Introduction:
The capacitance is uniformly distributed over the entire length of the line. However, in order to make the calculations simple, the line capacitance is assumed to be lumped or concentrated in the form of capacitors shunted across the line at one or more points. Such a treatment of localizing the line capacitance gives reasonably accurate results. The most commonly used methods (known as localised capacitance methods) for the solution of medium transmissions lines are : (i) End condenser method (ii) Nominal T method (iii) Nominal π method.
It is well known that line constants of the transmission line are uniformly distributed over the entire length of the line. However, reasonable accuracy can be obtained in line calculations for short and medium lines by considering these constants as lumped. If such an assumption of lumped constants is applied to long transmission lines (having length excess of about 150 km), it is found that serious errors are introduced in the performance calculations. Therefore, in order to obtain fair degree of accuracy in the performance calculations of long lines, the line constants are considered as uniformly distributed throughout the length of the line. Rigorous mathematical treatment is required for the solution of such lines.
In any four terminal network, the input voltage and input current can be expressed in terms of output voltage and output current. Incidentally, a transmission line is a 4-terminal network; two input terminals where power enters the network and two output terminals where power leaves the network. Therefore, the input voltage (VS) and input current (IS) of a 3-phase transmission line can be expressed as :
Vs = A VR + B IR and IS = C VR + D IR
here A, B, C and D (generally complex numbers) are the constants known as generalized circuit constants of the transmission line. The values of these constants depend upon the particular method adopted for solving a transmission line. Once the values of these constants are known, performance calculations of the line can be easily worked out.
Learning Objectives:
- To identify and differentiate different types of transmission lines
- To know mathematical modeling of medium transmission lines and different methods
- To familiarize with different methods of solving transmission line performance
- To understand and determine generalized circuit constants of transmission line
Lecture Contents:
- Medium Transmission Lines and solution methods
- Nominal T Method
- Nominal π Method
- Long Transmission Lines
- Analysis of Long Transmission Line (Rigorous method)
- Generalized Circuit Constants of a Transmission Line
- Determination of Generalized Constants for Transmission Lines
Learning Outcomes:
The students will be able to
- classify different types of transmission lines
- formulate and apply different methods of solving and calculating transmission line performance
- understand generalized circuit constants and determine their quantity
