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

为了减小三相电路中的线路损耗，需添加两个变压器：在电源端添加升压变压器，在负载端添加降压变压器。
它们的匝数比倒数可确保负载电压和电流的稳定性。
左侧变压器的次级电压是其初级电压的十倍，而从初级侧观察，连接到右侧变压器次级的阻抗被放大了100倍。
现在，将电路替换为单网孔电路，网孔电流即代表支路电流。
流入左侧变压器次级端的电流等于负的线路电流，而在初级端，该电流是次级电流负值的十倍。
同理，流入右侧变压器初级端的电流等于线路电流，而在次级端，该电流为初级电流的十倍。
确定负载处的相电压，然后计算电源输出的功率以及传递给负载的功率。
估算线路中的功率损耗表明，电源提供的功率中有 99.5% 传输到了负载，仅有 0.5% 在线路中损耗。

减少线路损耗

在三相电路中，线路损耗是传输线中的电阻以热量的形式进行耗散的能量指标。为了能够解决这个问题，在系统中安装变压器（在电源处安装升压变压器，在负载处安装降压变压器）便是一个战略性的解决方案。为了能够改善这一问题，便引入了两台三相变压器。

在电源处使用升压变压器，电压会增加，并以此来减少传输线中的电流，由于传输线中的功率损耗与电流的平方成正比，电流的减少会导致线路损耗的减少。

线电流的计算：

线电流的计算方法是将阻抗反射负载（变压器的匝数比）除以变压器的次级电压。

线电流为：

<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;">

其中，n 是变压器的匝数比，Z_load 是次级侧的实际负载阻抗。

负载中相电压的计算：

如果变压器的初级匝数与次级匝数之比为 N_p:N_s，那么负载处的相电压可通过以下公式来进行计算：

<img alt="Equation 3" src="/files/ftp_upload/15136/15136_Equation_3.svg" style="text-align: center; height: 34px;">

其中：

V_phase 是负载处的相电压，

V_primary 是变压器初级侧的相电压

在两侧都有变压器的 Y 形-Y 形（星型-星型）三相系统中，由于 Y 形配置中的线电压之间存在相移，因此位于负载处完整的线间电压可以通过将相电压乘以根号 3 来进行计算：

<img alt="Equation 4" src="/files/ftp_upload/15136/15136_Equation_4.svg" style="text-align: center; height: 20px;">

在三项系统中，电源输出的实际功率 P为：

<img alt="Equation 5" src="/files/ftp_upload/15136/15136_Equation_5.svg" style="text-align: center; height: 18px;">

其中：

P 是电源实际输出的总功率。

V_L 是线间电压。

I_L 是线电流。

cos(θ) 是功率因数。

为减少三相电路中的线路损耗，需增加两个变压器：在电源端添加升压变压器，在负载端添加降压变压器。

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Three-Phase Circuits

三相电路

KEY TERMS AND CONCEPTS

关键术语与概念

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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