10 Questions
What is the expression for instantaneous power in the time domain?
$p(t) = V_m I_m [\cos(\theta_v - \theta_i) + \cos(2\omega t + \theta_v + \theta_i)]$
What is the complex power defined as?
$S = P + jQ$
In which form is complex power often expressed?
$S = V I \cos\theta + j V I \sin \theta$
What do the real and reactive power components of a generator's complex power represent?
Real power represents the ability to perform useful work, while reactive power supports the system electromagnetically.
In normal system operation, what dynamics are decoupled from each other?
Frequency/real-power dynamics are decoupled from voltage/reactive-power dynamics.
What is the average power expression for instantaneous power?
$P = V_m I_m \cos(\theta_v - \theta_i)$
What is the complex power defined as?
$S = P + jQ$
In normal system operation, which dynamics are decoupled from each other?
Voltage/reactive-power dynamics from frequency/real-power dynamics
What is the expression for instantaneous power in the time domain?
$p(t) = [\cos(\theta_{vi}) - \cos(2\omega t - \theta_{vi})]/2$
What do the real and reactive power components of a generator's complex power represent?
Real power is able to perform useful work, Reactive power supports the system electromagnetically
Study Notes
Reactive Power and Phase Shift
- Reactive power is related to the phase shift between voltage and current.
- The phase shift affects the current required to provide real power, with a higher reactive power causing a higher current.
Instantaneous Power and Average Power
- Instantaneous power is the product of instantaneous voltage and current.
- Instantaneous power can be decomposed into two terms: real power and reactive power.
- Real power is the average power consumed by a load, while reactive power is the power that does not perform any useful work.
- The average power is the fixed average component of the instantaneous power.
Steady-State Frequency-Domain Model
- The steady-state frequency-domain model is represented by S = V I* = P + jQ.
- P is the real power, and Q is the reactive power.
- The existence of Q causes current to be higher than necessary to provide P, which can "clog up the system".
Instantaneous Electric Power
- Instantaneous electric power is represented by p(t) = Vmax Imax sin(ωt) sin(ωt - θ).
- The power can be decomposed into two terms: a fixed average term and a zero average term.
Power Decomposition
- Power can be decomposed into two terms: P (1-cos(2wt)) and Q sin(2wt).
- P is the real power, and Q is the reactive power.
- The values of P and Q are given by P = 0.275 PU Watts and Q = 0.205 PU VARS.
Test your knowledge on reactive power with this quiz. From understanding the definition to its mathematical representation, this quiz covers various aspects of reactive power.
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