Electricity Generation and Transmission Notes

Transmission of Electricity

Key Concepts

Sinusoidal AC Voltages: AC voltages are produced by the uniform rotation of a loop in a constant magnetic field. These voltages can be described using several parameters:
- Frequency ( $f$ ): The number of complete cycles per second, measured in Hertz (Hz).
- Period ( $T$ ): The time taken for one complete cycle, related to frequency by the equation: $T = \frac{1}{f}$ .
- Amplitude: The maximum variation from zero, also known as the peak voltage ( $V{peak}$ ) or peak current ( $I{peak}$ ).
- Peak-to-Peak Voltage ( $V{p-p}$ ): The difference between the maximum and minimum voltages in a cycle. For a symmetrical AC voltage, $V{p-p} = 2V_{peak}$ .
- Peak-to-Peak Current ( $I{p-p}$ ): The difference between the maximum and minimum currents in a cycle. For a symmetrical AC current, $I{p-p} = 2I_{peak}$ .
RMS Voltage ( $V{RMS}$ ): The root mean square voltage is the DC voltage that would produce the same power as the AC voltage across the same resistance. It is related to the peak voltage by: $V{RMS} = \frac{V{peak}}{\sqrt{2}}$ . Similarly, the RMS current ( $I{RMS}$ ) is $I{RMS} = \frac{I{peak}}{\sqrt{2}}$ .

Transformers

Transformer Action: Transformers use electromagnetic induction to change AC voltages. The key equation for an ideal transformer is: $\frac{N1}{N2} = \frac{V1}{V2} = \frac{I2}{I1}$ , where:
- $N_1$ is the number of turns in the primary coil.
- $N_2$ is the number of turns in the secondary coil.
- $V_1$ is the RMS voltage in the primary coil.
- $V_2$ is the RMS voltage in the secondary coil.
- $I_1$ is the current in the primary coil.
- $I_2$ is the current in the secondary coil.
Step-Up Transformer: A transformer that increases voltage from primary to secondary ( $V2 > V1$ ), thus $N2 > N1$ .
Step-Down Transformer: A transformer that decreases voltage from primary to secondary ( $V2 < V1$ ), thus $N2 < N1$ .
Ideal Transformer: A transformer with 100% efficiency, meaning $V1 \times I1 = V2 \times I2$ . In real transformers, energy losses occur due to copper losses (resistance in wires) and eddy currents in the core.

Power Distribution and Transmission Line Losses

Transmission Losses: Power loss in transmission lines is given by $P_{loss} = I^2R$ , where $I$ is the current and $R$ is the resistance of the wires. To minimize power loss, electricity is transmitted at high voltages and low currents.
Power Supply Analysis: Considers transmission losses across transmission lines. High voltage transmission is used to reduce current and thus power loss ( $P_{loss} = I^2R$ ).

Important Definitions

Period (T): The time it takes for a source to produce one complete wave.
Frequency (f): The number of times a wave repeats itself every second. Measured in Hertz (Hz).
Amplitude: The maximum variation from zero of a periodic disturbance.
Peak Voltage: The amplitude of an alternating voltage.
Peak Current: The amplitude of an alternating current.
RMS Voltage: The value of the constant DC voltage that would produce the same power as the AC voltage across the same resistance.
Direct Current (DC): An electric current that flows in one direction only.
Alternating Current (AC): An electric current that reverses direction at short, regular intervals.
Peak-to-Peak Voltage: The difference between the maximum and minimum voltages of a DC voltage.
Power Rating: The total electrical power required for an appliance or machine to operate normally.
Transformer: A device in which two multi-turn coils may be wound around an iron core to produce an output AC voltage that is different from the input AC voltage.
Galvanometer: An instrument used to detect small electric currents or to detect the direction of current.
Electromagnetic Induction: The generation of an electromotive force (EMF) in a coil as a result of a changing magnetic field.
Step-Up Transformer: A transformer where the output (secondary) voltage produced is greater than the input (primary) voltage.
Step-Down Transformer: A transformer where the output (secondary) voltage produced is less than the input (primary) voltage.
Ideal Transformer: A transformer that is 100% efficient, meaning its input power is equal to its output power.
Eddy Current: An electric current induced in the iron core of a transformer by changing magnetic fields.

Energy and Power Calculations

Power Dissipated in Wires: $P_{loss} = VI = I^2R$
Ohm’s Law: $V = IR$
Power Formula: $P = VI$
Energy Unit Conversion:
- $1 \text{ watt} = 1 \text{ joule per second}$
- $1 \text{ joule} = 1 \text{ watt} \times 1 \text{ second} = 1 \text{ watt second}$
- $1 \text{ kWh} = 3.6 \times 10^6 \text{ joules} = 3.6 \text{ MJ}$

Transformers: Practical Considerations

Real transformers are not 100% efficient. Energy losses occur due to:
- Copper Losses (I²R losses): Heat generated in the wires of the primary and secondary coils due to resistance.
- Eddy Currents: Currents induced in the iron core due to changing magnetic fields. These are minimized by using laminated cores (layers of iron sandwiched between thin layers of insulation).

Transmission Systems: Victorian Context

Electricity is generated at varying voltages (e.g., 20 kV in Yallourn, 24 kV in Newport).
Voltages are stepped up to 500 kV for long-distance transmission to Melbourne.
Voltages are then stepped down through various stages (66 kV, 22 kV) to 230 V for domestic use.

Methods to Reduce Resistance in Transmission Cables

Make the wires thicker: Increases material and support costs.
Use a better conductor: Limited by the economic values of different metals; gold and silver are too expensive.

High-Voltage DC (HVDC) Transmission

HVDC is used for long distances (e.g., Basslink between Tasmania and Victoria).
Uses voltage source converters instead of transformers.
Advantages include more stability and no need for synchronization between networks.