Loading Impíd Tonnáin is a very essential parameter when it comes to the study of power systems as it is used in the prediction of maximum loading capacity of lines trasnmission.
However before understanding SIL, we first need to have an idea of what is Impíd Tonnáin (Zs). It can be defined in two ways one a simpler one and other a bit rigorous.
Modh 1
Is eolas ginearálta é go bhfuil lines trasnmission fada (> 250 km) le díobhú inductance agus capacitance mar a chuid íogaireach. Nuair a lánraítear an líne, cuireann an comhbhailt capacitance cumhacht reacóideach isteach ar an líne agus glanann an indúilt cumhacht reacóideach. Anois, más ghearr a dhéanamh an iarmhéid de na cúpla cumhacht reacóideach, tagaimis ar an chothromóid seo leanas
Capacitive VAR = Inductive VAR
Áit,
V = Vocht fhasa
I = Cúr Líne
Xc = Reacóid Capacitance per phase
XL = Reacóid Inductive per phase
Upon simplifying
Áit,
f = Fréimeach an chórais
L = Inductance per unit length of the line
l = Oiread an líne
Hence we get,
This quantity having the dimensions of resistance is the Impíd Tonnáin. It can be considered as a purely resistive load which when connected at the receiving end of the line, the reactive power generated by capacitive reactance will be completely absorbed by inductive reactance of the line.
It is nothing but the Characteristic Impedance (Zc) of a lossless line.
Modh 2
From the rigorous solution of a long transmission line we get the following equation for voltage and current at any point on the line at a distance x from the receiving end
Áit,
Vx and Ix = Voltage and Current at point x
VR and IR = Voltage and Current at receiving end
Zc = Characteristic Impedance
δ = Propagation Constant
Z = Series impedance per unit length per phase
Y = Shunt admittance per unit length per phase
Putting the value of δ in above equation of voltage we get
Áit,
We observe that the instantaneous voltage consists of two terms each of which is a function of time and distance. Thus they represent two travelling waves. The first one is the positive exponential part representing a wave travelling towards receiving end and is hence called the incident wave. While the other part with negative exponential represents the reflected wave. At any point along the line, the voltage is the sum of both the waves. The same is true for current waves also.
Now, if suppose the load impedance (ZL) is chosen such that ZL = Zc, and we know
Thus
and hence the reflected wave vanishes. Such a line is termed as infinite line. It appears to the source that the line has no end because it receives no reflected wave.
Hence, such an impedance which renders the line as infinite line is known as impíd tonnáin.It has a value of about 400 ohms and phase angle varying from 0 to –15 degree for overhead lines and around 40 ohms for underground cables.
The term impíd tonnáin is however used in connection with surges on the line trasnmission which may be due to lightning or switching, where the line losses can be neglected such that
Now that we have understood Impíd Tonnáin, we can easily define Loading Impíd Tonnáin.
SIL is defined as the power delivered by a line to a purely resistive load equal in value to the surge impedance of that line. Hence we can write
The unit of SIL is Watt or MW.
When the line is terminated by surge impedance the receiving end voltage is equal to the sending end voltage and this case is called flat voltage profile. The following figure shows the voltage profile for different loading cases.
It should also be noted that impíd tonnáin and hence SIL is independent of the length of the line. The value of impíd tonnáin will be the same at all the points on the line and hence the voltage.
In case of a Compensated Line, the value of impíd tonnáin will be modified accordingly as
Áit, Kse = % of series capacitive compensation by Cse
KCsh = % of Shunt capacitive compensation by Csh
Klsh = % of shunt inductive compensation by Lsh
The equation for SIL will now use the modified Zs.
Déan Comhrá: Meastar an bunreacht, maith iad na haislinge a thugtar amach, má tá briseadh cinn, déan teagmháil chun scrios.
