Power and Power factor

• In a purely resistive AC circuit, the energy delivered by the source will be dissipated as heat by the resistor.
• In a purely capacitive or purely inductive circuit, all of the energy will be stored during a half cycle, and then returned to the source during the other – there will be no net conversion to heat.
• When there is both a resistive component and a reactive component, some energy will be stored, and some will be converted to heat during each cycle.

Power equations

Purely resistive circuit

Suppose a circuit with load resistance is supplied a voltage of .

Instantaneous power dissipated by the load is given by:

Always: .

Purely inductive circuit

Suppose a circuit with inductor is supplied a voltage of .

Instantaneous power dissipated by the load is given by:

Purely capacitive circuit

Suppose a circuit with inductor is supplied a voltage of .

Instantaneous power dissipated by the load is given by:

The capacitive reactive power is given by:

General load

Consider a general load with both resistive and reactive components. Depending on how inductive or capacitive the reactive component, the phase shift between voltage and current phasor lies between and .

Suppose the circuit is supplied a voltage of . And the current phasor shifts in phase angle.

This ends up with:

Average over 1 cycle

Types of power

Active power

Aka. true power, resistive power. In all electrical and electronic systems, it is the true power (the resistive power) that does the work.

Note

In a question, if “power” is asked to be calculated, that means “active power”.

Reactive Power

Power delivered to/from a pure energy storage element (inductors and capacitors) is known as reactive power.

• Average power consumed by a pure energy storage element is .
• Current associated with it is not . Transmission lines, transformers, fuses, etc. must all be designed to be capable of withstanding this current.
• Loads with energy storage elements will draw large currents and require heavy duty wiring even though little average power is consumed.
• Shuttles back and forth between the source and the load.

Apparent power

Combination of active and reactive power.

The apparent power is essentially the effective power that the source “sees”.

The Beer Analogy

• Beer - Active power
  Liquid beer is useful power. The power that does the work.
• Foam - Reactive power
  Wasted or lost power.
• Mug - Apparent power
  Demand power, that is being delivered by the utility.

Power factor

If is the phase angle difference between and , is called the power factor.

Power factor appears in the equation of .

Power factor is:

• leading when leads
• lagging when lags

Power triangle

• Take phasor as the reference.
• Draw and phasors.