Performance of Transmission lines

Name of the Subject : Power Systems-IN. R. Dagade

Electrical Engineering Department NBNSSOE, Ambegaon, Pune

Introduction

• An electric transmission line conductor has four parameters: R, L, C, and G

• These are uniformly distributed along the whole length of the line and representation of these parameters at any point on the line is not possible.

• These are usually expressed as resistance, inductance, capacitance and conductance per kilometre.

Performance of Transmission Line

The transmission lines are categorized as three types-1) Short transmission line

The line length is up to 80 km with an operating voltage up to 20 kV

2) Medium transmission line The line length is between 100 km and 250 km with an

operating voltage ranging from 20 kV to 100 kV3) Long transmission line

The line length above 250 km and operating voltage above 100 kV

Performance of Transmission Line

• performance of transmission line can be determined by its efficiency and voltage regulation.

• Power sent from sending end - line losses = Power delivered at receiving end.

• Voltage regulation of transmission line is measure of change of receiving end voltage from no-load to full load condition.

ABCD Parameters of Transmission Line

• The circuit of a 2 port network is shown in the diagram below.

• Vs, Is – supply end voltages and currents • VR, IR– receiving end voltages and currents • ABCD parameters or the transmission line parameters

provide the link between Vs, Is and VR, IR considering the circuit elements to be linear in nature.

ABCD Parameters of Transmission Line

Parameter Specification UnitA = VS / VR Voltage ratio Unit less

B = VS / IR Short circuit resistance Ω

C = IS / VROpen circuit conductance mho

D = IS / IR Current ratio Unit less

Short Transmission Line

• The transmission lines which have length less than 80 km are generally referred as short transmission lines.

• For short length, the shunt capacitance of this type of line is neglected and other parameters like electrical resistance and inductance of these short lines are lumped, hence the equivalent circuit is represented as given below,

Short Transmission Line

• Is = Ir.• Now if we observe the vector diagram carefully, we

will get, Vs V≅ r + Ir.R.cosφr + Ir.X.sinφr

• Vs V≅ r + Ir.R.cosφr + Ir.X.sinφr as the it is assumed that φs φ≅ r

Vs = Vr + IrZ and Is = Ir

• Compairing with

• A = 1, B = Z, C = 0 and D = 1.• AD-BC=1

Short Transmission Line

• Regulation of Short Transmission Line

• Efficiency of Short Transmission Line

Medium Transmission Line

• When the length of an overhead transmission line is between 100 km and 250 km with an operating voltage ranging from 20 kV to 100 kV, it is considered as a medium transmission line.

• Due to the line length being considerably high, admittance Y of the network does play a role in calculating the effective circuit parameters

• For this reason the modelling of a medium length transmission line is done using lumped shunt admittance along with the lumped impedance in series to the circuit.

Medium Transmission Line

• These lumped parameters of a medium length transmission line can be represented using two different models, namely-

1)Nominal Π representation.2)Nominal T representation.

Medium Transmission Line-Nominal Π representation.

• Now applying KCL, at node P, we get.• (1)• Similarly applying KCL, to node Q.

(2)

Medium Transmission Line-Nominal Π representation.

• Now substituting equation (2) to equation (1)

• Now by applying KVL to the circuit,

• Now substituting equation (4) to equation(3), we get•

Medium Transmission Line-Nominal Π representation.

• Comparing equation (4) and (5) with the standard ABCD parameter equations

• We get,

Medium Transmission Line-Nominal T Representation

• Vs and VR is the supply and receiving end voltages respectively, and

• Is and IR is the supply and receiving end currents respectively

• Let M be a node at the midpoint of the circuit, and the drop at M, be given by Vm.

Medium Transmission Line-Nominal T Representation

• Applying KVL to the above network we get,

• Rearranging the above equations

Medium Transmission Line-Nominal T Representation

• Now the sending end current is,(9)

• Substituting the value of VM to equation (9) we get,

• Again comparing equation (8) and (10) with the standard ABCD parameter equations,

Questions1. Resistivity of a wire depends on

A. materialB. lengthC. cross section areaD. all of above

Ans: A2. Shunt capacitance is usually neglected in the analysis of

(A) Short transmission lines (B) Medium transmission lines (C) Long transmission lines(D) Medium as well as long transmission lines.

Answer: A

Questions3. In overhead transmission lines the effect of capacitance

can be neglected when the length of line is less than (A) 200 km (B) 160 km (C) 100 km (D) 80 km. Answer:D4. In a transmission line following arc the distributed

constants (A) resistance and inductance only(B) resistance, inductance and capacitance (C) resistance, inductance, capacitance and short

conductance. Answer: C

Questions5. A 30 km transmission line carrying power at 33 kV is known

as (A) short transmission line(B) long transmission line (C) high power line (D) ultra high voltage line. Answer: A6. In terms of constants A, B, C and D for short transmission

lines, which of the following relation is valid ? (A) A = B = 1 (B) B = D = 0 (C) A = C = 1 (D) C=0. Answer: D

Questions7. Which of the following relationships is not valid for short

transmission lines ? (A) B = Z = C (B) A = D = 1 (C) Is = Ir (D) None of the above. Answer: A8. Which of the following short circuit is the most dangerous ? (A) Line to line short circuit (B) Dead short circuit(C) Line to ground short circuit (D) Line to line and ground short circuit. Answer: B•

Questions9. In the analysis of short transmission lines which of the following is

neglected ? (A) I2 R loss (B) Shunt admittance (C) Series impedance (D) All of the above. Answer: B10. In medium transmission lines the shunt capacitance is taken into

account in (A) Tee method (B) Pie method (C) Steinmetz method (D) all of the above. Answer: D

Questions11. In nominal T method A. full charging current flows over full the line B. half charging current flows over the full the lineC. full charging current flows over half the line D. half charging current flows over half the line Answer: C12. Which combination is true for short lines A. A =1, B=Z, C=0, D=1B. A=0, B=1, C= Z, D=1C. A=1, B=1, C= Z, D=0D. A=0, B=0, C=1, D=Z

Answer: A

Thank You.