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Alternating Current |
Alternating Current
[!quote] Alternating current (AC) is electric current that reverses direction periodically. The voltage and current in an AC circuit oscillate in a sinusoidal manner. The frequency of the oscillation is the number of complete cycles per second measured in hertz (Hz). The frequency of the AC power grid in the United States is 60 Hz.
- Ungrounded conductor - "Hot"
- Grounded conductor - "Neutral"
3-Phase Power
The conductors between a voltage source and a load are called lines, and the voltage between any two lines is called line voltage. The voltage measured between any line and neutral is called phase voltage.
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Poles vs Phases vs Wires
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3Ø = 3PH 3W
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3ØY = 3PH 4W
[!info] Phase Abbreviations
- PH
- Φ (capital phi)
- Ø (latin O with stroke)
Formula
Active Power
The formula for active power in a three phase system is given by
P = \sqrt{3} \times V_{L} \times I_{L} \times \text{PF}
where:
- $P$ is the active power,
- $V_{L}$ is the line voltage,
- $I_{L}$ is the line current,
- $\text{PF}$ is the power factor.
Apparent Power
The formula for apparent power in a three phase system is given by
S = \sqrt{3} \times V_{L} \times I_{L}
I_{L} = \frac{S}{\sqrt{3} \times V_{L}}
where:
- $S$ is the apparent power,
- $V_{L}$ is the line voltage,
- $I_{L}$ is the line current.
Voltage Systems
120/240V 1-Phase 3-Wire:
- 120V 1-Phase 2-Wire --- Line to Neutral
- 240V 1-Phase 2-Wire --- Line to Line
208Y/120V 3-Phase 4-Wire:
- 120V 1-Phase 2-Wire --- Line to Neutral
- 208V 1-Phase 2-Wire --- Line to Line
- 208V 3-Phase 3-Wire --- Line to Lines
480Y/277V 3-Phase 4-Wire:
- 277V 1-Phase 2-Wire --- Line to Neutral
- 480V 1-Phase 2-Wire --- Line to Line
- 480V 3-Phase 3-Wire --- Line to Lines
Wiring Configurations
- 1-Phase 2-Wire --- Line to Line (2-Pole) or Line to Neutral (1-Pole)
- 1-Phase 3-Wire --- Line to Line and Line to Neutral (2-Pole)
- 3-Phase 3-Wire --- Line to Lines (3-Pole)
- 3-Phase 4-Wire --- Line to Lines and Line to Neutral (3-Pole)
Active and Reactive Power
As a consequence of the periodic nature of AC, and the electromagnetic "inertia" of inductance and capacitance, inherent of all matter, the power in an AC circuit is divided into two components:
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Active Power (abbreviated
P, measured in watts) also known as real power, is power that does work. -
Reactive Power (abbreviated
Q, measured in volt-amperes reactive (VAR)) transfers no net energy to the load.
derived from these components are others:
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Complex Power (abbreviated
S, measured in volt-amperes (VA)) is the vector sum of the active and reactive components. It is "complex" because it exists on the real and imaginary axes of active and reactive power respectively. -
Apparent Power (abbreviated
|S|, measured in volt-amperes (VA)) is the magnitude of the complex power vector. -
Power Factor (abbreviated
\text{PF}, unitless) is the ratio of active power to apparent power.
P = S \times \text{PF}, \quad S = \frac{P}{\text{PF}}, \quad \text{PF} = \frac{P}{\text{S}}
Power Factor Correction
Capacitance and inductance can both be measured in VAR, but their effects cancel each other out rather than add.
Ferroelectric Hysteresis
The Venn Diagram of ferroelectric and ferromagnetic materials has a large but not complete intersection.