three phase grid-connected inverter using current.pdf

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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976

6545(Print), ISSN 0976 6553(Online) Volume 4, Issue 2, March April (2013), IAEME

293

THREE-PHASE GRID-CONNECTED INVERTER USING CURRENT

REGULATOR

Tran Quang Tho, Truong Viet Anh

Faculty of Electrical & Electronic Engineering,

HCM City University of Technical Education

ABSTRACT

This paper presents an approach for a three-phase grid-connected inverter using

current regulator. The switching frequency of hystereris in the current modulation is fixed by

comparing the current error with carrier wave with the constant frequency of the multiple of

3. The LCL filter is installed at the inverter output to offer high harmonic attenuation. In

order to determine simply the parameters of PI regulators, the methods of PSO, GA and the

conventional Ziegler-Nichols are used to search the best values with high global stability. Thesimulation results in Simulink/Matlab show that the PI regulators designed by PSO method

demonstrate better results than Ziegler-Nichols and even GA technique.

Keywords: gen algorithm (GA), particle swarm optimization(PSO)

I. INTRODUCTION

The demand of renewable energy sources such as solar energy is becoming more

popular for sustainability and environment with enormous potentials [1]. In order to convert

solar DC source to three-phase AC power needs to have 3-phase inverters that have been well

researched in recent years [2].

The current modulation plays an important role in power electronic systems,especially in voltage source inverters [3]. The advantages of current regulator are very

simple, fast response, high robust and overload protection. In addition, it also keeps power

factor unity and does not depend on voltage drop of switches [15]. However, the hysteresis

PWM has unfixed switching frequency that increases loss of switches and current THD [16].

The elimination of common mode voltage in VSIs aims to reduce THD by using

compensation circuitry [4], harmonic filters [5], [6], [7] and carrier wave phase shift [8] is

very complicated. In order to meet grid-connected standard IEEE Std 929-2000 [9] with

INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING

& TECHNOLOGY (IJEET)

ISSN 0976 6545(Print)ISSN 0976 6553(Online)

Volume 4, Issue 2, March April (2013), pp. 293-304 IAEME:www.iaeme.com/ijeet.aspJournal Impact Factor (2013): 5.5028 (Calculated by GISI)

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IJEET

I A E M E


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294

harmonic attenuation [10], LCL filter is installed at inverter output. The simulation results

discussed show that the PI regulators designed by PSO demonstrate better results than

Ziegler-Nichols and even GA method.

II. MODEL OF GRID-CONNECTED THREE PHASE INVERTER AND CONTROL

STRATEGY

The principle diagram of grid-connected three phase system is shown in Fig 1.

Fig 1: Simplified model of the grid-connected inverter with L filter

II.1. Current regulationThe three phase AC quantities Ia, Ib and Ic in the stationary frame are transformed into

the DC components Id and Iq in the synchronously rotating frame by the phase angle ofPLL. With L filter in grid-connected VSI as Fig 1, voltage equation of phase A in the

stationary frame is:

)1(ViRVdtdiL gaagia

a =

And phases B and C are similar. When neglecting resistor Rg, equation (1) became:

)2(VVdt

diL gaia

a =

The equation (2) shows that phase current can be regulated by amplitude and phase angle

of Vi at inverter output with constant Vg as Fig 2.

Fig 2: Relationship between Vi and Ig in dq frame


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295

Active and reactive powers in dq frame are calculated as (3) and (4).

( )

( ) )4(IVIV23Q

)3(IVIV2

3P

gqgdgdgq

gqgqgdgd

=

+=

With reference P_refand Q_ref, currents Idp and Iq can determine as:

( ))5(

V

V

PQ

QP

VV3

2

I

I

gq

gd

ref_ref_

ref_ref_

2

gq

2

gdq

dp

+=

The current Idp depends on DC source power status of solar. So:

)6(PP dcref =

For optimization of generation, only active power is to be injected in the grid and

reference Iq is zero. Pdc and Idp can be determined by MPPT technique. To obtain the closed

loop response, Id and Iq are taken from the outputs of the inner loop PI regulator, as (7).

Where Id and Iq are the reference currents. Kp and Ki are the proportional and integral gain

constants respectively. These gain constants are determined by tuning the regulators for

optimal response with methods of Ziegler-Nichols, GA and PSO.

)7(II

II

s

KK0

0s

KK

I

I

qgref_q

dgref_d

iq_i

iq_p

id_i

id_p

*

q

*

d

+

+=

The LCL filter of the inverter output is proposed as Fig 3.

Fig 3: The proposed diagram of three phase inverter with LCL filter


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296

II.2. DC link voltage control

The DC voltage is held at a constant value by using a PI regulator which provides the

real current reference as (8). Where V*dc is the DC voltage of MPPT.

[ ] )8(VVsKKII dc

*dc

dc_idc_pdpref_d

+=

II.3. PWM modulation

Current error: )9(III gref_gerror_ =

Then:( )

)10(VVdt

IdL iref_i

error_=

Current errors are compared with carrier wave of fixed frequency and amplitude. If

the current error is positive and larger than the carrier wave, the switches are activated to

apply +Vdc. On the other hand, if current error is positive and smaller than the carrier wave,

the switches are activated to apply Vdc as Fig 4.

Fig 4: PWM modulation

II.4. Tuning parameters of PI regulator:With LCL filter, parameters of PI regulators effect significantly on THD of inverter

output current [11].

The conventional tuning methods of PI regulator such as Ziegler-Nichols rules and

GA have been applied to tune the controller recently. Randomly searching technique such as

GA that has high efficient computational and global searching capabilities has been applied

successfully to optimize the complex problems. But the premature convergence of GA

degrades its performance and reduces its searching capabilities. The PSO algorithm is

proposed in this paper to tune PI regulator.

The Ziegler-Nichols method:

Fig 5: Single phase equivalent circuit of LCL filter


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297

In Fig 5, when assuming no harmonic at PCC, then Vg=0. For a balanced system the

transfer function of the LCL filter for every phase is given by (11).

;RRC;RRCLLC

;RLCRLCC;LLCC:where

)11(CsCsCsC

1sRCsLC

)s(V

)s(I

ig4igfig3

gifigf2igf1

43

2

2

3

1

gf

2

gf

i

i

+=++=

+==

+++

++=

and Ri and Rg are resistors of inductances Li and Lg respectively.

System parameters: Vdc=650V; Ldc=3mH; Rdc=1; Cdc=500F; grid voltage =380V;

50Hz; short-circuit power=40KVA; Lg=1mH; Rg=0.1; Cf=5F; Li=2mH; Ri=0.2; carrierwave frequency fc=9KHz.

Kgh=30 and Tgh=3.888 are determined by Ziegler-Nichols method in (11).

In the GA method with flowchart in Fig 6a

Fig 6a: GA flowchart Fig 6b: PSO flowchart

In the PSO method, velocity and position are updated by equations (12) and (13) in flowchart

in Fig 6b.

)13(V.PP

)12()PP(R.)PP(R.)t(V.wV

curcurcur

curglobes2curlobes1cur

+=

++=

Results of tuned parameters are shown in table 1

Method Kp_Id Ki_Id Kp_Iq Ki_Iq

Ziegler-

Nichols13.5 4.182 13.5 4.182

GA 5.6208 200.046 3.4441 1.0156

PSO 4.3523 179.534 2.442 4.0112

Table 1: parameters of PI regulators


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298

III. SIMULATION RESULTS AND DISCUSSION

Fig 7: Simulation model in Simulink/Matlab.

The current Id increases from 5A up to 10A at 3.803s.

III.1. Results with Ziegler-Nichols:

Fig 8a: Three-phase voltage (V)

Terminator3

PI_Idq

PI_idq

PI_Vdc

PI_Vdc

0

Iq=0

Idp

[gates]

Goto

[Vdc_ref]

From6

[Vdc]

From5

[Iabc]

From4

[Iabc]

From3

wt

From2

wt

From1

abc

wt

dq0

abc_dq0

Embedded

MATLAB Function1

dq

wt

abcdq0_abc

Embedded

MATLAB Function

9KHz

I*_abc

Carrier

I_abc

gates

6 xung

wt

wt

650

Vsol

A

B

C

Three-Phase Source

VabcA

B

C

a

b

c

Three-Phase

V-I Measurement

IabcA

B

C

a

b

c

Three-Phase

I Measurement

a

b

c

A

B

C

Ri_Li

a

b

c

A

B

C

Rg_Lg

Gates

Vso

VDCA

B

C

Inverter

[Iabc]

I

Vdc

Goto3

[gates]

From

a b c

A B C

C

Vabc (pu)wt

3-phase PLL

3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83 3.84 3.85

x 105

-400

-300

-200

-100

0

100

200

300

400

3-phase voltage (V)


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299

Fig 8b: Three-phase current (A)

Fig 8c: Active power P (w) and reactive power Q (var)

Fig 8d: THD spectrum of current

3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83 3.84 3.85

x 105

-10

-5

0

5

10

3-phase current (A)

0 1 2 3 4 5 6 7

x 105

-2000

0

2000

4000

6000

3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.7 3.71 3.72

-4

-2

0

2

4

FFT window: 5 of 288.7 cycles of selected signal

Time (s)

0 200 400 600 800 10000

1

2

3

4

Frequency (Hz)

Fundamental (50Hz) = 4.521 , THD= 5.20%

Mag(%ofFun

damental)


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300

III.2. RESULTS WITH GA:




3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83 3.84 3.85

x 105

-400

-300

-200

-100

0

100

200

300

400

3-phase voltage (V)

3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83 3.84 3.85

x 105

-10

-5

0

5

10

3-phase current (A)

0 1 2 3 4 5 6 7

x 10

5

-2000

0

2000

4000

6000

P (w) & Q (var)


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301


III.3. RESULTS WITH PSO:



3.61 3.62 3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.7-5

0

5


Time (s)

0 200 400 600 800 10000

0.5

1

1.5

2

2.5

Frequency (Hz)


Mag(%ofFundamental)

3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83 3.84 3.85

x 105

-400

-300

-200

-100

0

100

200

300

400

3-phase voltage (A)

3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83 3.84 3.85

x 105

-10

-5

0

5

10

3-phase Current (A)


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302



thod % THD of output current

Ziegler-Nichols 5.20

GA 3.41

PSO 2.93

Table 2: THD of output current at PCC

IV. DISCUSSION

Parameters of PI regulators in GA and PSO methods always give Kp_Id Kp_Iq and

Ki_Id Ki_Iq.

Power responses in figures 8c, 9c and 10c demonstrate that GA and PSO methods

give results better than Ziegler-Nichols method.

The output currents harmonics in figures 8d, 9d and 10d also show that PSO method

in the table 2 gives the best result current THD is 2.93%.

0 1 2 3 4 5 6 7

x 105

-2000

0

2000

4000

6000

P (w) & Q (var)

3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.7 3.71 3.72

-5

0

5


Time (s)

0 200 400 600 800 10000

0.5

1

1.5

2

Frequency (Hz)


Mag(%ofFundamental)


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303

V. CONCLUSION

This paper presents an approach for a three-phase grid-connected inverter using

current regulator with low current THD by using LCL filter at inverter output and good

response.

The PSO algorithm is proposed in this paper to tune parameters of PI regulator gives

global results better than Ziegler-Nichols and even GA method.

Control strategies proposed is a good alternative to implement an inverter system

control with reduced harmonic content injected into the grid and less computational load than

other methods.

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three phase grid-connected inverter using current.pdf

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