Fine-Grained Mobility Characterization: Steady and Transient State Behaviors
Transient Component Steady-State...
Transcript of Transient Component Steady-State...
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Transient Component Steady-State Component
Now we focus on steady-state power calculations.
We are primarily interested in the average power delivered to or supplied
from a pair of terminals as a result of sinusoidal voltages and currents.
Other measures, such as reactive power, complex power, and apparent
power, will also be presented.
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We are operating in the sinusoidal steady state, so we may choose any
convenient reference for zero time. This reference system requires a shift of
both the voltage and current by 𝜃𝑖, Thus:
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Figure 10.2 Instantaneous power, voltage, and current versus v(t ) for steady-state sinusoidal operation.
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Unit for reactive power is
VAR (volt-amp reactive).
Unit for real power is
W (watt)
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The instantaneous real power can
never be negative.
Power cannot be extracted from a
purely resistive network.
Rather, all the electric energy is
dissipated in the form of thermal
energy.
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In a purely inductive circuit, the average
power is zero. Therefore no transformation
of energy from electric to nonelectric form
takes place.
The instantaneous power at the terminals
continually exchanged between the circuit
and the source driving the circuit
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The average power is zero, so there is no
transformation of energy from electric to
nonelectric form.
The power is continually exchanged
between the source driving the circuit and
the electric field associated with the
capacitive elements
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The average power and the reactive power
can be written in terms of effective values:
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Complex power is the complex sum of real power and reactive power
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The magnitude of complex power is referred to as apparent power.
Apparent power, like complex power, is measured in volt-amps. The
apparent power, or volt-amp, requirement of a device designed to
convert electric energy to a nonelectric form is more important than the
average power requirement. Although the average power represents the
useful output of the energy-converting device, the apparent power
represents the volt-amp capacity required to supply the average power.
𝑺 = 𝑷𝟐 + 𝑸𝟐𝟐
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𝑺 = 𝑽𝒆𝒇𝒇. 𝑰𝒆𝒇𝒇∗
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𝑺 = 𝑽𝒆𝒇𝒇. 𝑰𝒆𝒇𝒇∗
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𝑺 = 𝑽𝒆𝒇𝒇. 𝑰𝒆𝒇𝒇∗
X is positive for an inductor
and negative for a capacitor
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For maximum average power transfer, 𝑍𝐿 must be equal to the conjugate of the Thévenin impedance