Lecture 25 Complex Power

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Lecture 25Complex Power

• ECE 205
• Prof. Ali Keyhani

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Complex Power

• In power circuit analysis phasor magnitudes
  are expressed in terms of root mean square (rms)
  values

Complex power Product of the voltage phasor
times the conjugate of the current phasor
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Complex Power
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Complex Power

• Power Triangle

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Example 1

• Determine the average power, reactive power
  and apparent power for the given voltage and
  current.

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Complex Power
Since
We have
Reactive Power positive inductive load, lagging
power factor Reactive Power negative capacitive
load, leading power factor
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Example 2

• At 480V, a load draws 300kVA of apparent power
  with p.f. 0.9 lagging, what is the active,
  reactive, and complex power of the load?

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Example 2

• Solution

Q gt 0 because p.f. is lagging
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Example 3

• Consider a 480V, 180kVA load with pf 0.0
  leading, what is the active, reactive, and
  complex power of the load?

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Example 3

• Solution

Q lt 0 because p.f. is leading.
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Load Flow

• Load Flow Adjust the source so that a
  required complex power is delivered to the load
  at a specified interface voltage magnitude
• Conservation of complex power
• In a linear circuit operating in steady state
  the sum of the complex powers produced by each
  independent source is equal to the sum of the
  complex power absorbed by each two-terminal
  element in the circuit.

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Example 4

• Source textbook
• Compute the complex power absorbed by each
  branch of the circuit. Also calculate the power
  produced by the source.

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Example 4

• Solution

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Example 5

• Calculate the complex power delivered by each
  source.

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Example 5

• Solution