Name: cutting heat loss in three-phase lines
Uploaded: 2024-07-08T13:19:58.000Z
Duration: 1 min 18 s
Channel: JoVE

Pour minimiser les pertes de ligne dans les circuits triphasés, deux transformateurs sont ajoutés : un transformateur élévateur à la source et un transformateur abaisseur à la charge.
Leurs rapports de rotation inverses assurent une tension et un courant de charge constants.
La tension secondaire du transformateur gauche est dix fois supérieure à sa tension primaire, et l'impédance connectée à la tension secondaire du transformateur droit, vue du primaire, est multipliée par un facteur de 100.
Maintenant, en remplaçant le circuit par un circuit à maille unique, le courant de maillage représente le courant de ligne.
Le courant entrant à l'extrémité secondaire du transformateur gauche est égal au courant de ligne négatif, tandis qu'au primaire, il est dix fois le courant secondaire négatif.
De même, le courant entrant à l'extrémité primaire du transformateur droit est égal au courant de ligne, tandis qu'à l'extrémité secondaire, il est dix fois le courant primaire.
La tension de phase à la charge est déterminée, puis calculée la puissance délivrée par la source et à la charge.
L’estimation de la puissance perdue dans la ligne révèle que 99,5 % de l’énergie fournie par la source atteint la charge, avec seulement 0,5 % perdu dans la ligne.

réduire la perte de ligne

Dans un circuit triphasé, la perte de ligne est un indicateur de l'énergie dissipée sous forme de chaleur en raison de la résistance des lignes de transmission. Pour résoudre ce problème, l'intégration de transformateurs dans le système (un transformateur élévateur à la source et un transformateur abaisseur à la charge) est une solution stratégique. Deux transformateurs triphasés sont introduits pour améliorer cela.

Avec un transformateur élévateur à la source, la tension est augmentée, réduisant ainsi le courant dans les lignes de transmission puisque la perte de puissance dans les lignes de transmission est proportionnelle au carré du courant, cette réduction du courant entraîne une diminution des pertes en ligne.

Calcul du courant de ligne :

Le courant de ligne est calculé en divisant la charge réfléchie par l'impédance (en tenant compte du rapport de transformation du transformateur) par la tension secondaire du transformateur.

Le courant de ligne est :

<img alt="Equation 1" src="/files/ftp_upload/15136/15136_Equation_1.svg" style="text-align: center; height: 36px;">

<img alt="Equation 2" src="/files/ftp_upload/15136/15136_Equation_2.svg" style="text-align: center; height: 18px;">

Où n est le rapport de transformation du transformateur et Zload est l'impédance de charge réelle du côté secondaire

Calcul de la tension de phase à la charge :

Si le rapport des spires primaire/secondaire du transformateur est donné comme Np:Ns, alors la tension de phase à la charge peut être trouvée par :

<img alt="Equation 3" src="/files/ftp_upload/15136/15136_Equation_3.svg" style="text-align: center; height: 34px;">

où:

Vphase est la tension de phase à la charge,

Vprimary est la tension de phase du côté primaire du transformateur

Dans un système triphasé Y à Y (étoile à étoile) avec transformateurs des deux côtés, la tension complète entre phases à la charge peut être trouvée en multipliant la tension de phase par sqrt 3, en raison de la déphasage entre les tensions de ligne dans une configuration Y :

<img alt="Equation 4" src="/files/ftp_upload/15136/15136_Equation_4.svg" style="text-align: center; height: 20px;">

La puissance réelle P délivrée par la source dans un système triphasé est :

<img alt="Equation 5" src="/files/ftp_upload/15136/15136_Equation_5.svg" style="text-align: center; height: 18px;">

Où:

P est la puissance réelle totale délivrée par la source.

VL est la tension ligne à ligne.

IL est le courant de ligne.

cos(θ) est le facteur de puissance.

Réduire la perte de ligne

Pour minimiser les pertes de ligne dans les circuits triphasés, deux transformateurs sont ajoutés : un transformateur élévateur à la source et un transformateur abaisseur à la charge.
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Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

Three-Phase Circuits

Circuits triphasés

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

Reducing Line Loss

cutting heat loss in three-phase lines

Three-phase power systems can lose energy as heat in transmission lines because the wires have resistance. This line loss becomes important when electricity travels over a distance. A common solution is to use transformers to change the voltage and current in the system.

The setup uses two three-phase transformers. A step-up transformer is placed at the source, and a step-down transformer is placed at the load. Raising the voltage at the source lowers the current in the transmission lines, and that reduces line loss because power loss in the lines depends on the square of the current.

The line current can be found by dividing the reflected load impedance by the transformer secondary voltage. In this calculation, the turns ratio affects the load as it appears on the transformer side. The actual load impedance on the secondary side is represented as Z load, and n is the transformer's turns ratio.

The load phase voltage is found from the primary-to-secondary turns ratio, written as N p:N s. In a Y-to-Y, or star-to-star, three-phase system, the load line-to-line voltage is the phase voltage multiplied by sqrt 3. This factor comes from the phase shift between line voltages in a Y connection.

The real power delivered by the source is calculated with the three-phase power equation. It uses the line-to-line voltage, the line current, and the power factor, cos(theta). Together, these relationships show how transformer choice can help lower line loss while still delivering power to the load.

Cutting Heat Loss in Three-Phase Lines

three-phase circuits

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generation of three-phase voltage

Three-Phase AC Generator Windings

A three-phase AC generator uses rotating magnet windings and a stationary stator to make three-phase voltage. The rotor carries a magnet that spins inside the stator. The stator holds the three-phase winding, and mutual induction creates the voltage. The stator windings are spread evenly around the inside of the stator. They are placed 120 electrical degrees apart. These windings consist of three separate coils, or groups of coils, called phases. The phases can be connected in a Y, or star,...

three-phase voltages

Three-Phase Power Connections

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the y-to-y circuit

Balanced Wye-to-Wye Neutral Current

A balanced wye-to-wye circuit uses three wye-connected sinusoidal voltage sources and three wye-connected loads. A neutral wire links the neutral node of the source to the neutral node of the load. The load impedance is connected across each phase of the load. The source and load can be connected in either a four-wire or a three-wire arrangement. A three-phase system is balanced when each phase has the same load. In that case, the current flow and phase angle are uniform across the system. If...

the y-to-delta circuit

Wye Source and Delta Load Currents

A balanced wye source and delta load form a common three-phase circuit with no neutral line connection. The source is Y-connected, and the load is delta-connected. To analyze the circuit, the first step is to assume a positive phase sequence. These phase voltages are then used to find the line voltages that appear across the delta load impedances. In the wye source, the phase voltages are V an, V bn, and V cn. In the delta load, the line voltages are V ab, V bc, and V ca. These line voltages...

the delta-to-delta circuit

Balanced Delta-Delta Power Circuit

A balanced delta-delta power circuit uses a delta-connected source and a delta-connected load. The two deltas form a closed loop that creates three separate phases. In this setup, the phase voltages are the same as the line voltages. If the source is in positive sequence, the phase voltages can be written directly, and no neutral wire is needed. The delta-connected load current is found by dividing the phase voltage by the impedance of each phase. For line current, Kirchhoff’s Current Law...

the delta-to-y circuit

Delta-Wye Source and Load Connections

A balanced delta-wye circuit connects a delta-connected source to a wye-connected load. In this setup, the phase voltage of the delta source equals the line voltage of the wye load. The source also sets the line currents that flow into the load. For a balanced system, the phase difference between currents makes it possible to find one line current from the other by using the positive sequence of phases. In the wye-connected load, each phase current equals the line current from the delta source.

power in a three-phase circuit

Balanced Three-Phase Power Calculation

Balanced three-phase power calculation depends on the wye and delta connections used in the circuit. A wye, or star, configuration can use three wires or four wires. A delta configuration connects the components in a closed loop. These connection types change how voltages and currents are arranged, but both are used in three-phase systems. In a balanced three-phase system, instantaneous power is the power at one exact moment. Even though the power in each phase changes over time, the total...

power distribution in three-phase and single phase circuits

power-distribution-in-three-phase-and-single-phase-circuits

Single-Phase vs. Three-Phase Power Loss

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line loss

Reducing Power Loss in Three-Phase Lines

Three-phase power lines can lose energy as electricity travels from the source to the load. This line loss affects how efficiently power reaches the load. In balanced three-phase circuits, the symmetry makes the analysis easier because one phase can represent the whole system. The source-load connection can use wye, also called star, or delta configurations. These setups change the relationship between line voltage, phase voltage, line current, and phase current. A per-phase equivalent circuit...

reducing line loss

Three-phase power systems can lose energy as heat in transmission lines because the wires have resistance. This line loss becomes important when electricity travels over a distance. A common solution is to use transformers to change the voltage and current in the system. The setup uses two three-phase transformers. A step-up transformer is placed at the source, and a step-down transformer is placed at the load. Raising the voltage at the source lowers the current in the transmission lines, and...

key terms and concepts

See how step-up and step-down three-phase transformers lower line loss by reducing current, and learn the key voltage, current, and power equations.

Cutting Heat Loss in Three-Phase Lines | 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

Cutting Heat Loss in Three-Phase Lines

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