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

Для минимизации потерь в линии в трехфазных цепях добавляются два трансформатора: повышающий трансформатор у источника и понижающий трансформатор у нагрузки.
Их обратные передаточные числа обеспечивают постоянное напряжение и ток нагрузки.
Вторичное напряжение левого трансформатора в десять раз превышает его первичное напряжение, а импеданс, подключенный к вторичной обмотке правого трансформатора, как видно с точки зрения первичной обмотки, умножается в 100 раз.
Теперь, заменив цепь на цепь с одной сеткой, ток сетки представляет собой линейный ток.
Ток, поступающий на вторичный конец левого трансформатора, равен отрицательному линейному току, в то время как на первичной обмотке он в десять раз превышает отрицательный вторичный ток.
Точно так же ток, поступающий на первичный конец правого трансформатора, равен линейному току, в то время как на вторичном конце он в десять раз превышает первичный ток.
Определяется фазное напряжение на нагрузке с последующим расчетом мощности, подаваемой источником и на нагрузку.
Оценка мощности, теряемой в линии, показывает, что 99,5 процента мощности, подаваемой источником, доходит до нагрузки, и только 0,5 процента теряется в линии.

уменьшение потерь на линии

В трехфазной цепи потери на линии - это показатель энергии, рассеиваемой в виде тепла из-за сопротивления линий электропередачи. Чтобы решить эту проблему, стратегическим решением является включение в систему трансформаторов — повышающего трансформатора в источнике и понижающего трансформатора в нагрузке. Для улучшения этой ситуации введены два трехфазных трансформатора.
При наличии повышающего трансформатора в источнике напряжение увеличивается, тем самым снижается ток в линиях передачи, поскольку потери мощности в линиях передачи пропорциональны квадрату тока, такое снижение тока приводит к уменьшению потерь в линии.
Расчет линейного тока:
Линейный ток рассчитывается путем деления нагрузки, отраженной импедансом (с учетом коэффициента трансформации трансформатора), на вторичное напряжение трансформатора.
Линейный ток составляет:
<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;">
Где n — коэффициент трансформации трансформатора, а Z_load — фактическое сопротивление нагрузки на вторичной обмотке.
Расчет фазного напряжения на нагрузке:
Если соотношение витков первичной и вторичной обмотки трансформатора задано как Np:Ns, то фазное напряжение на нагрузке можно найти по формуле:
<img alt="Equation 3" src="/files/ftp_upload/15136/15136_Equation_3.svg" style="height: 34px;">
где:
V_фаза – фазное напряжение на нагрузке,
V_primary — фазное напряжение на первичной стороне трансформатора.
В трехфазной системе Y-Y (звезда-звезда) с трансформаторами с обеих сторон полное линейное напряжение на нагрузке можно найти, умножив фазное напряжение на квадратный корень из 3, поскольку фазовый сдвиг между линейными напряжениями в конфигурации Y выглядит как:
<img alt="Equation 4" src="/files/ftp_upload/15136/15136_Equation_4.svg" style="height: 20px;">
Реальная мощность P, подаваемая источником в трехфазной системе, равна:
<img alt="Equation 5" src="/files/ftp_upload/15136/15136_Equation_5.svg" style="height: 18px;">
Где:
P — полная активная мощность, отдаваемая источником.
V_L – линейное напряжение.
I_L – ток линии.
cos(θ) — коэффициент мощности.

Для минимизации потерь в линии в трехфазных цепях добавляются два трансформатора: повышающий трансформатор у источника и понижающий трансформатор у нагрузки.
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Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

Three-Phase Circuits

Трехфазные цепи

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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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