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

To minimize line losses in three-phase circuits, two transformers are added: a step-up transformer at the source and a step-down transformer at the load.
Their inverse turn ratios ensure consistent load voltage and current.
The left transformer&#39;s secondary voltage is tenfold its primary voltage, and the impedance connected to the right transformer&#39;s secondary, as seen from the primary, is multiplied by a factor of 100.
Now, replacing the circuit with a single-mesh circuit, the mesh current represents the line current.
The current entering the left transformer&#39;s secondary end equals the negative line current, while at the primary, it is ten times the negative secondary current.
Similarly, the current entering the right transformer&#39;s primary end equals the line current, while at the secondary end, it is ten times the primary current.
The phase voltage at the load is determined, followed by calculating the power delivered by the source and to the load.
Estimating the power lost in the line reveals that 99.5 percent of the power supplied by the source reaches the load, with only 0.5 percent lost in the line.

reducing line loss

In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system&#8212;a step-up transformer at the source and a step-down transformer at the load&#8212;is a strategic solution. Two three-phase transformers are introduced to improve this.
With a step-up transformer at the source, the voltage is increased, thereby reducing the current in the transmission lines since power loss in transmission lines is proportional to the square of the current, this reduction in current leads to a decrease in line losses.
Calculation of Line Current:
The line current is calculated by dividing the impedance-reflected load (considering the transformer's turns ratio) by the secondary voltage of the transformer.
The line current is:
<img alt="Electrical formula, IL = Vsecondary / Zreflected, transformer equation diagram." src="/files/ftp_upload/15136/15136_Equation_1.svg" style="text-align: center; height: 36px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
<img alt="Electrical impedance formula, Z_reflected=Z_load*n^2, diagram for study of circuit reflection analysis." src="/files/ftp_upload/15136/15136_Equation_2.svg" style="text-align: center; height: 18px;" data-altupdatedat="1762173717000" data-alt="Equation 2" />
Where n is the transformer's turns ratio and Zload is the actual load impedance on the secondary side
Calculation of Phase Voltage at the Load:
If the primary to secondary turns ratio of the transformer is given as Np:Ns, then the phase voltage at the load can be found by:
<img alt="Electrical transformer voltage ratio equation, Vphase=Vprimary&#183;(Ns/Np), for circuit analysis." src="/files/ftp_upload/15136/15136_Equation_3.svg" style="text-align: center; height: 34px;" data-altupdatedat="1762173717000" data-alt="Equation 3" />
where:
Vphase is the phase voltage at the load,
Vprimary is the phase voltage at the primary side of the transformer
In a Y-to-Y (star-to-star) three-phase system with transformers on both sides, the full line-to-line voltage at the load can be found by multiplying the phase voltage by sqrt 3, due to the phase shift between line voltages in a Y configuration:
<img alt="Voltage equation for three-phase system, Vline-to-line=&#8730;3&#183;Vphase, electrical engineering formula." src="/files/ftp_upload/15136/15136_Equation_4.svg" style="text-align: center; height: 20px;" data-altupdatedat="1762173717000" data-alt="Equation 4" />
The real power P delivered by the source in a three-phase system is:
<img alt="Three-phase power equation P=&#8730;3*VL*IL*cos(&#952;), formula, electrical engineering concept." src="/files/ftp_upload/15136/15136_Equation_5.svg" style="text-align: center; height: 18px;" data-altupdatedat="1762173717000" data-alt="Equation 5" />
Where:
P is the total real power delivered by the source.
VL is the line-to-line voltage.
IL is the line current.
cos(&#952;) is the power factor.

Reducing Line Loss

To minimize line losses in three-phase circuits, two transformers are added: a step-up transformer at the source and a step-down transformer at the load.
...

Education

JoVE Core

Electrical Engineering

Unit 1

Three-Phase Circuits

KEY TERMS AND CONCEPTS

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...

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