Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Define a three-phase system and list its advantages.
• Describe how three-phase voltages are generated.
• Differentiate between Star (Y) and Delta (Δ) connections.
• State the relationships for voltage and current in each connection.
• Calculate voltages and currents in balanced Star and Delta loads.

Lesson summary

Three-phase electrical systems are the backbone of electricity distribution and powering large industrial and commercial facilities in South Africa. From the lights in your school to the machinery in factories producing goods, and even the pumps delivering water to your homes, three-phase systems are essential. Understanding these systems is crucial for anyone pursuing a career in electrical engineering, technology, or even related fields. As South Africa aims for increased industrialisation and reliable power infrastructure, knowledge of three-phase systems becomes even more valuable.

Lesson notes

What is a Three-Phase System? A three-phase system is an electrical power system that uses three alternating currents, each 120 electrical degrees out of phase with the other two. Imagine three separate single-phase generators connected to the same shaft and rotating together. Each generator produces a voltage waveform. If these waveforms are perfectly synchronized but shifted by 120 degrees, you have a three-phase system. Why Three-Phase over Single-Phase?

Higher Power Capacity: For the same physical size and weight, a three-phase motor or generator can deliver significantly more power than a single-phase equivalent. Think of it as three people pushing a car versus one – more power! This is vital for large industrial motors and generators used in South African industries like mining and manufacturing.

Smoother Power Delivery: In a single-phase system, the power delivered pulsates, dropping to zero twice in each cycle. In a three-phase system, the power delivery is much smoother and more constant, leading to more efficient operation of motors and equipment. This reduces vibrations and extends the lifespan of machinery.

Smaller Conductors: For the same power delivery, three-phase systems require smaller conductors (wires) compared to single-phase systems. This reduces the cost of materials, especially over long distances, which is a significant advantage in South Africa's vast landscape.

Improved Motor Starting Torque: Three-phase motors generally have higher starting torque than single-phase motors. This is essential for applications requiring a lot of force to start, such as pumps in irrigation systems or conveyor belts in mines. Generation of Three-Phase Voltages Three-phase voltages are generated using a three-phase alternator (generator). The alternator has three sets of windings (coils) physically spaced 120 degrees apart on the stator (the stationary part). As the rotor (rotating part) spins, it induces a voltage in each set of windings. Because of the physical displacement of the windings, the generated voltages are 120 degrees out of phase with each other.

We can represent the three phases as: Va = Vm sin(ωt) Vb = Vm sin(ωt - 120°) Vc = Vm sin(ωt + 120°)

Where: Va, Vb, Vc are the instantaneous voltages of phases A, B, and C, respectively. Vm is the peak voltage. ω is the angular frequency (2πf, where f is the frequency – typically 50 Hz in South Africa). t is time. Star (Y) and Delta (Δ) Connections There are two primary ways to connect the three phases of a three-phase system: Star (Y) and Delta (Δ).

Star (Y)

Connection: In a star connection, one end of each of the three windings is connected to a common point called the neutral point (or star point). The other end of each winding is connected to a line conductor.

Line Voltage (VL): The voltage between any two line conductors.

Phase Voltage (VP): The voltage across each individual winding (from line to neutral).

Line Current (IL): The current flowing through each line conductor.

Phase Current (IP): The current flowing through each individual winding.

Relationships in a Star Connection: VL = √3 VP IL = IP Delta (Δ)

Connection: In a delta connection, the windings are connected in a closed loop, forming a triangle. Each corner of the triangle is connected to a line conductor.

Line Voltage (VL): The voltage between any two line conductors.

Phase Voltage (VP): The voltage across each individual winding.

Line Current (IL): The current flowing through each line conductor.

Phase Current (IP): The current flowing through each individual winding.

Relationships in a Delta Connection: VL = VP IL = √3 IP Important

Note: These relationships hold true for balanced three-phase systems, where the loads connected to each phase are equal.

Worked example

Example 1: Star Connection

A balanced star-connected load is connected to a 400V, 50Hz three-phase supply. The impedance of each phase is (8 + j6) ohms.

Calculate:

a) Phase Voltage (VP)

b) Phase Current (IP)

c) Line Voltage (VL)

d) Line Current (IL)

Solution: