Fourth-Order Buck Converter for Maximum Power Point Tracking Applications

Fourth-Order Buck Converter

for Maximum Power Point

Tracking Applications

MUMMADI VEERACHARY, Senior Member, IEEE

Indian Institute of Technology Delhi

Photovoltaic arrays (PVAs) need an intermediate maximum

power point tracker as their v-i characteristics are nonlinear.

Application of switch-mode dc-dc converters are popular in

this area and the buck topology is widely used in these power

tracking applications. However, the buck converter with an

input L-C filter, with insufficient damping, will exhibit unwanted

oscillations, or it may operate at suboptimal power points for

certain solar insolations. Suitable damping must be designed

otherwise the maximum power point (MPP) becomes unstable.

Because of the variable impedance characteristic of PVA the

design of optimal damping, suitable for all solar insolations, is a

complex task. In order to eliminate these problems a fourth-order

buck converter, which will track maximum power (MP) at all

solar insolations, is proposed for the photovoltaic (PV) power

tracking applications. Mathematical models of the proposed

converter are formulated and then boundary conditions, under

which the converter capable of tracking MP, are obtained. The

combined PV power tracking scheme is simulated in PSIM and

then power tracking performance characteristics are generated.

Performance of the proposed topology is compared with the buck

converter with input filter. The proposed converter effectiveness,

in power tracking applications, is verified through experimental

studies. Micro-controller, dsPIC30F6010, is employed in the

real-time implementation of the perturb and observe (P & O)

tracking algorithm.

Manuscript received June 15, 2008; revised May 22, 2009; released

for publication November 6, 2009.

IEEE Log No. T-AES/47/2/940820.

Refereeing of this contribution was handled by S. Mazumder.

Author’s address: Dept. of Electrical Engineering, Indian Institute

of Technology Delhi, Hauz Khas, New Delhi 110016, India, E-mail:

([email protected]).

0018-9251/11/$26.00 c° 2011 IEEE

I. INTRODUCTION

Clean and renewable energy source such as

photovoltaic (PV) power generation is expected

as one of the key technologies to mitigate global

warming. Since the PV source’s exhibit nonlinear

v-i characteristics their power output mainly depend

on the nature of the load connected to it. Hence,

direct load connection to the PV array (PVA) system

results in poor overall efficiency. As the solar panels

are still expensive their life cycle cost minimization

is essential. To achieve some of these goals, direct

connected PV systems are being replaced by PV

systems having an intermediate maximum power

point tracking (MPPT) converter. Several MPPT

algorithms with different converter combinations

[1—17] have been proposed and used to extract

maximum power (MP) from the PVA under different

operating conditions. Some of the well-established

power tracking methods are: 1) perturb and observe

algorithm (P & O), 2) incremental conductance

method (ICM), 3) voltage-based method (VBM), and

4) search-based methods (SBM). All these methods

have evolved one after another to overcome some

of the disadvantages present in other methods. Each

one of these schemes, mentioned above, has their

own advantages as well as limitations. However, the

suitability and its final selection is mainly decided

by the application and operating conditions. Hence,

the designer has to make an exercise before choosing

a particular scheme for the tracking purpose. The

main concern while choosing a tracking scheme

is the accuracy and tracking speed requirement.

Thus, a tradeoff design should be chosen so that

it results in better dynamic response as well as

the minimum steady-state oscillations in the PV

power.

The performance of a PV system depends on

several factors, of which the most important ones

are: 1) type of power converter used, 2) tracking

methodology employed, and 3) nature of filters

employed. Hence, each one of these elements is

equally responsible for the overall performance

improvement. In this direction, the designer has to

make substantial efforts while performing the PV

system design. Several studies have been conducted

and reported on the usage of intermediate power

converters for power tracking applications, which are:

conventional buck, boost, and buck-boost topologies.

In power supply application buck based derived

topologies have been reported in the literature [18]

to realize improved performance in the step-down

conversion. Exhaustive studies were also made on

the MPPT methods and their improvement. However,

in PV applications there is still a need to look into

the intermediate power converters suitability and

evolving alternative topologies in order to find a better

matching converter.

896 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 2 APRIL 2011

Several topologies have been proposed in the

literature for the PV, and most of them are dealing

quantitatively without having much mathematical

orientation. However, there are certain issues in

PV, from the converter performance point of view,

those can only be addressed and understood through

mathematical analysis. PV power tracking using

buck converters is also reported by several authors,

wherein the buck converter based power tracking

characteristics were presented and then compared

with experimental characteristics. However, there

is no discussion reported on the tracking issues,

mathematical analysis applicable to power tracking

aspects, conditions for satisfactory power tracking,

etc. From the converter performance improvement

point of view, ripple reduction through zero-ripple

filter is more popular in the dc-dc conversion [20—22],

PV power conversion, and several other power

conditioning systems. This ripple mitigation technique

has also been applied recently in energy efficient fuel

cell conversion [23—24], wherein it is demonstrated

that the zero-ripple filter significantly reduces the

input low- and high-frequency current ripples. Thus,

such solutions result in better reliability and enhanced

durability to the fuel cell power system.

The purpose of this investigation is to analyze the

buck topologies in the MPPT applications and then

evolve a modified buck topology, which will track

MP at all solar insolations leading to an improved

performance over the buck converter with input

filter (BCIF). In this direction, a fourth-order buck

converter (FOBC) is proposed for PV tracking

applications. As this converter contains the inductor

on the input side, the PVA current is smooth

and exhibits low ripple content as in comparison

with the conventional buck converter. To reduce

the ripple current even more, without using any

additional passive components, a coupled inductor

(CI) arrangement is proposed for the FOBC. This

CI arrangement not only reduces the core size but

also improves the converter performance, by way of

ripple reduction, for certain values of inductance and

coupling coefficients combination. Further, the CI in

FOBC also eliminates the problem of right half of

s-plane (RHP) zeros.

II. PHOTOVOLTAIC SYSTEM

The PV system consists of several PVA modules,

which are normally connected in series and parallel

fashion in order to realize the required voltage and

current demands, an intermediate power converter to

extract maximum available power, and a load. The

load may be of: 1) stand-alone sink type, 2) battery,

3) up-stream converters, and 4) combinations of

above. In any case to understand the whole tracking

process as well as the conditions under which a

particular converter performs its function for optimal

operation, it is necessary to model the complete

PV system. Detailed discussions of PVA modeling

aspects were already reported [12]—[16]. The PV

generator exhibits a nonlinear insolation dependent v-i

characteristic, mathematically expressed for the PVA

consisting of Ns cells in series and Np cells in parallel

as

VA =¡IARsÃNsNp

!+

μNs¤

¶ln

(1+

NpIph¡ IANpIoc

)(1)

where ¤= (q=AKT), q–electric charge;

A–Completion factor; K–Boltzmann’s constant;

T–Absolute temperature; Rs–cell series resistance;

Iph–photo current; Ioc–cell reverse saturation

current; and IA, VA are the PVA current and voltage,

respectively. As (1) gives dependence of vA¡ iA withinsolation, it is used in the simulation studies.

III. MAXIMUM POWER POINT TRACKING WITHBUCK TOPOLOGIES

Conventionally, buck converters are widely used

in PV applications, such as in: 1) front end step-down

applications, 2) battery charging, and 3) maximum

power point (MPP) tracker. However, simple

buck converter generates a lot of electromagnetic

interference (EMI) noise on account of pulsating

source current waveform. The best way to minimize

these problems is to add a low-pass filter on the

source side. Various possible filter combinations

available for dc-dc converters are: 1) connecting a

capacitor filter, 2) connecting single-stage L-C filter,

or 3) multiple-stage filters. Multiple filter stages

are recommended only when the single stage filter

is unable to meet the requirements or its design is

very large and impractical. Although the system

performance can be improved by an input filter,

they alter the converter dynamics. Numerous papers

dealing with input filter interactions on the converter

dynamics have been reported in the literature [25, 28].

Normally the input filter affects the downstream

converter stability. Appropriate care should be taken

while designing the filter stage such that its output

impedance is less than the downstream converter

input impedance jZoj< jZinj, to ensure the combinedsystem stability. Further, the components must be

designed to handle large ripple currents, and be

capable of providing sufficient damping. Insufficient

damping causes the frequency response plots to

have multiple crossover frequencies, less than

control-loop crossover frequency, leading to system

instability.

Buck converter with simple C-filter was proposed

and used in many MPPT applications. However,

this solution requires large capacitance value,

and sometimes it may not be possible to meet the

requirements as determined by the input-output

VEERACHARY: FOURTH-ORDER BUCK CONVERTER FOR MAXIMUM POWER POINT TRACKING APPLICATIONS 897

Fig. 1. Buck topologies for PV power tracking scheme. (a) BCIF based. (b) FOBC based.

impedance stability criteria. Other possible filter

configurations are: 1) parallel damped filter, 2) series

damped filter, 3) two-stage filter, etc. However,

L-C filter with shunt damping network provides an

alternative solution to the buck converter from the

EMI noise problem. This filter converter combination

can be used in the PV MPPT applications. However,

in MPPT applications obtaining the suitable filter,

which results in optimal operation at all solar

insolations, is a complex task. Further, the magnitude

of ripple current flowing in the front-end side

filter components is high resulting in more losses

and hence the efficiency of conversion becomes

low.

Although the buck converter with input

filter, Fig. 1(a), may be stable while performing

current/voltage regulation, but it may become

unstable in the PV power tracking applications.

Main important reasons for this destabilization, while

performing the MPPT task, are: 1) variable impedance

characteristics of the solar cell array, which is a

function of insolation and temperature, 2) damping

provided by the filter may not be sufficient at all

tracking points of PV, and 3) selection of MPPT

algorithm parameters. Even if input filter design that

yields optimum tracking performance is possible, the

power loss due to ripple currents flowing through the

damping resistors can’t be eliminated. This ultimately

results in lower converter efficiency, which is not

desirable in PV applications. Further, the value of

the dc blocking capacitance used in the damping

network is very large, and hence its size and cost

are the limiting factors. To eliminate some of the

above problems a fourth-order buck converter, shown

in Fig. 1(b), is proposed for the PV power tracking

applications in this paper. This topology, however,

has the following major advantages: 1) lower source

current ripple and hence EMI requirements are lower,

2) voltage conversion ratio is the same as simple buck

converter, and 3) simplicity in converter control due to

single switch topology.


IV. MATHEMATICAL THEORY OF FOBC FOR MPPTAPPLICATIONS

The proposed FOBC topology, shown in Fig. 1(b),

can be operated in several operating modes depending

on the load, switching frequency, and supply voltage.

However inductor current (iL1) must be continuous;

otherwise the benefits obtained from this converter

are lost. As a result the converter is analyzed here

for the continuous inductor current mode (CICM) of

operation only. Mathematical analysis of the converter

is developed in this section under the following

assumptions: 1) switching devices are ideal, 2) passive

energy storage parameters are assumed to be linear

time invariant, and 3) averaging of the converter

states has been done on the small-ripple assumption.

In CICM operation the circuit has two operating

modes: Mode-1: S-ON (0< t < dT); Mode-2: S-OFF

(dT < t < T). In each mode of operation the circuit is

linear and its behavior can easily be described by the

state-space average model [26] given by

_x= [A][x]+ [B][u], v0 = [P][x] (2)

where, [x] = [iL1 iL2 vc1 vc]t, [u] = [Vg], A=§DjAj ,

B =§DjBj , P = §DjPj , j = 1,2. The final state-space

matrices for CICM of operation are given below for

ready reference.

[A] =

0BBBBBBBBBBB@

¡ [a1L2 + aL2e]Le

¡ (aL2e¡ a2M)Le

¡ (D1M +D2L2)

Le

aL2ercLe

¡ (aL1e¡Mr1)Le

¡ (aL1e+ a2L1)Le

(D1L1 +D2M)

Le

aL1ercLe

D2C1

¡D1C1

0 0

a

rcC

a

rcC0

¡1C(R+ rc)

1CCCCCCCCCCCA[B]t =

μL2Le

¡ MLe

0 0

¶

where a1 = (D1r1 +D2r1c1), a2 = (D1r2c1 +D2r2),

L1e = (L1¡M), L2e = (L2¡M), Le = (L1L2¡M2),

r1c1 = (r1¡ rc1), r2c1 = (r2¡ rc1), a= Rrc=(R+ rc).This FOBC topology is simple and gives a voltage

transformation ratio almost identical to the buck

converter. In this process, the converter unit actually

replaces the constant load by an equivalent load that

corresponds to the effective load requirement of

the PVA at which it can deliver MP to the load. It

may not be possible, sometimes, to replace all the

values of constant loads by an equivalent value that

corresponds to the MPP load line. Achieving the

true MPPT depends on: 1) the type of switch-mode

converter used, 2) nature of load present on the

converter, 3) status of converter operation, etc. The

mathematical analysis of the proposed converter

and the desirable conditions for satisfactory MPPT

operation is discussed in the following lines. From (2)

we can easily establish the steady-state voltage gain

expression of the FOBC as

V0VA= kD (3)

where k = R=[R+D2(r1 + r2)+ r2(1¡ 2D) ¡ rc1¢D(D¡ 1)(2D¡ 1)], and VA and V0 are the averagevalues of the PVA voltage and converter load

voltage, respectively. This steady-state relationship

is derived based on the small-ripple assumption.

Under steady-state the FOBC transfers most of the

power extracted from the PV to the load, except a

small portion is going to be lost in the converter

nonidealities and in any case the power balance,

VAIA = V0I0 + losses, is ensured at all solar insolations.

The above equation together with FOBC efficiency

definition [27—28] V0I0 = ´VAIA, gives the basis for

establishing the relationship between the FOBC load

current and PVA source current as

IA =kDI0´

(4)

where I0 is the load current, and ´ is the efficiency of

the converter. From the expressions (3) and (4) the

equivalent load appearing across the PVA terminals

can be written as

VAIA= Req =

´R

k2D2(5)

and it can be controlled smoothly over wide ranges

with the help of duty ratio modulation. Here the

role of the FOBC is to force the fixed load line to

coincide with the line that intersects at the MPP

(Vm,Im) of the PVA i-v characteristic. At this MPP, the

effective equivalent impedance Req offered at the input

terminals of the converter should be equal to the load

line Rmp of the PV array, i.e.,

Rmp =´R

k2D2: (6)


The duty ratio corresponding to MPP operation is

Dmp =

s´R

k2Rmp: (7)

In all of the above equations, the terms ´ and k are

present, which gives an indication that the power

tracker performance depends on the converter

nonidealities. Assuming ´ = 100%, k = 1, then

Dmp < 1 for the case when Rmp > R. If Rmp <

R then Dmp > 1, which will not fall within the

converter control range. Therefore, if the converter

is operating in MPPT mode then Dmp < 1, R < Rmpand the corresponding FOBC tracking zone pictorial

representation is shown in Fig. 2. For given PVA

parameters and known MPP quantities, one can

compute the expected duty ratio of the converter

from (7), and the appropriate value of the load should

satisfy R < Rmp condition.

Under ideal conditions the reflected equivalent

load appearing at the input terminals of the PVA will

be either 1 or R for the duty ratio’s zero and one,

respectively. In order to achieve satisfactory MPPT

performance, with FOBC, the connected load value

(CLV) must be less than the value of Rmp at that solar

insolation. For loads R > Rmp the converter settles

to a duty ratio, extreme limits set by the designer,

at which the power output from the array is less

than the MP. The above discussion is under ideal

conditions, i.e., duty ratio variation is (0<D < 1).

In practice the operating duty ratio is restricted to

the Dmin ·D ·Dmax range, for better utilization ofthe converter capabilities, and the corresponding load

range is

k2D2minRmp

´< R <

k2D2maxRmp

´: (8)

However, the practical D range is (0.1—0.9) and ´ is

about 90%. For these values, the approximate load

range becomes (0:011k2Rmp < R < 0:9k2Rmp). The

above discussion is valid only when the converter

is supplying a constant resistive load. However, in

most of the cases the energy extracted from the PV

sources is stored in the batteries. In that situation the

above discussion is equally valid. The explanation

for this is as follows. The basic equivalent circuit

of the battery to be charged consists of a voltage

source in series with an internal resistance and a

parallel combination of a capacitor and resistor.

Effectively this combination presents a variable

impedance/resistance across the load terminals.

However for steady-state analysis purposes, the

battery can be treated as an equivalent resistive

load and this value depends on the state-of-charge

condition of the battery. As a result the battery load

can be represented by a variable load, a function of

its voltage and current, with maximum and minimum

limits (Rbmin · Rb = f(vb, ib)· Rbmax). Here Rbmin,

Fig. 2. Load tracking region of FOBC through MPPT operation.

Rbmax corresponds to minimum charge voltage,

regulation voltage of the battery, respectively. The

variables vb, ib are battery voltage and current,

respectively. Power supplied to the battery, under the

current control case, is almost varied linearly and its

power storage variation is determined by the regulated

current value, dynamic impedance characteristic of

the battery. In case of stand-alone loads, for a given

solar insolation, the MPPT converter reaches to a

steady-state duty ratio value in short time, while for

battery loads the duty ratio variation persists until it

is fully charged. As a result, in the PV battery energy

storage systems, the MPPT should be continuously

on and one should not put a constraint such as

termination of MPPT loop to avoid the steady-state

oscillations.

V. RIPPLE CANCELLATION THROUGH COUPLEDINDUCTOR

Ripple steering/cancellation using CI is well

known in the dc-dc converters [20]. A set of two

or more inductors placed on a common magnetic

core results in a CI, and it not only requires fewer

numbers of cores, but also improves the converter

performance. Ripple reduction in the inductor current

is possible both during charging and discharging

periods. Applying the ripple reduction principles

discussed in [20] to the FOBC one can easily establish

di=dt expressions for switch-ON and switch-OFF

durations, respectively

di1dt=(L2¡M)Le

(Vg ¡V0) (9)

di1dt=(M ¡L2)V0

Le: (10)

Equations (9) and (10) represent the ripple current

flowing in the inductor L1 during switch-ON and


OFF states, respectively. Both equations indicate

that if L2 =M then di1=dt= 0, which means that the

inductor current (i1) is essentially a constant value or

the ripple ¢i1 ¼ 0. That means the ripple reductionis possible for the entire switching period as shown

in Fig. 9. This perfect ripple compensation theory

is valid only under ideal conditions and the exact

zero-ripple steering depends on the compensation of

the nonidealities of the system.

VI. PERFORMANCE COMPARISON OF BCIF ANDFOBC TOPOLOGIES

An FBOC and a BCIF, parameters listed in

Table III, were designed, simulated using PSIM,

built and tested. The source ripple current is slightly

higher in FOBC, while it is low in BCIF because of

L1¡C1 elements directly connected to the sourceside. In both the converters the peak current/voltage

stress on the switch and diode is identical. The FOBC

circuit structure gives an impression that the ripple

current flowing in capacitor C1 is larger in magnitude,

but actually the magnitude of current flowing in it

is identical to that flowing in the BCIF. Hence, the

I2R-losses, contributed by the series resistance of

the L1 and C1 elements, in both the converters are

almost the same. In both the topologies the ac losses

contributed by the inductor L2 series resistance is

also the same because of the identical peak-to-peak

ripple current waveforms. However, after adding the

losses occurring in the damping network of the BCIF,

its efficiency is close to the efficiency of FOBC.

In conclusion, both BCIF and FOBC circuits show

almost identical performance, from the steady-state

point of view, and their efficiencies are also of the

same order.

Development of the small-signal model (SSM) for

the converters FOBC and BCIF [18, 25], is essential

in order to study their dynamical properties in the

power tracking process. The PV supplied converters

SSM consists of a linearized model of the converter

and on the input side the PVA is being replaced by

the incremental impedance jZsj= Rmpp. Due to paperlength restrictions the full SSM development is not

discussed here and the readers can easily obtain these

models employing the methodology presented in the

references. To have a fair comparison, small-signal

transfer functions (TFs) of the BCIF and FOBC are

derived using the signal flow graph small-signal

linearization method and are tabulated in Tables I and

II, respectively. The converters important small-signal

TF frequency response characteristics (the figures

were not given here due to space limitation) were

plotted, and these observations reveal that almost

all the TFs listed in Table I and II, show similar

variation except for v0=d, i1(s)=d(s) TFs and their

significance is explained here. The control-to-output

TFs exhibit complex pole-zero pairs and so there

TABLE I

Small-Signal TFs of BCIF

TFs Expression

v0(s)

vsa(s)

RD1x¢b

v0(s)

i0(s)

R[(x1¡Zs)(x2x4 +D21)+ x2]x¢b

vsa(s)

isa(s)

Zs[R+ x+ x2x3 +Rx1x4 + x1x3D21]

x¢b

vsa(s)

d(s)

[x3D1Vc1 + I2(R+ x2x3)]

x¢b

Note: x1 = (r1 + sL1), x2 = (r2 + sL2), x3 = (1+ sRC2), x4 = sC1,

x= x1x2x3x4, Zs = Rmpp, D1 =D, D2 = (1¡D1), ¢b =[x+ x2x3 + x1x3D

21+Rx1x4 +R¡Zsx2x3x4¡Zsx3D21 ¡RZsx4]=x.

TABLE II

Small-signal TFs of FOBC

TFs Expression

v0(s)

vsa(s)

[RL2D2Ld1m+RL2(K2K4 +D1Ld1m)¡RM(K1K4 +D2Ld2m)]K¢f

v0(s)

i0(s)

R[K1K2K4 +K2D2Ld2m +K1D1Ld1m¡ZsL2K2K4]K¢f

vsa(s)

isa(s)

K¢f

L2[K234 +D1K3Ld1m +RK4L1m]

vsa(s)

d(s)

[ZsL2Vc1[K234 +L1K3D21+RK4L1m +MD1D2K3]

+[(K2K3 ¡RL1m)Ld2mZsI1 +RI1ZsL2mLd1m]+ZsI2[Ld2m(K2K3 +RL1m) +RL2mLd1m]

+[ZsL1K4Vc1(D1Ld2m ¡RL2m)]+ZsMVc1[RK4L2m ¡D1K3Ld2m]

¡ZsMVc1[K234 +L1K3D21 +RK4L1m +MD1D2K3]]=¢fNote: E = (L1L2 ¡M2), K1 = (r1L2 + sE), K2 = (r2L1 + sE),

K3 = (1+ sCR), K4 = sC1, K = K1K2K3K4, K234 = K2K3K4,

L1m = (L1 ¡M), L2m = (L2¡M), Ld1m = (L1D1 +MD2),Ld2m = (L2D2 +MD1), ¢f = [K +K2(L1K1D

21¡L2K2D22)

+R(L1 ¡M)(K1K4 ¡MD21)+R(L2 ¡M)(K2K4 +MD22)+RD1D2(2L1L2 ¡M(L1 +L2))¡MD1D2K3(K1 +K2)¡ZsL2K1K3K4+R(L1 ¡M)(L2D22 +L2K2Zs) +RL1D21(L2¡M)¡L1L2K2ZsD21+MD1D2(R(L1 +L2 ¡ 2M)¡L2K4Zs)]=K.

will be a glitch in the magnitude plot. In the case of

BCIF the zeros pair may enter into RHP for which

the phase characteristic will orient towards ¡540±.However, there is no such problem of RHP zero in

the CI FOBC, as shown in Figs. 3—5, as the mutual

inductance restricts the movement of zeros to the left

half of s-plane(LHP).

VII. DESCRIPTION OF EXPERIMENTAL DATAACQUISITION SYSTEM

For the demonstration and validation of the

proposed theory, an experimental prototype has

been built in the laboratory environment. The solar


Fig. 3. Bode plot of control-to-output [v0(s)=d(s)] transfer function (D : 0:1! 0:9). (a) BCIF. (b) FOBC.

system is realized by the PV panel illuminated with

incandescent lamps. The converter is made up of

IRF540 MOSFET, fast recovery diode MUR820. The

MOSFET is driven by IR2110 IC. The real-time PVA

quantities, voltage and current, are sensed through

the voltage and current sensors and these quantities

are scaled such that they can readily be given to

analog-to-digital converter channels of the dsPIC

controller. A dsPIC30F6010 micro-controller [30] is

employed for realizing the MPPT algorithm as well

as to generate a pulse width modulation (PWM) gate

signal to the converter.


Fig. 4. Pole-zero movement of i1(s)=d(s) TF [FOBC; D : 0:2! 0:9]. (a) Without mutual coupled inductance.

(b) With mutual coupled inductance.

VIII. DISCUSSION OF SIMULATION ANDEXPERIMENTAL RESULTS

In order to verify the theoretical analysis

developed in the preceding sections, a simulation

profile of the proposed system was formulated in

PSIM power electronic simulator. The PV system

and converter parameters are listed in Table III. A

simulation diagram involves a model development

of: 1) PVA, 2) converter, 3) load, and 4) MPPT

algorithm. Among these, the converter and resistive

load modeling are straight forward, but models

need to be developed for the remaining two. If the

load is battery, then again, its accurate simulation

model formulation is essential for carrying out the

performance studies. The PVA simulation model,

reported in [16], is transformed into the PSIM

platform, while the tracking algorithm, P & O, was


Fig. 5. Comparison of i1(s)=d(s) TF frequency response plot.

TABLE III

Converter, PVA and Tracking Parameters

Converters Parameters PVA Parameters

Parameter BCIF FOBC Parameter Value

L1 60 ¹H 60 ¹H

L2 35 ¹H 35 ¹H

M – 30 ¹H Maximum Power (Pm) 30 W

C1 87 ¹F 87 ¹F Open circuit voltage (Voc) 21 V

C2 220 ¹F 220 ¹F Short circuit current (Isc) 3 A

r1 35 m− 33 m− MPP voltage (Vm) 12 V

r2 20 m− 19 m− MPP current (Im) 2.5 A

rC1 200 m− 205 m− Module size = 0:4£ 0:6 mrc 171 m− 174 m−

fs 40 kHz 40 kHz

Tsampling 0.185 ms 0.13 ms

¢D 0.68% 0.27%

Fig. 6. Simulated power tracking characteristics of PVA against

solar insolation change (FOBC).

implemented in C-language program and linked to the

PSIM [29] simulation model through a dynamic link

library (DLL) block.

Exhaustive simulations have been performed to

verify the validity of the theoretical analysis. These

studies reveal that the proposed converter can track

MP from the PVA for all solar insolations. However,

for demonstration the simulated power tracking

characteristics are reported here for the following

cases: 1) variable solar insolations, 2) load changes,

and 3) with battery load. These results are plotted in

Figs. 6—8. Power output of PVA depends on the solar

insolation, and it increases with an increase in solar

insolation (ª2!ª1) as shown in Fig. 6. Variation in

the load immediately reflects on the PVA input side

and hence its power output will change accordingly.

However, the presence of MPPT loop brings the

operating point back to the original one, by changing

the duty ratio, so that the power output of the PVA

is maintained at constant value. During this tracking

process the converter undergoes dynamics, and hence

it is reflected on the power output characteristic of

the PVA as shown in Fig. 7 for load changes from


Fig. 7. Simulated power tracking characteristics of PVA against

load disturbances (FOBC).

3:7! 1:7 − and then back. As discussed in the theory

presented in Section IV, the converter extracts MP

from the PVA provided that the load on the converter

is well within the range, R < Rmp. This phenomenon

is also verified through simulations by changing the

load from nonoptimal value to optimal value; these

observations are not included in order to restrict the

paper length, but these observations reveal that for

loads other than the optimal range, the PVA operates

at a suboptimal power point. The tracking capability

of the converter supplying the battery loads is also

verified and these observations are shown in Fig. 8.

In order to verify the simulation performance

of the proposed scheme, a 30 W experimental

prototype PV system was built and then experimental

investigations were carried out. Initially, the

steady-state performance waveforms of the FOBC,

source and load side current ripple, were measured.

Steady-state performance comparison of BCIF and

FOBC is tabulated in Table III. These observations

indicate that the source current without coupling,

¢is, is continuous, which is the salient feature of

the proposed FOBC. Further, inclusion of coupling

among the existing inductors has reduced the source

current ripple ¢isc to almost 70% in comparison

with the noncoupled case. This ripple reduction

(experimentally measured results are shown in

Fig. 9) calls for reduced input filtering requirements,

particularly the terminal capacitance. However, not

Fig. 9. FOBC current drawn from PV array (experimental).

Fig. 8. Simulated power tracking characteristics of PVA with

battery load (FOBC).

much ripple reduction is observed in the load voltage.The measured steady-state performance comparison

of BCIF and FOBC such as the switch voltage

stress, PV voltage, and current ripple are plotted

in Fig. 10. Prototype BCIF and FOBC converters’

efficiency variation with the duty ratio is measured

and these measurements show that their efficiencies

are almost in the same range. Detailed comparison

and experimental verification of BCIF and FOBC

based tracking, given in Table IV, is discussed in the

following paragraphs.

In the PV systems, the MPPT may become

unstable for the following cases: 1) improper dampingprovided by the input filter of the converter, and

2) improper sampling time period and incremental

duty ratio selection. The MPP depends on the solar

insolation and to extract this MP the intermediate

converter needs to be controlled such that its

equivalent input impedance, offered by the converter,

must be equals to the PVA MPP impedance. However,

in case of converters having input filters, the

impedance criterion jZoj< jZinj has to be satisfied,otherwise the system may result in unwanted

oscillations. Use of L1¡C1 input filter is the commonpractice in the buck based PV system. However,

simple L1¡C1 filter alone often leads to sustainedoscillations [25], and to mitigate these oscillations a

damping network needs to be added. Although the

damping can be provided through several different

ways, but Rd ¡Cd series combination is popular for


Fig. 10. Steady-state performance comparison of BCIF and FOBC (experimental). (a) PV and load voltage. (b) Switch voltage stress.

(c) PV and capacitor current.

the buck converter. The only main disadvantage

of this method of damping realization is that a

larger value of dc blocking capacitor Cd is needed

to avoid the power loss in the series resistance Rd.

Applying the impedance criterion jZoj< jZinj tothe input filter and buck converter results in the

condition Rd¿ R=D2. In case of power supply

applications the converter is essentially performing

fixed voltage conversion and hence the duty ratio

is almost constant. Hence, one can easily choose

the Rd value satisfying the constraint. However, in

the PV-MPPT applications for a given load the duty

ratio is continuously changing with solar insolations

and as a result the Rd requirement also changes.


TABLE IV

Performance Comparison of the BCIF and FOBC

Parameter BCIF FOBC

MCR Two One

ICR Lesser than FOBC Little bit more than BCIF

DPVS Almost same as FOBC Almost same as BCIF

CE Almost same as FOBC Almost same as BCIF

TCR Large Very small

Cost Little bit higher Lower than BCIF

Damping Required No-need

CMI Same as basic converters Additional flexibility due

to CI

SDT ground isolated ground isolated

MPTE 91—96% 95—98.5%

Note: MCR: Magnetic cores required, ICR: input current ripple,

DPVS: device peak voltage stress(switch/diode), CE: converter

efficiency, TCR: terminal capacitance requirement, CMI: converter

matching impedance, SDT: wwitch driver type, MPTE: MPPT

efficiency.

Fig. 11. Experimental power tracking characteristics with

improper P & O parameters (BCIF).

Damping design in this case involves computing

the Rd values for the expected duty ratios and then

choosing minimum value, which ensures the constraint

Rd¿ R=D2 at all solar insolations. However, use of

too small values for the Rd is also not recommended

as it increases the output impedance of the filter

again and may intersect with the input impedance

characteristic of the buck converter, leading to

unstable oscillations. In certain cases, such as in the

fixed resistive loading case, although it is possible

to choose a damping resistance value satisfying the

constraint Rd¿ R=D2, for certain solar insolations

the resulting value may be too low and hence the

MPP is forced to exhibit oscillations. Hence a

trade-off value must be chosen to avoid unwanted

oscillations.

Fig. 12. Experimental power tracking characteristics with

improper damping (BCIF).

Fig. 13. Experimental power tracking characteristics with proper

damping (BCIF).

While performing the MPPT with different

converters, using the P & O algorithm, an identical

set of tracking parameters, sampling frequency,

and incremental duty ratios may not be suitable as

different converters will be having different dynamic

characteristics. Under such conditions suitable P & O

tracking parameters need to be chosen, otherwise

the MPPT may become unstable. However, for a

higher order converter self-tuning process is the best

tuning methodology for arriving at optimal P & O

parameters. In this paper these parameters, for the two

converters BCIF and FOBC, have been obtained by

the self-tuning process, and they are listed in Table III.


Fig. 14. Experimental power tracking characteristics of PVA

during starting (FOBC).


against solar insolation change (FOBC).

Exhaustive experimental MPPT investigations have

been conducted, using BCIF and FOBC, to verify

the above-mentioned points. These studies show that

fulfilling the sampling time and incremental duty

ratio requirement is sufficient for certain converter

configurations, like in FOBC, but in some cases

input filter interactions also need to be considered for

realizing the stable MPPT schemes. Fig. 11 shows

the tracking characteristics, with improper MPPT

control parameters (¢D = 1%, Tsampling = 0:08 ms),

of BCIF wherein the MPP is continuously oscillating.

In case of BCIF, it has been observed that the MPPT

is stable for certain solar insolations and becomes

unstable or settling to suboptimal power point at

some other insolations. This is mainly due to an

insufficient damping provided by the input filter.

This issue has been experimentally verified by

having two different damping networks and these

results are plotted in Fig. 12. At a solar insolation


against load disturbances (FOBC).


against nonoptimal/optimal loads (FOBC).

of ª3 the BCIF is exhibiting stable MPPT, while

showing unstable oscillations at solar insolation ª1as evidenced by the observations shown in Fig. 12.

This behavior is due to insufficient damping, damping

resistance Rd = 10 −, provided by the input filter

section of the BCIF. In order to stabilize the MPP,

now the damping resistance has been changed

from 10 to 1.2 −, without changing the P & O

parameters, and then measurements were recorded

for variable solar insolation conditions. For these filter

parameters, the MPPT is stable at all solar insolations

as demonstrated by Fig. 13. Hence, the damping

design plays a key role in the BCIF adaptability for

the PVA power tracking applications. Since the PVA

exhibits a highly nonlinear capacitance variation,

which again depends on the environmental factors,

fine tuning of optimal damping is one of the issues

of the BCIF used in the power tracking applications.

To overcome these problems a FOBC is proposed


Fig. 18. Experimental power tracking characteristics of PVA with

battery load (FOBC).

in this paper and its experimental power tracking

performance characteristics are discussed in the

following paragraphs.

Power tracking performance of the proposed

converter was verified experimentally and for

validation measured characteristics are provided

here for almost identical simulation conditions,

which are: 1) tracking during starting, 2) variable

solar insolations, 3) load changes, 4) load variation

from nonoptimal to optimal, and 5) with a battery

load. Fig. 14 shows the power tracking starting

characteristics while Fig. 15 shows solar insolation

changes. Tracking characteristics for load variations

are plotted in Fig. 16. Tracking characteristics against

nonoptimal to optimal load variation is shown in

Fig. 17, and it is clear that the converter is capable of

tracking MP only when the connected load is within

the optimal range. The proposed scheme is capable

of tracking MP with the battery load also, as shown

in Fig. 18. However, the battery voltage must be

within the range such that the resistance offered by

the battery must be within the optimal range for which

the converter tracks MP. For battery voltages falling

out of this range the converter settled to a suboptimal

power point. The measured MPPT efficiency, with the

proposed converter, is ranging between 93—98%.

In all these cases, the experimental characteristics

are in agreement with those obtained through

simulations. In simulations the processing time is

almost zero and hence the response time is low.

However, in the experimental system the definite

amount of time is required for: 1) sensing and

converting the real-time signals, voltage and current,

and 2) computation of the MPPT control loop.

Because of these factors and additional processing

time requirements, there is a slight mismatch

of dynamic response time in the simulation and

experimental results.

IX. CONCLUSIONS

The power tracking studies with BCIF showedthat sufficient damping must be designed in order toensure MPPT and to eliminate unwanted oscillationsor suboptimal power operation. In order to track PVpower through buck topology, a novel CI FOBCwas proposed for power tracking applications andits features were verified through simulation andexperimental observations. Use of FOBC reducedthe source current ripple in comparison with buckconverter and exhibiting identical steady-stateperformance to that of BCIF. Additional ripplereduction was achieved by CI. Analysis aspectssuch as ripple reduction and conditions under whichpower tracking is successful were also explored.The combined PV system was modeled in PSIMand then it’s performance simulated. Various powertracking characteristics have been generated and thenrange of loads, for which the converter is capable oftracking MP, obtained through mathematical analysis,have been verified through simulation as well asexperimental investigations.

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Mummadi Veerachary (M’94–SM’04) was born in Survail, India, in 1968.He received the Bachelor’s degree from the College of Engineering, Anantapur,

Jawaharlal Nehru Technological University (JNTU), Hyderabad, India, in 1992,

the Master of Technology degree from the Regional Engineering College,

Warangal, India, in 1994, and the Dr. Eng. Degree from the University of the

Ryukyus, Okinawa, Japan, in 2002.

From 1994 to 1999, he was an assistant professor with the Department of

Electrical Engineering, JNTU College of Engineering, Anatapur. From October

1999 to March 2002, he was a research scholar with the Department of Electrical

and Electronics Engineering, University of the Ryukyus. Since July 2002, he

has been with the Department of Electrical Engineering, Indian Institute of

Technology Delhi, New Delhi, India, where he is currently an associate professor.

His fields of interest are power electronics and applications, modeling and

simulation of large power electronic systems, design of power supplies for

spacecraft systems, control theory application to power electronic systems, and

intelligent controller applications to power supplies.

Dr. Veerachary was the recipient of the IEEE Industrial Electronics Society

Travel Grant Award for the year 2001, Best Paper Award at the International

Conference on Electrical Engineering (ICEE-2000) held in Kitakyushu,

Japan, and Best Researcher Award for the year 2002 from the President of the

University of the Ryukyus. He is an editorial member of IET Proceedings on

Power Electronics, Institution of Engineering & Technology, U.K., and the Journal

of Power Electronics. He is a member of the IEEE Industrial Electronics Society

and the Institution of Engineers India. He is currently serving as an Associate

Editor of the IEEE Transactions on Aerospace and Electronic Systems and the

IEEE Transactions on Industrial Electronics. He is listed in Who’s Who in Science

and Engineering 2003.


Documents

Fourth-Order Buck Converter for Maximum Power Point Tracking Applications