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Chapter 8: Three-Phase Circuits Back To Chapter

8.3: Three-Phase Voltages

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Three-Phase Voltages

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8.2: Generation of Three-Phase Voltage

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8.4: The Y-to-Y Circuit

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In three-phase four-wire systems, three Y-connected voltage sources generate balanced phase voltages.

There are two phase sequences based on the order in which the phase voltages reach their maximum values.

The first, abc or positive sequence, involves phasors rotating anticlockwise, with V_an leading V_bn, which leads V_cn. This sequence occurs when the rotor rotates counterclockwise.

The second, acb or negative sequence, has phasors rotating anticlockwise, and V_an leads V_cn, which leads V_bn. This sequence corresponds to clockwise rotor rotation.

Like voltage sources, the three loads can be Y-connected or delta-connected.

In balanced load configurations, the phase impedances are equal in magnitude and phase.

The Y-connected loads can be transformed to delta-configuration and vice versa.

Based on the configurations of the three-phase source and load, four possible connections exist.

Delta-connected loads are more common than Y-configuration due to the ease of adding and removing loads from individual phases without causing excessive imbalances.

However, delta-connected sources are less common than Y-connected sources due to the circulating current in the delta-mesh when the three-phase voltages are slightly unbalanced.

8.3: Three-Phase Voltages

A three-phase generator produces three voltages that are equal in magnitude but have a phase difference of 120 degrees. This identical magnitude and equal phase separated voltages are known as the balanced voltages and help to minimize power loss while ensuring a steady delivery of energy to connected loads. As voltage sources in a three-phase system can be configured in a wye or a delta formation, the loads connected to these systems can also be arranged in either configuration. This flexibility in load configuration is not just a design choice but a way to exert control over the system. Delta-connected loads have one end of each phase winding connected to a common neutral point. Conversely, in delta-connected loads, the ends of the phase windings are connected in a continuous loop, forming a triangle. A three-phase system uses four- and three-wire systems through star and delta connections. Three-phase voltages in wye configuration are:

Equation 1

Equation 2

Equation 3

Understanding the logical sequence of the three phases is key. When in the positive and a-b-c sequences, the phasors rotate anticlockwise, with V_an leading V_bn, followed by V_cn. This sequence, resulting from the rotor rotating counterclockwise, is a clear and orderly progression.

In the negative sequence a-c-b, the phasors rotate clockwise, with V_anleading V_cn and V_bn following last. This indicates a reversed-phase order compared to the positive sequence, which corresponds to clockwise rotor rotation.

Each configuration, whether wye-connected or delta-connected, allows for a balanced load condition and influences the circuit's distribution and management of voltages and currents. During the balanced load configurations, the impedances connected across each phase are equal in magnitude and phase, giving the power to manage your system effectively.

The star-connected loads can be transformed into delta configuration and vice versa. Based on the connection types of the source and load, the system can be configured in four main ways: wye-wye, wye-delta, delta-wye, and delta-delta.

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