Mppt With Incremental Conductance

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A Novel Stand-alone PV Generation System Based onVariable Step Size INC MPPT and SVPWM Control

Jiyong Li 1 and Honghua. Wang 2

1 College of Electrical engineering, Hohai University, Nanjing, 210098, China2 College of Electrical engineering, Hohai University, Nanjing, 210098, China

Abstract- T he power available at the output of photovoltaic (PV)cells keeps changing with solar irradiation and ambienttemperature because PV cells exhibit a nonlinear current-voltagecharacteristic. So its maximum power point of photovoltaic cellsvaries with solar irradiation and ambient temperature. Maximumpower point tracking (MPPT) techniques are used in PV systems tomake full utilization of PV array output power which depends onsolar irradiation and ambient temperature. Compared with the

conventional fixed step size the incremental conductance (INC)method, this paper proposes a variable step size INC MPPTalgorithm which can effectively improve the MPPT speed andaccuracy simultaneously. Inverter control is another key aspect inPV generation system. This paper proposes Space Vector PulseWidth Modulation (SVPWM) control scheme for three-phasePWM inverter is used in PV generation system. A novelstand-alone PV generation system based on a variable step sizeINC MPPT method and SVPWM control scheme for three-phasevoltage source PWM inverter is built in Matlab/Simulink softwarein this paper. Results of simulation show that the novel stand-alonePV generation system can have good performance of MPPT andthe high quality of output voltage.

Index Terms- Maximum power point tracking (MPPT),photovoltaic generation, simulation, space vector pulse widthmodulation (SVPWM).

I. I NTRODUCTION Solar energy is a clean, a maintenance-free, and an abundant

source of energy. The rapid trend of industrialization of nationsand increased interest in environmental issues has recently toconsideration of the use of renewable forms such as solar energyand wind energy. Photovoltaic (PV) arrays produce electric

power directly from sunlight. Photovoltaic (PV) generation is becoming increasingly important as a renewable source since itoffers many advantages such as incurring no fuel costs, not

being polluting, requiring little maintenance, and emitting nonoise. Because of the nonlinear relationship between the currentand the voltage of the photovoltaic cell, it can be observed thatthere is a unique maximum power point (MPP) at a particularenvironment, and this peak power point keeps changing withsolar illumination and ambient temperature [1]. An importantconsideration in achieving high efficiency in PV powergeneration system is to match the PV source and load impedance

properly for any weather conditions, thus obtaining maximum

power generation. The technique process of maximum power point is been tracking which is called maximum power pointtracking (MPPT). In recent years, a large number of techniqueshave been proposed for maximum power point tracking(MPPT), such as the constant voltage tracking (CVT) [2], the

perturb-and-observe (P&O or hill-climbing) method, theincremental conductance (INC) method, and so on. At last, thesealgorithms modify the actual voltage in order to increase the

power output.The CVT is very simple and can be easy implemented. But the

constant voltage can’t track MPP when solar illuminationchanges so the constant voltage method is not often used in thetrue MPPT strategy. The P&O method is based on the principleof perturbation and observation [3]. However, this method hasseveral drawbacks such as slow tracking speed and oscillationsabout MPP, making it less favorable for rapidly changingenvironmental conditions. The INC method is based on the factthat the slope of the PV array power curve is zero at the MPP,

positive on the left of the MPP, and negative on the right [4]. The INC algorithm decrements or increments V ref to track the

new MPP when atmospheric conditions change.It must be pointed out that all the conventional trackingmethods use fixed, small iteration steps, determined by theaccuracy and tracking speed requirements. If the step-size isincreased to speed up the tracking, the accuracy of trackingsuffers and vice versa. To overcome above limitation, a variablestep size INC method is applied in MPPT of photovoltaic (PV)generation in this paper. The proposed scheme offers the fastMPPT and accurate MPP over the existing schemes.

Inverter’s control is another key aspect in PV generationsystem. With the development of power electronic, technologyof pulse width modulation (PWM) has been widely applied ininverter. The sine PWM technology is applied into many aspects

by its simplicity, easy implementation. However, when the inputDC voltage is rated, the foundational wave amplitude of outputline voltage of is only 0.866 times of it, this restricts thedevelopment seriously. On the contrary, the space voltagevector pulse width modulation (SVPWM) differs from it, andSVPWM has low total harmonic distortion (THD). SVPWM hasmany advantages such as constant switching frequency,well-defined output harmonic spectrum, optimum switching

patterns, and excellent dc-link voltage utilization [5].In order to improve efficiency and gain better quality of

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output power in PV power generation system, a novelstand-alone PV generation system based on a variable step sizeINC MPPT method and SVPWM control scheme forthree-phase source PWM inverter is proposed in this paper.

II. CHARACTERISTIC OF PV CELL Photovoltaic cells consist of a silico n P-N junction that when

exposed to light releases electrons arou nd a closed electricalcircuit. The circuit equivalent of a PV cell can be modeledthrough the circuit shown in Fig. 1. This is modeled by the lightgenerated current source ( I ph). The intrinsic P-N junctioncharacteristic is introduced as a diode in the circuit equivalent[6].

Fig. 1. Photovoltaic cell equivalent circuit The photo current I ph generated in the PV cell is proportional

to level of solar illumination. I is the output current of photovoltaic cell. The current ( I d ) through the bypass diodevaries with the junction voltage V j and the cell reverse saturationcurrent I 0. V is the output of the photovoltaic cell. R sh and R s arethe parallel and series resistances, respectively. Parallelresistance R sh is very large while the series resistance R s is small.When the number of cell in series is n s, and the number of cellsin parallel is n p. There are relevant mathematical equationsexpressing as following:

( / )

0

/[ 1]

s sq V n IR s snkT

p ph p sh

V n IR I n I n I e

R

++

= − − − (1)

( ) ( )1000 ph sc T ref

S I I C T T = + − (2)

Where1 1

[ ( - )]3

0 ( ) g

ref

qE

nk T T do

ref

T I I e

T = , 191.6022 10q C −= × is the

electronic charge, n is the emission coefficient of diodes,23 11.3807 10 JK k − −= × is Boltzmann’s constant, T is ambient

temperature in Kelvin, and ref T is reference absolute

temperature. sc I is the short current, S is the level of solarillumination, g E is the energy of the band gap for silicon which

is (1~3) eV, T C is the short-circuit-current temperature

coefficient(=0.0016A/K), do I is the reverse current of diode.The output power of a PV array is the product of current I and

terminal voltage V ; thus( / ) 2

0

/[ 1] )

s sq V n IR s snkT

p ph p sh

V n VIR P n VI n VI e

R

++

= − − − (3)

From above equations, it is known that the characteristic ofPV will be changed when S and T change. Changes in thesevariables S and T cause the current-voltage ( I-V ) curves of

photovoltaic array to change as well. As illustrated in Fig. 2.Besides the solar illumination, another important factor

influencing the characteristics of a photovoltaic module isambient temperature, as shown in Fig. 3. At the same time, it can

be seen that the solar illumination and ambient temperature willinfluence the output power of a PV module. The output power ofa PV changes with the solar illumination’s variation whentemperature is constant 40 , as shown in Fig. 4.

Fig. 2. Current versus voltage curves of PV array influenced by solar

illumination

Fig. 3. Current versus voltage curves of PV array influenced by temperature

Fig. 4. Power versus voltage curves influence by the solar illuminationAnd the characteristic of output power changes with the

ambient temperature’s variation when the solar illumination isconstant 1000W/m 2, as shown in Fig. 5.

From Fig. 4 and Fig. 5, it can be seen that the output power ofa PV module is influenced by the solar illumination and ambienttemperature. So the MPP will be change when peripheralcondition is changed. MPP is more difficult to search accurate

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track MPP by above conventional tracking methods when thesolar illumination and ambient temperature change. In order toquick and accurate track MPP under any weather conditions, avariable step size INC MPPT algorithm is applied in PV powergeneration system in this paper.

Fig. 5. Power versus voltage curves influence by temperature

III. THE VARIABLE STEP SIZE INC MPPT ALGORITHM The INC MPPT algorithm is based on the fact that the slope of

the PV array power curve is zero at the MPP, positive on the leftof the MPP, and negative on the right.

/ 0, at MPP

/ 0, left of MPP

/ 0, right of MPP

dP dV

dP dV

dP dV

=

>

<

(4)

By derivation, it can be gained the relationship between theinstantaneous conductance ( I/V ) and the incrementalconductance ( I / V ). The MPP can be tracked by comparing

I /V to I / V , as shown in equation (5)./ / , at MPP

/ / , left of MPP

/ / right of MPP

I V I V

I V I V

I V I V

∆ ∆ = −

∆ ∆ > −

∆ ∆ < −

(5)

It can be supposed that V ref equal to V MPP at the MPP. Oncethe MPP is reached, the operation of the PV array is maintainedat this point unless a change in I is noted. The algorithmdecrements or increments V ref to track the new MPP when theatmospheric condition changes[4]. The INC MPTT algorithmusually uses a fixed iteration step size, the power drawn from thePV array with a lager step size contributes to faster dynamics butexcessive steady state oscillations, resulting in a comparativelylow efficiency. If iteration step size is small, then the powerdrawn from the PV array will have slower dynamics. To solvethese dilemmas, a modified INC MPPT with variable step size isapplied in this paper. The step size is automatically tunedaccording to the inherent PV array characteristics. If theoperating point is far from MPP, it increases the step size whichenables a fast tracking ability. If the operating point is near to theMPP, the step size becomes very small that the oscillation iswell reduced contributing to a higher efficiency. The flow chartof the variable step size INC MPPT algorithm is shown in Fig. 6,where the Variable step size V δ is automatically tuned.Variable step size adopted to reduce the problem mentionedabove is shown as following,

1 1

1

N N N N

N N

V I V I V N

V V δ − −

−

−=

− (6)

where coefficient N is the scaling factor which is tuned at thedesign time to adjust the step size.

Fig. 6. Flowchart of the variable step size INC MPPT algorithm

IV. PRINCIPLE OF SVPWMIn recent years, Space Vector Pulse Width Modulation

(SVPWM) technology gradually obtains widespreadapplications in the power electronics and the electrical drives.Comparing to the conventional Sine Pulse-Width Modulation(SPWM), its DC voltage utilization ratio has been enhancedvery much and it is also easier to realize digitally. The powercircuit topology of a three-phase voltage source inverter (VSI) isshown in Fig. 7. Each switch in the inverter leg is composed oftwo back-to-back connected semiconductor devices.

Fig. 7. Topology of a three-phase voltage source inverterThere are totally eight possible switching patterns and each of

them determines a voltage space vector. As shown in Fig. 8,eight voltage space vectors divide the whole space into sixsectors, I ~ VI. Except two zero vectors, V0 and V7, becauseinverter’s output voltage is zero as it is (000) or (111) state,

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nonzero effective denoted by { iV →

,i=1,……6} as it is in the othersix states, all other active space vectors have the samemagnitude of (2/3) V dc [7][8]. That is 2 / 3, 1,......,6i dcV V i= = .

Phase voltage space vectors are shown as in table I.

Fig. 7. Voltage space vector graph and sectors TABLE I

PHASE VOLTAGE SPACE VECTORS

State Switch on Phase voltage space vectors

1 1,6,2 (2/3) V dc

2 1,3,2 (2/3) V dcexp(j /3)

3 4,3,2 (2/3) V dcexp(j2 /3)

4 4,3,5 (2/3) V dcexp(j )

5 4,6,5 (2/3) V dcexp(j 4/3)

6 1,6,5 (2/3) V dcexp(j 5/3)

0 and 7 1,3,5 or 4,6,2 0

In SVPWM, the reference voltage vector should besynthesized by the adjacent vectors of the located sector in order

to minimize the switching times and to minimize the currentharmonics [9]. If a reference voltage vector ref V V =

in some

sectors with sustaining (sampling) period T , then we can expressit by using its neighboring effective voltage vectors iV and 1iV + with appropriate operating times T i and T i+ 1 as follows

1 1 , 1......, 6i i i iV T V T VT i+ ++ = =

(7)The SVPWM algorithm is firstly to get its two correspondingcomponent equations in α β − reference frame for (7), and thento solve the operating times of the neighboring effective voltagevectors. An example of the synthesizing procedure in sector I(0~60°), i. e., i=1, as described in Fig. 7, suppose a reference

voltage vector ref V V =

, where T is the PWM period, T 1 and T 2 are time durations of two active vectors in each PWM cycle. Thecorresponding component equations in α β − reference of (7)are as follows [10]:

1 1 2 2

2 2

cos60

sin 60

oa

o

V T T V T V

V T T V β

= +

=

(8)

Where V V are the corresponding axis components of V .Solving (8) for T 1 and T 2 gives the operating times as (9).

1

2

31( 3 )

2

3

s

dc

s

dc

T T V V

V

T T V

V

α β

β

= −

=

(9)

T 0 is the time duration of zero active vectors in each PWMcycle and equals to ( T -T 1-T 2). In order to obtain fixed switching

frequency and optimum harmonic performance, each leg shouldchange its state only once in one switching period. This isachieved by applying zero state vector followed by two adjacentactive state vector in half switching period. The next half of theswitching period is the mirror image of the first half [11]. Fig. 8shows the method of PWM generation corresponding to the caseshown in Fig. 7. Using the same approach, we can calculate theother relative vectors’ operating time in the other sectors.

Fig. 8. Generation of three phase PWM

V. SIMULATION OF A NOVEL STAND -ALONE PV GENERATIONSYSTEM

The block diagram of a stand-alone PV generation system based on a variable step size INC MPPT method and SVPWMcontrol scheme for three-phase source PWM inverter is shownin Fig. 9. It consists of PV module, dc link capacitor, DC-DCconverter, three phase voltage source inverter (VSI), L-C filter,and load. The first stage is DC-DC converter for MPPT. Thesecond stage is inverter with SVPWM control strategy.

Fig. 9. Schematic diagram of the proposed stand-alone PV system In order to verify the novel PV generation system proposed in

this paper. Simulation has been performed in Matlab/Simulinksoftware when solar illumination rises from 400 W/m 2 to 1000W/m 2 at 0.03 second and decrease from 1000 W/ m 2 to 400W/m 2 at 0.1 second. Voltage-curves of MPPT with different stepsize can be seen in Fig. 10, and power-curve can be seen in Fig.11.

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Fig. 10. Output voltage of PV module with different step size

Fig. 11. Output power of PV module with different step size

From the output performance of INC MPPT with differentirradiation step size, comparing with the MPPT with fixed stepsize of 1, the MPPT with fixed step size of 10 exhibits a gooddynamic performance but larger steady state oscillations. Thevariable step size method solves the dilemma. We can see thevariable step size INC method have more dynamic performanceand smaller steady state than that of fixed step size.

Fig. 12. Output line voltage of system for SPWM

Fig. 13. The THD of output voltage for SPWM

Fig. 14. Output line voltage of system for SVPWM

Fig. 15. The THD of output voltage for SVPWMFig. 12 and Fig. 13 show the output line voltage Vab and the

total harmonic distortion (THD) for SPWM. Fig. 14 and Fig. 15show the output line voltage Vab and THD for SVPWM. FromFig. 14 and Fig. 15, we can know that the inverter output voltageis sinusoidal with a THD of 3.4% when control strategy ofinverter is applied with SVPWM, then THD of the outputvoltage with SPWM control strategy is 7.5%.

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VI. CONCLUSIONS In this paper, a stand-alone PV generation system based on a

variable step size INC MPPT method and SVPWM controlscheme for three-phase voltage source PWM inverter is

proposed. Both fixed step size and the proposed variable sizeINC MPPT methods are implemented with Matlab/Simulink forsimulation. From results of simulation, it can be seen that the

variable step size INC MPPT algorithm which is able to improvethe dynamic and steady state performance of the PV systemsimultaneously. At the same time, output results of inverter withSVPWM control strategy have better power quality than that ofinverter with SPWM control strategy, and simulation results ofsystem demonstrate that the novel PV system has the fast andeffective response under changing atmospheric condition. Sothe stand-alone PV generation system based on a variable stepsize INC MPPT method and SVPWM control for three-phasevoltage source PWM inverter is feasible and effective.

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[3] S. Jain, and V. Agarwal, “Comparision of the performance of maximum power point tracking schemes applied to single-stage grid-connected photovoltaic systems,” IET Electr. Power Appl. , Vol. 1, No. 5, pp. 753-762,September 2007.

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[9] Vineeta Agarwal, and Alck Vishwakarma, “A Comparative Study of PWMSchemes for Grid Connected PV Cell,” IEEE The 7th InternationalConference on Power Electronics and Drive Systems (IEEE PEDS2007),

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[11] Wang Xu, Huang Kaizheng, Yan Shijie, and Xu Bin, “Simulation ofThree-phase Voltage Source PWM Rectifier Based on the Space VectorModulation,” 2008 Chinese Control and Decision Conference , July 2-5,2008, Yantai, China, pp. 1881-1884.

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