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

3상 회로에서 라인 손실을 최소화하기 위해 소스의 승압 변압기와 부하의 강압 변압기의 두 개의 변압기가 추가됩니다.
역 권선 비율은 일관된 부하 전압과 전류를 보장합니다.
왼쪽 변압기의 2차 전압은 1차 전압의 10배이며, 1차에서 볼 수 있듯이 오른쪽 변압기의 2차 전압에 연결된 임피던스에 100을 곱합니다.
이제 회로를 단일 메쉬 회로로 교체하면 메쉬 전류는 라인 전류를 나타냅니다.
왼쪽 변압기의 2차 끝으로 들어가는 전류는 음의 라인 전류와 같고 1차측에서는 음의 2차 전류의 10배입니다.
마찬가지로 오른쪽 변압기의 1차 끝으로 들어가는 전류는 라인 전류와 같고 2차 끝에서 1차 전류의 10배입니다.
부하의 위상 전압이 결정된 다음 소스와 부하에 의해 전달되는 전력을 계산합니다.
라인에서 손실되는 전력을 추정하면 소스에서 공급되는 전력의 99.5%가 부하에 도달하고 라인에서 손실되는 것은 0.5%에 불과하다는 것을 알 수 있습니다.

회선 손실 줄이기

3상 회로에서 선로 손실은 전송선의 저항으로 인해 열로 소산되는 에너지를 나타내는 지표입니다. 이 문제를 해결하기 위해 변압기(소스에 승압 변압기, 부하에 강압 변압기)를 시스템에 통합하는 것이 전략적 해답입니다. 이를 개선하기 위해 2개의 3상 변압기가 도입되었습니다.

소스에서 승압 변압기를 사용하면 전압이 증가하여 전송선의 전력 손실이 전류의 제곱에 비례하므로 전송선의 전류가 감소하고 이러한 전류 감소는 선로 손실의 감소로 이어집니다.

라인 전류 계산:

선전류는 온저항 반영 부하(변압기의 권선비 고려)를 변압기의 2차 전압으로 나누어 계산합니다.

라인 전류는 다음과 같습니다.

<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;">

여기서 n은 변압기의 권선비이고 Z_load는 2차측의 실제 부하 온저항입니다.

부하에서의 위상 전압 계산:

변압기의 1차 권선과 2차 권선비가 N_p:N_s로 주어지면 부하의 위상 전압은 다음과 같이 구할 수 있습니다.

<img alt="Equation 3" src="/files/ftp_upload/15136/15136_Equation_3.svg" style="height: 34px;">

어디:

V_phase는 부하의 위상 전압이고,

V_primary는 변압기 1차측의 상 전압입니다.

양쪽에 변압기가 있는 Y-to-Y(스타-투-스타) 3상 시스템에서 부하의 전체 선간 전압은 위상 전압에 sqrt 3을 곱하여 찾을 수 있습니다. Y 구성에서 라인 전압 간의 위상 변이:

<img alt="Equation 4" src="/files/ftp_upload/15136/15136_Equation_4.svg" style="height: 20px;">

3상 시스템의 소스에서 전달되는 실제 전력 P는 다음과 같습니다.

<img alt="Equation 5" src="/files/ftp_upload/15136/15136_Equation_5.svg" style="height: 18px;">

어디:

P는 소스가 전달하는 총 실제 전력입니다.

V_L은 선간 전압입니다.

I_L은 라인 전류입니다.

cos(θ)는 역률입니다.

3상 회로에서 라인 손실을 최소화하기 위해 소스의 승압 변압기와 부하의 강압 변압기의 두 개의 변압기가 추가됩니다.
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Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Three-Phase Circuits

3상 회로

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

How Three-Phase Power Delivers Electricity

Three-phase power is a major part of AC power distribution, especially where steady and efficient electricity delivery is needed. AC systems are grouped into single-phase, two-phase, and three-phase systems. These categories help describe how power moves from the source to the load. Single-phase circuits are common in homes. They usually use a two-wire system that connects one AC source to loads. These circuits can supply everyday appliances such as lamps, televisions, and microwaves at 120 V...

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

Three-phase power connections use balanced voltages that are equal in magnitude and separated by 120 degrees. A three-phase generator produces these voltages, and the balance helps reduce power loss while keeping energy delivery steady to connected loads. Three-phase sources can be arranged in either wye or delta form. The loads connected to the system can also use wye or delta. This flexibility gives control over how the system is designed and managed. In a wye connection, one end of each...

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

Single-phase and three-phase circuits distribute electrical power in different ways. Single-phase power is common in homes, while balanced three-phase power is widely used in industrial settings with heavy machinery. Both systems deliver energy, but their current flow and wire needs are not the same. A single-phase circuit usually uses a two-wire system. The current depends on the power absorbed by the load and the line voltage. Because wire loss from resistance follows the square of the...

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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