. 3 that duty
ratio affects the equivalentresistance differently in DCM and CCM.
In other words, theeffect of duty ratio variation on the slope of
load line differsfrom CCM to DCM. This effect is discussed in
detail inFig. 5 corresponding to three different converter
configurationsnamely case A, B and C as specified in Table II and
for twodifferent conditions for solar panel irradiation. Solar
panel wasirradiated with Sun and a 500W hallogen lamp separately
toget different characteristics of 10W polycrystalline solar
panel[4]. Consider case A of boost converter operation as
specifiedin Table II. Owing to low value of ‘k’ DCM operation
isobserved for a wide range of duty ratio from 0.05 to 0.85 asshown
in Fig. 5(a). This is as expected from Fig. 4. For case B‘k’ value
is higher, this gives narrow range of DCM operationas shown in Fig.
5(b). However for case C as ‘k’ value is largeenough, it doesnot
intersect CCM-DCM boundary as shownin Fig. 4. Thus Fig. 5(c) shows
complete CCM operation asduty ratio varies from 0 to 1. It can be
observed that forboth CCM and DCM operation as d increases the
slope ofload line increases, therefore even if there is a
transition fromCCM to DCM still complete I-V curve can be traced.
However
0 5 10 15 200
5
10
15
20
25
30
V(V)
P(W
) P increasesV increases
MPP
P decreases
V increases
W
X Y
Z
Fig. 6. Power voltage characteristics for an array of PV panels,
marked withMPP and a boundary which divides two sides of hill. W,
X, Y, Z mark fourpossible operating points on the power - voltage
curve.
accuracy of tracking MPP will differ. This calls for
definationof a term called as sensitivity of MPP tracking. This is
definedas change in power compared to change in duty ratio
aroundMPP. Sensitivity can be physically interpreted by how
denselyload lines cover MPP region. Higher density corresponds
tohigher sensitivity. Fig. 5(a) shows better sensitivity comparedto
Fig. 5(b). Fig. 5(a) also corresponds case A with lowerinductance
value compared to case B with higher inductance.Therefore for a
system, selection of L can be done consideringeffective range of Ro
which for this case is Ro ≥ 160Ω, assmaller L can give both cost
and MPPT benefits.
Sensitivity can also be improved by going for a smallerstep size
∆d, but this increases tracking time. As step size isreduced from
0.05 in Fig. 5(c) to 0.01 in Fig. 5(d) sensitivityimproves from
0.15W for 0.05 to 0.02W for 0.01. Last twocases shown in Fig. 5
correspond to laboratory setup whereinbetter control over
irradiation conditions is achieved by usinga hallogen lamp. Results
for step size of 0.05 are shown inFig. 5(e) and for 0.01 in Fig.
5(f) showing better sensitivity.
B. The MPPT algorithm
Consider power-voltage curve of a PV panel as shown inFig. 6. On
left side of MPP, power (P) and voltage (V) are inphase, on right
side power and voltage are out of phase [3]. Bymaking a small
perturbation in the duty ratio, a new operatingpoint is obtained.
If P and V increase with this perturbationthe operating point is in
the left side of MPP, and furthermovement in the direction of
perturbation will lead it to topof the hill. If P reduces with
perturbation, V either increasesor decreases. In both cases the
direction of ‘d’ perturbationneeds to be changed. From Section II-A
it is known that as‘d’ increases load line moves up in
anti-clockwise direction.These facts can be combined in a flowchart
as given in Fig. 7.Fig. 7 shows that for a ‘∆d’ there are 4
possibilities for powerand voltage to increase or decrease. Based
on changes in Vand P one can judge the way the operating point has
moved onthe sides of hill, and then increase or decrease ‘d’
further toreach the top of the hill which corresponds to the MPP.
HereW, X, Y, Z correspond to operating points shown in Fig. 6.
-
0 5 10 15 20
0.20.40.60.81
I(A)
V(V)
0 5 10 15 200
10
20
P(W)
V(V)
DCM
(a)
0 5 10 15 2000.20.40.60.8
I(A)
V(V)
0 5 10 15 200
10
20
P(W)
V(V)
DCM
(b)
0 5 10 15 200.20.40.60.81
I(A)
V(V)
0 5 10 15 200
5
10
P(W)
V(V)(c)
0 5 10 15 2000.20.40.60.8
I(A)
V(V)
0 5 10 15 200
5
10
P(W)
V(V)(d)
0 5 10 150
0.1
I(A)
V(V)
0 5 10 150
1
2
P(W)
V(V)(e)
0 5 10 150
0.1
0.2
I(A)
V(V)
0 5 10 150
1
2
P(W)
V(V)(f)
Fig. 5. Measured Current-Voltage (I-V) characteristics of 10W
solar panel superimposed with family of load lines for varying duty
ratio for a boost converter.Duty ratio increases from 0 to 1 in
fixed step ∆d. (a) Case A : Ro = 160Ω, L = 100µH , Ts = 50µs. ∆d =
0.05. Projection on P-V curve shows DCMoperation for d = 0.05 to
0.85. (b) Case B : Ro = 200Ω, L = 700µH , Ts = 50µs. ∆d = 0.05.
Projection on P-V curve shows DCM operation for d =0.25 to 0.40.
(c) Case C : Ro = 300Ω, L = 1200µH , Ts = 50µs. ∆d = 0.05. For
complete d variation only CCM operation observed. Projection onP-V
curve shows MPP region (d = 0.60-0.65). (d) Same as (c) with ∆d =
0.01. Projection on P-V curve shows MPP region covered more densely
(d =0.62-0.64). MPP occurs at d = 0.63. (e) Case C, ∆d = 0.05, MPP
region projected on P-V curve. (f) Boost converter case C. ∆d =
0.01. MPP tracked withhigher accuracy at d = 0.25. Panel’s I-V and
P-V curve shown in (a), (b), (c) and (d) measured on 15/11/13,
12:30pm, Bangalore, panel temperature 40oC.Panel’s I-V and P-V
curve in (e) and (f) measured with panel irradiated with 500W
hallogen lamp placed at 0.3m height from panel.
-
OUT dn
IN Vn, InPn = Vn˟In
IS Pn>Pn-1
IS Vn>Vn-1
W to X Z to Y Y to Z X to W
ISVn>Vn-1
dn = dn-Δd dn = dn+Δd dn = dn-Δddn = dn+Δd
yes no
yes no yes no
Fig. 7. Flowchart for duty ratio based P & O MPPT
algorithm.
TABLE IIIBOOST CONVERTER PARAMETERS
Output Load Resistance (Ro) 300ΩBoost Inductance (L) 1.2 mH
Switching Frequency (fsw) 20 kHzInput Filter capacitance (Cf )
150 µF
Output Filter capacitance (Cdc) 4400 µFInput Stray Resistance
(Rs) 22.23 mΩInput Stray Inductance (Ls) 7.08 µH
C. Implementation and results
1) Implementation: This algorithm was coded in VHDLand
implemented on a FPGA platform, which further con-trolled the boost
converter fed by a 10W PV panel via a LCLfilter. The LCL filter
ensures that boost inductor current rippleis not carried over to
the PV panel and hence leads to panel’slong life. To emulate sun, a
500W halogen lamp is arranged,which irradiates the panel at a
distance of 0.3m. The intensityof light is controlled by an
autotransformer which feeds thehalogen lamp. Converter parameters
are chosen so as to ensureCCM operation throughout duty ratio
variation, they are givenin Table III, circuit diagram along with
MPPT block is shownin Fig. 8. Hardware setup is shown in Fig.
9.
2) Results: Table IV shows the results with the experimen-tally
tracked maximum power point for laboratory setup. Thisincludes a
10W polycrystalline PV panel irradiated with a500W halogen lamp.
Boost converter specifications are givenin Table III. Table IV
quantifies the tracked maximum powerpoint for the given setup. Fig.
10 shows maximum power
PVmodule
L D
R0Cf
Ls Rs
Sw
MPPTI
Ipv
Vpv
V d
Cdc V0
Fig. 8. Circuit showing implementation of MPPT.
HalogenFLamp
10WFPVFPanel
InverterF+FBoostFConverter ResistiveFLoad
1.2mHFInductor
FPGA
ACFVariac
Fig. 9. Hardware setup for MPPT.
TABLE IVRESULTS WITH MPP TRACKED
Input Voltage 16.6VInput Current 0.12ADuty Ratio 0.24
Output Voltage theoretical(ideal) 21.8 VOutput Voltage
theoretical(practical) 21 V
Output Voltage measured 20.4 V
point tracked in steady state for duty ratio perturbation
stepsize of 0.01. It shows panel voltage, current and duty
ratio.Results were also obtained for ∆d = 0.05 and that gives∆P =
0.2W , which matches theoretically expected value asmentioned in
Section IIA. Fig. 11 shows filtering by LCL filter,it shows panel
current, which is 0.12A dc and boost currentwhich has 0.2A
peak-peak ripple. MPP tracking is shown onpower-voltage plane in
Fig. 12. Fig. 13 shows effect of varyingintensity of light on
tracking of maximum power point againon power-voltage plane. It
shows as the light intensity reducesto zero, locus of MPP shifts
from 16V, 2W to 0V, 0W.
CH1CH2
CH4
Fig. 10. Panel voltage (CH1), panel current (CH2) and duty ratio
(CH4)using the boost switch gating pulse showing the tracking of
MPP and steadystate operation. Scale :: CH1 - 2V/div, sensor gain -
0.3V/V, Vmpp = 16.6V;CH2 - 0.5V/div, sensor gain - 6.67V/A, Impp =
0.12A; CH4 - 5V/div, timescale - 10µs/div, duty ratio = 0.24.
-
CH1CH2
CH4
Fig. 11. Panel voltage (CH1), panel current (CH2) and boost
inductor current(CH4) showing filtering by LCL filter at the input.
Scale :: CH1 - 2V/div,sensor gain - 0.3V/V, Vmpp = 16.6V; CH2 -
0.5V/div, sensor gain - 6.67V/A,Impp = 0.12A; CH4 - 10mV/div,
sensor gain - 0.1V/A, ILmean = 0.12A,ILpk−pk = 0.2A.
V
P
Fig. 12. PV panel power voltage plane (power-y axis, voltage-x
axis),showing traking of maximum power point with steady state
operation.Scale :: X axis : CH1 - 2V/div, sensor gain - 0.3V/V,
Vmpp = 16.6VY axis : CH2 - 0.5V/div, scaling - 0.4V/W, Pmpp =
2W.
III. CONCLUSION
The incorporation of LCL filter between PV panel andboost
converter results in lower boost inductance value whichleads to
reduced cost and size benefits. But reduction ininductance leads to
higher probability of DCM operation ofboost converter. The direct
duty ratio based MPPT algorithm isfound capable of tracking MPP
despite of mode changes, as inboth modes duty ratio increase
traverses I-V curve of PV panelin same direction. However it has
been found that sensitivityof MPP tracking depends on the mode of
operation. This issueis resolved by changing the perturbation step
size of duty ratiofor desired sensitivity. Experimental results
show the filteringaction of LCL filter and maximum power point
tracking forCCM operation with a duty ratio perturbation step size
of 0.01.It has been observed that a higher step size perturbs the
powerin a wider range thereby giving lower tracking accuracy,
lower
V
P
Fig. 13. Tracking of MPP with varying intensity of light, shown
onpower-voltage plane. MPP moves towards origin as light intensity
reduces.Scale :: X axis : CH1 - 2V/div, sensor gain - 0.3V/V,
voltage varies from16.6V to 0V; Y axis : CH2 - 0.5V/div, scaling -
0.4V/W, power varies from2W to 0W.
average power output but higher tracking speeds.
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