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EE8402

EE8402. TRANSMISSION AND. DISTRIBUTION. OBJECTIVE. •. To become familiar with the function. of different. components Distribution. used levels. in of. Transmission. and and. power. systems. modeling of these components. OBJECTIVES To develop expression for computation

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EE8402

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  1. EE8402 TRANSMISSION AND DISTRIBUTION

  2. OBJECTIVE • To become familiar with the function of different components Distribution used levels in of Transmission and and power systems modeling of these components.

  3. OBJECTIVES To develop expression for computation of fundamental parameters of lines. To categorize the lines into different classes and develop equivalent circuits for these classes. Toanalysethevoltagedistributionin insulatorstringsandcablesandmethods toimprovethesame. • • •

  4. INTRODUCTION

  5. INTRODUCTION Of.:S:F,JlA'nOS STATION [ HYl)llQFl,L;Cl"R IC I)\_\) !\ I - J &,;,,..;II- 2JOK\'TR,"S�IISSl01' Sii ncurso STATION _....;� 2:f3l0KV�IJSSI M� L \ 1II1St. K,NVs-i11ss1m-. \l'-�O:s' SYS'll·.\1 I SYSTEM 1 -----;;::-...-- � JI\ ZJOKV SWITCHYARD l;J" IIO.\IE USl:.R r_=._f}w1 )\l�lfltl,:1\Il'l)lSIRI\I

  6. INTRODUCTION • Various levels such as generation, transmission and distribution.

  7. INTRODUCTION • HVDC High voltage direct current (HVDC) is used to transmit large amounts of power over long distances or for interconnections between asynchronous grids. When electrical energy is required to be transmitted over very long distances, it is more economical to transmit using direct current instead of alternating current.

  8. INTRODUCTION EHV AC transmission • Hydro-electric and coal or oil-fired stations are located load centres for various very far from reasons which requires the transmission of the generated electric power over very long distances. This requires very high voltages for transmission. The very rapid strides taken by development of dc transmission since 1950 is playing a major role in extra-long- distance transmission, complementing or supplementing EHV AC transmission.

  9. INTRODUCTION Technical performance and reliability Considerations in the design of a power line: • • • • The amount of active power it has to transmit The distance over which the power must be carried The cost of the power line Aesthetic considerations, urban congestion, ease of installation, expected load growth • • • •

  10. INTRODUCTION Application of HVDC transmission system HVDC Light, is utilising state of the art semiconductors, control and cable insulation and can offer many new transmission opportunities as has been demonstrated by actual projects above. It offers a lot of possibilities to enhance the power systems. Wind power, even big parks, can easily be connected to the grid. In many cases HVDC Light can give new opportunities to trade electric energy in the new deregulated markets. As HVDC Light has been developed to minimise environmental impact and impact on the connecting grids, the licence procedure is generally more favourable than more traditional solutions. • • • •

  11. INTRODUCTION • FACTS Issues Issues VoltageIunu-, I ranxrcnt Stubil uv Damping P,l" er "" Ill!!" P,l-;t-(' ont ingcnc, Voltage Control Voltage ",tahdit) I imirs Limit, I henna! '>rnhilit, Shedding Fixed C 01n pensat ion Enhanced PowerTransfer and Stability Line Better Protection Increased

  12. INTRODUCTION • TCSC The Thyristor Controlled Series Capacitor (TCSC) seems to be one of the members within the FACTS family, beside the SVC that was established long ago, which has attracted the most interest so far. One reason may be that a distinctive quality of the TCSC concept is that it uses an extremely simple main circuit topology. The capacitor is inserted directly in series with the transmission line and the thyristor controlled inductor is mounted directly in parallel with the capacitor. Thus no interfacing equipment like e.g. high voltage transformers is required. This makes TCSC much more economical than some other competing FACTS technologies.

  13. INTRODUCTION • • SVC Static variable capacitor Parallel-connectedstaticvargenerator absorber or Output is adjusted to exchange capacitive or inductive current. Maintainor controlspecificparameters of the electricalpowersystem(typically bus voltage). Thyristor-based Controllers Lower cost alternative to STATCOM

  14. INTRODUCTION STATCOM • Static Synchronous Compensator (STATCOM) • • Parallel-connected static var compensator Capacitive or inductive output current controlled independently of the ac system voltage

  15. INTRODUCTION • UPFC Unifiedpowerflowcontroller(UPFC)is oneoftheFACTSdevices,whichcan controlpowersystemparameterssuch terminalvoltage,lineimpedanceand phaseangle.Therefore,it canbeused onlyforpowerflowcontrol,butalsofor powersystemstabilizingcontrol. as not

  16. TRANSMISSION LINE PARAMETERS Parameters in the transmission line resistance r, inductance L,capacitance C L and C are due to the effects of magnetic and electric fields around the conductor Overhead transmission line ANSI voltage standard: 69kV, 115kV, 138kV, 161kV, 230kV, 345kV, 500kV, 765kV line-to-line extra-high-voltage (EHV): >230kV, ultra-high-voltage (UHV): 765kV bundling: use more than one conductor per phase, usually used at voltage > 230kV advantage of bundling: increase effective radius of line conductor, reduce electric field strength and reduces corona power loss, audio loss and radio interference, and reduces line reactance     Energy Conversion Lab

  17. LINE RESISTANCE Transmission line resistance dc flow: resistance of solid round conductor is given by Rdc=l/A ac flow: the current distribution is not uniform, the current density is greatest at surface of the conductor, this is called skin effect, therefore, Rac > Rdc temperature: resistance increases when temperature increases Transmission line inductance definition of inductance L: L=/I, is flux linkage magnetic field density: Hx=Ix/2x, x is the radius of circle, Ix induces magnetic field density Hx Energy Conversion Lab

  18. INTERNAL INDUCTANCE Derivation of internal inductance Lint consider the flux Ia flowing inside intensity: linked by the portion x r of current a cylinder of radius x, the magnetic   Hdl Ienclosed 2 2 x x Since therefore 2xH I   I , I  a x r2 r2 magnetic flux density Bx: Bx=oHx=oxI /2r2 o is the permeability of free space: 410-7 H/m since current flowing into the circuit of x is only a fraction of Ia, the effectiveturn is equivalent to the fraction N = x2/r2    Energy Conversion Lab

  19. INTERNAL INDUCTANCE Derivation of internal inductance Lint x2/r2turns of the current Ialinked by flux: dx= (x2/r2) dx =(x2/r2) (Bx1dx) =(x2/r2)(oxI/2r2)1dx = (oI) x3/(2r4) dx total flux linkage in the inductor: oI oI r 3 0  xdx int 2r4 8 inductor due to the internal flux: Lint=o/8=(1/2)10-7 H/m inductor Lint is independent of the conductor radius r Energy Conversion Lab

  20. EXTERNAL INDUCTANCE Derivation of external inductance Lext consider Hx external to conductor at x>r, since the circle at radius x enclose entire current, Ix=I ( see Fig.4.4 ): Bx=oHx=oI/2x the entire current I is linked by the flux outside the conductor, dx=dx = Bxdx*1=oI/(2x)*dx external flux linkage between D1and D2: oI D2 D 1 x D2  dx  2 107 I ln  Wb/m ext  2 D1 1 inductance between two points D1 and D2 due to the external flux: D2 D1 L 2107ln H/m ext Energy Conversion Lab

  21. INDUCTANCE OF A SINGLE-PHASE LINE Single-phase line inductance in conductor 1 (L1) consider one meter length of two solid round conductors, radius r1 and r2 in the figure below: r1 r2 D =(1/2)10-7 internal inductance: L1(int) inductance beyond D links anet current of zero and doesn’t contribute to net magnetic flux linkage, thus 210-7*ln(D/r1) the external inductance L1(ext)= total inductance of conductor 1: 1072107ln 2107ln12107ln 1 D D 1 LL L 1(ext ) 1 1(int) r' 2 r 1 4 1 1 ' where r1 r1e Energy Conversion Lab

  22. INDUCTANCE OF A SINGLE-PHASE LINE Single-phase line inductance total inductance of conductor 2: L  2 107 ln 1 2 107 ln D 1 H/m 2 r' 2 if r1=r2=r, the line: inductance per phase per meter length of L  2 107 ln 1 2 107 ln D 1 H/m r' the first term is only the fraction of conductor radius the second term is dependent only on conductor spacing the term r’=re-1/4 is called self-geometric mean distance of a circle with radius r by GMR GMR is called geometric mean radius Energy Conversion Lab

  23. FLUX LINKAGE IN TERMS OF SELF AND MUTUAL INDUCTANCES Flux linkage in a single-phase two-wire line flux linkage: 1  (L11 L12 )I1 2  (L21 L22 )I2 self and mutual inductance: ln 1 ln 1 ln 1 L 2107 L 2107 L 2107 , , 11 22 12 r' r' D 1 for a group 2 of n conductors: I1+I2+…+In=0 i the flux linkage n of conductor : Lij I j j1 i   j Lii Ii i   n I j1 1 1   2 107 I ln ji ln   i j i r' D   i ij Energy Conversion Lab

  24. INDUCTANCE OF THREE-PHASE TRANSMISSION LINES 3-phase line with three symmetrical spacing conductors, the  single-phase inductance L balanced three-phasecurrents:Ia+Ib+Ic=0 total flux linkage of phase a (seefig.4.7):  ln 1 ln 1 ln 1   2 107 I I I   a a b c ' r D D   substituting for Ib+Ic=-Ia, flux linkage of phase a:  ln 1 ln 1 D r'    2 107 I  2 107 I I ln   a a a a r' D  per-phase per kilo-meter length L:  D D L0.2ln 0.2ln mH/km 1 4 ' r  re inductance per-phaseof a three-phasecircuitwith equal isthesameas one conductor of asingle-phase circuit spacing  Energy Conversion Lab

  25. INDUCTANCE OF THREE-PHASE TRANSMISSION LINES 3-phase line with three asymmetrical spacing conductors even in balanced three-phase currents, the voltage different line inductance will be unbalanced thephase a, b and cflux linkages: drop due to   1 1 1  2 107 I  ln I ln I ln a a b c ' r D12 D13     1 1 1  2 107 I  I ln I ln ln b a b c ' D12 1 r D23    1 1  2 107 I I ln  I ln ln c a b c ' D D r   use=LI 13 23 thephase a, b, and cinductances:    1 1 1 2107ln a2ln  a a ln L a ' Ia  r D12 D13     1 1 1  2 107 a ln  ln a2ln  b L b ' I D12 r D23  b  1  1 1 L c 2107a2ln ln  a ln c ' Ic D13 D23 r   where,a=1120o,thephase inductance contain imaginary term Energy Conversion Lab

  26. INDUCTANCE OF THREE-PHASE TRANSMISSION LINES Transpose line practical transmission lines cannotmaintain symmetricalspacing due to theconstruction considerations one waytoregain symmetryand to obtain a per-phasemodel is to consider transposition transposition arrangement: interchange phase every one-third the length (see Fig.4.9) for complete transposed lines, the inductance is the average value of L=(La+Lb+Lc)/3 note a+a2=1120o+1240o=-1      7    2 10 3ln1 ln1ln1ln1H/m L    ' r D12 D23 D13  3  and we obtain ( pp.114-115 ): rearrange equation L  D D D GMD 3 2107ln12 23 13  2 107 ln L H/m r' GMR GMD is geometric mean distance (equivalent conductor spacing)  GMR is geometric mean radius (equivalent conductor radius)  Energy Conversion Lab

  27. INDUCTANCE OF COMPOSITE CONDUCTORS In practical transmission line, stranded conductors and bundled conductors are used. The inductance of the composite conductors are analyzed with GMR and GMD A bundled case of single phase line with n strands in x conductor and m strands in y conductor currentis assumed equally divided among strands(sub- conductor), currentperstrand in xis I/n, currentperstrand is I/m in y flux linkage about strand a: (from mD D D Eq. 4.43 pp.116) 2107Iln aa' ab' am a ' rx DabDac Dan inductance of strand a: mD D D   2n 107 ln aa' ab' am a L  a I / n r' D D D n x ab ac an  Energy Conversion Lab

  28. INDUCTANCE OF COMPOSITE CONDUCTORS inductance of strand n: mD D D   2n 107 ln na' nb' nm n L  n I / n r' D D D n x na nb nc average of the inductance in any strand in x La Lb Lc Ln L  av n the equivalent inductance of conductor strands x in n La Lb Lc Ln Lav  2 107 ln GMD L   H/m x n2 n GMR X where GMD  GMD and GMRx are as follow: (Daa ' Dab' Dam )(Dna' Dnb' Dnm ) mn n2 GMR (D D D )(D D D ) X aa ab an na nb nn Energy Conversion Lab

  29. GMD AND GMR OF COMPOSITE CONDUCTORS Definition of GMD: mn th root of D’s product about any strand in x to strands in y Definition of GMRX: nn th root of rx’ product about any strand to the other strands in x GMR of the sevenidentical strands in a conductor see example 4.1 a large number of strands in GMR calculation would be tedious, usually GMRs are available in manufacturer’s data Energy Conversion Lab in x

  30. GMR OF BUNDLED CONDUCTORS Extra high voltage transmission lines are constructed with bundled conductors Advantages of the bundling: reduce line reactance increase power capability reduce reduce Common voltage surface gradient and corona surge impedance loss conductor bundling arrangement two sub-conductor bundling GMR: three sub-conductor bundling GMR: four sub-conductor bundling GMR: b   Ds d (D d d )3 Ds Db 9 s s 1 16 (D d d d  22 )4 Db s s Energy Conversion Lab

  31. INDUCTANCE OF THREE-PHASE DOUBLE CIRCUIT A three phase double circuit line consists of two identical three-phase circuits The circuits are operated with a1-a2, b1-b2, c1-c2 in parallel as figure 4.13 Geometric arrangement of three-phase double circuit unbalanced with different spacing, cause unbalanced voltage drop to achieve balance, use transpose arrangement To obtain inductance of three-phase double circuit line, we must consider consider combine Energy Conversion Lab transpose effect of L bundle effect of L transpose and bundle effects together

  32. INDUCTANCE OF THREE-PHASE DOUBLE CIRCUIT CalculationoftheGMD: starting from the calculation of per-phase GMD: group identical phase together find GMD between each phase group D D D D D 4  AB a1b1 a1b2 a2b1 a2b2 D D D D D 4 BC b1c1 b1c2 b2c1 b2c2 D D D D D 4 AC a1c1 a1c2 a2c1 a2c2 equivalent GMD per phase is GMD DAB DBC DAC 3  Energy Conversion Lab

  33. INDUCTANCE OF THREE-PHASE DOUBLE CIRCUIT CalculationoftheGMR: starting from the calculation of per-phase group identical phase together GMR: find GMR between each phase group b b 2     DSA (Ds Da1a 2 ) Ds Da1a 2 DbD 4  D (DbD )2 )2 4 SB s b1b2 s b1b2 D (DbD DbD 4 SC s c1c2 s c1c2 b where Ds is the two-subconductor distance bundled equivalent GMR per phase is  GMRL DSADSB DSC 3 Energy Conversion Lab

  34. INDUCTANCE OF THREE-PHASE DOUBLE CIRCUIT The per-phase inductance of the transpose line D D D GMD 3 L  2 107  2 107 ln ln122313 H/m  ' r GMRL where GMD: where GMR: GMD DAB DBC DAC DSADSB DSC 3 GMRL 3 for the inductance per-phase in mH/km GMD L  0.2ln mH/km  GMRL Energy Conversion Lab

  35. REVIEW OF LINE INDUCTANCE Internal inductance Lint=o/8=(1/2)10-7H/m External inductance D L 2107 ln2 H/m  ext D1 Single-phase line inductance D 7 L210 ln H/m  r' Three-phase line inductance spacing (symmetrical D r' 7 L210 ln H/m  Energy Conversion Lab

  36. REVIEW OF LINE INDUCTANCE Three-phase line inductance (transpose line) D D D GMD 3 L  2 107  2 107 ln ln122313 H/m  r' GMR Inductance of composite conductors in x group (n conductor in x, m conductor in y) GMD 7 210 ln Lav H/m  GMR X where where GMD (Daa ' Dab' Dam )(Dna' Dnb' Dnm ) mn n2 GMRX ( Daa Dab Dan )( Dna Dnb Dnn ) Inductance of three-phase double-circuit line (per-phase) D D D GMD 3 L  2 107  2 107 ln lnABBCCA H/m  GMR D D D 3 L SA SB SC Energy Conversion Lab

  37. LINE CAPACITANCE Derivation of the line capacitance consider a long round conductor with radius charge of q coulombs permeterlength: r , carrying a  D1 x D2 electric flux density at D = q/A = q/(2x) electric field intensity E = D/0 = q/(20x)ois the permitivity of a cylinder of radius x:    freespace: 8.8510-12 F/m  potential difference between cylinders from D1 to D2  q dxqD2 D2 D2  D D V Edx ln 12 2x 2 D 1 1 0 0 1 Energy Conversion Lab

  38. CAPACITANCE OF SINGLE-PHASE LINE Derivation of the line capacitance consider two charge of q1 in conductor conductors with radius r , carrying a coulombs/meter in conductor 1 and q2 q2 q1 D 2 voltage between conductor 1 and 2 by q1or q2 q1 ln D q2 ln D   V V 12( q1 ) 21( q2 ) 2 2 r r 0 0 potential difference due to q1 and q2 (q1=-q2) q1lnDq2lnr q lnr V V V    12 12( q1 ) 12( q2 ) 2 2 D  r D 0 0 0 capacitance between conductors  20 0 C  C F/m F/m or 12 D D ln ln r r Energy Conversion Lab

  39. CAPACITANCE OF THREE-PHASE LINES Derivation of the line capacitance consider one meter length of a three-phase line with three long conductors with radius r , transposed spacing shown in figure 4.18 a balanced three-phase system: qa + qb+ qc I = 0 voltage between phase a and b in section   D r 1 D ln23 q ln12  q q V ln ab( I ) a b c 20 r D12 D13  a and ln13  voltage between phase b in section II   D r 1 D q ln23  q q V ln ab( II ) a b c 20 r D23 D12  voltage between phase a and b in section III   D r 1 D ln12 q ln13  q ln q V ab( III ) a b c 20 r D13 D23  Energy Conversion Lab

  40. CAPACITANCE OF THREE-PHASE LINES Derivation of the line capacitance (continue) Vab average value of : 1 1 GMD r r V V  V V q q ln ln  ab ab( I ) ab( II ) ab( III ) a b 2 3 GMD  0 Vac similarly, : 1 1 GMD r r V V  V V q ln q ln  ac ac( I ) ac( II ) ac( III ) a c 2 3 GMD  0 for qb+ qc=- qa, Vab+Vac : 1 2q lnGMD 3qa lnr GMD r VV q  GMD2 ln  ab ac a a 2 r   0 for balanced three-phase voltages Vab+Vac=3Van from Eq.4.83 the capacitance per-phase to neutral qa20 C  F/m GMD r Van ln Energy Conversion Lab

  41. EFFECT OF BUNDLING Derivation of the line capacitance (bundling) rb the effective radius of bundled conductor is the capacitor per phase for bundled conductor where r effective bundle spacing 20 b C F/m, GMD ln rb for two-subconductor bundle : rb  r d for three-subconductor bundle : rd2 rb 3 for four-subconductor bundle : rb  1.094 r d 3 Energy Conversion Lab

  42. CAPACITANCE OF THREE-PHASE DOUBLE-CIRCUIT LINES Derivation of the line capacitance (three-phase) the effective radius of bundled conductor is GMRc the equivalent per-phase capacitance to neutral 20 C F/m, where GMRc is for phase group GMD ln GMRc GMRcper-phase to neutral : GMRc  effective rArB rC 3 radius for phase A, B, and C : r rbD A a1a 2 r rbD B b1b2 r rbD C c1c2 Energy Conversion Lab

  43. EFFECT OF EARTH ON THE CAPACITANCE The electric flux lines for an isolated charged conductor are radial and are orthogonal to cylindrical equipotential surfaces Earth level is likeequipotential surface To simulate effect of equipotential surface, the earth level is replaced by a fictitious charged conductor with charge equal and opposite to the charge on actual conductor at a depth below the surface of the earth the same as the height of the actual conductor above earth The effect of the earth can increase capacitance normally due to the height >> distance between conductors, therefore, effect of earth is negligible forbalanced steady-stateanalysis, effectof earthis neglected forunbalanced faults, earth’s effectis considered Energy Conversion Lab

  44. INDUCTION Magnetic field induction transmission line magneticfields affectobjectscloseto theline reason:line currentproduce magneticfield, magnetic field induces voltage in objects that have a long length parallel to line Magnetic field have been harm) human blood growth, behavior immune systems neuralfunctions Electrostatic induction reported to affect (long term transmission line electricfieldsaffectobjectscloseto theline reason: high voltage produce electric field, electric field induces currents in objects in the area of the electric field Concern of the Electrostatic induction (instant harm) human body may be exposed to steady current or spark discharge from charged objects Energy Conversion Lab

  45. CORONA Corona thepartial ionization surrounding theconductor surface reason:whensurfacepotential gradient of a conductor exceeds occurs the dielectric strength of the surrounding Corona effect produce powerloss produce audible noise radio interferencein theAM band Corona is affected by conductordiameter, bundling typeof conductor air, ionization condition of surface:air dust, Corona can be reduced by increasing theconductor size conductorbundling Energy Conversion Lab humidity, wind

  46. UNIT 3 MODELLING AND PERFORMANCE OF TRANSMISSION LINES 1

  47. Introduction Analyze the performance of single phase and balanced three-phase transmission lines under normal steady-state operating conditions. Expression of voltage and current at any point along the line are developed, where the nature of the series impedance and   shunt admittance is Theperformanceof measuredbased on andlineloadability. taken into account. transmission line is the voltage regulation  2

  48. Transmission Line Representation Is ABCD IR s + + V VR - - A line is treated which the ABCD as two-port network parameters and an for equivalent π circuit are derived. 3

  49. Transmission Line Representation To facilitate the performance calculations relating to a transmission line, the line approximated as a series–parallel interconnection of the relevant parameters. Consider a transmission line to have: is A A A sending end and a receiving end; series resistance and inductance; and shunt capacitance and conductance 4

  50. Transmission Line Representation The relation between sending–end and receiving–end quantities of the two–port network can be written as:   BI VS IS AVR CVR R DIR B VR VS A          IS  DIR  C 5

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