begin notes on ac

uni/mmme/2051_electromechanical_devices/ac_power.md

@@ -0,0 +1,51 @@
+---
+author: Akbar Rahman
+date: \today
+title: MMME2051 // AC Power
+tags: [ ac, alternating_current, power ]
+uuid: c269b4b7-7835-4b50-8d4f-ff5bc63a8a3d
+lecture_slides: [ ./lecture_slides/MMME2051EMD_Lecture3B.pdf ]
+exercise_sheets: [ ./exercise_sheets/Exercise Sheet 4 - Power factor and three phase.pdf ]
+---
+
+# Definitions
+
+- Phase voltage - voltage across any phase
+- Line voltage - voltage between two live lines
+- Phase current - current through any phase
+- Line current - current through any live line
+
+# Three-Phase Load
+
+$$P = \sqrt{3} V_lI_l\cos\gamma$$
+
+![](./images/vimscrot-2023-02-17T13:12:48,739518484+00:00.png)
+
+- 3-phase devices (source and load) are usually balanced, meaning that the impedance in each
+  phase is equal ($Z_1 = Z_2 = Z_3$).
+- For loads, this means that the voltage across them are the same, apart from the phase angles:
+
+  \begin{align*}
+  v_{1N} = V\cos{2\pi ft} \\
+  v_{2N} = V\cos{2\pi ft - \frac{2\pi}{3} \\
+  v_{3N} = V\cos{2\pi ft + \frac{2\pi}{3}
+  \end{align*}
+
+- Balanced loads and sources ensure that line/phase currents have equal magnitudes and that the
+  neutral current is 0
+
+## Star Load
+
+![](./images/vimscrot-2023-02-17T13:14:49,017883457+00:00.png)
+
+$$|V_\text{line}| = \sqrt 3 |V_\text{phase}|$$
+
+$$I_\text{line} = I_\text{phase}$$
+
+## Delta Load
+
+![](./images/vimscrot-2023-02-17T13:15:12,490943631+00:00.png)
+
+$$|V_\text{line}| = |V_\text{phase}|$$
+
+$$I_\text{line} = \sqrt 3 I_\text{phase}$$