Name: wye source and delta load currents
Uploaded: 2024-07-08T13:19:57.000Z
Duration: 1 min 19 s
Channel: JoVE

在电力系统中，平衡的星形-三角形电路具有星形连接的电压源和三角形连接的负载，通常不包含中性线。
假设为正相序，通过相电压来表示以估算线电压。
这些线电压等于负载阻抗两端的电压，有助于计算相电流，相电流具有相似的幅值且相位互差120度。
在三角形连接的负载节点处应用基尔霍夫电流定律，可以揭示线电流与相电流之间的关系。
计算得到的线电流幅值为相应相电流幅值的√3倍，且线电流滞后相电流30度。
分析Y型到三角形系统的另一种方法是将三角形连接的负载转换为其对应的Y型配置。
然后可以通过考虑其单相等效电路并确定线路电流，来分析所得到的平衡Y型到Y型系统。
相电流的幅值和相位角通过相应的线电流，采用适当的三角形-星形变换来计算。

y 形-三角形电路

平衡的星形-三角形电路是由平衡的 Y 形连接电压源和三角形连接负载所组成的，并且没有中性线进行连接。
分析星形-三角形电路的第一步是将其假设为正相序。然后利用这些相电压来直接计算连接到三角形连接负载阻抗上的线电压。V_an、V_bn 和 V_cn 是星形电路中的相电压，而 V_ab、V_bc 和 V_ca 则分别是三角形电路中的线电压。在星形-三角形电路中，线电压之间的关系可以用以下公式来进行计算：
<img alt="Equation 1" src="/files/ftp_upload/15130/15130_Equation_1.svg" style="text-align: center; height: 13px;">
<img alt="Equation 2" src="/files/ftp_upload/15130/15130_Equation_2.svg" style="text-align: center; height: 13px;">
<img alt="Equation 3" src="/files/ftp_upload/15130/15130_Equation_3.svg" style="text-align: center; height: 13px;">
在欧姆定律中，这些负载阻抗中的电压将会被用于计算相电流。由于电路具有平衡性，这些相电流的大小是相同的，但相位差为 120 度。
基尔霍夫电流定律（KCL）适用于三角形连接负载的节点，以此来推导处线电流和相电流之间的关系。
在一个平衡的星形-三角形系统中，线电流的幅度与相电流的幅度的关系为3的平方根。在三角形配置中，线电流会比其相应的相电流滞后 30 度。
分析星形-三角形电路的另一种方法是将三角形连接的负载转换为等效的星形配置。这会将电路转换为平衡的星形-星形系统，同时还可以将其简化为单相等效电路来进行分析。这样就可以根据其相应的线电流来估算出相电流，同时还会得出由变换所带来的相移。
详细了解相电流和线电流以及星形连接电源和三角形连接负载之间的关系，这对于设计和操作一个高效的电气系统来说是至关重要的。

Y 形-三角形电路

在电力系统中，平衡的星形-三角形电路具有星形连接的电压源和三角形连接的负载，通常不包含中性线。

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Three-Phase Circuits

三相电路

KEY TERMS AND CONCEPTS

关键术语与概念

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 are the voltages across the load impedances. They are used with Ohm's law to calculate the phase currents in the delta branches.

Because the circuit is balanced, the phase currents all have the same magnitude. They are also separated by 120 degrees. Kirchhoff's Current Law, or KCL, is then applied at the nodes of the delta load to connect line currents and phase currents. In a balanced wye-to-delta system, the line current magnitude is related to the phase current magnitude by a factor of square root of 3.

The line currents also lag their matching phase currents by 30 degrees in the delta configuration. Another way to study the circuit is to transform the delta-connected loads into an equivalent wye. This changes the problem into a balanced wye-to-wye system. That form can be reduced to single-phase equivalent circuits, which makes the current analysis simpler.

Wye Source and Delta Load Currents

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

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

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

Learn how balanced wye sources and delta loads work, including phase voltages, line voltages, KCL, and the 30-degree shift in line currents.

Wye Source and Delta Load Currents | 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

Wye Source and Delta Load Currents

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