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Complex Algebra and Load Power

Complex Algebra and Load Power. EE341 Ali Keyhani Circuit Theory Lecture #3. Complex Numbers. i. b. b. . . a. a. 0. 0. r. r. A complex number is a quantity of the form of. (1). Where a and b are real numbers, and. a : real part b : imaginary part.

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Complex Algebra and Load Power

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  1. Complex Algebra and Load Power EE341 Ali Keyhani Circuit Theory Lecture #3

  2. Complex Numbers i b b   a a 0 0 r r A complex number is a quantity of the form of (1) Where a and b are real numbers, and a: real part b: imaginary part is called the conjugate of z

  3. Complex Numbers A complex number can also be written in phasor form: (2) (3) (4) where - Modulus (or norm) - Argument (or phase)

  4. Complex Numbers b  a 0 r Conversion between two forms: i (5) (6) (8) (7)

  5. Complex Numbers Operation Addition / Subtraction: (9) Multiplication: (10) (11) A complex number times its conjugate  the square of its modulus.

  6. Complex Numbers Operation Division: (12) Addition and subtraction can be easily done in regular form. While multiplication and division are a little bit complicated.

  7. Complex Numbers Operation Multiplication: (13) Division: (14) Multiplication and division are much easier to be done in phasor form.

  8. Electric Power For DC circuit: (15) For single-phase AC circuit: (16) Let Impedance angle So (17)

  9. Electric Power Since We have (18) (19) For three-phase AC circuit: (20)

  10. Electric Power For AC circuit: (21) Complex power: VA, kVA, MVA Active power: W, kW, MW Reactive power: Var, kVar, MVar (22) (24) (23) (25)

  11. Power Factor Power factor is defined as: (26) Lagging: Q > 0,  > 0, inductive Leading: Q < 0,  < 0, capacitive

  12. Electric Load Example 1 Consider a three-phase 480V, 300kVA load with p.f. = 0.9 lagging, what is the active, reactive, and complex power of the load? Solution: Known: To compute: P, Q, from S lagging

  13. Electric Load Example 1 According to eqn (24), According to eqn (25), Q > 0 because p.f. is lagging.

  14. Electric Load Example 2 Consider a three-phase 480V,240kW load with pf = 0.8 lagging, what is the active, reactive, and complex power of the load? Solution: Known: To be compute:Q, S from P lagging

  15. Electric Load Example 2 According to eqn (24), According to eqn (25), Q > 0 because p.f. is lagging.

  16. Electric Load Example 3 Consider a three-phase 480V,180kVA load with pf = 0.0 leading, what is the active, reactive, and complex power of the load? Solution: Known: Compute be:P, Q, from S leading

  17. Electric Load Example 3 According to eqn (24), According to eqn (25), Q < 0 because p.f. is leading.

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