Name: lossless lines and voltage behavior
Uploaded: 2024-11-21T14:54:26.000Z
Duration: 1 min 23 s
Channel: JoVE

Consider a lossless line with a purely imaginary propagation constant, resistive characteristic impedance, and established ABCD parameters.
Its equivalent pi circuit has imaginary series impedance and shunt admittance. When the beta and length product is less than pi, it exhibits inductive series impedance and capacitive shunt admittance, making it lossless.
The wavelength, or distance required to change the voltage or current phase by 2-pi, is calculated using the velocity of propagation.
Surge impedance loading is the power delivered to a load resistance equal to the surge impedance.
Here, voltage remains constant along the line, and constant real power flows from the sending to the receiving end, with zero reactive power flow.
Real power delivered is determined using the rated voltage and surge impedance.
In reality, power lines are not terminated by their surge impedance, causing non-flat voltage profiles that vary depending on load conditions.
At no load, voltage increases from the sending to the receiving end, while for short circuits, it decreases to zero at the receiving end. The full-load profile is higher than the short-circuit profile.

verliesloze lijnen

In de elektrotechniek wordt een verliesvrije transmissielijn gekenmerkt door een puur denkbeeldige voortplantingsconstante en een resistieve karakteristieke impedantie. De ABCD-parameters, die het verband tussen de ingangs- en uitgangsspanningen en -stromen beschrijven, geven een equivalent π-circuit aan met een denkbeeldige serie-impedantie en een shunt-admittantie. Dit resulteert in een transmissielijn die, wanneer het product van de faseconstante (bèta) en de lengte van de lijn kleiner is dan pi, inductieve serie-impedantie en capacitieve shunt-admittantie vertoont, waardoor deze verliesvrij blijft.

Golflengte en voortplanting

De golflengte is de fysieke lengte waarover de spanning of stroomfase verandert met 2π. Dit wordt bepaald met behulp van de voortplantingssnelheid van het signaal. Voor een verliesvrije lijn is de golflengte cruciaal bij het bepalen van de elektrische lengte van de lijn en de fasekarakteristieken ervan.

Piekimpedantiebelasting

Overspanningsimpedantiebelasting (SIL) is een concept dat wordt gebruikt om het vermogen te beschrijven dat kan worden geleverd aan een belastingsweerstand die gelijk is aan de overspanningsimpedantie van de transmissielijn. Voor een transmissielijn met een resistieve karakteristieke impedantie wordt de SIL berekend met behulp van de nominale spanning en de overspanningsimpedantie:

<img alt="Equation1" src="/files/ftp_upload/16147/16147_Equation 1.svg" style="height: 36px;" />

In deze toestand blijft de spanning over de lijn constant en is er een constante stroom van echt vermogen van de verzendende kant naar de ontvangende kant, met een reactieve stroom van nul.

Spanningsprofielen en belastingomstandigheden

In praktische scenario's worden transmissielijnen zelden beëindigd met hun piekimpedantie, wat leidt tot niet-uniforme spanningsprofielen langs de lijn. Onder nullastcondities neemt de spanning toe van het verzendende uiteinde naar het ontvangende uiteinde vanwege het Ferranti-effect. Omgekeerd daalt de spanning in een kortsluitconditie naar nul aan het ontvangende uiteinde. Bij volledige belasting ligt het spanningsprofiel tussen deze twee uitersten, over het algemeen hoger dan het kortsluitprofiel maar lager dan het nullastprofiel.

Deze kenmerken van verliesvrije transmissielijnen zijn van essentieel belang voor het ontwerp en de analyse van energiesystemen. Ze zorgen voor een efficiënte en betrouwbare energielevering met minimale verliezen en stabiele spanningsprofielen onder wisselende belastingomstandigheden.

Verliesloze lijnen

Consider a lossless line with a purely imaginary propagation constant, resistive characteristic impedance, and established ABCD parameters.
Its equivalent ...

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Lossless Lines

lossless lines and voltage behavior

Lossless transmission lines in electrical engineering are described by a purely imaginary propagation constant and a resistive characteristic impedance. Their ABCD parameters show an equivalent pi circuit with an imaginary series impedance and a shunt admittance. When the product of beta and line length is less than pi, the line has inductive series impedance and capacitive shunt admittance, which keeps it lossless.

Wavelength is the physical length over which voltage or current phase changes by 2π. It depends on the signal’s propagation velocity. For a lossless line, wavelength helps define the electrical length of the line and its phase behavior.

Surge impedance loading, or SIL, is the power that can be sent to a load resistance equal to the line’s surge impedance. For a line with resistive characteristic impedance, SIL is found from the rated voltage and the surge impedance. In this condition, voltage stays constant along the line, and real power flows from the sending end to the receiving end with zero reactive power flow.

In practice, transmission lines are often not terminated with their surge impedance, so the voltage profile is not uniform. Under no-load conditions, the voltage rises from the sending end to the receiving end because of the Ferranti effect. Under short-circuit conditions, the receiving-end voltage drops to zero. At full load, the voltage profile falls between these two cases, and these line properties are important for efficient and reliable power-system design.

Lossless Lines and Voltage Behavior

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lossless lines

Lossless transmission lines in electrical engineering are described by a purely imaginary propagation constant and a resistive characteristic impedance. Their ABCD parameters show an equivalent pi circuit with an imaginary series impedance and a shunt admittance. When the product of beta and line length is less than pi, the line has inductive series impedance and capacitive shunt admittance, which keeps it lossless. Wavelength is the physical length over which voltage or current phase changes...

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Explore lossless transmission lines, wavelength, surge impedance loading, and how voltage profiles change under no-load, full-load, and short-circuit conditions.

Lossless Lines and Voltage Behavior | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Lossless Lines and Voltage Behavior

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