Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Define a three-phase system and its advantages.
• Describe and draw Star (Y) and Delta (Δ) connections.
• Identify voltage & current relationships in Star and Delta.
• Explain phase sequence and its importance.
• Perform basic calculations for line and phase values.

Lesson summary

Three-phase systems are the backbone of electrical power distribution in South Africa and globally. From powering our homes and schools to running large industrial machinery in mines and factories, three-phase electricity is essential for our modern way of life. Understanding how these systems work is crucial for any aspiring electrician or engineer, as it forms the basis for many advanced electrical applications. Consider the impact of load shedding (or "dumploading" as it is sometimes known) on businesses and households – three-phase systems play a crucial role in ensuring a stable and efficient power supply, and understanding them is a step towards solving our country's energy challenges.

Lesson notes

2.1 What is a Three-Phase System? A three-phase system consists of three alternating current (AC) voltages that are out of phase with each other by 120 electrical degrees. Imagine three single-phase generators, each producing a voltage, but their outputs are timed so that each reaches its peak voltage at a different point in time. This is the basic idea behind a three-phase system.

Advantages over Single-Phase: Higher Power Capacity: Three-phase systems can deliver more power for a given size and weight of equipment compared to single-phase systems. This is why heavy machinery in factories, mines (like those in Rustenburg and Kimberley), and large-scale industries in Gauteng rely heavily on three-phase power.

Smoother Power Delivery: The power delivered by a three-phase system is more constant and smoother than single-phase power. This reduces vibrations and improves the performance of motors and other electrical equipment. Think of a pump at a water treatment plant supplying drinking water; consistent power ensures the pump operates reliably.

More Efficient Motors: Three-phase motors are generally smaller, lighter, and more efficient than single-phase motors for the same power output. This translates to energy savings and lower operating costs.

Improved Voltage Regulation: Three-phase systems provide better voltage regulation, meaning the voltage remains more stable under varying load conditions. This is crucial for sensitive electronic equipment. 2.2 Star (Y) and Delta (Δ) Connections There are two main ways to connect the three phases of a three-phase system: Star (Y)

Connection: In a star connection, one end of each of the three phases is connected to a common point called the neutral point (or star point). The other ends of the phases are connected to the lines.

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

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

Line Current (IL): The current flowing in the lines.

Phase Current (Iph): The current flowing through each phase winding. Relationships in a balanced star connection: `VL = √3 Vph` (Line voltage is √3 times the phase voltage) `IL = Iph` (Line current is equal to the phase current)

Think of it like this:* The voltage is "shared" between two phases to get the line voltage, hence the multiplication by √

3. The current only has one path to follow, so the line current is the same as the phase current. Delta (Δ)

Connection: In a delta connection, the three phases are connected in a closed loop, forming a triangle. Relationships in a balanced delta connection: `VL = Vph` (Line voltage is equal to the phase voltage) `IL = √3 Iph` (Line current is √3 times the phase current)

Think of it like this:* The voltage is directly applied to the line from a single phase, hence line voltage equals phase voltage.

However, the line current "splits" to feed current into two phases, hence the multiplication of phase current by √

3. Visual Representations: It is VERY important to be able to draw star and delta connections. Search on the internet or in textbooks for labelled diagrams showing clearly how the phases are interconnected in each configuration. Practice drawing these until you can do so from memory. 2.3 Phase Sequence The phase sequence refers to the order in which the three phases reach their maximum positive voltage. The standard phase sequence is either A-B-C or A-C-B. Reversing the phase sequence can have serious consequences, especially when dealing with three-phase motors. For example, reversing the phase sequence of a three-phase motor will cause it to rotate in the opposite direction. This can be dangerous if the motor is driving a pump, fan, or other equipment where the direction of rotation is critical. Imagine the chaos if the pumps providing irrigation water on a farm rotated in the wrong direction! 2.4 Worked Examples Example 1: Star Connection A three-phase, star-connected generator has a phase voltage of 230

V. Calculate the line voltage.

Solution: Given: `Vph = 230 V` Formula: `VL = √3 * Vph` Calculation: `VL = √3 * 230 V ≈ 398.4 V` Answer: The line voltage is approximately 398.4

V. Example 2: Delta Connection A three-phase, delta-connected load has a line current of 20

A. Calculate the phase current.

Solution: Given: `IL = 20 A` Formula: `IL = √3 * Iph` => `Iph = IL / √3` Calculation: `Iph = 20 A / √3 ≈ 11.55 A` Answer: The phase current is approximately 11.55

A. Example 3: Star Connection - Power Calculation (Simplified) A balanced three-phase star connected load is connected to a 400V supply. The phase current is 10

A. What is the phase voltage? (This doesn't give power, but builds understanding)

Solution: Given: `VL = 400V`, `Iph = 10A` Formula: `VL = √3 * Vph` => `Vph = VL / √3` Calculation: `Vph = 400V / √3 ≈ 230.94 V` Answer: The phase voltage is approximately 230.94

V. Guided Practice (With Solutions)

Question 1: A three-phase star-connected motor is connected to a 415 V supply.