Questions and Answers
What is the formula for instantaneous power in a time domain?
$p(t) = \frac{1}{2} V_m I_m \cos(\theta_v - \theta_i) + \frac{1}{2} V_m I_m \cos(2\omega t + \theta_v + \theta_i)$
What is the complex power, S, defined as?
$S = V I cos\theta + jV I sin\theta$
What do the real and reactive power, P and Q, represent in the power system?
P represents the ability to perform useful work and Q supports the system electromagnetically.
In normal system operation, which dynamics are decoupled from each other?
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What does the single system frequency, f, represent in a power system?
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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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