max power point control sdarticle

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A group of PV cells connected in series to provide a sig-nicant voltage (typically P 20 V) is called a PV module.Series or parallel combinations of PV modules form a solarpanel, and again, a group of PV panels results in a PVarray. This is depicted in Fig. 1(b). PV systems are populardue to the many advantages they offer. Not only are theypollution free, but also, they do not incur any maintenance

and running cost. The major deterrent factor in their use isthe high initial investment required [3]. However, withgradual reduction in the cost of PV modules, the conver-sion of solar energy into electrical energy is becoming moreand more affordable.

Because of the high initial investment and limited lifespan of a PV array, it is important to utilize it effectively

Nomenclature

k Insolation levelI pv average PV array output currentV pv average PV array output voltage

I ph photo generated currentI o reverse saturation currentDX diode (X = 1, 2, pr)D duty cycleSW xx bi-directional switchc constantq electronic chargek Boltzmann’s constantg diode ideality factorT ambient temperature (K or C)R s cell series resistance (X)AI ref reference current amplitudeb approximate MPP tracking variableV p amplitude of grid voltage V ac

I p amplitude of grid current i gI ref reference current wave formx angular frequency of fundamental grid voltage

(radians)bg reference b value for MPP trackingAI ref(new) new value of AI ref

AI ref(old) old value of AI ref

L buck-boost inductorT s high frequency switching time periodvout average voltage across (grid) capacitor ( C f )

when device is OFF

DI current tolerance denoting hysteresis bandtk turn ON switching instants during k th intervalt 0k turn OFF switching instants during k th interval

f c lower cut off switching frequency in hysteresisband

C f lter capacitor across grid

L f lter inductorek energy transferred during k th switching intervalx state parametervac grid voltage as function of time

SubscriptsC capacitorL inductor

Superscript0 d/d t

AbbreviationsCCM continuous conduction modeJDCM just discontinuous current modeDCM discontinuous current modePV photovoltaicOP operating pointMPP maximum power pointMPPT maximum power point trackingKCL Kirchoff’s current lawKVL Kirchoff’s voltage lawi – v current–voltage p – v power–voltageSSSP single stage single phase

FFT fast Fourier transformSPWM sine triangle pulse width modulation

Parabolicconcentrator

Rs

PV Cell

Module

Panel

Array

(b)(a)

Fluidcylinder

Sun rays

Basestructure

Load(R L)

Fig. 1. PV energy utilization in the form of (a) thermal energy and (b) in the form of electrical energy through photovoltaic cells.

626 S. Jain, V. Agarwal / Energy Conversion and Management 48 (2007) 625–644



and extract the maximum possible power. However, aneffective utilization of the PV array poses several challengesdue to the following reasons:

(1) Because of the continuous revolution and rotation of Earth [4], there is no unique position of the PV array

that will receive direct, vertical solar insolation at alltimes. PV panels are made to track the movement of the Earth with respect to the Sun with the help of stepper motors (or some other arrangement) toensure the maximum insolation at all times. Thisarrangement, called mechanical tracking, increasesthe generated electrical energy.

(2) Because of the non-linear i – v characteristics of the PVarray ( Fig. 2), the power extracted from a PV sourcedepends on its operating point on the load line. Fromthe p – v characteristics given in the gure, it can beobserved that for a given insolation ( k) and tempera-ture (T), there exists a unique operating point corre-sponding to the maximum power point (MPP) of the PV array. Therefore, to extract maximum powerfrom the PV array, it is necessary to operate at thecorresponding MPP as k and T vary. This is calledelectrical tracking of the maximum power point orsimply maximum power point tracking (MPPT). Itis this aspect of the PV power conditioning withwhich this paper is concerned.

1.1. Electrical MPP tracking

As mentioned earlier, due to the non-linear i – v charac-teristics of the PV array, electrical tracking is essential.Power generated by a PV array depends on various envi-ronmental conditions like temperature, insolation, windspeed, etc. Fig. 2 shows the i – v and p – v characteristics of

a PV array for different levels of insolation and tempera-ture. Let the operating point OP R 1( k 1) be the MPP corre-sponding to insolation k1 and temperature T 1 with RL =R1 (Fig. 1). Now, if the insolation and temperature changeto k2 and T 2, respectively, both the i – v and p – v character-istics shift as shown in Fig. 2. If RL continues to be R1, it

can be observed that the new operating point, OP R 1( k 2) isno longer the MPP. The actual MPP corresponding to k2and T 2 is OPR 2( k 2) . To operate the PV array at OP R 2( k 2)

(corresponding to power P R 2( k 2)), RL must be changed toR2 as shown in Fig. 2. Thus, for any variation in the envi-ronmental conditions (insolation, temperature, etc.), a suit-able adjustment of RL is required to track the maximumpower point of the PV array. This is the objective of electri-cal tracking of the MPP.

Electrical tracking of the MPP is achieved throughpower conditioning converters (switching converters) asan interface between the load and source as shown inFig. 3. The switching converters are suitably controlled tomatch the load impedance with the varying PV sourceimpedance. There are several algorithms for control of the switching converters to achieve MPPT. Some of thewidely used schemes are the hill climbing method [5], incre-mental conductance method [6], ripple based method [7]and the constant voltage method [8].

The hill climbing method is based on the principle of perturb and observe . In this algorithm, perturbations areperiodically introduced into the control signal of the switch-ing converter, and the resulting effect on the PV power out-put is observed. If the ‘present’ value of power is more thanthe ‘previous’ value, the perturbation in the control signal is

assumed to be a step in the right direction. Otherwise, thedirection of perturbation is reversed. As this algorithm exe-cutes, it gives an appearance that the operating point isclimbing the p – v curve (hill) and, hence, the name ‘hillclimbing method’. This is shown in Fig. 2. The operating

Array Operating Voltage(V)

P V A r r a y

P o w e r ( W

a t t s )

OP R1( λ 1)OP R1( λ 2)

i-vcurve[ λ 1,T1]

i-vcurve [ λ 2,T2]

P R1( λ 2)

PR1( λ 1)

Hill-climbingmethod

Load line(R1)

Load line (R2)

P R2( λ 2)

P V A r r a y

C u r r e n t ( A )

= Operating point for fixedresistive load

0>∂∂

V

P

(MPP)Positive slope Region

NegativeSlope

Region0=

∂∂

V P

0<∂

∂

V P

p-vcurve[λ 2,T2]

p-vcurve [ λ 1,T1]

OPR2( λ 2)

ISC [λ 1,T1]

ISC [λ 1,T1]

VOC[ λ 1,T1]VOC[ λ 2,T2]

VMPP

[λ 1,T1]

IMPP [λ 1,T1]

Fig. 2. i – v and p – v characteristics of the PV array for different insolation and temperature levels. The load lines corresponding to resistive loads R1 and R2

are also shown.

S. Jain, V. Agarwal / Energy Conversion and Management 48 (2007) 625–644 627



point eventually reaches the top of the p – v curve (MPP) andkeeps oscillating around it, the latter being a demerit of thismethod. The incremental conductance method is based onthe principle of impedance matching between the PV sourceand the effective load across it. This algorithm controls thepower converter so as to match the panel impedance withthe converter input impedance. The ripple based methodutilizes the phase relationship between the PV voltage andpower to achieve the MPP. The MPP divides the p – v char-acteristics into two regions – the positive and negative sloperegions as shown in Fig. 2. The phase relationship betweenthe voltage and power is utilized to determine the operatingregion, which is then utilized by the algorithm to drive theoperating point towards the MPP.

A major challenge in MPPT arises from the fact that ini-tially there is no way of determining the direction in whichthe PV operating point should be driven to achieve the MPPor how far the MPP is from the current operating point.

Because of this, all the MPPT algorithms described aboveutilize a small xed incremental step change in the controlsignal (of the switching power converter) to reach theMPP. This reduces the tracking speed. There are someapproximate methods that can be used for fast tracking.One of the methods in this category is the constant voltagemethod, which utilizes the fact that in a PV source, the ratioof its open circuit voltage ( V oc ) to its MPP voltage ( V MPP ) isnearly a constant ( %0.76). This method is suitable for loca-tions having small variations in environmental conditions.

An analogous method, called the constant currentmethod, also exists that utilizes the fact that I sc /I MPP % 0.88,where I sc is the short circuit (i.e. when the PV output isshorted) current and I MPP is the PV output current corre-sponding to the MPP. The problem with the constant volt-age method is that the load must be repeatedly disconnectedfrom the PV source to determine the V oc . Similarly, the con-stant current method requires that the PV source output isfrequently shorted to determine I sc . Some loads may notallow open circuiting or short circuiting of the PV source.In such a case, a pilot cell method may be used in which asample PV cell is separately monitored for its V oc or I sc valueand used for MPPT.

Another fast tracking algorithm [9] has been recentlyproposed by the authors. The details of this algorithm

are presented in a subsequent section.

1.2. Types and operating modes of DC–DC converters

DC–DC converters transform a given (usually unregu-lated) DC voltage to another level of regulated DC voltage.This is achieved with the help of energy storage elementslike the inductor and capacitor and ON–OFF switchingdevices like transistors and diodes. Usually, the ON–OFFsequence is repeated in a periodic manner at a certainfrequency f s (=1/ T s) (Fig. 3), where T s = T ON + T OFF .There are three basic types of DC–DC converters [10]:(1) boost or step up converter; (2) buck or step down con-verter; (3) buck-boost converter.

The basic operating principle of any of these convertersis the same [10]. As an example, a boost converter is drawnin Fig. 3(b). It works in the following manner. When thetransistor S is turned ON, the input supply stores energyin inductor LB . When S is turned OFF, the stored energyis transferred to the load. Noting that the average voltage

across inductor LB over a switching cycle must be zero[10], the following expressions can be written:V in Â D þ ð V in À V oÞ Â ð1 À DÞ ¼0 ) V o ¼ V in=ð1 À DÞSimilarily; I o ¼ ð1 À DÞ Â I inand Rin ¼ V in= I in ¼ ðV o= I oÞ Â ð1 À DÞ2 ¼ Ro Â ð1 À DÞ2

9>=>;ð1Þ

where D is T ON /(T ON + T OFF ), Ro is the load resistance fedby the DC–DC converter and R in is the Thevenin’s equiv-alent resistance appearing at the PV array terminals. Theoperation of the other two converters can be explainedon similar lines. The pertinent expressions for these con-verters are:Buck: V o ¼ D Â V in ) Rin ¼ Ro Â ð1= DÞ2

Buck-boost : V o ¼ ð D=ð1 À DÞÞ ÂV in ) Rin ¼ Ro Â ðð1 À DÞ= DÞ2)ð2Þ

These expressions show that by varying the duty cycle ‘ D0

,the load presented to the PV source can be suitably con-trolled to match the PV source impedance. These convert-ers can be operated in various operating modes dependingon the inductor current ( i L ) waveform as shown in Fig. 4.These modes are continuous conduction mode (CCM), justdiscontinuous conduction mode (JDCM) and discontinu-

ous conduction mode (DCM). The converter is said to

(b)

v pv

V o

Control

pulses

R o

I o I in

V in

PV Array

Vpv (V MPP )

i pv

i pv

R in =V in /I in S

LB

D or V ref Controlcircuit

MPPTAlgorithm

T ON T OFF

T s(=1/f s )

(a)

L o a d

Controlcircuit

PV Array

Vpv (V MPP )

i pv

v pv i pv

MPPTAlgorithm

D or V ref Control pulses

DC-DC or DC-AC powerconditioning circuit

Fig. 3. PV power conditioning system. (a) General block diagram and (b) PV system with Boost converter.




operate in the CCM when the inductor current i L neverreaches a zero value. The JDCM is the critical case inwhich the decaying inductor current i L just touches zero be-fore the start of the next switching pulse. The converter issaid to operate in the DCM when i L rises from zero (duringT ON ) and decays to zero (during T OFF ) and remains zerofor a non-zero, nite duration before the next switchingpulse comes.

1.3. PV loads

Basically, there are two types of electrical loads – DCand AC loads. PV systems can be used to feed either of these loads. For certain DC load applications, the PV arraycan be directly connected to the load (e.g. DC pumps).Some other applications, however, may require condition-ing of the generated solar power (through a power elec-tronic stage [11]). A battery back up is usually requiredalong with the PV sources to provide power when solarinsolation is not available. AC loads can either be standalone or grid connected types. The generated solar powerwould usually require at least two conditioning stagesbefore it can be fed into an AC load, as shown in Fig. 5.MPPT is not always fruitful in the case of stand alone

loads, as the load may not be able to absorb all the gener-ated power unless a provision for energy storage (e.g. bat-tery) exists. On the other hand, a grid connected PV systemcan make full use of MPPT, since the grid can absorb anyamount of power generated by the PV source. No batteryback up is required. Hence, grid connected PV systems

are very popular. Grid connected PV systems also enablelocal power generation to meet local power requirements(viz. distributed generation applications). This avoidstransmission losses, reduces the load on the central gener-ating station and improves voltage regulation.

1.4. Grid connected PV systems

Grid connected PV systems typically have two or morestages. The rst stage is a DC–DC converter which is meantfor boosting the array voltage and for MPPT. The secondstage is meant for DC to AC conversion. Several congura-tions [12–14] have been proposed for such systems. Thispaper is concerned only with grid connected PV systems.The number of stages involved in a grid connected PV sys-tem is an important issue, as it determines the overall effi-ciency, reliability and control complexity in such systems.A multiple stage system may be undesirable on account of low efficiency and reliability (owing to increased partcount). Thus, it is desirable to reduce the number of stagesin such systems. There are two major alternatives to achievethis – either use a step up transformer [15] at the output of the power inverter (just before feeding power into the grid)or use PV arrays with large dc voltages [16]. The rst optionadds to the bulk of the system, apart from adding losses.The second option may lead to hot spots during partialshading of the array, reducing the safety and increasingthe probability of leakage current through the parasiticcapacitance between the panel and the system ground. Thisimplies that the ideal solution is to have a low voltage PVarray with only a single stage of intermediate power conver-sion as shown in Fig. 6. This single stage [17] should notonly boost the PV array voltage and invert it into high qual-ity ac waveforms but should also have the provision forextracting maximum power from the given PV array. It isexpected that such a system will be more efficient and reli-able on account of its lower part count.

Time (s)

i L ( A m p s )

i L ( A m p s )

i L ( A m p s )

Switchingpulses

CCM

JDCM

DCM

T OFFT ON

T OFFT ON

T OFFT ON

(a)

(b)

(c)

Fig. 4. Inductor current waveforms for (a) CCM; (b) JDCM and (c)DCM.

Grid orstand

alone acload

MPPT +Boost(boost

or buck-boost

topology)

Inverter

PV Array Stage# 1

Stage# 2

λ

Fig. 5. General topology showing a PV system feeding the grid.




1.5. MPPT in grid connected PV systems

Limited literature [16,18,19] is available that deals withMPPT techniques for single stage grid connected systemswith CCM operation. In such systems, the inverter shouldtake care of MPPT, apart from feeding sinusoidal powerinto the grid. This becomes quite challenging on accountof the non-linear i – v characteristics of the PV array. MPPTcan be achieved either by controlling the operating voltageor current of the PV array. Accordingly, the reference valueof the operating current or voltage is utilized to computethe reference grid current (the current that can be fed intothe grid). To determine the reference current for MPPT insingle stage grid connected PV systems, an incrementalconductance method [16,18,19] has been applied. It is agood approach, as it directly provides the value of the ref-erence grid current, which can then be used by the control-

ler to feed the appropriate sinusoidal current into the grid.It also prevents oscillation of the reference current aboutthe MPP, thereby preventing the icker problem. The samealgorithm, with slight modication in the control scheme,in which the PV array voltage is controlled for MPPT(instead of current) as given by Liang et al. [16] has alsobeen applied to a single stage conguration. Here, the ref-erence voltage is utilized to calculate the reference gridcurrent.

All these algorithms seem to work well when the PVarray is operating in the negative slope region or voltagesource region of the p – v characteristics. The controller,based on these algorithms, is designed using the fact thatthe reference voltage and reference grid current are inver-sely proportional in the region of operation (i.e. voltagesource region). This relationship no longer holds as thePV array enters into the current source region. Thus, thecontroller fails, and the system collapses when the operat-ing point shifts to the positive slope region due to a suddenenvironmental change. There is no method by which thesystem can be restored immediately. Algorithms such asincremental conductance and hill climbing use a smallincremental step size for MPPT. Further, a change in thestep size can be done only after the completion of the ongo-ing grid voltage cycle, to avoid asymmetry in the grid cur-

rent (i.e. feeding DC current into the grid). The tracking

speed with these algorithms is also slow. On the whole,the existing MPPT algorithms for single stage grid con-nected PV systems suffer from the following drawbacks:

1. They mainly control sinusoidal current fed into the grid,which directly governs the power drawn from the PV

source. Problems may arise when the reference currentamplitude turns out to be more than what can be drawnfrom the array. Further, under this condition, it is notpossible to judge whether the system has really goneunstable. This prevents any protective measures frombeing initiated in time.

2. Only a constant incremental change in reference param-eter is allowed to track the optimum power pointexactly.

3. A change in amplitude is allowed only after one funda-mental frequency cycle of the grid voltage to prevent dccurrent injection into the grid. With the existing MPPTtechniques, this constraint results in very slow tracking.

4. It is not possible to predict the reference value (whichthe PV array can provide) due to the non-linear v – i characteristics.

In view of the above, a new algorithm is proposed in thispaper, which can overcome all the above mentioned draw-backs and provide rapid tracking of the MPP by makinguse of an intermediate variable b [9]. This algorithm canpredict the amplitude of the reference current, i.e. it is ableto judge the power that can be drawn from the PV array. Ithas been applied to a new single stage single phase (SSSP)grid connected PV system conguration recently proposed

by the authors [20]. The proposed conguration uses a min-imum number of switches and can be operated in differentmodes as described below.

2. Control strategy for the proposed system

The proposed conguration can be operated in variousmodes depending on the inductor current waveform asshown in Fig. 4. Whether the converter operates in aCCM or DCM, the main objective is to feed the maximumpossible power (with high quality sinusoidal current) intothe grid. This can be achieved by applying a proper controlstrategy for the different operating modes as discussedbelow.

2.1. CCM operation

Fig. 7 shows the schematic diagram of the SSSP topol-ogy [20] considered. The circuit can be visualized as aparallel combination of two buck boost converters witha common PV array input and the outputs tied in anti-parallel. The resultant circuit acts as a current source inver-ter that feeds sinusoidal current into a low value capacitoracross the grid. If this conguration is made to operate inthe CCM, the method of determining the reference current

waveform through inductor, L , is described next.

MPPT + Boost +inversion(boostor buck-boost

+invertingtopology) Grid orstand

alone acload

PV Array Stage# 1

λ 0

v ac i g

Pgrid

V pv I ref (t)

Fig. 6. Single stage topology of PV system feeding the power grid.




Assuming 100% efficiency and unity power factor oper-ation of the inverter ( Fig. 6):

PV output power ¼ Power injected into the gridi:e: V pv Â I ref ¼ V p Â I p Â sin2ðx t Þ

ð3Þ

therefore I ref ¼V p Â I p Â sin2ðx t Þ

V pv

ð4Þ

where V pv is the PV array voltage, which is assumed to beripple free, V p and I p correspond to the amplitude of thegrid voltage and current, respectively, and I ref I ref (t) isthe reference current waveform, which the inductor current

(i L ) must track as depicted in Fig. 6. x is the angular fre-quency of the fundamental grid voltage in rad/s. Eq. (4)shows that to feed a sinusoidal, unity power factor currentinto the grid, the buck boost inductor current should bemade to track a double sinusoidal current reference wave-form. In other words, the energy transferred during eachswitching interval is a double sinusoid.

In SSSP PV systems with CCM operation, to feed sinu-soidal power into the grid, the buck boost inductor currentmust follow the waveform given by Eq. (4). This can beachieved by using hysteresis or bang-bang control [14]. Withthis control strategy, the inductor current i L is restricted

DSP Block

C p I ph V ac

L

X 4p (i Lp )

C f X 3 (V f )

Lf

X 1(i g )

L

X 5 ( v pv ) SW p1

SW p2

SW n1

SW n2

D1

D2

i pv

kV ac

v pv

PV Array eq. circuit

model

Unit Amplitudesine-wave }

SW p1

SW n1SW n2

SW p2

V pv

i pv kV ac

I fb

I ref }

Comparator

LogicalControl

Ckt

FFT

FFT

MPPTBlock

I pv

I ref

Bang-Bangcontrol

X 4n (i Ln )

a b

cd

e f

ghi

jDPV

I fb

Fig. 7. Schematic circuit diagram of the proposed, single-stage PV inverter topology operating in CCM.

t k t k+1

Time (s)

Amps

I

I

I sense

Upper limit

Lower Limit

I ref 2sin ( ) AI t I ref ω × + Δ

2sin ( ) AI t I ref ω × − Δ

2sin ( ) AI t ref ω ×

inV

Lout V

L

'Δ = −t t t k k

k t ′

Fig. 8. A section of reference inductor current waveforms along with the hysteresis band.


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within a certain tolerance band (2 · DI ) as shown in Fig. 8.In other words, turn ON and turn OFF of the switch ( SW p1

or SW n1) is decided on the basis of the deviation of i L fromI ref (i.e. difference between the reference inductor currentand the actual inductor current, i L À I ref ). The inductor cur-rent i L is maintained within the upper and lower limits

around the reference current waveform. When i L ‘bangs’the lower limit as shown in Fig. 8, the switch is turnedON to increase i L . When the inductor current i L ‘bangs’the upper limit, the switch is turned OFF to decrease i L .

Basically, there are two modes of operation when a con-verter operates in the continuous conduction mode (CCM).During Mode I or charging mode, the controlled switchSW p1(or SW n1) during the positive half (or negative half)of the grid voltage is turned ON. Energy is stored in theinductor during this mode. The PV array voltage appearsacross the inductor, which results in an increase of i L .. ByFaraday’s law

V pv¼ Lt Dt ! 0 LDi LDt

¼ Ldi Ldt

) V pv ¼ Lð AI ref Â sin2ðx t 0k Þ þ D I Þ À ð AI ref Â sin2ðx t k Þ ÀD I Þ

t 0k À t k 9>>=>>;ð5Þ

As i L increases and hits the upper limit of the toleranceband, mode II begins. During this mode SW p1(or SW n1)is turned OFF, D1 (or D2) gets forward biased and theinductor current i L decreases as per the followingexpressions:

V f ¼ L ð AI ref Â sin2

ðx t 0k Þ ÀD I Þ À ð AI ref Â sin

2

ðx t k Þ þ D I Þt k þ 1 À t 0k ð6Þ

where V pv is the average input voltage across inductor L(operating voltage of PV array) and V f is the average volt-age across the capacitor during the device OFF time.

The power device SW p1 is switched at high frequency,while SW p2 is kept continuously ON during the positivehalf cycle. When SW p1 is ON, energy is stored in ‘L’ by

the capacitor C pv and the PV source. When SW p1 isOFF, D1 gets forward biased, discharging the stored induc-tor energy into capacitor C f , which feeds sinusoidal currentinto the grid. If the current i L passes through an inductor of value L , then the energy stored ðeÞ ¼ 1

2 Â L Â i2 L is propor-

tional to the square of current ( i L ). If the grid voltage cycle

is divided into ‘n’ high frequency switching cycles, theenergy transferred during the ‘ k th’ switching interval isgiven by

ek ¼ 12 Â L Â ði2

Lðt 0k Þ À i2 Lðt k þ 1ÞÞ

ek ¼ 12 Â L Â ½ð AI ref Â sin2ðx t 0k Þ þ D I Þ2

Àð AI ref Â sin2ðx t k þ 1Þ ÀD I Þ2

9>>=>>;ð7Þ

where n is any positive integer. Assuming t k % t 0k % t k þ 1 andapplying it to the above equation yields:

ek ¼ 12 Â L Â ½4 Â AI ref Â sin2ðx t 0k Þ ÂD I

ek F ðsin2ðx t 0k ÞÞ 9=;ð8Þ

where ‘F ’ denotes the mathematical function.Thus, during each switching interval, the energy trans-

ferred is a double sinusoidal function, which is necessaryfor feeding sinusoidal current into the grid with unitypower factor.

2.2. DCM operation

In the DCM operation, the inductor current alwaysstarts from zero and settles down to zero before the next

switching pulse commences ( Fig. 4(c)). Thus, there is acomplete transfer of inductor energy into capacitor C f (connected across the grid) during each switching interval.To feed sinusoidal power into the grid ,the energy trans-ferred during each switching interval from the buck boostinductor L to capacitor C f should be a double sinusoidalfunction. This can be achieved by using simple sine trianglepulse width modulation (SPWM) [11]. Let the rectied sinewave in SPWM be divided into ‘ n’ intervals. The energy, ek ,transferred during the k th interval ( k 6 n) is given by

Table 1States of power devices and circuit equations during the respective modes for DCM operation [Figs. 7 and 9]Mode State of the device Circuit equations

SW p1 SW p2 D1

I ON ON OFF ipv ¼ C p dvpv

dt þ i Lp ðby KCL at node ‘ a ’ Þ; vpv ¼ L

di Lp

dt ðby KVL in loop abcd Þ;

C f dv f

dt þ ig ¼ 0 ðby KCL at node ‘ e’ Þ; v f ¼ L f

dig

dt þ vac ðby KVL in loop efghÞ

II OFF ON ON ipv ¼ C p dvpv

dt ðby KCL at node ‘ a ’ Þ; Àv f ¼ L

di Lp

dt ðby KVL in loop jehiÞ;

C f dv f

dt þ ig ¼ i Lp ðby KCL at node ‘ e’ Þ; v f ¼ L f

dig

dt þ vac ðby KVL in loop efghÞ

III OFF ON OFF ipv ¼ C p dvpv

dt ðby KCL at node ‘ a ’ Þ; 0 ¼ L

di Lp

dt ðvoltage across inductor L Þ;

C f dv f

dt

þ ig ¼ 0 ðby KCL at node ‘ e’ Þ; v f ¼ L f dig

dt

þ vac ðby KVL in loop efghÞ




ek ¼12

Â L Â i2 pk

¼ ðV 2pv Â M 2Þ=ð2 Â LÞ Âsin2ðp Â k =nÞ

C Â F ðsin2½p Â k =n Þ ð9Þ

where i pk ¼ V pvt on

Lðt on ¼ M Â sinðp Â k =nÞÞ, M (= V s( p)/V tri( p))

is the modulation index used for SPWM and V s( p) andV tri( p) are the amplitudes of the rectied sine wave and tri-angular wave, respectively. F denotes a suitable functionand C is a constant.

DCM operation has three modes, Modes I and II beingthe same as Modes I and II of the CCM operation andMode III is an additional ‘no energy transfer’ mode. Oper-ations in Modes I and II are the same as those in CCM, i.e.charging and discharging of the inductor takes place inthese two modes. Mode III corresponds to a no energy

transfer mode in which capacitor ( C f ) comes across the gridand the PV array charges capacitor ( C P ) across it. The cir-cuit equations corresponding to these three modes aregiven in Table 1 . In Table 1 , v f is the voltage across capac-itor C f . V ac and i g are the grid voltage and current,

L f

C p I ph

L

x 4n

L

x 5

SW p1

SW p2

SW n1

SW n2

D1

D2

i pv

PV Array

v pv

I fb x 4p

V ac

C f x 3

x1

(b)

SW n2

SW n2

C p I ph

L L f

x 4n

L

x 5

SW p1

SW p2

SW n1

D1

D2

i pv

PV Array

v pv

I fb x 4p

V ac

C f x 3

x1

(c)

C p I ph

L L f

x 4n

L

x 5

SW p1

SWp2

SW n1

D1

D2

i pv

PV Array

v pv

I fb x 4p

V ac

C f x 3

x1

(a)

a b

cd

e f

h g

a

d

e

h

f

g

j

i

e f

h g

a

d

Fig. 9. Circuit diagram showing active current paths with bold lines during various operating modes (a) Mode I, (b) Mode II and (c) Mode III.




respectively. Fig. 9 shows the active current paths (boldlines) during each mode.

This paper is mainly concerned with the CCM operationof the proposed SSSP grid connected PV system and itsdesign and simulation in MATLAB.

3. Design procedure for CCM operation

The design of the proposed topology requires determi-nation of the values of the buck boost inductor, L , andthe grid capacitor, C f . The design procedure for theCCM operation is presented next.

3.1. Design of buck boost inductor, L

The design of inductor L is governed by the fact that hys-teresis control is required for the inductor current to trackthe reference current waveform. Let DI be the tolerance cur-rent denoting the hysteresis band. From Fig. 8, we have

V pv

L¼

ð AI ref Â sin2ðx t 0k Þ þ D I Þ À ð AI ref Â sin2ðx t k Þ ÀD I Þt 0k À t k

ð10Þ

V pv

L¼

AI ref Â ðsin2ðx t 0k Þ Àsin2ðx t k ÞÞ þ 2 Â D I t 0k À t k

ð11Þ

where V pv is the average input voltage across inductor L(operating voltage of PV array). tk and t 0k are the switchinginstants as shown in Fig. 8. Assuming, t 0k À t k ¼Dt on ; sinðx ðt 0k À t k Þ Þ % ðx Â Dt on Þ; t 0k þ t k % 2t k and simpli-fying Eq. (11), we have

V pv

L¼ ðÀ AI ref Â sinð2x t k Þ Âx Â Dt on Þ þ ð2 Â D I Þ

Dt onð12Þ

) Dt on ¼2 Â D I Â L

V pv þ AI ref Â sinð2x t k Þ Âx Â Lð13Þ

Similarly, the device OFF time can be calculated as

Dt off ¼2 Â D I Â L

V f þ AI ref Â sinð2x t k Þ Âx Â Lð14Þ

T s ¼Dt on þ Dt off ¼ 2 Â D I Â L

Â1

V pv þ AI ref Â sinð2x t k Þ Âx Â L

þ1

V f þ AI ref Â sinð2x t k Þ Âx Â Lð15Þ

where T s is the switching time period and V f is assumed tobe nearly equal to the grid voltage (i.e. jV f j % jvac j =jV p · sin(x tk )j). At the peak of the grid voltage (i.e.sin(2x tk ) % 0 and sin(x tk ) % 1), Eq. (15) simplies to thefollowing:

T s ¼ L Â2 Â D I

V pvþ L Â

2 Â D I V p

L ¼1

f sðmaxÞ Â 2 Â D I Â

1

V pv

þ1

V p

À19>>>=>>>;

ð16Þ

It should be noted that T s (1/ f s) is a minimum (i.e. maxi-mum switching frequency f s(max) ) when V f is a maximumand vice versa.

3.2. Design of capacitor, C f on the grid side

The design of C f requires the value of the maximumenergy that is transferred through the buck boost inductor.If V is the voltage across the capacitor of value ‘ C ’, then theenergy stored ðeÞ ¼ 1

2 Â C Â V 2 is proportional to thesquare of the voltage. As unity power factor operation isassumed, the maximum energy is transferred at the peakof the grid voltage. Equating the decrease in the energyof the inductor with the increase in energy of the capacitorduring the turn OFF period near the peak of the grid volt-age yields the following:

12 Â L Â ðð AI ref ðmaxÞ þ D I Þ2 À ð AI ref ðmaxÞ À D I Þ2Þ

¼12 Â C f Â ððV p þ DV Þ

2

À ðV p þ DV Þ2

Þ

C f ¼ L Â AI ref ðmaxÞ Â D I

V p Â DV 9>>>>>=>>>>>;

ð17Þ

where AI ref(max) is the maximum amplitude of the referencecurrent corresponding to rated power of the PV array andDV is the maximum ripple voltage across capacitor C f .

3.3. Design of inductor, L f

The design of L f is akin to the design of a low pass lterwith a cut off frequency lower than the minimum switching

frequency. L f can be calculated as

f c ¼1

2 Â p Â ffiffiffiffiffiffiffi L f Â C f p L f ¼

1ð2 Â p Â f cÞ

2 Â C f

9>>>=>>>;ð18Þ

where f c is the cut off frequency and C f is the grid capacitoras dened earlier.

3.4. Design example

The design of the proposed SSSP grid connected PVconguration can be done using Eqs. (16)–(18). As canbe seen from Eq. (14), design of the buck boost inductorrequires advance knowledge of the maximum switching fre-quency and the amount of ripple current it has to handle.Let the maximum switching frequency and ripple current( DI ) be 30 kHz and 2 A respectively. Let the optimum

Table 2Design specications and parameter values for the proposed gridconnected system operating in CCM

DV f c DI AI ref(max.) V p L C f L f

50 V 750 Hz 2 A 30 A 325 V 0.7 mH 2.56l F 18 mH


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operating voltage ( V pv ) of the PV array, when delivering itsrated power, be 105 V and the maximum average voltageacross capacitor ( C f ) during turn OFF be approximatelyV p. With this information and the given specications,design of the important parameters of the system can bedone and is shown in Table 2 .

4. Theory and algorithm of the proposed MPPT techniquefor CCM operation

The electrical equivalent model of a PV cell consists of acurrent source ( I ph ) with a diode connected in anti-parallelas shown in Fig. 7 [21]. The v – i characteristic equation of aPV array is given by [21]:

I pv ¼ I ph À I o Â ðecÂðV pv þ I pv Â RsÞ À 1Þ ð19Þ

where I pv and V pv are the average PV array output currentand voltage, respectively. I ph is the photo generated cur-

rent, I o is the reverse saturation current, c = q/(g ÆK ÆT ),where ‘q’ is the electronic charge, K is Boltzmann’s con-stant, g is the diode ideality factor, T is the ambient temper-ature in Kelvin and R s is the cell series resistance in Ohms.The PV array output power P pv given by

P pv ¼ I pv Â V pv ð20Þ

Taking the derivative of Eq. (20) with respect to V pv , we geto

o V pv P pv ¼

o

o V pvð I pv Â V pvÞ ð21Þ

Substituting Eq. (19) in Eq. (21) yields

o

o V pv P pv ¼ À I o Â ecÂðV pvþ I pvÂ RsÞc Â 1 þ

o I pvo V pv

Â Rs Â V pv þ I pv

ð22Þ

At the MPP, oo V pv

P pv ¼ 0, and therefore, Eq. (22) yields,

À I o Â ecÂðV pvþ I pv Â RsÞc Â 1 þo I pvo V pv

Â Rs ¼I pv

V pv

ð23Þ

Simplifying the above expression by taking the logarithmof both sides and neglecting R s, results in

lnðÀ I o Â cÞ ¼lnI pv

V pvÀ c Â V pv ¼ b ð24Þ

The expression ln( ÀI o · c) is independent of the insolationbut depends on temperature. The variable b at the MPP [9],for dened bounded environmental conditions, lies withina xed, narrow band of the overall variation of b , as theoperating point varies from open circuit to short circuitcondition. This is depicted in the conceptual diagram of Fig. 10. b has a monotonically increasing, one to one rela-tionship with the operating voltage. Thus, the operatingvoltage for MPPT can be controlled by controlling b suchthat b lies in a pre-determined narrow band.

V pv (Volts)

p-v curve

Positive sloperegion

Negative sloperegion

versus AI ref curve

P pv (Watts)

AI ref (Amps)

min.

max.

versus V pv curve

i-v curve

current sourceregion

voltage sourceregion

lim.

AI ref(i)

β ββ

ββ

value

Fig. 10. Typical v – p and v – i curves of a PV array. Variations of b with AI ref and V pv are also plotted.




4.1. Application of the fast MPPT scheme [9] for the proposed SSSP grid connected PV system operating in CCM

As described in the previous section, MPPT can be per-formed by tracking b [9]. However, a relationship between

b and the corresponding current reference amplitude ( AI ref )must be determined. This was achieved with the help of repeated MATLAB/SIMULINK simulations, whichresulted in the following observations:

(1) b reaches a stable value or have injective relationshipwith the reference current amplitude ( AI ref ) when thearray is operating in the negative slope region of the p – v characteristics. It can also be used to verify thesteady state of the system.

(2) b changes continuously and does not settle at a stablevalue when AI ref is greater than the PV array capacityor the system is operating in the unstable region, i.e.the positive slope region of the p – v characteristics. Ascan be seen from Fig. 10, b does not have a stablevalue in the current source region

The following conclusions are drawn from the aboveobservations:

(1) For stable operation, large increments in AI ref

should be allowed only when the array is operatingin the voltage source region, while smaller incre-ments should be allowed near the optimum powerpoint. Operation in the voltage source region canbe conrmed from the lowest value of b

Start

Read V pv , I pv

Calculate ß = ln (I pv /V pv ) - V pv

Check ß for thesteady state

Switch over to hill climbing or other method withconstant small-step change in AI ref

Calculate AI ref(new) = AI ref(old) + error . m

NO

NO

YES

YES

Check whether ß is within the

range (between ß max and ß min )error = ß g - ß

Implement AI ref(new)

ImplementAI ref(i)

Check for the end of

fundamental cycleof the grid voltage

YES

NO

Check ß for

the instability

NO

YES

Fig. 11. Flow chart of the proposed MPPT algorithm.




(bmin ) (Fig. 10) corresponding to the b band at theMPP.

(2) b can be used to arrive at an approximate value of AI ref , as the former has an injective relationship withAI ref when the array is operating in the voltage sourceregion.

(3) The b versus AI ref curve has a minimum slope nearthe optimum power point. This means only smallincrements in the current reference amplitude shouldbe allowed near the optimum power point, i.e. theband of b near the MPP.

Since b at or around the MPP lies within a xed bandfor xed variations in the panel temperature, it is possibleto determine a new value of AI ref . After deciding a ‘refer-ence’ b value (bg) [9], an error function can be determinedthat, when multiplied with a suitable value ( m) and addedto the current value of AI ref , renders a new value of AI ref

as shown below

error ¼ bg À b ð25Þ AI ref ðnewÞ ¼ AI ref ðoldÞ þ error Â m ð26Þ

where AI ref(new) and AI ref(old) correspond to the new and oldvalues, respectively, of AI ref . Eqs. (25) and (26) are applica-ble only when the array is operating in the voltage sourceregion. It is important to note that when b lies within the(bmax À bmin ) band (i.e. the array is near the optimumpower point), only small, incremental steps in the AI ref

amplitude should be allowed for MPPT to avoid instabil-ity. Small, incremental steps result in the exact determina-tion of the MPP, preventing oscillations (about the MPP)and instability. It is also important to restrict b fromincreasing beyond b lim (Fig. 10). b lim corresponds to thatpoint on the b versus V pv curve beyond which the systemgets unstable. Thus, as b approaches b lim , the AI ref ampli-tude is set equal to a pre-dened initial (minimum)value,AI ref( i ) (Figs. 10 and 11 ).

Another signicant parameter is m, which decides thenew I ref amplitude as per Eq. (26). It should be so chosenthat AI ref(new) ensures the new operating point be withinthe voltage source region. To avoid operation in the posi-tive slope region of the p – v characteristics, m is calculatedas the ratio of the minimum difference in AI ref to the max-

imum difference in b as shown below

m ¼ AI ref MPP ðminÞ À AI ref ðiÞ

bg À bhighð27Þ

where AI ref_MPP(min) is the amplitude of the current refer-ence for the MPP at minimum insolation and maximumtemperature. bhigh is the highest value of b corresponding

to AI ref( i ) at maximum insolation and minimum tempera-ture. The ow chart for the proposed algorithm is shownin Fig. 11.

5. Simulation of the system with the proposed MPPTalgorithm

The proposed algorithm was applied to the SSSP gridconnected PV system shown in Fig. 7. The whole system,along with the control algorithm, was simulated usingMATLAB/SIMULINK. The PV array was modeled usingthe MATLAB function block [22]. Each half of the circuit

(i.e. one buck boost converter) operates for one half cycleof the fundamental grid voltage. The reference currentwaveform ( I ref ) of unit amplitude is generated by sensingthe grid voltage. It is then multiplied with AI ref (providedby the MPPT algorithm) to yield I ref . The inductor currentis made to track I ref using the hysteresis control. The aver-age values of vpv and i pv required for the MPPT algorithmare generated using the FFT (fast Fourier transform) blockset.

The circuit equations shown in Table 1 can be convertedinto state equations by replacing the circuit parameterswith the corresponding state parameters ( Fig. 7) as shownin Table 3 . During the positive half cycle, the power deviceSW 1( p) is switched at high frequency. The switching takesplace as per the requirement of the hysteresis control.

Table 4Table showing state equations used for simulation of proposed topology

State equations duringpositive half cycle

State equations duringnegative half cycle

Combined state equation for the twohalves of the grid voltage cycle

ipv ¼ C p x05 þ Ux4 p ipv ¼ C p x0

5 þ Ux4n ipv ¼ C p x05 þ U ðc x4n þ c x4 p Þ

Lx04 p ¼ Ux5 À ð1 À U Þ x3 Lx0

4n ¼ Ux5 þ ð 1 À U Þ x3 c Lx04 p þ c Lx0

4n ¼ Ux5 þ ð 1 À U Þ x3ðÀc þ cÞC f x0

3 þ x1 ¼ ð1 À U Þ x4 p C f x03 þ x1 ¼ ð1 À U Þ x4n C f x0

3 þ x1 ¼ ð1 À U Þðc x4n þ c x4 p Þ x3 ¼ L f x0

1 þ vac x3 ¼ L f x01 þ vac x3 ¼ L f x0

1 þ vac

c is ‘1’ during positive half cycle and ‘0’ during negative half cycle of the grid voltage.c is ‘0’ during positive half cycle and ‘1’ during negative half cycle of

the grid voltage.

Table 3Circuit parameters with their corresponding state parameters used inFig. 7

S. no. State parameter Corresponding circuit parameter

1 x5 vpv

2 x4 p i Lp

3 x4n i Ln

4 x3 v f

5 x1 i g


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SW 2( p) is kept ON for a complete positive half cycle. SW 1( n)

and SW 2( n) are switched in the same manner during the

negative half cycle. Various state equations during the posi-

tive half cycle of the grid voltage are obtained.

v f or x3 (Volts)

1.42 1.425 1.43 1.435 1.44-400

-200

0

200

400

1.4245 1.425 1.4255250

300

350

400

1.42 1.425 1.43 1.435 1.440

5

10

15

20

25

30

35

1.4245 1.425 1.425524

26

28

30

32

34i L ( x 4p or x 4n ) (Amps)

i L ( x 4p or x 4n ) (Amps)Iref

(a) (c)

(b) (d)

vac

v f or x3 (Volts)

v f or x3 (Volts)v f or x3 (Volts)

1.42 1.425 1.43 1.435 1.44-400

-200

0

200

400

1.4245 1.425 1.4255250

300

350

400

1.42 1.425 1.43 1.435 1.440

5

10

15

20

25

30

35

1.4245 1.425 1.425524

26

28

30

32

34

v f or x3 (Volts)

1.42 1.425 1.43 1.435 1.44-400

-200

0

200

400

1.4245 1.425 1.4255250

300

350

400

1.42 1.425 1.43 1.435 1.440

5

10

15

20

25

30

35

1.4245 1.425 1.425524

26

28

30

32

34i L ( x 4p or x 4n ) (Amps)

i L ( x 4p or x 4n ) (Amps)Iref

(a) (c)

(b) (d)

vac

v f or x3 (Volts)

v f or x3 (Volts)

Time (s) Time (s)

Time (s)Time (s)

Fig. 13. Simulation results showing (a) waveforms of voltage across capacitor C f ; (b) current through inductor L for CCM operation; (c), (d) expandedviews of (a) and (b), respectively.

0 0.5 1 1.5 2 2.5 30

1

2

0 0.5 1 1.5 2 2.5 30

500

1000

0 0.5 1 1.5 2 2.5 3-120

-100

-80

-60

0 0.5 1 1.5 2 2.5 30

5

10

150 0.5 1 1.5 2 2.5 3

0

20

Temperature/25(ºC)Insolation (Suns)

P pv(Watts)

Amplitude of referencecurrent waveform ( AI ref )

i pv(Amps)

V pv / 10 (Volts)

Variable

Time (s)

Fig. 12. Waveforms of various parameters on the PV source side of the proposed conguration operating in CCM. Proximity to MPP can be veried bythe reduction in power ripple.




When the switch is turned ON, inductor L (with

state parameter x4 p (Fig. 7) comes across the PV source,

where, xm (m = 1, 3,4 p, 4n,5) represents state parameters

as shown in Figs. 9 and 7 . Using Table 3 in conjunc-

500

1000

-500

0

500

-10

0

10

1.3 1.305 1.31 1.315 1.32 1.325 1.33 1.335 1.340.055

0.06

0.065

THD of current fed into the grid

Current fed into the grid(Amps)

v f or x3 (Volts)

Reactive power fed into the grid (Vars)

Active power fed into the grid (Watts)

Time (s)

1.3 1.305 1.31 1.315 1.32 1.325 1.33 1.335 1.34

1.3 1.305 1.31 1.315 1.32 1.325 1.33 1.335 1.34

1.3 1.305 1.31 1.315 1.32 1.325 1.33 1.335 1.34

Fig. 15. Expanded view of the waveforms shown in Fig. 14.

0 0.5 1 1.5 2 2.50

500

1000

0 0.5 1 1.5 2 2.5-500

0

500

0 0.5 1 1.5 2 2.5-10

0

10

0 0.5 1 1.5 2 2.50.04

0.06

0.08

Reactive power fed intothe grid (Vars)

Active power fed intothe grid (Watts)

THD of current fed into thegrid


Time (s)

v f or x 3 (Volts)

Fig. 14. Waveforms of various parameters on the grid side for the proposed conguration operating in CCM.




1.495 1.5 1.505 1.51 1.515 1.52 1.525 1.530

500

1000

1.495 1.5 1.505 1.51 1.515 1.52 1.525 1.530.072

0.074

0.076

0.078

1.495 1.5 1.505 1.51 1.515 1.52 1.525 1.53-10

-5

0

5

10

Active power fed into the grid (Watts)

Grid-current (Amps)

THD of grid-current

Time (s)

Reactive power fed into the grid (Vars)

Fig. 17. Expanded view of the waveforms shown in Fig. 16.

0 0.5 1 1.5 2 2.5 30

500

1000

0 0.5 1 1.5 2 2.5 30.05

0.1

0.15

0.2

0 0.5 1 1.5 2 2.5 3-10

-5

0

5

10

Active power fed into the grid(Watts)Reactive power fed into the

grid (Vars)



Time (s)

Fig. 16. Simulation results showing grid side waveforms for the proposed topology operating in JDCM.




1.4 1.405 1.410

100

200

300

400

500

1.403 1.404 1.405 1.406 1.407

200

300

400

500

1.4 1.405 1.410

20

40

60

1.4001 1.4002 1.4003 1.4004 1.40050

1

2

3

v f or x 3 (Volts)

v f or x 3 (Volts)

vac

Time (s) Time (s)

Time (s) Time (s)

i L ( x 4p or x 4n )(Amps)

i L ( x 4p or x 4n ) (Amps)

(a) (c)

(b) (d)

Fig. 19. Simulation results showing (a) waveforms of voltage across capacitor C f ; (b) current through inductor L for JDCM operation; (c), (d) expanded

views of (a) and (b), respectively.

0 0.5 1 1.5 2 2.5 30

1

2

0 0.5 1 1.5 2 2.5 30

500

1000

0 0.5 1 1.5 2 2.5 3

-120

-100

-80-60

0 0.5 1 1.5 2 2.5 30

5

10

150 0.5 1 1.5 2 2.5 3

0

50

p pv(Watts)

Amplitude of referencecurrent waveform

i pv(Amps) V pv / 10 (Volts)

Variable ß

Insolation(Suns) Temperature/25(ºC)

Time (s)

Fig. 18. Simulation results showing PV side waveforms of the proposed conguration operating in JDCM.




0 0.5 1 1.5 2 2.5 30

50

0 0.5 1 1.5 2 2.5 30

500

1000

0 0.5 1 1.5 2 2.5 3-10

0

10

0 0.5 1 1.5 2 2.5 30

0.05

0 0.5 1 1.5 2 2.5 3-500

0

500

Reactive power fed intoActhe grid (Vars)tive power fed into the grid

(Watts)

Current fed into the grid (Amps)


i L ( x 4p or x 4n) (Amps)

v f or x 3(Volts)

Time (s)

Fig. 21. Simulation results of the proposed topology operating in DCM showing grid side waveforms. Sudden change and high value of THD is the result

of a sudden, large change in modulation index during the tracking phase, immediately after an environmental condition (e.g. insolation) has changed.

0 0.5 1 1.5 2 2.5 30

1

2

3

0 0.5 1 1.5 2 2.5 30

500

1000

0 0.5 1 1.5 2 2.5 3-120-100

-80-60-40-20

0 0.5 1 1.5 2 2.5 30

10

20

300 0.5 1 1.5 2 2.5 3

0

5

Insolation(Suns)

Temperature/25(ºC)

p pv(Watts)

Amplitude of reference sine wavein sine-triangle PWM

i pv(Amps)

v pv /5 (Volts)

Variable

Time (s)

Fig. 20. Simulation results for the proposed topology operating in DCM. PV side waveforms are shown. Proximity to MPP can be identied with thereduction in power ripple.




tion with Table 1 , the following state equations can bederived:

When switch is turned ON When switch is turned OFFipv ¼ C p x0

5 þ x4 p ; x5 ¼ Lx04 p

C f x03 þ x1 ¼ 0; x3 ¼ L f x0

1 þ vac

ipv ¼ C p x05; À x3 ¼ Lx0

4 p

C f x03 þ x1 ¼ x4 p ; x3 ¼ L f x0

1 þ vac

ð28Þ

With the help of the switching ‘ U ’, dened below, a gener-alized equation for both the negative and positive half cy-cles of a grid voltage cycle can be derived as shown in Table4.

U ¼1 when c error > þ D I

0 when c error < ÀD I ð29Þ

where

c error ¼ I sense À I ref ð30Þ

with I sense denoting the actual, sensed current. The com-bined set of equations shown in Table 4 are simulated usingMATLAB/SIMULINK [21,22]. The simulation results areshown in Figs. 12–15.

The grid connected circuit was also simulated for itsoperation in the other modes such as the discontinuouscurrent mode (DCM) and the just discontinuous currentmode (JDCM) for comparison with the CCM operation.The design, modeling, simulation and MPPT for theJDCM operation was done along similar lines as the CCMwith proper modications. On the other hand, the DCMoperation was designed and simulated using the xed fre-quency, sine triangle PWM strategy to achieve both MPPTand current shaping based on the concept of controlling b

[9,20]. The simulation results for the JDCM and DCMoperations are shown in Figs. 16–21 and are compared withthe CCM results. The proposed conguration works atnear unity power factor [20] as can be observed in the sim-ulation results given in Figs. 14, 16 and 21. During theCCM, although the current stress on the devices is less,complete demagnetization of the buck boost inductor

during each half cycle of the grid voltage must be ensured.Table 5 summarizes the salient features of the variousmodes of operation for the purpose of comparison.

6. Conclusions

This paper presented some of the basic aspects of PVenergy with focus on PV systems. The basic back groundneeded to understand the working of PV systems, such asmaximum power point tracking (MPPT), DC–DC convert-ers and CCM and DCM operating modes have been pre-sented. The focus has been on grid connected PV systemsoperating in the CCM. Operation, analysis and the designprocedure for a new SSSP grid connected PV system in theCCM has been presented. A new MPPT technique, suitablefor CCM operation has also been proposed. Tracking of anintermediate variable b makes the convergence of the sys-tem to the MPP faster. A comparison has also been pre-sented between various modes of operation, viz. CCM,DCM and JDCM. The following conclusions emerge fromthis study:

1. Switching and conduction losses are lower in the case of CCM operation compared to those in DCM or JDCMoperations.

2. Peak current stress on the devices is drastically reduced(to nearly half) in the case of CCM operation comparedto JDCM or DCM operation for the same poweroutput.

3. In view of (1) and (2), CCM operation is more efficientthan the other two.

4. Because of higher peak currents in the DCM or JDCM,the system is more prone to EMI/EMC problems thanin the CCM.

5. DCM operation has the advantage of feeding high qual-ity current waveforms (nearly unity power factor) intothe grid as compared to the CCM or JDCM operations.Also, MPPT in the DCM operation is indirectly basedon array voltage control, which results in stable opera-tion of the system over the entire i – v characteristics of the PV array. However, with proper control strategies,these drawbacks of the CCM operation can beminimized.

CCM operation improves the over all efficiency of thePV system with minor trade offs with power factor andTHD (total harmonic distortion) of grid current. In con- junction with a fast MPPT algorithm, suitably modiedfor CCM operation, the efficiency of the whole system isincreased during the MPP tracking phase. The proposedalgorithm is able to predict the AI ref that can be drawnfrom the PV array. With variable, large step changes inAI ref , an approximate MPP is reached within a few itera-tion steps, drastically reducing the tracking time as com-pared to conventional techniques, which take up to 10 sor more (typically) to reach the MPP. With the proposed

algorithm, it takes less than 2 s. In addition to this, the

Table 5Comparison between various modes of operation

S. no. Parameter Mode of operation

CCM JDCM DCM1 C pv (l F) Low Medium High2 L (mH) High Medium Low3 Switching frequency

variationLow High 0

4 THD of grid current 6–8% 5–7% Less than 5%5 MPPT control strategy Current

controlCurrentcontrol

Voltagecontrol

6 Reactive power fedinto the grid

Less More Negligible

7 Buck-boost inductorcurrent

Low Medium High

8 Stress on switchingdevice

Low Medium High

9 Switching losses Low Medium High




proposed algorithm is able to detect quickly any instabilitycondition that may arise due to a sudden decrease ininsolation.

References

[1] Schmitz M et al. Assessment of the potential improvement due tomultiple apertures in central receiver systems with secondaryconcentrators. Solar Energy 2006;80(1):111–20.

[2] Gruber DP et al. Spatial distribution of light absorption in organicphotovoltaic devices. Solar Energy 2005;79(6):697–704.

[3] Hua C et al. A modied tracking algorithm for maximum powertracking of solar array. Energy Convers Manage 2004;45(6):911–25.April.

[4] Karimov Kh S et al. A simple photo-voltaic tracking system. SolarEnergy Mater Solar Cells 2005;87(1–4):49–59. May.

[5] Bose BK et al. Microcontroller control of residential photovoltaicpower conditioning system. IEEE Trans Industry Appl 1985;21(5):1182–91.

[6] Hussein K et al. Maximum photovoltaic power tracking: an algo-rithm for rapidly changing atmosphere conditions. IEE Proc – G1995;142:59–64.

[7] Calais M et al. A ripple-based maximum power point trackingalgorithm for a single-phase, grid-connected photovoltaic system.Solar Energy 1998;63(5):277–82.

[8] Salameh ZM et al. Step-down maximum power point tracker forphotovoltaic systems. Solar Energy 1991;46(5):279–82.

[9] Jain Sachin, Agarwal Vivek. A new algorithm for rapid tracking of approximate maximum power point in photovoltaic systems. IEEEPower Electron Lett 2004;2(1):16–9.

[10] Mohan Ned. Power electronics – Converters applications and design.second ed. John Wiley; 2001.

[11] Walker GR et al. Cascaded DC–DC converter connection of photovoltaic modules. IEEE Power Electron Specialists Conf 2002;2:1015–20. June.

[12] Kang F et al. Photovoltaic power interface circuit incorporated witha buck-boost converter and a full-bridge inverter. Applied Energy2005;82(3):266–83.

[13] Shinohara H et al. Development of a residential use, utility interac-tive PV inverter with high-frequency isolation. Solar Energy MaterSolar Cells 1994;35(11):429–36. September.

[14] Calais M et al. A cascaded inverter for transformerless single-phasegrid-connected photovoltaic systems. Renew Energy 2001;22(1–3):255–62.

[15] Kang F et al. A new control scheme of a cascaded transformer typemultilevel PWM inverter for a residential photovoltaic powerconditioning system. Solar Energy 2005;78(6):727–38. June.

[16] Liang TJ et al. Single-stage photovoltaic energy conversion system.IEE Proc Electric Power Appl 2001;148(4):339–44.

[17] Kasa N et al. Maximum power point tracking with capacitoridentier for photovoltaic power system. IEE Proc Electric PowerAppl 2000;147(6):497–502.

[18] Yeong-Chau Kuo et al. A high-efficiency single-phase three-wirephotovoltaic energy conversion system. IEEE Trans IndustrialElectron 2003;50(1):116–22.

[19] Liang TJ et al. Novel maximum-power-point-tracking controller forphotovoltaic energy conversion system. IEEE Trans IndustrialElectron 2001;48(3):594–601.

[20] Sachin Jain, Annual Ph.D. progress report, August 2004, Departmentof Electrical Engineering, IIT-Bombay, India.

[21] Walker G. Evaluating MPPT converter topologies using a MATLABPV model. J Electrical Electron Eng Australia IE Aust 2001;21(1):49–56.

[22] Pires VF, Silva JF. Teaching nonlinear modeling, simulation, andcontrol of electronic power converters using MATLAB/SIMULINK.IEEE Trans Educ 2002;45(3):253–61.


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