Introduction
The design and operation of a transmission line is greatly influence by the voltage drop line losses and efficiency of transmission system. All these factors related to transmission system are dependent on the line parameters that is resistance (R), inductance (L), and capacitance (C) of the transmission line. Depending on the values of these constants the voltage drop along the line will be changed and the resistance is the important factor while considering power loss in the line and its efficiency. And the very important problem in the design and operation of a power system is the maintenance of the voltage within specified limits at various points in the system.
Types of Transmission line
Two types of system are used for the transmission
- Over head system
- Underground system
Overhead system
Overhead system transmission of electrical power is by using overhead transmission lines over long distances. Thus system the appropriate spacing is provided between the conductors at the supports as well as at the intermediate points. The spacing provides insulation which avoids an electric discharge to occur between the conductors. The transmission lines are subjected to the faults occurring due to lightening, short circuits, and breakage of line etc., overhead lines can be easily repaired compared to underground system. It is also true that though such faults are rear, if occurred it is very difficult to find exact point of fault as transmission lines are very long to the overhead system the insulation must be provided between the conductors and supporting structure. Since the maximum stress exists between conductor and earth.
The parameters of resistor, capacitor, inductor associated with any transmission line are distributed uniformly along the whole length of line and series impedance is formed by the resistance and the inductance. In this case of single phase circuits capacitance is present between conductors whereas in case of three phase circuits conductor to neutral forms a shunt path throughout the length of line. By proper capacitor introduce to makes the transmission line calculations more complexity. And more different ways in which capacitance can be taken into account. The overhead transmission line is classified as followed
- Short transmission line
- Medium transmission line
- Long transmission line
Short transmission line:
If the transmission line length is about 50km and the line voltage is low that is about 20kV or less than that the line is treated as short transmission line and length is small and the voltage is also less the capacitive effects are small. This cause to this effect of capacitance is neglected. So the only resistance and inductance is to be taken into account while analyzed.
Medium transmission line
During the length of transmission line is lying between 50 to 150 km and the line voltage is normally high that is in between 20kV and 100 kV it is treated as medium transmission line and the capacitance is taken into account as the line length is a responsible. To simplest way in the calculations the distributed capacitance of the line is divided and is lumped across the line at one or more points.
Long transmission line system
During the length of transmission line is more than 150km and the line voltage is very high that is above 100kV the line is considered as long transmission line. In the analysis of such lines the line constant are considered uniformly distributed over the whole length of line. To handle careful methods are applied to obtain the solution.
When a short and medium transmission lines through and we are taking the line parameters as lumped one instead of distributed throughout the length of line sufficient accuracy is obtained.
Transmission line system representation:
In this ort transmission lines the capacitive effects are small and rejected with some loss in the precious. It is necessity to consider only the resistance and inductance of the line. Fig shows the star connected generator supplying a balanced Υ connected load through a short transmission line.
Such as the parameters R and L are distributed it making no difference. so far as measurements at the ends of the line are connected to the generator is represented by an impedance connected in series with the generate emf of each phase.
In case of medium length transmission line R and L are taken as lumped with half the capacitance to neutral of the line lumped at each end of the equivalent circuit. The shunt conductance G is neglected as the current is same throughout the line while calculating voltage and current.
The long transmission lines the parameters connected with the line are taken as distributed one to achieve high degree of accuracy was obtained.
The transmission lines are commonly operated with balanced three phase loads and the lines may not be spaced equilaterally and not transposed. The unsymmetrical obtained is less and phases are said to be balanced.
Transmission line related terms and performance
The voltage regulation and transmission efficiency are the most important factors while analyzing the performance of transmission lines.
Voltage Regulation:
The cause of the current carried by the transmission line due to voltage drop in the line because of resistance and inductance connected with the line. And the finally result at the receiving end the voltage is usually less than the voltage at the sending end. The drop in the voltage (Vs –VR) of the line is expressed as a percentage of receiving end voltage VR known as “Regulation”.
By the difference of no load voltage and full load voltage ration of the full load voltage and its express as percentage.
Voltage Regulation = (V no load – V full load / V full load) * 100 %
At no load there is no drop in the line and since
VR = Vs
At full load is voltage drop in the line and the voltage is VR.
Voltage regulation = (Vs – VR / VR) * 100 %
The voltage regulation of a transmission line must be as low as possible and with increase in load current and the change in receiving end voltage
Transmission efficiency
The transmission efficiency always some power loss taking place in line resistance. This offence to this power determined at the receiving end of the line is generally less than that obtained at the sending end.
Transmission efficiency is the ration of the receiving end power to sending end power it expressed as percentage.
Transmission efficiency η = (receiving end power/sending end power) * 100 %
Performance Analysis of Short Transmission Lines
In the review of short transmission lines the capacitive effects are small and neglected. The resistance and inductance of the line are only taken into consideration. The parameters are taken to be lumped instead of distributed for the analysis.
Where
I = Load current
R = Resistance of the loop that is resistance of both conductors
XL = inductive loop reactance
VR = Receiving end voltage
cos ΦR = Receiving end power factor
Vs = sending end voltage
cos Φs = sending end power factor
ZL = Load impedance
Transmission efficiency = (power delivered/power silent)*100
η = (VR IR cos ΦR / VR IR cos ΦR + I2R) * 100
Three Phase Short Transmission Line
Generally transmission of electrical power is done using 3phase system. It consider as three single phase units with each conducting unit transmitting one third of the total power. The method of 3 phase system is done by considering only one phase as similar conditions can be obtained in three phase system.
The expressions obtained for regulation efficiency in this case of single phase system are valid in case of 3 phase system. Here we have to take the phase voltages for V s and VR. similarly R and XL are resistance and inductive reactance per phase respectively.
Medium Transmission Line
By over comet the short transmission lines have smaller lengths and the power transmitted by these lines are comparatively at lower voltages. Due to this while analyzing short transmission lines the effect of capacitance is neglected. With increase in length and voltage of transmission line the capacitive effects are dominant and they cannot be neglected.
The medium transmission lines are having lying between 20 to 150km and they operated at voltage greater than 20kV. Since its making the analysis of medium transmission line we have to take into account the effect of capacitance for better accuracy and the capacitance is uniformly distributed along the length of transmission line. For the simplicity in the calculations the line capacitance is considered to be limped at one or more points. This is known as localizing of line capacitance and it gives fairly accurate results. Its also classified as
- End condenser method
- Nominal T method
- Nominal π method
End condenser method
End condenser system is the line capacitance is lumped or concentrated near the load or at the receiving end. This method over estimates the effect of capacitance.
For a 3phas systems it is always convenient to represent a single phase instead of line to line values
Where
Vs = sending end voltage
VR = Receiving end voltage
IR = Load current per phase
XL = Inductive reactance per phase
C= Capacitance per phase
cos ΦR = Receiving end power factor
Now
Voltage regulation = (Vs – VR)/VR) * 100 %
Transmission efficiency = (power delivered/phase)/ (power sent/phase + losses /phase) * 100
η = (VR IR cos ΦR / VR IR cos ΦR + Is2 R) * 100 %
This method is having some limitations. When this method is simple to operate.
Advantages:
This method assumes the capacitance to be lumped near the receiving end. During actual practice it is distributed along its length. Due to this there is considerable error of about 10% in the calculations.
The effects of line capacitance are over estimated in this method.
Nominal T Method
This method is used for the analysis of medium transmission line. In this method the total line capacitance is lumped or concentrated at the midpoint of the line. The resistance and reactance of the line are divided with half the resistance and reactance on one side and remaining half on other side of capacitor. Half of the line carries full charging current with this arrangement. It desirable work in phase instead of line values.
Nominal π method
This method to construct capacitance. In which capacitance is divided into two halves with one half lumped near sending end and other half near the receiving end.
To near the capacitor the sending end does not contribute any line voltage drop but it should be added with line current to get total sending end current.
Long Transmission Lines
In the short and medium analysis we are assuming that the capacitance associated with the line is combined or concentrated at one or more point when its actual practice it is distributed along the length of line. If same assumption is made performance parameters. So the better accuracy the line constants in case of long transmission line are considered to be uniformly distributed throughout the length of line.
The total length of the transmission line can be separated into n sections with each section having the line constants 1/n times that for total line.
The resistance and the inductive reactance forms the series elements whereas the leakage susceptance and leakage conductance make shunt elements. Because of the capacitance existing between line and neutral the leakage susceptance is appeared. The leakage taking place over the conductors or due to corona effect between the conductors forms leakage conductance. The leakage current through shunt admittance is maximum at the sending end and decreases continuously towards the receiving end.
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