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

Para minimizar as perdas de linha em circuitos trifásicos, dois transformadores são adicionados: um transformador elevador na fonte e um transformador abaixador na carga.
Suas relações de giro inversas garantem tensão e corrente de carga consistentes.
A tensão secundária do transformador esquerdo é dez vezes maior que sua tensão primária, e a impedância conectada ao secundário do transformador direito, vista do primário, é multiplicada por um fator de 100.
Agora, substituindo o circuito por um circuito de malha única, a corrente da malha representa a corrente da linha.
A corrente que entra na extremidade secundária do transformador esquerdo é igual à corrente de linha negativa, enquanto na primária é dez vezes a corrente secundária negativa.
Da mesma forma, a corrente que entra na extremidade primária do transformador direito é igual à corrente da linha, enquanto na extremidade secundária é dez vezes a corrente primária.
A tensão de fase na carga é determinada, seguida pelo cálculo da potência fornecida pela fonte e para a carga.
A estimativa da energia perdida na linha revela que 99,5% da energia fornecida pela fonte atinge a carga, com apenas 0,5% perdida na linha.

reduzindo a perda de linha

Em um circuito trifásico, a perda na linha é um indicador da energia dissipada na forma de calor devido à resistência das linhas de transmissão. Para resolver isso, incorporar transformadores ao sistema – um transformador elevador na fonte e um transformador abaixador na carga – é uma solução estratégica. Dois transformadores trifásicos são introduzidos para melhorar isso.
Com um transformador elevador na fonte, a tensão é aumentada, reduzindo assim a corrente nas linhas de transmissão, uma vez que a perda de potência nas linhas de transmissão é proporcional ao quadrado da corrente, esta redução na corrente leva a uma diminuição nas perdas na linha.
Cálculo da Corrente da Linha:
A corrente de linha é calculada dividindo a carga refletida pela impedância (considerando a relação de espiras do transformador) pela tensão secundária do transformador.
A corrente de linha é:
<img alt="Equation 1" src="/files/ftp_upload/15136/15136_Equation_1.svg" style="height: 36px;">

<img alt="Equation 2" src="/files/ftp_upload/15136/15136_Equation_2.svg" style="height: 18px;">
Onde n é a relação de espiras do transformador e Z_load é a impedância real da carga no lado secundário
Cálculo da Tensão de Fase na Carga:
Se a relação de espiras primária e secundária do transformador for dada como N_p:N_s, então a tensão de fase na carga pode ser encontrada por:
<img alt="Equation 3" src="/files/ftp_upload/15136/15136_Equation_3.svg" style="height: 34px;">
onde:
V_fase é a tensão de fase na carga,
V_primary é a tensão de fase no lado primário do transformador
Em um sistema trifásico Y-para-Y (estrela-estrela) com transformadores em ambos os lados, a tensão total linha-linha na carga pode ser encontrada multiplicando-se a tensão de fase por sqrt 3, devido ao mudança de fase entre tensões de linha em uma configuração Y:
<img alt="Equation 4" src="/files/ftp_upload/15136/15136_Equation_4.svg" style="height: 20px;">
A potência real P entregue pela fonte em um sistema trifásico é:
<img alt="Equation 5" src="/files/ftp_upload/15136/15136_Equation_5.svg" style="height: 18px;">
Onde:
P é a potência real total fornecida pela fonte.
V_L é a tensão linha a linha.
I_L é a corrente de linha.
cos(θ) é o fator de potência.

Reduzindo a perda de linha

Para minimizar as perdas de linha em circuitos trifásicos, dois transformadores são adicionados: um transformador elevador na fonte e um transformador abaixador na carga.
...

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

Three-Phase Circuits

Circuitos Trifásicos

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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

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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

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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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