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What is the 3-phase Circuit Formula?

Author: Apogeeweb
Date: 16 Jun 2021
 2483
three phase circuit equations

Introduction

A three-phase circuit consists of a three-phase source, a three-phase load, and a three-phase transmission line. The most basic characteristic of this circuit is that it has one or more groups of power supplies. Each group consists of three sinusoidal power supplies with the same amplitude, the same frequency, 120° phase difference, and the power supply and the load are connected in a specific way. Three-phase circuits are widely used in power systems such as power generation, transmission, distribution, and high-power electrical equipment.

What does 3 phase mean?

Catalog

Introduction

Ⅰ Three-phase Circuit Basics

1.1 Three-phase Circuit Characterized

1.2 Three-phase Circuit Terms

1.3 Three-phase Voltage & Current

1.4 Three-phase Circuit Advantages

Ⅱ Symmetrical vs Asymmetrical

2.1 Symmetrical Three-phase Circuit

2.2 Three-phase Asymmetry

Ⅲ Power in Three Phase Circuit Formulas

Ⅳ Frequently Asked Questions about Three-phase Circuit


Ⅰ Three-phase Circuit Basics

The three phases could be supplied over six wires, with two wires reserved for the exclusive use of each phase. However, they are generally supplied over only three wires, and the phase or line voltages are the voltages between the three possible pairs of wires. The phase or line currents are the currents in each wire. Voltages and currents are usually expressed as rms or effective values, as in single-phase analysis.

three-phase voltage and current phasor diagram

1.1 Three-phase Circuit Characterized

Special power supply
Special load
Special connection
Special solution

1.2 Three-phase Circuit Terms

Three Phase Circuit Diagram

1) End wire (fire wire)
2) Neutral line
3) Line current
4) Line voltage
5) Phase current
6) Phase voltage
7) Three-phase three-wire system and three-phase four-wire system

1.3 Three-phase Voltage & Current

  • Star Connection

star connection

Summery: Line Voltage vs Phase Voltage
1) The line current is equal to the corresponding phase current.
2) If the phase voltage is symmetrical, the line voltage is also symmetrical.
3) The line voltage is equal to √3 times the phase voltage.
4) The phase of the line voltage leads the corresponding phase voltage by 30°.

 

  • Delta Connection

delta connection

Summery: Line Current vs Phase Current
1) The line voltage is equal to the corresponding phase voltage.
2) If the phase currents are symmetrical, the line currents are also symmetrical.
3) The line current is equal to √3 times the phase voltage.
4) The phase of the line current lags behind the corresponding phase voltage by 30°.

1.4 Three-phase Circuit Advantages

Power generation: Three-phase power is increased by 50% compared to single-phase power.
Transmission: 25% less material than single-phase circuit transmission. That is, under certain conditions, transmitting a certain amount of power by three-phase only requires 75% of the copper of single-phase transmission.
Power distribution: More economical than single-phase transformers and easier to connect to the load.
Transportation: simple structure, low cost, reliable operation, convenient maintenance.
In addition, three wires are usually seen in high-voltage transmission lines, whether on towers or poles, with pin or suspension insulators. Some high-voltage lines are now DC, since solid state devices make it easier to convert to and from AC. The DC lines are free of the problems created by phase, as well as eliminating the skin effect that reduces the effective area of the conductors. It is not nearly as easy to manage long-distance electrical transmission as might be thought.

three-phase circuit in delta connection three-phase circuit in star connection

Ⅱ Symmetrical vs Asymmetrical

2.1 Symmetrical Three-phase Circuit

A symmetrical three-phase power source is usually generated by a three-phase synchronous generator, as shown in Figure (a). Among them, the three-phase windings differ by 120° in space. When the rotor rotates at a uniform angular velocity ω, an induced voltage is generated in the three-phase winding, thereby forming a symmetrical three-phase power supply as shown in Figure (b). Among them, the three ends of A, B, and C are called the start end, and the three ends of X, Y, and Z are called the end. When you connect a load to the three wires, it should be done in such a way that it does not destroy the symmetry.

symmetrical three-phase power supply

Instantaneous Voltage Calculation of Three-phase Power

Instantaneous Voltage Calculation of Three-phase Power

In the formula, take the phase A voltage uA as the reference sine quantity. The three-phase voltage waveform diagram is shown in Figure (a).
The key to understanding three-phase is to understand the phasor diagram for the voltages or currents. The phasor of the three-phase power supply can be represented by the Figure (b).

phasor diagram for the voltages or currents


The characteristics of the symmetrical three-phase power supply can be derived from the above formula:

From the above formula, the sum of the instantaneous value of the three-phase power supply and the sum of the phasor are always zero.

positive sequence and reverse sequence

The sequence in which each phase of the three-phase power passes through the same value (such as the maximum value) is called the phase sequence of the three-phase power, and the phase sequence of the above-mentioned three-phase voltage is called the positive sequence. Conversely, if phase B exceeds 120° of phase A and phase C exceeds 120° of phase B, this phase sequence is called reverse sequence. If there is no special instructions, it will generally default to positive order.

2.2 Three-phase Asymmetry

1) In a three-phase circuit, as long as there is asymmetrical part, it is called a three-phase asymmetry.
2) The complex power absorbed by the three-phase load is equal to the sum of various complex powers.
3) The instantaneous power of a three-phase circuit is the sum of the instantaneous power of each phase load.
4) In a three-phase three-wire circuit, whether symmetrical or not, two power meters can be used to measure three-phase power.
When the power supply voltage in the three-phase circuit is asymmetrical or the parameters in the circuit are asymmetrical, the current in the circuit is generally asymmetrical. This kind of circuit is called three-phase asymmetry. There are a lot of asymmetry parts in three-phase circuits, and the causes are different. For example, there are many low-power single-phase loads in a three-phase circuit, it is difficult to make them into a completely symmetrical circuit. When a three-phase circuit is broken or short-circuited, it is also a three-phase asymmetry circuit. In addition, some electrical equipment and instruments formally use three-phase asymmetry to work.
For example, the most common low-voltage three-phase four-wire system. Due to the large number of single-phase loads in the low-voltage system, the equivalent impedances ZA, ZB, and ZC of the three phases circuit are generally different from each other, and the power supply voltage can generally be considered symmetrical. In this way, a symmetrical three-phase power supply converts to an asymmetrical three-phase load.

three-phase four-wire system

The circuit shown in the figure has two nodes, and the voltage between the two nodes can be directly calculated according to the node voltage method.

node voltage

Although the power supply voltage in the above formula is symmetrical, the voltage between the neutral point of the power supply and the neutral point of load is not zero due to the load asymmetry, that is, UNN≠0. According to Kirchhoff's voltage law, the phase voltage of the load can be obtained as:

load voltage

The phasor diagram of each voltage corresponding to the above formula is as follows:

voltage  phasor diagram

Ⅲ Power in Three Phase Circuit Formulas

1. Average Power
Suppose the power absorbed by a phase load in a symmetrical three-phase circuit is equal to Pp=UpIpcosφ, where Up is the phase voltage and Ip is the phase current of the load. Then the total three-phase power is: P=3UpIpcosφ
Pay Attention To
1) φ in the above formula is the phase difference angle (impedance angle) of phase voltage and phase current.
2) cosφ is the power factor of each phase, in a symmetrical three-phase system:
cosφA=cosφB=cosφC=cosφ
3) The formula calculates the circuit power (or the power absorbed by the load).
When the load is in a star connection, the line voltage line voltage and line current line current at the load end are substituted into the above formula:

When the load is in a delta connection, the line voltage line voltage and line current line current at the load end are substituted into the above formula:

2. Reactive power
The reactive power absorbed by the load in a symmetrical three-phase circuit is equal to the sum of the reactive power of each phase:

3. Apparent Power

4. Instantaneous Power
Suppose the voltage and current of phase A of the three-phase load are:

Then the instantaneous power of each phase is:
It can be proved that their sum is

The above formula shows that the instantaneous power of a symmetrical three-phase circuit is a constant, and is equal to the average power. This is one of the advantages of a symmetrical circuit. For example, on a three-phase motor, a balanced electromagnetic torque is obtained and mechanical vibration is avoided, which is not available in single-phase motors.

 

Ⅳ Frequently Asked Questions about Three-phase Circuit

1. What is a 3 phase circuit?

Three-phase power is a three-wire ac power circuit with each phase ac signal 120 electrical degrees apart. ... three-phase is that a three-phase power supply better accommodates higher loads. Single-phase power supplies are most commonly used when typical loads are lighting or heating, rather than large electric motors.

 

2. How many wires are in a 3 phase?

four wires
The three-phase system has four wires. Three are conductors and one is neutral.

 

3. What is the 3 phase power formula?

3-Phase Calculations. For 3-phase systems, we use the following equation: kW = (V × I × PF × 1.732) ÷ 1,000.

 

4. What is the advantage of three-phase system?

A three-phase circuit provides greater power density than a one-phase circuit at the same amperage, keeping wiring size and costs lower. In addition, three-phase power makes it easier to balance loads, minimizing harmonic currents and the need for large neutral wires.

 

5. What is meant by 3 phase balanced load?

A balanced three-phase voltage or current is one in which the size of each phase is the same, and the phase angles of the three phases differ from each other by 120 degrees. ... With such a balanced load, if a balanced three-phase supply is applied, the currents will also be balanced.

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