58 lines
1.6 KiB
Markdown
Executable File
58 lines
1.6 KiB
Markdown
Executable File
---
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author: Akbar Rahman
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date: \today
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title: MMME2051 // AC Power
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tags: [ ac, alternating_current, power ]
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uuid: c269b4b7-7835-4b50-8d4f-ff5bc63a8a3d
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lecture_slides: [ ./lecture_slides/MMME2051EMD_Lecture3B.pdf ]
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exercise_sheets: [ ./exercise_sheets/Exercise Sheet 4 - Power factor and three phase.pdf ]
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---
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This section builds on [introduction to AC](/permalink?uuid=0c90c691-cbf8-43e9-bfa5-7b277c853151).
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# Definitions
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- Phase voltage - voltage across any phase
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- Line voltage - voltage between two live lines
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- Phase current - current through any phase
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- Line current - current through any live line
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# Three-Phase Load
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$$P = \sqrt{3} V_lI_l\cos\gamma$$
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- 3-phase devices (source and load) are usually balanced, meaning that the impedance in each
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phase is equal ($Z_1 = Z_2 = Z_3$).
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- For loads, this means that the voltage across them are the same, apart from the phase angles:
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\begin{align*}
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v_{1N} = V\cos{2\pi ft} \\
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v_{2N} = V\cos{2\pi ft - \frac{2\pi}{3}} \\
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v_{3N} = V\cos{2\pi ft + \frac{2\pi}{3}}
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\end{align*}
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- Balanced loads and sources ensure that line/phase currents have equal magnitudes and that the
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neutral current is 0
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## Star Load
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$$|V_\text{line}| = \sqrt 3 |V_\text{phase}|$$
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$$I_\text{line} = I_\text{phase}$$
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## Delta Load
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$$|V_\text{line}| = |V_\text{phase}|$$
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$$I_\text{line} = \sqrt 3 I_\text{phase}$$
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# Power Factor (PF)
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$$\text{PF} = \cos{\gamma} = \cos{\left(\Phi_v-\Phi_i\right)}$$
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