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

Um Leitungsverluste in Drehstromkreisen zu minimieren, werden zwei Transformatoren hinzugefügt: ein Aufwärtstransformator an der Quelle und ein Abwärtstransformator an der Last.
Ihre inversen Windungsverhältnisse sorgen für eine konstante Lastspannung und einen konstanten Laststrom.
Die Sekundärspannung des linken Transformators beträgt das Zehnfache ihrer Primärspannung, und die Impedanz, die mit der Sekundärspannung des rechten Transformators verbunden ist, wird vom Primärtransformator aus gesehen mit dem Faktor 100 multipliziert.
Wenn wir nun die Schaltung durch eine Einzelmaschenschaltung ersetzen, stellt der Netzstrom den Netzstrom dar.
Der Strom, der am Sekundärende des linken Transformators eingeht, entspricht dem negativen Leitungsstrom, während er am Primärende das Zehnfache des negativen Sekundärstroms beträgt.
In ähnlicher Weise entspricht der Strom, der in das Primärende des rechten Transformators eintritt, dem Netzstrom, während er am Sekundärende das Zehnfache des Primärstroms beträgt.
Die Phasenspannung an der Last wird bestimmt, gefolgt von der Berechnung der von der Quelle und an die Last gelieferten Leistung.
Die Schätzung der in der Leitung verlorenen Leistung zeigt, dass 99,5 Prozent der von der Quelle gelieferten Leistung die Last erreicht, während nur 0,5 Prozent in der Leitung verloren gehen.

leitungsverlust reduzieren

In einem Dreiphasenstromkreis ist der Leitungsverlust ein Indikator für Energie, die aufgrund des Widerstands der Übertragungsleitungen als Wärme abgegeben wird. Um dies zu beheben, ist die Integration von Transformatoren in das System – ein Aufwärtstransformator an der Quelle und ein Abwärtstransformator an der Last – eine strategische Lösung. Um dies zu verbessern, werden zwei Dreiphasentransformatoren eingeführt.

Mit einem Aufwärtstransformator an der Quelle wird die Spannung erhöht und dadurch der Strom in den Übertragungsleitungen reduziert, da der Leistungsverlust in Übertragungsleitungen proportional zum Quadrat des Stroms ist. Diese Stromreduzierung führt zu einer Verringerung der Leitungsverluste.

Berechnung des Leitungsstroms:

Der Leitungsstrom wird berechnet, indem die impedanzreflektierte Last (unter Berücksichtigung des Windungszahlverhältnisses des Transformators) durch die Sekundärspannung des Transformators geteilt wird.

Der Leitungsstrom beträgt:

<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;">

Wobei n das Windungszahlverhältnis des Transformators und Z_load die tatsächliche Lastimpedanz auf der Sekundärseite ist

Berechnung der Phasenspannung an der Last:

Wenn das Windungszahlverhältnis von Primär- zu Sekundärseite des Transformators als N_p:N_s angegeben ist, kann die Phasenspannung an der Last wie folgt ermittelt werden:

<img alt="Equation 3" src="/files/ftp_upload/15136/15136_Equation_3.svg" style="text-align: center; height: 34px;">

wobei:

V_phase die Phasenspannung an der Last ist,

V_primary die Phasenspannung an der Primärseite des Transformators ist

In einem Y-zu-Y-Dreiphasensystem (Stern-zu-Stern) mit Transformatoren auf beiden Seiten kann die volle Leiter-zu-Leiter-Spannung an der Last durch Multiplikation der Phasenspannung mit Quadratwurzel 3 ermittelt werden, aufgrund der Phasenverschiebung zwischen den Leiterspannungen in einer Y-Konfiguration:

<img alt="Equation 4" src="/files/ftp_upload/15136/15136_Equation_4.svg" style="text-align: center; height: 20px;">

Die von der Quelle gelieferte Wirkleistung P in ein Dreiphasensystem ist:

<img alt="Equation 5" src="/files/ftp_upload/15136/15136_Equation_5.svg" style="text-align: center; height: 18px;">

Wobei:

P die gesamte Wirkleistung ist, die von der Quelle geliefert wird.

V_L die Spannung zwischen den Leitern ist.

I_L der Leitungsstrom ist.

cos(θ) der Leistungsfaktor ist.

Leitungsverlust reduzieren

Um Leitungsverluste in Drehstromkreisen zu minimieren, werden zwei Transformatoren hinzugefügt: ein Aufwärtstransformator an der Quelle und ein Abwärtstransformator an der Last.
...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

Three-Phase Circuits

Dreiphasenschaltungen

KEY TERMS AND CONCEPTS

WICHTIGE BEGRIFFE UND KONZEPTE

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

Description

Transcript

Tags