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Fundamentals of Power System

• Basic Circuit Elements: Three basic circuit elements used in electrical and electronic circuits:

  • Resistor (R): Converts electrical energy into heat energy.

    • Equations:

      • Voltage and current relationship: V ∝ I

      • Power dissipated: P = I²R or P = V²/R

      • Electrical energy converted into heat: W = I²Rt or W = V²t/R

    • Factors affecting heat production:

      • Resistance (R) of the conductor (higher resistance = more heat).

      • Time (t) for which current flows (longer time = larger heat).

      • Current (I) (higher current = more heat).

  • Inductor (L): A wire of finite length twisted into a coil.

    • Equations:

      • Voltage and current relationship: V ∝ di/dt

      • Stored energy in magnetic field: W = 1/2 Li²

    • Properties:

      • Stores energy in a magnetic field during the positive half-cycle and releases it during the negative half-cycle.

  • Capacitor (C): Stores electrical energy in the form of an electric field.

    • Equations:

      • Capacitor current: i = C * dV/dt

      • Stored energy: W = 1/2 CV²

Single Phase Transmission System

• Instantaneous Voltage: v(t) = Vm * sin(wt)

• Instantaneous Current: i(t) = Im * sin(wt - Ф)

• Instantaneous Power:

  • P(t) = v(t) * i(t) = Vm * sin(wt) * Im * sin(wt - Ф)

    • Expanded to express active (P) and reactive (Q) power.

Power Analysis

• Active Power (P): Useful power transmitted (Watt); never negative.

• Reactive Power (Q): Positive for inductive circuits, negative for capacitive circuits; can be represented by sinusoidal functions.

Relationship Between Reactive Power and Stored Energy

• For an inductor:

  • Equation: dW/dt = Q * sin(2(wt - Ф))

• For a capacitor:

  • Equation: dW/dt = -Q * sin(2(wt + Ф))

Three Phase Transmission System

• Balanced System:

  • Voltages and currents are balanced:

    • Phase a: i_a = Im sin(wt - Ф)

    • Phase b: i_b = Im sin(wt - 120° - Ф)

    • Phase c: i_c = Im sin(wt + 120° - Ф)

• Instantaneous Power:

  • P(t) = i_a * v_a + i_b * v_b + i_c * v_c

  • Total instantaneous 3-phase power is constant and equates to 3 times the real power per phase.

Complex Power in Circuits

• Relation: S = VI* = P + jQ

  • Represents apparent power (VA), with distinction based on circuit type (inductive, capacitive, resistive).

Load Characteristics and Classification

• Types of Loads:

  1. Heavy Loads: ~70% (factories, motors)

  2. Medium Loads: ~25% (heating and lighting)

  3. Light Loads: ~5% (electronic devices)

• Load Classification:

  • Lumped Loads: Defined by resistive and reactive properties based on voltage and frequency.

  • Composite Loads: Non-linear, with no direct relationship.

Power Quality and Transmission Systems

• Good Quality Supply: Reliability and limits within ±10% voltage and ±0.1% frequency.

• Electrical Power Transmission:

  • Involves generating plants sending power to consumers over long distances, primarily using HVAC and HVDC systems (alternating current and direct current).

HVAC vs HVDC

• HVAC:

  • Ranges from 33 kV to 230 kV.

• HVDC:

  • Ranges from 100 kV to 800 kV.

  • Transmits electric power as DC; losses less than 3% per 1000 km.

DC Transmission Systems

• Monopolar and Bipolar Links:

  • Monopolar Link: One conductor; economical.

  • Bipolar Link: Two conductors; allows for independent operation in case of faults.

AC and DC Distribution Systems

• AC System Features:

  • Voltage drop due to resistance, inductance, and capacitance; currents summed arithmetically.

• DC System:

  • Voltage drop due to resistance alone; currents summed vectorially.

Conclusion

• Advantages of HVDC over HVAC:

  • Reduced losses, flexibility, and improved performance under load.

Problems and Examples

The exercises listed at the end outline scenarios for the application of the concepts covered, including voltage calculations, bridge circuits, and load current distributions.