WIND ENERGY SYSTEMS - Cd3wd

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Chapter 5—Electrical Network 5–12 + ♠ ✏ ✏✏ ✏ E a n ♠✏✏ ✏✏ + E b + E ab − + b − E ca a ♠E c E bc + − + c Figure 6: Balanced three-phase source. The symbol V will be used for other types of voltages in the circuit. This will become more evident after a few examples. The line to line voltage E ab is given by E ab = E a − E b = |E a |(1/0 o − 1/ − 120 o ) = |E a |[1 − (−0.5 − j0.866)] = |Ea|(1.5+j0.866) In a similar fashion, = |Ea| √ 3/30 o V (21) E bc = √ 3|E a |/ − 90 o V These voltages are shown in the phasor diagram of Fig. 7. E ca = √ 3|Ea|/ − 210 o V (22) When this three-phase source is connected to a balanced three-phase wye-connected load, we have the circuit shown in Fig. 8. The current I a is given by Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
Chapter 5—Electrical Network 5–13 E c E ca ❍❨ ❆❑ ❍ ❍ ❍ ❆ ❍ ❍ ❆ ❍ ❍ ❆ ❍✟ ❆ ✟✟✟✟✟✟✟✟✯ ✲ E a ✁ ✁ ✁ ✁ ✁☛ E b E ab ❄ E bc Figure 7: Balanced three-phase voltages for circuit in Fig. 5.6. ✲ I a a b ✟ ✲ I b ❍ ✟ ✟ ❍❍❍ ✟ ✟ ❍ ✠ ✟ ❍❍ ❍ ✟ ❍ ✟ ♠ ♠✟ ❍ ✟✟ ❍ ✁ ✁✁ ❆✟ ✟✟ ❆ E ❆ b Z ❍ ❍✟ ✟✟✟ ❍ ❍ ❍ ❍✁ ✁✁ Z ❍ ❍✟ ✟✟ ❆ ❆✟ ✟✟ ❆ ✛ I n n E a ♠E c Z c ✲ I c Figure 8: Balanced three-phase wye-connected source and load. I a = E a Z = |E a| |Z| / − θ = |I a|/ − θ A (23) The other two currents are given by I b = |I a |/ − θ − 120 o A I c = |I a |/ − θ − 240 o A (24) The sum of the three currents is the current I n flowing in the neutral connection, which can Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
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WIND ENERGY SYSTEMS Electronic Edit
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