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2.1. Basic Principles of AC Signals
· Active power equals the products of the instantaneous voltages and currents, averaged over a period of time.
With AC power, a phase difference occurs between the voltage and current if a capacitive or inductive load is introduced. If the instantaneous voltage u(t) and instantaneous current i(t) are sinusoidal and expressed as
, instantaneous AC power p is expressed as follows:
U: Voltage RMS I: Current RMS φ: Phase difference between voltage and current.
p is the sum of time-independent terms UIcosφ and the AC component of twice the frequency of the voltage or current -UIcos(2ωt-φ).
Since the power P consumed by the load per unit of time represents the average value of multiple instances of p, the AC component of p [-UIcos(2ωt-φ)] is 0, and the power P is P=UIcosφ[W]. Combining these findings, power per unit of time can be found using the expression below.
T: Input Cycle
Figure 1: Relationship between load type and voltage/current phase
· Active, Reactive, and Apparent Power
Even given the same voltage and current, the power consumed varies depending on the phase difference φ. Figure 1 shows the relationship between voltage and current when the load is resistive, inductive, or capacitive. The product of RMS voltage and RMS current, UI, is called the apparent power S (units: VA). Apparent power is used to express the electric capacity of the device. Within apparent power there is active power (or effective power, units: W), which is the power consumed by the load mentioned above, as well as reactive power (units: var) which is not part of the consumed power.
The following equation expresses the relationship between apparent, active, and reactive power.
Here, cosφ represents the proportion of the apparent power that is actually consumed by the load, and is called the power factor (λ).
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Figure 2: Relationship between apparent,
active, and reactive power
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