Name: balanced delta-delta power circuit
Uploaded: 2024-07-08T13:19:57.000Z
Duration: 1 min 17 s
Channel: JoVE

平衡的三角形-三角形系统具有三角形连接的电源和负载。
假设三角形连接的电源为正序，以表示相电压，其与线电压相同。
假设线路阻抗为零，相电压等于阻抗两端的电压。
相电流等于相电压与每相负载阻抗之比。
利用基尔霍夫电流定律，在三角形连接负载的节点处由相电流推导出线电流。
每条线路电流滞后于其对应的相电流30度，其幅值为相电流的√3倍。
或者，可以通过将电源和负载转换为其等效Y电路来分析Δ-Δ电路。
对于Y型连接的电源，其相应的相电压等于三角形连接电源各线电压除以根号3，且相位滞后30度。
星形连接的负载阻抗等于三角形连接的负载阻抗除以三。
现在，可以利用等效单相电路来确定三条线路电流。

三角形-三角形电路

The Delta-to-Delta Circuit

在三角形-三角形配置中，电源和负载将会以三角形的方式来进行连接，从而形成一个闭合回路，并将网络划分为三个不同的相位。这种配置中的相电压与线电压是相同的。假设电源为正序，那么相电压便可以直接进行表示，而无需中性线。
<img alt="Equation 1" src="/files/ftp_upload/15131/15131_Equation_1.svg" style="text-align: center; height: 13px;">
三角形连接负载中的相电流是通过将相电压除以每相的负载阻抗来进行计算的：
<img alt="Equation 2" src="/files/ftp_upload/15131/15131_Equation_2.svg" style="text-align: center; height: 32px;">
在这种配置中，基尔霍夫电流定律（KCL）能够将每条线电流作为其余两相电流的矢量和，从而能够得出每条线电流是三倍相电流幅值的平方根的一般原理。由于三角形连接会产生相位差，因此它会使相电流滞后 30 度。
对这类系统进行分析时，需要将电源和负载转换为它们的星形等效电路。这种转换能够将三相系统简化为单相等效电路。这种转换通常会涉及到调整三角形连接电源中线电压的幅度和相位：
<img alt="Equation 3" src="/files/ftp_upload/15131/15131_Equation_3.svg" style="text-align: center; height: 32px;">
<img alt="Equation 4" src="/files/ftp_upload/15131/15131_Equation_4.svg" style="text-align: center; height: 16px;">
此外，每个星形连接负载的阻抗是三角形连接负载阻抗的三分之一。
在工业应用中，大功率机械、变压器和电机控制中心都会采用平衡的三角形-三角形配置。这种配置能够实现远距离的高效电力传输，减少谐波失真，并通过保持稳定的电压水平而无需中性连接来促进三相电机的平稳运行。

一个平衡的三角形-三角形系统具有三角形连接的电源和负载。  
假设三角形连接的电源为正序，以表示……

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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 (KCL) applies at each node. The line current is the vector sum of the currents from the other two phases. In a balanced delta connection, each line current has a magnitude of square root of three times the phase current. It also lags the phase current by 30 degrees because of the phase shift in the delta network.

To analyze the system more simply, the source and load can be changed into wye-equivalents. A wye connection is a star-shaped circuit that makes three-phase analysis easier. This conversion turns the three-phase network into a single-phase equivalent circuit. The delta-connected source voltages must be adjusted in both magnitude and phase during the conversion. The impedance of each wye-connected load is one-third of the delta-connected load impedance.

Balanced delta-delta systems are common in industrial settings. They are used for high-power machines, transformers, and motor control centers. They also support long-distance power transmission and can help reduce harmonic distortion. In three-phase motors, the steady voltage levels help smooth operation without the need for a neutral connection.

Balanced Delta-Delta Power Circuit

three-phase circuits

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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...

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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

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

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power in a three-phase circuit

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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...

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key terms and concepts

Explore how balanced delta-delta power circuits work, including line and phase voltages, line current, wye-equivalent conversion, and industrial uses.

Balanced Delta-Delta Power Circuit | 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

Balanced Delta-Delta Power Circuit

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