The Flexible Transmission System Engineering Essay

A Inactive VAR compensator ( SVC ) is Flexible ac Transmission System ( FACTS ) device used to modulate the electromotive force on a transmittal line. The SVC uses reactive compensation in order to command the electromotive force. The SVC is made up of a Thyristor Controlled Reactor ( TCR ) and a Thyristor Switched Capacitor ( TSC ) . The TCR is used to absorb MVArs from the transmittal line in order to diminish the system electromotive force. The TSC is used to provide MVArs to the transmittal line in order to increase the system electromotive force. The SVC is made up of one or more of these devices depending on the system demands and installing of the SVC. These devices are connected in analogue to the coach through a transformer.

This study inside informations the design of the TCR every bit good as its shift of the thyristors and control strategy. The design of the harmonic filters used to extinguish the harmonics caused from the shift of the TCR is included. The design was modeled on the computing machine package plan PSCAD. Trials were done on the theoretical account to mensurate the public presentation of the TCR and the dependability of the control strategy.

FEASIBILITY STUDY

The job of the undertaking is to plan a SVC for electromotive force stableness control. This means that a SVC must be designed to the given specifications in order to keep the needed electromotive force at the having on of the transmittal line.

SVCs are used in to increase active power transportation capacity, to muffle power oscillations and to accomplish effectual electromotive force control. [ 10 ] SVCs have a faster response over the simple automatically switched compensation strategies. They are more dependable as they consist of no traveling parts, therefore the term inactive.

The SVC is made up of a TCR and TSC. “ When TCRs and TSCs are placed in parallel with each other and have the fire angles of their thyristors adjusted by a accountant, the device is referred to as a SVC. ” [ 1 ]

The TCR uses thyristors connected back-to-back as a bidirectional switch, in series with an induction to exchange the inductance in for a certain period of clip. A TSC consist of one or more capacitor Bankss in series with a bidirectional thyristor switch and a little inductance. The inductance is used to restrict the transients caused form shift of the TSC. [ 6 ]

If the burden on the transmittal line is a capacitive burden, the SVC will utilize the TCR to absorb MVArs from the system, in bend take downing the system electromotive force. If the connected burden is an inductive burden, the SVC will utilize the TSC to shoot MVArs into the system hence increasing the system electromotive force. The SVC can provide or devour MVArs depending on the burden connected to the system. The SVC is able to manage the varying loads because of the fast response of the accountant.

The SVC will be connected to a simple transmittal system rated at 400kV. The bulk of electricity transmittal is done at this kilovolt evaluation.

Information can be obtained from diaries and thesis found in the library or on the IEEE web site. Textbooks have information sing the SVC and the modeling and control thereof. PSCAD will be used as the simulation tool to pattern the design and is available on bulk of the computing machines within the university computing machine local area networks.

Theory

THYRISTOR CONTROLLED REACTOR

Figure. Basic construction of thyristor [ 2 ]

The operation of a thyristor ( Si controlled rectifier ) can be explained by mentioning to Figure 1 above. The thyristor consist of four beds of a semiconducting material stuff doing up p-n-p-n beds. Three junctions are produced designated J1, J2 and J3, and there are three terminuss, the Anode, Cathode and Gate. The thyristor can be thought of as pnp transistor ( J1 and J2 ) connected to a npn transistor ( J2 and J3 ) . To send on bias the thyristor, a electromotive force is applied to be positive on the anode and negative on the cathode. If no gate current is supplied, both transistors remain cut off. When a negative gate-cathode electromotive force is applied both transistors remain away. A positive gate-cathode electromotive force applied will send on prejudice npn transistor ( J2 and J3 ) and do it to carry on. Once this has started carry oning it will do the pnp transistor ( J1 and J2 ) to carry on. The first pnp junction so keeps the 2nd npn junction conducting, even when the gate pulsation has been removed. The ability for the thyristor to stay on once the gate pulsation has been removed is known as latching. Merely a brief pulsation to the gate is needed to exchange the thyristor on. The thyristor switches off on the negative half rhythm of the supply electromotive force when the anode to cathode electromotive force becomes zero. [ 9 ]

When two thyristors are connected in analogue with the anode of one connected to the cathode of another, the thyristors form a bidirectional switch. [ 2 ] Using a sinusoidal electromotive force across the two thyristors will do the one thyristor to carry on on the positive half rhythm, and the other thyristor will carry on on the negative half rhythm. When the electromotive force across the thyristor becomes negative, it will halt conducting and the other thyristor will get down carry oning. With this method the thyristors are said to be “ of course commutated ” [ 1 ] . The thyristors are turned on by firing pulsations sent to their several Gatess 180Es apart. This enables the thyristor to be controlled as a switch. A firing angle I± is used which causes the thyristors to carry on for a part of the sinusoidal electromotive force.

Figure. Basic elements of a TCR

Figure 2 above illustrates the basic elements of a TCR. A TCR is a reactor in series with a bidirectional thyristor switch. The thyristors conduct on opposite half rhythms of the cardinal frequence depending on the fire angle alpha I± which is used as a hold to trip the thyristors to exchange on. Alpha is measured from a zero crossing of electromotive force. A firing angle of 90A° consequences in full conductivity of the thyristors. Partial conductivity is obtained with firing angle between 90A° and 180A° . “ Open firing angles between 0A° and 90A° are non allowed as they produce asymmetrical currents with a dc constituent. ” [ 6 ]

A TCR acts as a governable susceptance, as. Full conductivity of the thyristors at 90A° consequences in the maximal value of susceptance from the TCR. The thyristors are none carry oning as 180A° ensuing in a nothing susceptance from the TCR. The susceptance of the TCR varies as a map of I± as shown by Equation ( 1 ) . [ 6 ]

( 1 )

The susceptance is switched into the system by the TCR for a “ governable fraction of every half rhythm depending on the fire angle ” . [ 6 ] Changing the sum of susceptance switched into the system determines the sum of MVAr that will be absorbed by the TCR. The TCR requires a control system to find the firing angle of the thyristors to accomplish the right susceptance value. The control system responds to an mistake signal in the electromotive force between a mention electromotive force Vref and a mensural electromotive force Vmeasured.

INITIAL DESIGN SPECIFICATIONS

TRANSMISSION LINE PARAMETERS

Figure. Single line diagram of transmittal line with SVC connectedFigure 3 above shows the SVC connected to a simple transmittal line. The transmittal line parametric quantities are given below in table 1. The transmittal line is fed from a 400kV 50 Hz beginning and is connected to a changing burden. The transmittal line is 200km long. The SVC is connected in shunt with the transmittal line through a transformer. The object of the SVC is to fit the magnitude of the having terminal electromotive force VR with directing terminal electromotive force VS within a certain per centum while the burden varies. ( Either being capacitive or inductive and at different MVAR evaluations ) .

Table. Transmission line parametric quantities

Parameter

Value

RL

2.45*10-2 I©/km

Forty

0.322 I©/km

BC

3.6323 uS/km

RL is the opposition, XL the inductive reactance and BC the capacitive susceptance. These values are given per kilometer of the transmittal line and must be multiplied by the line length in order to acquire the entire values. These values are calculated [ 3 ] in equations ( 2-4 ) below and are shown above in Figure 3.

( 2 )

( 3 )

( 4 )

The theoretical account of the SVC will be built in the computing machine simulation bundle PSCAD. The theoretical account considers the SVC as a shunt-connected variable susceptance BSVC, which changes automatically due to the accountant to accomplish electromotive force control. The tantamount susceptance Beq needed for reactive compensation is determined by the fire angle I± of the thyristors. [ 3 ] The shift of the thyristors causes harmonics which must be reduced utilizing harmonic filters. The decrease of harmonics will be discussed in more item in following subdivisions.

TCR ‘s behavior between a firing angle of I±=90Es to I±=180Es . When the fire angle is at I±=90Es the thyristors are to the full carry oning and when the fire angle I±=180Es , the thyristors are non carry oning. By commanding the firing angle of the thyristors, the susceptance is controlled and therefore the device is able to command the sum of MVAr consumed from the system. Controling the sum of MVAr being absorbed in bend controls magnitude of the electromotive force at the coach that it is connected to. As the burden alterations, the firing angle must alter by agencies of a control system. As the burden additions ( capacitive burden ) , the firing angle must diminish from 180Es towards 90Es so that more reactive power is consumed. The having terminal electromotive force VR, must be within scope of 5 % with regard to the directing terminal electromotive force VS.

SVC LIMITS

Figure 3 above illustrates a simple transmittal line with a changing burden connected. This burden was varied for different evaluations of MVAr and at different power factors. This allowed for a scope of tonss to be tested in order to find the bounds of the SVC. The rush electric resistance burden or SIL was calculated and used as a mention to find the tonss that the SVC will be able to counterbalance for. The SIL of a transmittal line is defined as “ the MW burden of a transmittal line at which a natural reactive power balance occurs. ” [ 5 ] This means that there is no reactive power flow along the transmittal line at the SIL. A transmittal line produces its ain reactance due to the reactive electrical capacity of the line ( XC ) . The transmittal line is besides able to absorb some of the reactance produced because of its inductive reactance ( XL ) . The point where the sum of reactive power produced by the transmittal line is equal to the sum of reactive power absorbed is shown below by Equation ( 5 ) [ 5 ] .

( 5 )

At this point there is no net reactive power flow into or out of the line.

The SIL can be calculated by Equation ( 6 ) below:

( 6 )

Using the parametric quantities given in table 2 above, the SIL of the transmittal line was calculated utilizing equations ( 5 ) and ( 6 ) .

From ( 5 )

From ( 6 )

When the burden from the transmittal line is P0=537.456 MW, there will be no reactive power flow through the transmittal line. Using this point as the mention, different tonss can be calculated for the transmittal line for different ratios of MVA/P0, as shown in Table 3 below.

Table. Changing tonss for transmittal line

integrity

A

0.9lead/lag

0.95lead/lag

MVA/Po

MVA

MVAr

MW

MVAr

0.01

5.37456

2.342716

4.837104

1.678206

0.05

26.8728

11.71358

24.18552

8.391029

0.1

53.7456

23.42716

48.37104

16.78206

0.5

268.728

117.1358

241.8552

83.91029

0.8

429.9648

187.4173

386.9683

134.2565

1

537.456

234.2716

483.7104

167.8206

1.3

698.6928

304.5531

628.8235

218.1668

1.5

806.184

351.4075

725.5656

251.7309

1.9

1021.166

445.1161

919.0498

318.8591

2

1074.912

468.5433

967.4208

335.6412

2.5

1343.64

585.6791

1209.276

419.5515

3

1612.368

702.8149

1451.131

503.4617

These deliberate tonss were so used in the PSCAD theoretical account. Each burden was tested in the theoretical account to see how it affects the having terminal electromotive force Vr. Vr was measured and tabulated as shown below in Table 4. The electromotive forces were measured to obtain a scope that the SVC will run at.

Table. Receiving terminal electromotive forces for different tonss

MVA/Po

0.9lead

0.95lead

Integrity

0.95lag

0.9lag

0.01

409.816

410.419

409.012

409.191

409.717

0.05

411.652

410.174

409.698

407.883

407.161

0.1

412.777

412.373

408.5305

406.211

405.639

0.5

425.1605

418.748

403.1364

390.4004

386.142

0.8

431.719

420.965

397.5366

379.138

372.314

1

435.0232

422.299

393.052

371.012

362.966

1.3

438.1196

420.795

386.001

358.146

349.799

1.5

439.645

420.26

379.474

350.311

340.795

1.9

438.866

413.852

367.604

333.69

323.842

2

438.634

412.644

363.669

330.528

319.845

2.5

431.673

401.419

346.439

310.743

299.269

3

417.9995

386.404

329.283

292.999

282.016

The electromotive forces in table 4 above were so plotted against the MVA/P0 and the consequence is shown below. This graph illustrates the scope of Vr against the MVA/P0 for different tonss connected in shunt to the transmittal line.

A: Maximal capacitive

reactance

Bacillus: Maximal inductive

reactance

Figure. Limits of operation of the SVC

The above graph illustrates the alteration in the electromotive force at the having terminal for the different tonss. The greatest difference in Vr exists for the 0.9 taking burden and the 0.9 dawdling burden as shown in Figure 4 above. Indicate A shows the maximal value that Vr reaches with the capacitive burden and point B shows the minimal value that Vr reaches with the inductive burden. The magnitudes of the tonss at these two points are shown below in Table 5. These two points determine the maximal reactive compensation needed for the TCR ( indicate A ) and TSC ( point B ) .

Table. Maximum bounds of operation

Point on Curve

MVA/Po

MVAr

MW

A

1.5

445.1161

919.0498

Bacillus

3

702.8149

1451.131

The sending terminal electromotive force Vs and the having terminal electromotive force Vr were measured at these two different tonss shown in the tabular array above to find the sum of MVAr to rectify the electromotive force difference. The capacitive tonss consequences are depicted in Figure 5.

Figure.Vs and Vr for point A burden

The electromotive forces shown above are in per unit ( plutonium ) . The intent of the SVC is to shoot or absorb reactive power into or from the transmittal line. The sum of MVAr required by the TCR to diminish Vr to 1 plutonium is 245 MVAr. This sum can be confirmed by Figure 6 below.

Figure.Vs and Vr for point A burden

Figure 7 below illustrates the difference in Vs and Vr for the maximal inductive burden.

Figure.Vs and Vr for point B burden

The sum of MVAr needed for the TSC to increase Vr to 1 plutonium is 1260 MVAr. This can be confirmed in Figure 8 below

Figure.Vs and Vr for point B burden

The size of the transformer used will be a 1300MVA 400kV/20kV star-delta. 1300 MVA is used to be able to provide the 1260 MVAr and 245MVAr from the TSC and TCR severally.

Design of SVC parametric quantities

THYRISTOR CONTROLLED REACTOR ( TCR ) VALUES

The TCR consist of an induction which value needs to be calculated in order to exchange in the right sum of reactance. The sum of MVAr needed ( QTCR ) to diminish Vr to 1 plutonium is 245MVAr.The TCR will be connected in delta ( to extinguish ternary harmonics ) so the sum of reactive power that each inductance can absorb ( QL ) must be calculated.

The TC R will necessitate to provide a upper limit of 81.667 MVAr across each stage of the delta connexion. The size of the inductance ( L ) was calculated as follows:

( 7 )

( 8 )

( 9 )

A 15.591 mH inductance will be connected in each stage of the TCR to absorb the right value of reactance needed to diminish Vr to 1 plutonium. This value of induction will do the TCR to absorb 245 MVArat full conductivity of the thyristors. Valuess below 245MVAr will be absorbed by altering the firing angle of the thyristors.

COMPARISON OF TCR SUSEPTANCE V FIRING ANGLE

The TCR susceptance ( BTCR ) was compared against the fire angle I± to see how the susceptance alterations as the firing angle alterations. The theoretical comparing was done by utilizing equation ( 1 ) . The equation was used in MATLAB to plot the consequences. The susceptance V firing angle curve is shown below in Figure 9. The MATLAB codification required to plot this curve can be found in Appendix A.

( 1 )

Figure.Theoretical Comparison of BTCR and I±

Table. Susceptance values at varied fire angles

Alpha

I_TCR

Volt

Susceptance

90

36.6371

179.629

0.203959828

95

32.5258

179.629

0.181072099

100

28.5378

179.629

0.158870784

105

24.6765

179.629

0.137374811

110

20.9895

179.629

0.116849172

115

17.5266

179.629

0.097571105

120

14.3331

179.629

0.079792795

125

11.4446

179.629

0.06371243

130

8.88625

179.629

0.049470019

135

6.67378

179.629

0.037153132

140

4.81373

179.629

0.026798178

145

3.30192

179.629

0.018381887

150

2.12253

179.629

0.011816188

155

1.24935

179.629

0.006955169

160

0.64746

179.629

0.003604429

165

0.273877

179.629

0.001524681

170

0.078444

179.629

0.0004367

175

0.005241

179.629

2.91757E-05

180

0.005666

179.629

3.1544E-05

The fake consequences were plotted as shown below in Figure 10. These were simulated in PSCAD by mensurating the electromotive force and the current in the line for different fire angles, and ciphering BTCR ( BTCR =ILINE/VSOURCE ) from these values..

Figure. Fake comparing of BTCR vs alpha

Operation OF TCR

The induction value calculated in Equation ( 9 ) is the size of the inductance that will be used in the TCR. The inductance in each stage of the TCR is split into two halves, one on each side of the anti-parallel affiliated thyristor brace, to forestall the full Ac electromotive force looking across the thyristor valves and damaging them if a short circuit mistake occurred across the reactors two terminal terminuss. The shift of the inductances at different firing angles changes the value of the susceptance, which causes a alteration in the sum of VARs absorbed.

The shift of the thyristors is based on the undermentioned circuitry shown in Figure 11 below. A PLL ( stage locked cringle ) generates a ramp signal theta, which varies between 0A° and 360A° . This signal theta is synchronized in stage with the input electromotive forces. The end products from the PLL are compared with the firing angle I± in the interpolated fire pulsation ( IFP ) to bring forth the right shift of the thyristors. The IFP generates an end product pulsation to turn on the thyristors. The end product of the interpolated fire pulsation is based on a comparing of high and low input signals. The low input is the firing angle i?? and the high input is theta from a phase-locked cringle.

The circuit diagram of the TCR connected to the transmittal line can be found in Appendix B. Figure 11 below illustrates the firing strategy.

Phase B ‘ , FP4

Phase C, FP5

Phase A, FP1

Phase A ‘ , FP2

Phase B, FP3

Phase C ‘ , FP6

Figure. PLL and Interpolated Firing Pulse Generation signals

The inputs from to the PLL are the line electromotive forces from the secondary side of the transformer. These are used alternatively of the line electromotive forces of the transmittal line to forestall the stage displacement of the electromotive forces through the transformer from impacting the firing strategy. A transformer is used to link the TCR to the transmittal line so that the TCR operates at lower electromotive forces ; therefore the constituents in the SVC are smaller, salvaging on cost. The IFP generates the fire pulsations based on the stage rotary motion. Phase A receives firing pulsations FP1 and FP2. Phase B receives FP3 and FP5. Phase C receives FP4 and FP6.

7.3.4 THYRISTOR Switch

Figure 12 illustrates the firing strategy of stage A when I±=90A° . At a firing angle of 90A° , there is full conductivity of the thyristors. This can be seen by the bottom graph in figure 12. It shows that the current is sinusoidal.

Figure. Phase A at alpha = 90 grades

Figure 13 below illustrates the shift of the thyristors at I±=135A°

Figure. Phase A at Alpha = 135 grades

Figure. Phase A at alpha = 180 grades

Figure 14 illustrates the shift of the thyristors at 180Es . It can be seen from the current curve that no current is fluxing and therefore the thyristor is non carry oning.

Design OF HARMONIC FILTERS

Harmonic currents in power systems shorten the equipment ‘s life anticipation and can interfere with communicating lines and sensitive equipment. The TCR generates harmonics from the shift of the thyristors. In a three stage system the TCR is connected in delta to forestall all ternary harmonics from come ining the line, the delta causes the ternary harmonics to go around in the closed delta. A filter is needed to take the lowest order harmonics that are non trapped by the delta connexion. A filter will be needed to pin down the 5th and 7th harmonics.

The size of the harmonic filter ( MVAr evaluation ) is set to be 19 % to that of the size of the TCR. This was selected as the optimal value. Specifically tuned filters were used to decrease the 5th and 7th order harmonics.

Qfilter=0.19 QTCR, the size of the TCR was determined in the old subdivision to be 245 MVAr. The undermentioned equations [ 7 ] are used to cipher the size of the harmonic filters.

Qfilter= 0.19*245

Qfilter= 45 MVAr

Qfilter ( 5th ) = 30 MVAr

Qfilter ( 7th ) = 15 MVAr

( 10 )

( 11 )

5th ORDER HARMONIC FILTER

From equation ( 10 ) ,

( a )

From equation ( 11 ) ,

( B )

From equation ( a ) ,

Sub equation ( B ) in equation ( a ) ,

7th ORDER HARMONIC FILTER

From equation ( 10 ) ,

( degree Celsius )

From equation ( 11 ) ,

( vitamin D )

From equation ( degree Celsius ) ,

Sub equation ( vitamin D ) in equation ( degree Celsius ) ,

COMPARISON OF HARMONICS

The harmonics were measured before and after the filters were placed into the circuit. A comparing was so made on hoe effectual the filters are at cut downing the 5th and 7th order harmonics. A FFT ( fast fourier transform ) block was used in PSCAD to mensurate the harmonics. The FFT receives the line current as the input and outputs the corresponding harmonics in that line. Figure 15 below shows the harmonics in each stage of the transmittal line for a firing angle of 130Es . The first column shows the current at the cardinal frequence ( 50Hz ) . The 2nd column shows the fifth order harmonic and the 3rd column shows the seventh order harmonic.

Figure. Harmonicss with no filter, Alpha=130 grades

Figure 16 below shows the magnitude of the harmonics when the filters have been placed into the circuit. The harmonics were measured at a firing angle of 130Es .

Figure. Harmonicss with filters, alpha = 130 grades

As can be seen from Figure 15 and 16 above, the harmonics have decreased with the inclusion of the filters. The fifth harmonic has decreased by 95 % and the 7th harmonic has decreased by over 99 % . Using tuned filters to the right frequence of the harmonics, consequences in the harmonics being eliminated. The filters are connected as shunt filters, and act as a short to earth at the severally tuned frequences. The circuit diagram demoing the connexions of the harmonic filters can be found in Appendix B.

SVC CONTROL

ABSORBTION MODE CONTROL

The TCR uses a control circuit to find the sum of MVAr to be absorbed organize the system. A electromotive force regulator loop continuously monitors the systems variables and generates an end product signal that is relative to the desired reactive power compensation. The undermentioned electromotive force regulator loop shown in Figure 17 below was used as the exchanging control for the TCR.

Figure. Voltage regulator for soaking up manners control

Vref is the mention electromotive force and is set to be 1 plutonium. Vmeasured is the mensural electromotive force on the HV side of the transformer. G is the inactive addition and is defined as the reciprocal of the current sag feature. The current sag is 1 % so G was set at 100. T is defined as the thyristor fire hold and is set to be 200ms [ 8 ] . These values were chosen for a critical damped system response. The Transfer map was limited in per unit between Bmax at 1pu and Bmin at 0.02pu [ 6 ] . The base used for susceptance was 0.204S calculated from Equation ( 8 ) . This transportation map acts on the electromotive force mistake between Vref and Vmeasured to bring forth a susceptance value within the scope of bounds. The non-linear transportation characteristic outputs the right fire angle depending on the susceptance value that is obtained from the mistake signal in electromotive force. The non-linear feature was measured in Section 6.3.2 and table 6 was used to supply values for the non- additive relationship.

Figure 18 below illustrates the relationship between the susceptance and the fire angle. If the end product from the transportation map is BTCR=1pu the non-linear features will direct an end product of 90A° to the interpolated fire pulsation. The minimal end product of Bmin=0.02 plutonium will match to a firing angle between 155A° and 160A° .

Figure. Non-Linear transportation characteristic tabular array

Testing ON CAPACITIVE LOAD VARIABLES

The first trial was done without the TCR connected to the transmittal line. A burden was placed on the having terminal of the transmittal line as shown below in Figure 19.

Figure. Capacitive tonss

Figure. Voltage measured at having terminal with no TCRAt clip t=0s, Circuit Breaker 1 ( CB1 ) was closed, CB2 was unfastened and CB3 was unfastened. At t=1s, CB1 was opened. At t=1.3s CB2 was closed. At t=2s CB2 was opened and CB3 was closed. This resulted in the undermentioned electromotive force at the having terminal.

As can be seen from figure 20 above, the electromotive force measured at the having terminal additions to 1.12pu as more capacitive burden is added to the transmittal line. With the TCR included, the mensural electromotive force stabilizes back to 1.017pu, shown below in Figure 21. This is within the acceptable bounds of 5 % .

Figure. Voltage measured at having terminal with TCR included

Figure 22 below illustrates the response of the accountant to this fluctuation in burden. The circuit ledgeman operations, BTCR and I± are shown.

Figure. Response of accountant with fluctuation in burden

VARIATION IN REFERENCE VOLTAGE

A measure alteration was applied to the mention electromotive force to see how the system responds. The having terminal electromotive force VR must follow Vref. Vref was ab initio set to 1.05pu. At a clip t=0.5s Vref was changed to 0.95pu. At t=1.5s, Vref was changed to 1pu. Figure 23 below illustrates the measure in Vref and the response caused by the accountant on VR.

Figure. Variation in Vref and response of Vr

Decision

The undertaking specifications have been presented in the study. The end of the SVC is to brace the electromotive force at the having terminal of the transmittal line. The SVC parametric quantities were calculated based on the specifications given for the transmittal line and the needed tonss that it will necessitate to counterbalance for. The TCR was designed to the given specifications and the control system to command the sum of MVArs being absorbed by the TCR was designed. The harmonic filters to extinguish the 5th and 7th harmonics was designed and tested to turn out that the harmonics are eliminated. The following stage of the design involves the design of the TSC and the TSC control strategy to command the sum of MVArs being injected into the system.

APPENDIX A

MATLAB CODE FOR PLOTTING SUSCEPTANCE VS FIRING ANGLE

& gt ; & gt ; w=2*pi*50 ;

& gt ; & gt ; Vs=20e3 ;

& gt ; & gt ; QL=245e6/3 ;

& gt ; & gt ; XL=Vs^2/QL ;

& gt ; & gt ; a=pi/2:0.01: pi ;

& gt ; & gt ; num= ( ( 2*pi ) – ( 2*a ) + ( wickedness ( 2*a ) ) ) ;

& gt ; & gt ; den=XL*pi ;

& gt ; & gt ; BL=num/den ;

& gt ; & gt ; secret plan ( a, BL )

b= [ 0.203959828

0.181072099

0.158870784

0.137374811

0.116849172

0.097571105

0.079792795

0.06371243

0.049470019

0.037153132

0.026798178

0.018381887

0.011816188

0.006955169

0.003604429

0.001524681

0.0004367

2.91757E-05

3.1544E-05 ]

& gt ; & gt ; alpha= [ 90:5:180 ] ;

& gt ; & gt ; alpha ‘ ;

& gt ; & gt ; keep on

& gt ; & gt ; secret plan ( alpha, B )

& gt ; & gt ; grid on

APPENDIX B

July 23, 2017