Reactive Power and Power Decomposition Quiz
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Questions and Answers

What is the formula for instantaneous power in a time domain?

  • $p(t) = \frac{1}{2} V_m I_m \cos(\theta_v - \theta_i) + \frac{1}{2} V_m I_m \cos(2\omega t + \theta_v + \theta_i)$ (correct)
  • $p(t) = \frac{1}{2} V_m I_m \cos(\theta_v - \theta_i)$
  • $p(t) = V_{max} I_{max} [\cos(\theta_{vi}) - \cos(2\omega t - \theta_{vi})]$
  • $p(t) = P + Q(t)$
  • What is the complex power, S, defined as?

  • $S = P + Q$
  • $S = V I$
  • $S = V_{max} I_{max} [\cos(\theta_{vi}) - \cos(2\omega t - \theta_{vi})]$
  • $S = V I cos\theta + jV I sin\theta$ (correct)
  • What do the real and reactive power, P and Q, represent in the power system?

  • P represents system voltage profile and Q supports the system electromagnetically.
  • P represents the ability to perform useful work and Q supports the system electromagnetically. (correct)
  • P represents system frequency and Q supports the ability to perform useful work.
  • P represents system frequency and Q supports system electromagnetically.
  • In normal system operation, which dynamics are decoupled from each other?

    <p>Voltage/reactive-power dynamics are decoupled from frequency/real-power dynamics.</p> Signup and view all the answers

    What does the single system frequency, f, represent in a power system?

    <p>None of the above</p> Signup and view all the answers

    Study Notes

    Reactive Power

    • Reactive power (Q) is the component of power that is 90 degrees out of phase with the voltage, causing current to be higher than necessary to provide real power (P)
    • Q is measured in VARS ( Volt-Amps-Reactive)
    • Q = 0.205 PU VARS in the given example

    Instantaneous Power

    • Instantaneous power is the product of voltage and current at a given time
    • p(t) = v(t) * i(t) = Vmax * Imax * sin(ωt) * sin(ωt - θ)
    • Instantaneous power can be decomposed into two terms:
      • Average power term: cos(θ)
      • Oscillating power term: -cos(2ωt - θ)

    Power Decomposition

    • Power can be decomposed into two terms:
      • Real power (P): P = 0.275 PU Watts
      • Reactive power (Q): Q = 0.205 PU VARS
    • Steady-state frequency-domain model: S = V * I* = P + jQ

    Importance of Q

    • Existence of Q causes current to be higher than necessary to provide P, "clogging up the system"
    • Q affects the system's efficiency and stability

    Phase Shift

    • The phase shift between voltage and current is the key to understanding reactive power
    • The phase shift can be expressed as θ (theta)

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    Description

    Test your knowledge of reactive power and power decomposition with this quiz. Determine the correct values and terms related to these concepts.

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