MATLAB/SIMULINK Based Modelling Photovoltaic Array Fed T-Source Inverter

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Photovoltaic Array Fed T-Source Inverter

G. Hemaprabha, R. Kiruthika, P. Vijayasalini

Assistant Professors, Department of EEE, Info Institute of Engineering, Coimbatore, India

International Journal of Research in Electrical & Electronics Engineering Volume 2, Issue 4, October-December, 2014, pp. 20-30

ISSN Online: 2347-5439 Print: 2348-0025, DOA : 19112014 © IASTER 2014, www.iaster.com

ABSTRACT

In order to utilize the solar energy for industrial, commercial and domestic applications the power conversion schemes plays an important role. The problem exists in conventional power conversion schemes are low efficiency, poor transient response, low voltage gain and more reactive components are being used .This paper proposes a single stage power conversion scheme called T-source inverter(TSI) to overcome these drawbacks. T-Source inverter (TSI) with simple boost control scheme is used as interface circuit between PV array and load. The PV array is analyzed under different irradiation and temperature value. The mathematical equations are verified with simulation and hardware. The verification shows the voltage gain of TSI was comparatively higher than ZSI. The reactive components in the circuit are less, fast transient response and low output ripple.

Keywords: PV cell, T-source Inverter-Source inverter, Voltage Source Inverter, Simple Boost Control.

1. INTRODUCTION

Due to increase in energy consumption and depleting of fossil fuels the renewable energy sources have become cynosure of all eyes. Nowadays solar and wind energy power generations are rapidly grown when compared to other renewable source. In India solar potential is high and wind power generations have the limitation of medium wind profile, low plant factor and saturation of optimal wind locations. Solar irradiation is abundant in India by figures (4 -7) kw/m2 per day in all over the country with 300clear sunny days in a year. The 70% of Indian population are involved in agricultural and living in rural areas. Still 1/3rd of Indian population are not connected to grid electric supply [*] for that reason photo voltaic distributed power generation is most popular.

Two methods are available to convert solar energy into alternating current (AC) supplies are 1.) Single stage conversion 2.) Two stage conversions. These days single stage conversions are more popular than two stage conversion because of reduced system size, cost and high efficiency.

DC to DC Boost Conversion DC to AC LOAD PV ARRAY DC TO AC TRANS- FORMER LOAD PV ARRAY

Fig.1.A Two Stage Power Conversion Fig 1.B Two Stage Power Conversion

DC TO AC LOAD PV

ARRAY

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Conventional methods of photovoltaic energy conversion systems are suffer from voltage buck boost capability in single stage. It is possible with Z-source inverter, but this type of inverter has some limitations like more reactive components, high ripple contents and occupies more space. When compared to z-source inverter T-z-source inverter has few reactive components and high voltage gain. High voltage gain is possible by adjusting the number of turns in coupled inductor of T-network. This T-source inverter has the L and C impedance network in T-shape combined with Voltage source inverter (VSI).

II. PV ARRAY MODEL

The equivalent electric circuit model of PV cell is used here for implementation in MATLAB. The equivalent circuit models of PV cells are connected in series and parallel combination to attain desired output voltage and power of PV array.

Fig.2.1 Equivalent Circuit of Photovoltaic Cell Fig: 2.1 show the simplest model of a PV cell. An equivalent circuit consists of an ideal current source in parallel with an ideal diode. The current source represents the current generated by photons (often denoted as Iph or IL), and its output is constant under constant temperature and constant incident

radiation of light. The photon generated current will follow out of the cell as a short-circuit current (Isc). Thus, Iph = Isc. Assume that output is in open-circuit, the photon generated current is shunted

internally by the intrinsic p-n junction diode. This gives the open circuit voltage (Voc). The output

current (I) from the PV cell is found by applying the Kirchoff‟s current law (KCL) on the equivalent circuit shown in Fig.2.1.

0 d sc d PV P V I I I R     ₍₁₎ Where:

Isc is the short-circuit current that is equal to photon generated current

Id is the current shunted through the intrinsic diode

Vd is the voltage across the diode (V)

RP=RSH is Parallel Resistance (ohm)

Table1: Electrical Characteristics of PV Array

S.No Parameter Value

1 Maximum power (Pmax) 180W

2 Voltage at Pmax (Vmpp) 35.8V 31.9V 3 Current at Pmax (Impp) 5.03A 4.02A 4 Short circuit current (Isc) 5.58A 4.52A 5 Open circuit voltage (Voc) 43.6V 39.7V

6 Module efficiency 14.4%

7 Tolerance -3/+5%

8 Nominal voltage 24V

9 Limiting reverse current 5.58A

10 Temperature coefficient of Isc (0.065±0.015)%/ºC 11 Temperature coefficient of Voc -(0.36±0.05) %/ºC 12 Temperature coefficient of Pmax -(0.5±0.05) %/ºC 13 Maximum series fuse rating 20A

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The diode current Id is given by the Shockley‟s diode equation:

I



I e

(



1)

Where:

Io is the reverse saturation current of diode (A)

q is the electron charge (1.602×10-19 C) Vd is the voltage across the diode (V)

K is the Boltzmann‟s constant (1.381×10-23 J/K),

T is the junction temperature in Kelvin (K)

Applying the Kirchoff‟s voltage law (KVL) on the equivalent circuit shown in Fig.2.1

V



V



R I

Replacing Id of the equation (1) by the equation (2) gives the current-voltage relationship of the PV

cell.

I

 

I

I e

(



1)

Where:

V is the voltage across the PV cell I is the output current from the cell

The reverse saturation current of diode (Io) is constant under the constant temperature and found by

setting the open-circuit condition as shown in Fig.2.5 (b). Using the equation (4), let I = 0 (no output current) and solve for Io.

/

1

I

I

e





To a very good approximation, the photon generated current, which is equal to Isc, is directly

proportional to the irradiance, the intensity of illumination, to PV cell. Thus, if the value, Isc, is known

from the datasheet, under the standard test condition, Go=1000W/m2 at the air mass (AM) = 1.5, then the photon generated current at any other irradiance, G (W/m2), is given by:

sc G sc Go o

G

I I

I I

G





  





The PV cell output is limited by both cell current and the cell voltage, and it can only produce a power with any combinations of current and voltage on the I-V curve. It also shows that the cell current is proportional to the irradiance. To realize the PV array characterics in MATLAB BP 4180T PV panel data sheet is used for simulation. The specification of PV panel is given in table 1.

BP 4180T PV panel are simulated using Matlab. The open circuit voltage, short circuit current and the maximum power are greatly affected by change in atmospheric conditions such as temperature and irradiation.

Fig2.4 illustrates the V-I Characteristics of the specified PV array, which is simulated with constant temperature (250 C) and different irradiation. From this we infer that irradiation is directly proportional to open circuit voltage and short circuit current.

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Fig. 2.2 V-I Characteristics of PV Panel With Irradiation of 1000 W/M2 and Different Temperature V-I characteristics of the specified PV module with respect to different temperature and constant irradiation(1000w/m2) is shown in fig.2.2 From the figure we infer that the significance of the temperature is, when temperature changes open circuit voltage get decreased and short circuit current is slightly increased.

Fig.2.5 P-V Characteristics of PV Panel with Temperature 250C and Different Irradiation

Fig.2.5 illustrates the P-V characteristics of BP 4180T PV panel with temperature of 250C and different irradiation condition .When the irradiation increases the PV panel output voltage and power gets increased.

III. T-SOURCE INVERTER

T – Source inverter (TSI) overcomes the limitation of traditional voltage source inverter and current source inverter. Both inversion and boost function are being accomplished in a single stage using the TSI, there by reducing conversion loss. Unlike the traditional inverter, TSI utilizes a unique impedance network that links the inverter main circuit with the PV (or DC) source. Fig. 2.3 P-V characteristics of PV panel with irradiation of 1000 w / m2 and different temperature.

P-V Characteristics of PV array with constant irradiation and variable temperature is shown in fig.2.3.By increasing temperature output voltage and maximum power point get decreased; the maximum power and open circuit voltage are inversely proportional to temperature at constant irradiations.

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Working Principle

The DC voltage (from PV) is fed as input to the impedance network of TSI which helps to achieve voltage buck and boost properties. Then the output of the impedance network is applied to the inverter main circuits which comprising of six switches. The voltage boost capability of TSI is facilitated by turning ON both the switches in the same phase leg simultaneously. Voltage boost capability of TSI is due to energy transfer from capacitors to inductors, during the shoot through state. Since, the capacitors may be charged to higher voltages than the source voltage, the diode „D‟ prevents discharging of capacitors through the source.

As with conventional ZSI, the TSI can handle shoot through states when both switches in the same phase leg are turned on. The T-network is used instead of the lattice impedance-network, for boosting the output voltage by inserting the shoot through states in the pulse width modulation (PWM) schemes. The operating principle of T – Source Inverter is same as that of conventional ZSI [2] but it differ from number of capacitor being used. In proposed TSI, only one capacitor is enough to handle shoot through state where as in ZSI two capacitor were used. The detailed operation of TSI is explained in two modes as: a) Non shoot through mode b) Shoot through mode

A) Non – Shoot Through Mode

Fig.3.1 illustrates the equivalent circuit of TSI in Non – shoot through mode of operation. In this mode capacitor is charged, the inverter bridge operate

in one of traditional active states, thus acting as a current source when viewed from T – source circuit. During active state current is zero because of open circiut. The open circuit voltage appear across inverter bridge. The diode conduct and carry current difference, between the inductor current and input DC current. Note that both the inductors have an identical current because of coupled inductors.

Fig.3.1: Non – Shoot Through Mode

Assume:

Drop across diode is negligible. For symmetrical T network L1=L2; VL1=VL2=VL,

Total switching period (Tt) = T1+T0

T1-Non shoots through time period (active state) T0-Shoot through time period (zero state)

From non-shoot through mode for the time period of T1 Vi = Vdc (3.1) Vi = VL1+Vc Vc = Vi- VL (3.2) VL = Vi-Vc Vout = Vc- VL2 Vout = Vc- VL Vout = 2Vc-Vdc; Vi=Vdc (3.3)

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B) Shoot Through Mode

This shoot through zero state prohibited in traditional voltage source inverter. It can be obtained in three different ways such as shoot through via any one phase leg or combination of two phase leg or combination of three phase leg. During this mode, Diode is reverse biased capacitor charges the inductor L2 separating DC link from the AC line.

Fig.3.2 Shoot Through Mode

Inverter in shoot through mode for the time period of T0 Vc = VL2 (3.4) VC = VL

Vout = 0 (3.5)

At steady state the average voltage of the inductor for one switching period (Tt) is zero. From equation (3.2) &(3.4)

( ) c V T +T V_{o 1} -V_c dc V =_L T = 0 1 -T Vc ₌ 1 V_dc T T₀ (3.6) 1 -T 1 V =_c V_dc T T₀ (3.7)

The average dc link voltage across T source inverter bridge is, dclink c dc 0 T + (2V -V ) T_{o 1} V = T _{dclink dc} 1 0 T₁ V =V T -T Vdc link = Vc (3.8) The Peak dc link voltage across inverter bridge can be written as

c = 2 c _dc V_{dc link peak}=V -V V -V L dc 1 0 T V_{dc link peak}=V T -T (3.9) = B Vdc (3.10) T B = T -To1 B = 1 To 1-2 T

1

(To / T)= D0 is shooting through duty ratio

Boost factor depends on shoot through zero time period (T0).The peak dc-link voltage is the equivalent dc-link voltage of inverter.

26 _i V_{dc link peak} V_ac=M 2 (3.11) i M -Modulation index

Peak phase value of out put voltage of inverter is

^ i V_dc V_ac=M B 2 (3.12) Bb = Mi B = (0 ~ ∞)

Bb - Buck boost (gain) factor

The capacitor voltage can expressed as

T0 T T0 T V =_c V_dc 1-2 (3.13)

IV. RESULTS AND DISCUSSION

Simulations were done with MATLAB software. PV array performance was analyzed by changing temperature and irradiation condition. Fig. 4.1 shows the circuit configuration of T-source inverter connected with PV array for three phase R-L load and Fig. 4.2 shows simulation waveforms, where PV array is simulated based on BP 4180T manufacturer data sheet. PV array voltage is, V0C=100V,at

standard temperature of 250C and1000w/m2 irradiation.

Fig.4.1 Circuit Configuration of T-Source Inverter

T source inverter consists of T network and voltage source inverter. T network consists of coupled inductor (L) and one capacitor(C) connected in T shape is illustrate in fig.4.1 The diode D used to block the revese current flow to load during shoot through zero state.T source inverter is connected to three phase RL load. The proposed system produces 3-phase 183 V rms from the PV array voltage of 100V dc. From Fig. 4.2, it is clear that the output line-to-line voltage is 150V rms or 259V peak. In this case, the modulation index was set to Mi=0.6, the shoot-through duty cycle was set to (D0=T0/T)

= 0.4, and its switching frequency to 5 kHz.

1 o T B = T -T ; B = To 1-2 T

1

27 ^ Vac 0.6 5 100 2    _; ^ Vac 150v ^

Vac- peak phase voltage of the inverter

V. SIMULATION RESULTS

Table 3.1 shows the system parameters used for simulation. The performance of the T-source inverter was tested under simple boost control method. Its characteristics and relative results are discussed in this section.

Table2: System Parameters

Parameter Specification

Input voltage(Vdc) 100 V

Modulation index (Mi) 0.6

Switching frequency 5000 Hz

Shoot through duty ratio (D0) 0.4

C 1000 μF

L1=L2=L 1 mH

RLoad 10 Ohms

LLoad 5 mH

The Input voltage(Vin), inductor current(IL),capacitor voltage(Vc),inverter line to line voltage without filter (VL),load current(IL),voltage across load (VLL),and transient voltage of capacitor for both ZSI and TSI (Vc) are shown in fig 4.2 from top to bottom respectively.

2200 2250 2300 2350 2400 2450 2500 -1000 -500 0 500 1000 Time(ms) V L (V )

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Transient response is good and ripple content is less in TSI when compared to ZSI because coupled inductor is used in TSI where as in ZSI separate inductors are used. One more advantage of coupled inductor is, it occupies less space hence there is reduction in its size and cost.

T –source inverter performance is analyzed by varying the shoot through duty ratio and modulation index, those results are shown in table3.Shoot through duty ratio (D0) is directly related to boost factor (B)by, increasing boost factor value, increases the output voltage. To maintain constant output voltage across the load irrespective of input voltage variation, the shoot through duty ratio (D0) is adjusted.

Table 3: System Parameter Variations with Respect to Modulation Index and Shoot through Duty Ratio

Mi D0 Vdc link Vrms Irms 0.6 0.4 304 183.5 6.4 0.3 241 134 5.2 0.2 197 93 4.3 0.1 167 57 2.9 0.7 0.3 238.7 136.5 5.3 0.2 190 94 4 0.1 152.2 58 2.5 0.8 0.2 188.6 97 3.9 0.1 144.2 61 2.2 0.9 0.1 140.8 61.5 2

Fig 4.3 Harmonic Spectrum of the Output Current

Fig 4.4 Harmonic Spectrum of the Output Voltage

Table4: Harmonic Profile

The harmonic profile of the output voltage and current of TSI with simple boost control method is given in Table 4. Total harmonic distortion of proposed TSI is low compared to Z-Source inverter of same rating. Fig4.3and Fig.4.4 illustrates the harmonic spectrum of load current and load voltage.

D0

ZSI Proposed TSI

V_thd I_thd V_thd I_thd

0.4 42.2 5.02 27.1 4.79

0.3 41.9 4.9 27.1 4.59

0.2 40.9 4.7 26.95 4.05 0.1 40.2 4.62 26.9 4.03

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VI. EXPERIMENTAL RESULT

The proposed inverter in this paper was verified experimentally using hardware. Captured waveform is same as proven conceptually in earlier sections. The figure show input voltage and output voltage of T-source inverter respectively, which are quite consistent with simulation results.

Fig.5.1 Input Voltage to T-source Inverter Fig 5.2 Output Voltage of TSI

VII. CONCLUSION

In this paper T-source inverter with simple boost control technique has been introduced for photovoltaic applications. The mathematical model of T-source inverter is derived and it is simulated in MATLAB software. The PV array simulations were done with BP4180T data sheet. By controlling modulation index and shoot through duty ratio, boost factor value gets varied; there by the designed output voltage can be obtained. Finally the proposed inverter is implemented in hardware, its performance under change in temperature and irradiation conditions were analyzed. The results shows proposed T-source inverter gives high voltage gain, improved transient response and reduction in Total harmonic distortion when compared to conventional z-source inverter.

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