Lecture 3 Transmission line Subject lecturer: Dr. XU Zhao Department of Electrical Engineering Hong Kong Polytechnic University Email: eezhaoxu@polyu.edu.hk R Room: CF632 Tel: 27666160 Outlines • • • • 2 Types Inductance of transmission line Capacitance of transmission line Transmission line model Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Types of power lines • Power lines classified according to voltage class – Low voltage (LV) lines – 120 V – 600 V • Lines are insulated conductors, conductors usually made of aluminium, aluminium often extended from local power mounted distribution transformers to service area of consumer • Lines may be overhead or underground – Underground cables found in metropolitan areas with grid providing dependable service in which some outages will not cause loss of load – Medium-voltage (MV) lines – 2.4 kV – 69 kV • Predominantly radial systems with lines spreading out from sub-stations to feed power to high-rise buildings, shopping centres and campuses – High-voltage (HV) lines - <230 kV • Lines composed of aerial conductors or underground cables – Extra-high-voltage (EHV) lines – operate at voltages up to 800 kV • Used when g generating g stations very y far from load centres • May be as long as 1000 km 3 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Component of HV transmission line • Conductors Aluminum outer strands 2 layers, 30 conductors Steell core strands, St t d 7 conductors – Stranded copper conductors or steel-reinforced aluminium cable (ACSR) • ACSR usually preferred because result in lighter and more economical lines • Insulators – Serve to support and anchor conductors and insulate them from ground • Usually made of porcelain, but glass and other synthetic insulating materials may be used – Must offer high resistivity to surface leakage currents – Must be sufficiently thick to prevent breakdown under high voltage stress 4 Electrical Engineering, HKPU Single-phase high-voltage cable with solid dielectric EE3741 Ass. Prof Zhao Xu Component of HV transmission line •Supporting structures – Keep conductors at safe height from ground and at adequate distance from each other • Wooden poles equipped with cross-arms used for voltages below 70 kV • For higher voltage two poles used to create H-frame • For very high voltage lines, steel tower used – Spacing between conductors must be sufficient to prevent arc-over under g p gusty y conditions and increased as distance between tower and line voltages become higher 5 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Resistance • DC Resistance at given temperature RDC,T = ρl/A l – length of conductor A – cross-sectional area of conductor ρ – resistivity of conductor – Resistivity will depend upon conductor material 6 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Resistance • If resistance of conductor at certain temperature know, DC resistance at other temperature given by: ⎛ M + T2 ⎞ ⎟⎟ RT 1 RT 2 = ⎜⎜ M + T1 ⎠ ⎝ M – temperature constant • Resistance of nonmagnetic conductors varies with frequency due to “skin skin effect” effect – Electric current distributions inside conductor not uniform As frequency increases, current tends to flow nearer to outer surface of conductor, conductor decreasing effective cross section E.g. RAC = K * RDC RAC ≈ (1.05 (1 05 ~ 1.10)* 1 10)* RDC @ 60Hz 60H 7 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Inductance • Series inductance of transmission line consists of two components – Internal inductance • Due to magnetic flux enclosed by conductor – External inductance • Due to magnetic flux outside conductor • Total inductance a combination of both these effects 8 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Internal Inductance L=λ/I Current carrying conductor •Magnetic field intensity around path, radius x, inside conductor 9 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Internal Inductance • Flux density around the path inside the conductor • Flux linkages are equal to fraction of current linked times flux per meter length. Thus the total flux linkages inside the conductor • The flux linkages and the consequent internal inductance of the conductor – THE INTERNAL INDUCTANCE IS CONSTANT!, IRRESPECTIVE OF CONDUCTOR DIAMETER 10 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu External inductance y to flux between p • Inductance due only points at D1 and D2 meters – Depends p comparative p distances from current carry y conductor 11 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Inductance of single phase line •Consider two wire transmission system –Conductor 1 is active conductor d t –Conductor 2 provide return path for current • “Neutral” conductor 2- wire transmission line system 12 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Inductance of single phase line • Inductance of two-wire circuit due to current flowing g in conductor 1 • Total T t l inductance i d t can b be simplified i lifi d tto: r’1=r1e−1/4 : GMR (geometric mean radius) of the conductor 13 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu r’1=rr1e−1/4 : GMR (geometric mean radius) of the conductor Inductance of single phase line •r1’ – (GMR) equivalent radius of conductor 1= 0.7788r1 – The impact of self inductance is to reduce the effective radius of the conductor • Inductance d off conductor d 2 • The inductance ind ctance of the complete ci circuit c it is then OR If r1 = r2 14 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Inductance of Three-Phase Circuit • Inductance due to current flow in phase a p • Inductance of phase b, c r’i=rie−1/4 : GMR (geometric mean radius) of the conductor 15 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu For a completely transposed transmission line, the average inductance of each conductor over a complete cycle is the same. Inductance of Three-Phase Circuit • If all three conductors have same radius –GMD – geometric mean distance = (D12D23D31)⅓ • For a three-phase, p , equilaterally q y spaced p transmission line, phase conductors have equal separation distances GMR of the conductor: r ’ = re-1/4 – D12 = D23 = D31 = D =2×10-7[1/4+ln(D/r)] H/m If 3-phase line not equilaterally spacedÆ different Φ and L, but small; assume transposed, eachHKPU conductor occupies the original positions of theAss. other 16 Electrical i.e. Engineering, EE3741 Prof Zhao Xu 16 conductors over equal distances. Examples • A single circuit, circuit fully transposed, transposed three-phase, three phase 60Hz transmission line consists of three conductors arranged as shown. The aluminium conductor has a diameter of 250mils, find the inductive reactance of the line p per kilometre p per p phase. • Note: 1 mil: 1×10-3 in; 1m = 39.36in 17 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Solution 1m = 39.36inches(in) Diameter: 250mils=0.25in=0.25/39.36=0.006352m Radius: r = 0.006352/2 0.006352/2=0.003176m 0.003176m De = (5×5 ×8)1/3=5.848m For each kilometre of length, the inductance is: L = 2[1/4 + ln(De/r)] ×10-7 ×103=1.544mH/km Inductive reactance per km is: XL=2πfL=377×1.544 ×10−3=0.5858Ω 18 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Verify the solution with GMR & GMD 19 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Inductance of Stranded Conductors • Stranded conductors have 2 or more elements or strands of wire that are electrically in parallel. • All strands t d are id identical, ti l shares h currentt equally. ll • La =Lb=Lc = 2×10-7 ln(GMD/GMR) GMR of stranded conductor: Equivalent radius or GMR (Geometric Mean Radius) of the conductor: r ’ = re-1/4 Dnn L=LX+LY 20 Electrical Engineering, HKPU GMR of the kth conducto G conductor:: Dkk = rk’ = rke-1/4 EE3741 Ass. Prof Zhao Xu Inductance of Bundled Conductors •La =Lb=Lc = 2×10-7 ln(GMD/GMRb) Two-conductor bundle GMRb = rb = d rc Three-conductor bundle rb = 3 d 2 rc Four-conductor bundle: rb = 1.09 4 d 3 rc rc: GMRc of individual conductor Bundled Conductors: have 2 or more conductors belong to the same phase and are close t together th in i comparison i with ith the th separation distances between the phases. 2-bundle 3-bundle 21 2-bundle conductor line 4-bundle Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Capacitance •When Wh voltage lt applied li d to t pair i off conducting d ti plates (separated by non-conducting medi m) charge medium) h ge accumulates m l te on each e h side ide of plate –Magnitude M it d off charge h on each h side id off plate l t equall –Charges on each side have opposing polarity •Magnitude Magnit de of charge cha ge deposited proportional p opo tional to applied voltage Q = CV –C – capacitance of line 22 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Capacitance •Potential difference between conductor in transmission line cause them to become charged like capacitors –Effective capacitance dependent upon size and separation i di distance off conductors d •AC power lines energized by time varying voltage –AC voltage causes charge on conductors to vary • “Charging” Charging current of line capacitance –Charging current effects • Power transmitted and operating power factor • Voltage drop along line 23 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Electric field around long conductor • Can consider transmission line as long g straight g conductor having uniform charge throughout length – Electric field intensity at point P some distance x from conductor given by: E = q / (2πεx) q – change of conductor [coloumbs/m] permittivity y of medium surrounding g conductor=εrε0 ε–p εr: relative permittivity (dielectric constant) =1 for air -9 -12 F/mEE3741 Ass. Prof Zhao Xu Electrical Engineering, HKPU ε24 0: permittivity of free space = 1/(36π)×10 =8.854×10 Electric field around long conductor •Instantaneous potential difference between two point, P1 and P2 around conductor –Found by considering change in electric field over radial path between two points 25 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Capacitance of single phase line • Consider C id active ti conductor d t and return path as two long lines of charge • Total voltage between lines – Superposition of: Voltage drop between lines due to charge on active conductor + Voltage drop between lines due to charge on return conductor 26 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Capacitance of single phase line 27 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Capacitance of single phase line εr: relative permittivity (dielectric constant) =1 for air ε0: permittivity of free space = 1/(36π)×10-9=8.854×10-12 F/m 28 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Capacitance of single phase line •Potential difference between each conductor and ground half the potential difference between two conductors –Capacitance to ground / Capacitance to neutral twice i capacitance i ffrom line li - line li εr: relative permittivity (dielectric constant) =1 for air ε0: permittivity of free space = 1/(36π)×10-9=8.854×10-12 F/m 29 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Capacitance of three-phase line •Capacitance Capacitance per phase given by: a D3 2 D1 GMD = (D12D23D31)⅓ =D provided conductors h have same diameter di t and are equilaterally spaced p 1 where c D23 b Bundled line capacitance 30 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Line reactance • Inductive reactance – Total T t l iinductive d ti reactance t proportional ti l to t li line llength th • Total line inductive reactance found by multiplying inductive reactance by line length • Capacitive reactance – Total capacitive reactance inversely proportional to line length • Total line capacitive reactance found by dividing capacitive reactance by y line length g – Total capacitive susceptance (admittance) proportional to line length Xc = Ω⋅m / m = Ω 31 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Transmission line model • Transmission lines are represented by an equivalent circuit with parameters on a per-phase basis – Voltages are expressed as phase-to-neutral – Currents are expressed for one phase – The three phase system is reduced to an equivalent single-phase • All lines are made up of distributed series inductance and resistance, and shunt capacitance and conductance – Line parameters: R, L, C, & G –Capacitance p between neighbouring g g conductors, line and ground – Inductance due to Stranded & Bundled Conductors • Three types of models – depend on the length and the voltage level – short, medium, and long length line models 32 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Transmission Line models • Classified according to length of line – Short line – less than 50 miles (80 km) (or up to 320 km for some applications depending upon whether line characteristics can still be represented by lumped components) – Medium line – 50 ~ 150 miles (80 ~ 240 km) – Long line 33 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Short Transmission Lines • Applicable to lines up to 80.45 km (50 miles) long • Equivalent circuit of short transmission line consists of series combination of line resistance and inductive reactance – Line capacitance ignored! 34 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Short Transmission Lines • No shunt branches – Cu Current e a at se sending d g end e d equal equa to o current cu e at a receiving ece g end e d Is = IR • Voltage at sending end given by: Vs = VR + IRZ • Voltage regulation – Increase I in i receiving i i end d voltage lt as load l d reduced d d from f full load to no load with sending end voltage held constant 35 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Two-Port model representation ABCD two p port model Vs = VR + IRZ Is = IR 36 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Medium Length Lines • For lines 80 km (50 miles) - 240 km (150 miles) capacitive reactance between lines and neutral (earth) not insignificant • Shunt admittance (usually pure capacitance) included in equivalent circuit – Allows formation of nominal π equivalent circuit • Line impedance p still represented p as lumped p components p 37 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Medium Length Line • Sending-end voltage and current expressed in terms of receiving end voltage and current using “ABCD” transmission parameters AD-BC = 1 A&D: dimensionless B’s unit: (Ω) C’s unit: siemens – ABCD parameters governed by line impedance and admittance 38 • They are a short-cut way of representing line characteristics Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Medium Length Line VS=AVR+BIR IS=CVR+DIR No load: IR = 0,, VS=AVR •Voltage Regulation (at specific power factor) –At At no lload, d receiving-end i i d voltage lt iis 1/A ti times sending end voltage Sending end power: = PS= 3VSISPFS Efficient of line: = ((PR//PS))100% 39 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Long transmission line • For lines greater than 240/250 km (150 miles) lumped components no longer provide required accuracy – Consider parameters distributed evenly throughout line l: length of line Z0 = SQRT(z/y): characteristic or surge impedance z: series impedance per unit length, Z=zl γ=SQRT(zy): constant y: shunt admittanceEE3741 per unit length, 40 Electrical propagation Engineering, HKPU Ass. Prof Zhao Xu Y=yl 40 Long transmission line •For lines greater than 240/250 km (150 miles) lumped components no longer provide required accuracy – Consider parameters distributed evenly throughout line •Modeling M d li off the th transmission t i i line li parameters – Accuracy obtained by using distributed parameters – The series impedance per unit length is z – The shunt admittance per unit length is y – The Th distance di t from f receiving i i end d is i x 41 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Long transmission line 42 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Long transmission line 43 Electrical Engineering, HKPU Wave equation for lossy line EE3741 Ass. Prof Zhao Xu Long transmission line • let d 2 I ( x) dx 2 = γ 2 I ( x) α-attenuation/damping constant β –phase p constant 44 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Two part model 45 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Two part model 46 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Wave propagation • Substitute V ( x) = A1eαx e jβx + A2 e −αx e − jβx • Transform back to time domain v( x, t ) = 2 Re A1eαx e j (ωt + βx ) + 2 Re A2 e −αx e j (ωt − βx ) -amplitude increases along positive x direction -amplitude decreases along positive x direction -incident incident wave -traveling traveling towards receiving end -reflected wave traveling backward to sending end Note: - α >0 for a line with resistance -Traveling sinusoidal waves in positive x direction 47 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Courtesy by Prof Goran Andersson ETH 48 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Wave propagation • Wave length: a voltage cycle corresponds to 2 π change of angular argument βx λ=2π/β • If loss neglected g=r=0, and β = ω LC C 1 1 λ= LC f LC • Using the equation for per unit length inductance and capacitance L and C, we can have 1 v≈ = 3 ×108 m / s u0ε 0 v = λ / T = 2πf / β = λ≈ 49 Electrical Engineering, HKPU 1 = 3 ×108 / 50 = 6km f u0ε 0 EE3741 Ass. Prof Zhao Xu Surge impedance • If loss neglected g=r=0 g=r=0, the characteristic impedance L -Surge impedance purely resistive C( • Surge u g impedance p da loading oad g (SIL) ) @ receiving g end d 2 3 V (kVrated ) 2 R * SIL = 3VR I R = = MW Zc Zc Zc = • @SIL, voltage and current along lines are constant in magnitude as sending di end d V ( x ) = (cos β x + j sin β x )V R = V R ∠ β x I ( x ) = (cos β x + j sin β x ) I R = I R ∠ β x • No reflected wave (A2=0) and reactive power in the line, and reactive loss due to shunt capacitance and series inductance offset each other • SIL indicate loading without itho t reactive eacti e compensation, compensation therefore the efo e reflecting capacity somehow: loading@ SIL compensation little, loading>> SIL-compensation needed • Zc for overhead line 400-600 ohm, cable: 30-50 ohm, overhead li line lloading di can > SIL, SIL while hil cable bl lloading di always l < SIL (SIL larger than cable thermal limit) 50 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Wave transient analysis are reflected wave @receiving end Let Zc=surge impendence Voltage reflection coefficient @ receiving end and SC termination, -1, open circuit termination +1. Since current reflection coefficient@receiving end is -ρ ρR When wave back to sending end, reflection coefficient@sending end 51 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Wave transient analysis-example • Refer to Page228-230 Power System analysis By John&William, McGraw-Hill 1994 • A DC source of 120v with negligible resistance is connected through a switch S to a lossless transmission line having Zc Zc=30 30 ohm. The line is terminated in a resistance of 90 (10) ohm. If S closes at t =0 , plot VR v.s. time until t=5T, where T is the time for a voltage wave to travel the length of line. line 52 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Wave transient analysis-example Incident wave starts to travel along line (Note: x from sending end here), ( ) is the unit step p where U(vt-x) function, equal to 1 when vt-x>0, and 0when vt-x<0 No reflection until wave reach receiving end with Zc=30, end, Zc=30 @ t= T, ρr =(90-30)/(90+30)=1/2 v-=120*1/2=60 V VR=120+60=180 V @t 2T ρs =(0-30)/(0+30)=-1 @t=2T, (0 30)/(0+30) 1 v-=-1*60=-60, Vs=120v always @t=3T, ρr =(90-30)/(90+30)=1/2 v-=1/2*-60=-30, 1/2* 60 30 VR=180-60-30=90 180 60 30 90 V … @t=5T, VR=135 v 53 Electrical Engineering, HKPU Lattice diagram EE3741 Ass. Prof Zhao Xu Wave transient analysis-example •ZR=10 ohm •Current lattice diagram can be drawn with reflection of current is negative value of voltage one 54 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Wave transient analysis • Reflection can occurs at the end, and also when a line has a junction of two different parts, or bifurcation • E.g. E g an overhead line connected to cable, cable the first part terminates at Zc of the second part cable. The part of wave which continues to travel and is not reflected back at the junction is called the refracted wave • When applies a voltage surge, a same shape voltage surge traveling backwards as seen in example occurs at end of the lossless line, • If ZR is not open circuit or SC, reflected wave has reduced magnitude. When ZR> Zc, the peak terminal voltage > voltage surge 55 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Wave transient analysis • Terminal equipment tends to overvoltage when surge applies in the circuit, and therefore protected by surge arrestor (lightening arrestor, surge divider) – Conducting at certain v above design rating v – Limit terminal voltage to its design value – Noncoducting again when line line-neutral neutral voltage drops below rating • Air gap type, difficult to extinguish current for AC • Air gap+ nonlinear resistor in series(ohm decreases quick when V rises) • silicon carbide carbide, zinc oxide is more popular without need of air gap 56 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Transmission power •Power transfer by transmission line VS = VS ∠δ ,VR = VR ∠0 A = A ∠θ A , B = B ∠θ B , I R = S R = PR + jQ R = 3VR I R = 3 VS VR * PR = QR = VS ( L − L ) VR ( L − L ) B VS ( L − L ) VR ( L − L ) B B ∠(θ B−δ ) − 3 cos(θ B−δ ) − A VR ( L − L ) sin(θ B−δ ) − A VR ( L − L ) B 2 ∠(θ B−θ A) cos(θ B−θ A) 2 sin(θ B−θ A) S R = PR + jQ R = 3VR I R PS = 57 Electrical Engineering, HKPU B ∠θ B 2 B B A VR VS ∠δ − A ∠θ A VR ∠0 QS = A VS ( L − L ) B IS = 2 cos(θ B−θ A) − B A VS ( L − L ) * 2 A ∠θ A VS ∠δ − VR ∠0 B ∠θ B VS ( L − L ) VR ( L − L ) B VS ( L − L ) VR ( L − L ) cos(θ B+δ ) sin(θ B−θ A) −EE3741 Ass. Prof Zhao Xu sin(θ B+δ ) B Transmission power • Real R l and d reactive ti power transmission t i i lloss PL = PS − PR QL = QS − QR • Power transfer by lossless line B = jX ' , θ A = 0, θ B = 900 , A = cos βl PS = PR = VS ( L − L ) VR ( L − L ) X ' sin δ QR = VS ( L − L ) VR ( L − L ) X ' cos δ − VR ( L − L ) B 2 cos βl • Power-delta P d lt curve: max power transfer t f @ 90 degree d • Actual stability is much lower [35,45]degree due to stability y consideration of generator, g , i.e. to withstand sudden loss of generator or load 58 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Transmission capability • Power transmission capability is limited by thermal and stability limits • Overloading may cause high temperature and irreversible stretching of conductor, i.e. physical sag of lines due to real power loss • Thermal limit specified in current carrying capability Ithemral from manufacture datasheet Sthermal = 3VφRated I thermal 59 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Other Limits Affecting Power Transfer Stability limit zAngle limits – while the maximum power transfer occurs when line angle difference is 90 degrees, degrees actual limit is substantially less due to multiple lines in the system and also the generator stability limits [35, 45]degree zVoltage stability limits – as power transfers increases, reactive losses increase as I2X. X As reactive power increases the voltage falls falls, resulting in a potentially cascading voltage collapse. 60 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Transmission line compensation • Self reactance and capacitance causing voltage variations and reactive flow • Loading variation cause voltage variations along the line line, e.g. eg – @ SIL, voltage profile are flat along line and no reactive flow – <SIL, voltage rise, line generate VARs – >SIL, >SIL voltage drops, drops line consume VARs • Shunt v.s. series compensation: Shunt reactors, Shunt capacitor, Series capacitor, FACTs devices… 61 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Transmission compensation • Compensate for voltage uneven distribution cause by line capacitance • Shunt reactors xLsh @end of long line • Solving for xLshh • If requiring q g VS=VR • Substitute b Xlsh • Voltage is uneven along the line, mid point voltage is, why? 62 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu Transmission compensation • Shunt capacitor for heavy loads with lagging power factor • Series capacitor connected in mid of line – reduce reactance – Reduce voltage g drop p – improve steady state and transient stability loading limit for EHV lines at very low costs comparing to new line costs PS = PR = VS ( L − L ) VR ( L − L ) X' sin δ is in percentage called percentage compensation – Drawbacks: special protection to prevent high current at SC fault occurrence, and SSR ( (resonant circuit causing oscillations ll when h stimulated by a disturbance) 63 Electrical Engineering, HKPU EE3741 Ass. Prof Zhao Xu