Lesson Notes By Weeks and Term v3 - Senior Secondary 3
Transmission systems
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Transmission systems
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Subject: Physics
Class: Senior Secondary 3
Term: 1st Term
Week: 1
Theme: Physics In Technology
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Students should be able to construct:- Simple transmission system explain why it is preferred to have a high p.d in stead of high current transmission over a long distance.
10% of the generated power is lost.
Scenario 2: High Voltage Transmission (e.g., 100,000 V) P_total = 10,000,000 W V = 100,000 V Current (I) = P_total / V = 10,000,000 W / 100,000 V = 100 A Power Loss (P_loss) = I2R = (100 A)2 1 Ω = 10,000 W = 0.01 MW Here, only 0.1% of the generated power is lost. Comparing Scenario 1 and 2, increasing the voltage by 10 times (from 10 kV to 100 kV) reduced the current by 10 times (from 1000 A to 100 A), but the power loss was reduced by 100 times (from 1 MW to 0.01 MW). This demonstrates the significant advantage of high voltage transmission.
Safety Considerations: While high voltage transmission is efficient, it is extremely dangerous. Hence, transmission lines are usually placed very high on tall pylons, and substations are fenced off with warning signs to prevent unauthorized access. Step-down transformers are essential to reduce the voltage to safe levels for domestic and industrial use. Worked
Examples: Example 1: Calculating Power Loss in Transmission Lines A power station generates 50 MW of power. It transmits this power at a voltage of 10 kV through transmission cables with a total resistance of 2 Ω. a) Calculate the current flowing through the cables. b) Calculate the power lost in the transmission cables. c) If the power is transmitted at 200 kV, what would be the new current and power loss?
Solution: a)
Current (I) at 10 kV: P_total = 50 MW = 50,000,000 W V = 10 kV = 10,000 V I = P_total / V = 50,000,000 W / 10,000 V = 5,000 A b) Power Loss (P_loss) at 10 kV: R = 2 Ω P_loss = I2R = (5,000 A)2 2 Ω = 25,000,000 2 W = 50,000,000 W = 50 MW This shows a catastrophic loss, meaning all generated power is lost as heat, which highlights why low voltage transmission over long distances is impractical. c)
Current and Power Loss at 200 kV: New V = 200 kV = 200,000 V New Current (I') = P_total / V' = 50,000,000 W / 200,000 V = 250 A New Power Loss (P'_loss) = (I')2R = (250 A)2 2 Ω = 62,500 2 W = 125,000 W = 0.125 MW By increasing the voltage from 10 kV to 200 kV (20 times), the current reduced 20 times, and the power loss reduced by 202 = 400 times (from 50 MW to 0.125 MW). This is a massive improvement in efficiency.
Definition of a Transmission System: An electrical power transmission system is a network of interconnected components designed to transport bulk electrical energy from generating stations (where electricity is produced) to electrical substations near population centers, where it is then distributed to consumers. Components of a Typical Transmission System:
1. Generating Station: Where electrical power is produced (e.g., hydroelectric power stations like Kainji Dam, thermal power stations like Egbin, or gas-fired power stations). Electricity is typically generated at a relatively low voltage (e.g., 11 kV to 25 kV).
2. Step-up Transformer: Located at or near the generating station. This transformer increases the voltage of the generated electricity to very high levels (e.g., 132 kV, 330 kV, 765 kV) for efficient long-distance transmission. Simultaneously, the current is significantly reduced.
3. Transmission Lines (High-Tension Cables): These are the overhead cables or underground lines that carry the high-voltage electricity across long distances. They are typically made of good conductors like aluminum or copper and are suspended by tall pylons or masts.
4. Step-down Transformer (Substation): Located closer to urban or industrial areas. These transformers reduce the high transmission voltage to lower, safer levels (e.g., 33 kV or 11 kV) suitable for local distribution.
5. Distribution Lines: Carry the medium-voltage electricity from substations to smaller transformers within communities.
6. Local Step-down Transformers: Further reduce the voltage (e.g., to 230 V or 400 V in Nigeria) for direct use by homes, offices, and small businesses.
7. Consumers/Users: The end-users who utilize the electrical energy. The Problem of Power Loss in Transmission (Joule Heating): When current flows through a conductor, some electrical energy is converted into heat due to the resistance of the conductor. This phenomenon is known as Joule heating or resistive heating. The power lost as heat (P_loss) in a transmission line is given by the formula: P_loss = I2R Where: P_loss = Power lost as heat (in Watts) I = Current flowing through the line (in Amperes) R = Total resistance of the transmission line (in Ohms) Since transmission lines are very long, they have considerable resistance (R). If a high current (I) is transmitted, the power loss (I2R) becomes substantial. This energy lost as heat is wasted and does not reach the consumers, leading to inefficiency and higher operational costs for electricity providers (e.g., TCN, DisCos).
The Solution: High Voltage Transmission: To minimize power loss (I2R) during long-distance transmission, the current (I) in the transmission lines must be minimized. The total electrical power (P_total) generated and transmitted is given by the formula: P_total = V x I Where: P_total = Total power (in Watts) V = Voltage (in Volts) I = Current (in Amperes) From this equation, for a constant amount of power (P_total) to be transmitted, if the voltage (V) is increased, the current (I) must decrease proportionally. By stepping up the voltage using a step-up transformer at the generating station, the current in the transmission lines is significantly reduced. Since power loss is proportional to the square of the current (I2), even a small reduction in current leads to a much larger reduction in power loss.
Mathematical Explanation: Assume a generating plant produces 10 MW (10,000,000 W) of power. Let the total resistance of the transmission line be 1 Ohm.
Scenario 1: Low Voltage Transmission (e.g., 10,000 V) P_total = 10,000,000 W V = 10,000 V Current (I) = P_total / V = 10,000,000 W / 10,000 V = 1,000 A Power Loss (P_loss) = I2R = (1,000 A)2 1 Ω = 1,000,000 W = 1 MW This means 10% of the generated power is lost.
Scenario 2: High Voltage Transmission (e.g., 100,000 V) P_total = 10,000,000 W V = 100,000 V Current (I) = P_total / V = 10,000,000 W / 100,000 V = 100 A Power Loss (P_loss) = I2R = (100 A)2 1 Ω = 10,000 W = 0.01 MW Here, only 0.1% of the generated power is lost. Comparing Scenario 1 and 2, increasing the voltage by 10 times (from 10 kV to 100 kV) reduced the current by 10 times Teacher Activities: Introduction (10 minutes): Initiate a discussion by asking students: "How does electricity get to our homes from places like Kainji Dam or Egbin Power Station?" Draw a simple block diagram on the board: Power Station -> Transmission Lines -> Homes. Introduce the term "Transmission System" and its importance.
Explanation of Components (15 minutes): Use a large diagram (pre-drawn on chart, projected, or drawn on the board) illustrating the entire transmission system from generation to consumption. Explain each component (generating station, step-up transformer, transmission lines, substations/step-down transformers, distribution lines, local transformers, consumers) with examples relevant to Nigeria (e.g., Kainji, 330kV lines). Emphasize the role of transformers at different stages. Demonstration/Conceptual Model Construction Guidance (20 minutes): Option A (Conceptual Diagrammatic Construction): Guide students to draw a detailed, labeled diagram of a transmission system, showing each component and its function, including voltage levels at each stage. Emphasize correct sequencing and labeling. Option B (Simple Physical Model - if resources permit): Demonstrate or guide students to construct a very simple low-voltage circuit representing the conceptual flow: Use a battery (generating station). Two long wires (transmission lines). A small light bulb (consumer).
Conceptual mention of step-up/step-down: Explain that in a real system, transformers would be at either end of the long wires to change voltage. Students can represent these with labeled blocks. This helps visualize the path. If miniature transformers (e.g., from old chargers, although not easily step-up/step-down) are available, connect them to a low voltage AC supply, showing how voltage can be changed. This is often resource-constrained in Nigerian schools, so Option A is more reliable.* Explaining Power Loss and High Voltage Transmission (25 minutes): Introduce the concept of resistance in wires and power loss due to heating (Joule heating). Write the formula P_loss = I2R on the board. Explain the P = VI relationship. Lead students through the logical reasoning: to minimize I2R, I must be minimized. To minimize I for a constant P, V must be maximized. Work through Example 1 (from Key Concepts) step-by-step on the board, contrasting low voltage vs. high voltage transmission and their respective power losses. Use concrete numbers to show the magnitude of efficiency improvement. Discuss the safety implications of high voltage.
Wrap-up and Q&A (10 minutes): Summarize key points. Address student questions.
Student Activities: Recall and Brainstorm: Participate in the initial discussion, recalling previous knowledge about electricity.
Observe and Engage: Pay close attention to the teacher's explanations and diagrams of the transmission system components.
Construct a Simple Model/Diagram: In groups or individually, students will draw a detailed, labeled diagram of an electrical transmission system, indicating the flow of electricity and the function of each component (meeting performance objective 1). If physical materials are available and teacher provides guidance, they can attempt a conceptual physical model.
Participate in Problem Solving: Actively follow the worked examples, attempting to replicate calculations and understand the implications of different voltage levels.
Explain the Rationale: Engage in discussions on why high voltage transmission is preferred, articulating the concept of power loss (I2R) and its reduction (meeting performance objective 2).
Question and Clarify: Ask questions to deepen their understanding. waste.
2. Economic Disadvantage: The energy lost as heat is unrecoverable and means less power reaches the consumers. This translates to substantial financial losses for power utility companies (like TCN) and makes electricity more expensive overall.
3. Overheating and Damage: High currents can cause the transmission cables to overheat excessively, leading to mechanical stress, sagging, and potential damage or failure of the transmission infrastructure.
4. Requirement for Thicker Cables: To carry high currents without overheating, exceptionally thick and heavy cables would be required, making construction and maintenance of transmission lines much more expensive and logistically challenging.
Commentary: This explicitly assesses the "explain why it is preferred to have a high p.d. instead of high current" objective.
Example 1: Calculating Power Loss in Transmission Lines
A power station generates 50 MW of power. It transmits this power at a voltage of 10 kV through transmission cables with a total resistance of 2 Ω.
a) Calculate the current flowing through the cables.
b) Calculate the power lost in the transmission cables.
c) If the power is transmitted at 200 kV, what would be the new current and power loss?
Solution:
a)
Current (I) at 10 kV:
P_total = 50 MW = 50,000,000 W
V = 10 kV = 10,000 V
I = P_total / V = 50,000,000 W / 10,000 V = 5,000 A
b) Power Loss (P_loss) at 10 kV:
R = 2 Ω
P_loss = I²R = (5,000 A)² 2 Ω = 25,000,000 * 2 W = 50,000,000 W = 50 MW
This shows a catastrophic loss, meaning all generated power is lost as heat, which highlights why low voltage transmission over long distances is impractical.
c)
Current and Power Loss at 200 kV:
New V = 200 kV = 200,000 V
New Current (I') = P_total / V' = 50,000,000 W / 200,000 V = 250 A
New Power Loss (P'_loss) = (I')²R = (250 A)² 2 Ω = 62,500 * 2 W = 125,000 W = 0.125 MW
By increasing the voltage from 10 kV to 200 kV (20 times), the current reduced 20 times, and the power loss reduced by 20² = 400 times (from 50 MW to 0.125 MW). This is a massive improvement in efficiency.
Teaching and Learning Activities
The Nigerian National Grid and Power Challenges: This topic directly explains the backbone of Nigeria's electricity supply system – the National Grid. Students can understand why grid collapses occur (often due to faults in transmission lines or substations, leading to system instability) and the role of TCN (Transmission Company of Nigeria) in maintaining the grid. It explains why power might be available at a power station but not reach consumers efficiently in Maiduguri or Calabar.
Rural Electrification Initiatives: Extending electricity to remote villages in Nigeria faces significant challenges. The lesson helps students understand that it's not just about generating power, but also the costly infrastructure (pylons, cables, transformers) required for efficient transmission and distribution, especially when consumer density is low, making the "last-mile" connection expensive and prone to losses. Economic Impact of Power Losses (Commercial vs.
Technical Losses): Beyond technical losses (I2R), transmission systems also suffer from commercial losses (e.g., meter bypass, theft). Understanding technical losses helps appreciate the overall efficiency challenges faced by Nigerian DisCos and the impact on their revenue and ability to invest in infrastructure improvement. Reducing technical losses is a key focus for improving electricity supply reliability and cost-effectiveness in Nigeria.