Name: single-phase vs. three-phase power loss
Uploaded: 2024-07-08T13:19:58.000Z
Duration: 1 min 17 s
Channel: JoVE

Рассмотрим двухпроводную однофазную систему, обеспечивающую электричеством дома, и трехпроводную сбалансированную трехфазную систему, питающую завод с тяжелым оборудованием.
В обеих системах используются провода одинакового материала и длины с резистивными нагрузками и имеют одинаковое линейное напряжение и потребляемую мощность.
В однофазной системе ток равен отношению поглощенной мощности к сетевому напряжению, при этом потери мощности пропорциональны квадрату поглощенной мощности, деленному на квадрат сетевого напряжения.
Для трехфазной системы ток делится на три провода, а общие потери мощности рассчитываются иначе.
В соотношении потерь мощности двух систем происходит подстановка сопротивлений в терминах радиусов проводов.
Если потери мощности одинаковы в обеих системах, то радиус провода в однофазной системе в два раза больше радиуса трехфазной системы.
Сравнивая материал, необходимый для двух систем, можно сказать, что однофазная система использует на 33% больше материала, чем трехфазная система.
Таким образом, при той же выходной мощности трехфазная система значительно минимизирует расход материала, повышая эффективность распределения мощности.

Распределение мощности в трехфазных и однофазных цепях

Распределение мощности внутри электрических цепей является основополагающим аспектом бытовых и промышленных энергетических систем. В то время как однофазное питание распространено в жилых помещениях, трехфазное питание является стандартом для промышленных помещений с тяжелой техникой. Каждая система уникальна и имеет свои преимущества, поэтому крайне важно понимать основные принципы распределения мощности и эффективности использования материалов.
Однофазное распределение электроэнергии:
Однофазные цепи типичны для бытовых условий; используется двухпроводная система. Ток в этой системе определяется мощностью, потребляемой нагрузкой, и напряжением сети:
<img alt="Equation 1" src="/files/ftp_upload/15134/15134_Equation_1.svg" style="height: 32px;">
Потери мощности в проводах из-за сопротивления пропорциональны квадрату тока:
<img alt="Equation 2" src="/files/ftp_upload/15134/15134_Equation_2.svg" style="height: 16px;">
 где R – сопротивление проводов.
Трехфазное распределение электроэнергии:
Сбалансированная трехфазная система, наиболее широко используемая в промышленных условиях. В этой системе ток делится между тремя проводами, что снижает ток в каждом проводе по сравнению с однофазной системой с тем же уровнем мощности. Если предположить, что ток и сопротивление в каждой фазе одинаковы, общие потери мощности представляют собой сумму потерь в каждой фазе.

Размер провода и расход материала:
При сравнении размеров проводов для равных потерь мощности в обеих системах площадь поперечного сечения проводов в однофазной системе должна быть больше, чем в трехфазной системе, чтобы выдерживать повышенный ток без увеличения потерь мощности. В частности, для однофазной системы требуются провода с площадью поперечного сечения, вдвое превышающей площадь поперечного сечения каждого фазного провода в трехфазной системе. Это означает, что однофазной системе потребуются провода с большей площадью поперечного сечения, чтобы выдерживать ту же силовую нагрузку, что и трехфазной системе, что приведет к увеличению количества проводящего материала примерно на 33%.

Рассмотрим двухпроводную однофазную систему, обеспечивающую электричеством дома, и трехпроводную сбалансированную трехфазную систему, питающую завод с тяжелыми ...

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

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

Three-Phase Circuits

Трехфазные цепи

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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 current, higher current can increase power loss in the wires.

A balanced three-phase system spreads the current across three wires. This lowers the current in each wire compared with a single-phase system delivering the same power. If the current and resistance in each phase are the same, the total power loss is the sum of the loss in each phase.

Wire size also changes between the two systems. To keep equal power loss, the single-phase system needs wires with a cross-sectional area twice that of each phase wire in the three-phase system. That means single-phase wiring uses about 33% more conducting material for the same power load.

Single-Phase vs. Three-Phase Power Loss

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

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

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...

key terms and concepts

Compare single-phase and balanced three-phase power distribution, wire current, resistance loss, and why single-phase systems need more conducting material.

Single-Phase vs. Three-Phase Power Loss | 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

Single-Phase vs. Three-Phase Power Loss

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