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Introduction to Power System Analysis

Introduction to Power System Analysis. ET2105 Electrical Power System Essentials. Prof. Lou van der Sluis. Test (1). The average power of the instantaneous power dissipated in an AC circuit is called Complex power S Apparent power |S| Active power P Reactive power Q. Test (2).

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Introduction to Power System Analysis

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  1. Introduction to Power System Analysis ET2105 Electrical Power System Essentials Prof. Lou van der Sluis Electrical Power System Essentials

  2. Test (1) • The average power of the instantaneous power dissipated in an AC circuit is called • Complex power S • Apparent power |S| • Active power P • Reactive power Q Electrical Power System Essentials

  3. Test (2) An inductive current leads lags the voltage A capacitive load supplies consumes reactive power Electrical Power System Essentials

  4. Electrical Power System Essentials Outline • Introduction to Power System Analysis • The Generation of Electric Energy • The Transmission of Electric Energy • The Utilization of Electric Energy • Power System Control • Energy Management Systems • Electricity Markets • Future Power Systems Electrical Power System Essentials

  5. The energy is stored in the Electromagnetic Field Electrical Power System Essentials

  6. Why…? Why AC and not DC ? Why a sinusoidal alternating voltage ? Why 50 Hz (or 60 HZ) ? Why three-phase systems ? Electrical Power System Essentials

  7. Why AC and not DC ? Break-even distance for HVDC Electrical Power System Essentials

  8. Why a Sinusoidal Alternating Voltage ? Triangular, sinusoidal and block Electrical Power System Essentials

  9. The choice of Frequency (1) 50 Hz and 60 Hz • Between 1885 and 1890 in the U.S.A.: • 140, 133⅓, 125, 83 ⅓, 66 ⅔, 50, 40, 33 ⅓, 30, 25 en 16⅔ Hz • Nowadays: • 60 Hz in North America, Brazil and Japan (has also 50 Hz!) • 50 Hz in most other countries • 25 Hz Railways (Amtrak) • 16⅔ Hz Railways • 400 Hz Oil rigs, ships and airplanes Electrical Power System Essentials

  10. The choice of Frequency (2) 50 Hz and 60 Hz • A too low frequency, like 10 or 20 Hz causes flicker • A too high frequency • Increases the hysteresis losses: • Increases the eddy current losses: • Increases the cable and line impedance Electrical Power System Essentials

  11. Three Phase Systems (1) Phase voltages in a balanced three-phase system (50 Hz) Electrical Power System Essentials

  12. Three Phase Systems (2) The magnetic field generated by a three-phase system is a rotating field Electrical Power System Essentials

  13. Some basics 3 phase systems Power Voltage levels Phasors Per unit calculation Power system structure Electrical Power System Essentials

  14. Three Single Phase Systems  One Three Phase System Electrical Power System Essentials

  15. Balanced Three Phase System (1) Vc Ic Va Ib Ia Vb • Voltages in the 3 phases have the same amplitude, but differ 120 electrical degrees in phase • Equal impedances in the 3 phases Electrical Power System Essentials

  16. Balanced Three Phase System (2) Vc Ic 0 Va Ic Ia Ib Ia Ib Vb Electrical Power System Essentials

  17. Balanced system  Single Phase calculation Vc Ic 120º Va Ib Ia 120º Vb Electrical Power System Essentials

  18. Line-to-Line Voltage Electrical Power System Essentials

  19. Three Phase Complex Power • 3 x 1-phase complex power Electrical Power System Essentials

  20. Power (1) P: Active power (average value viR) Q: Reactive power (average value viX) Electrical Power System Essentials

  21. Power (2) I* V  I Negative How to calculate P and Q from the voltage and current phasor ? • Inductive load consumes reactive power (Q>0) • Current lags the supply voltage • Capacitive load generates reactive power (Q<0) • Current leads the supply voltage Positive Electrical Power System Essentials

  22. Power (3) Electrical Power System Essentials

  23. Series / Parallel Electrical Power System Essentials

  24. Power Factor Power factor That part of the apparent power that is related to the mean energy flow Electrical Power System Essentials

  25. System Voltage Levels Electrical Power System Essentials

  26. Steady State Analysis: f = 50 Hz 6000 km L C/2 C/2 • f = 50Hz   = v/f = 3e8/50 = 6000km • Modelling with R, G, L and C Electrical Power System Essentials

  27. Steady State Analysis (1) 50 V 100 30° 86.6 Example: Electrical Power System Essentials

  28. Steady State Analysis (2) Power System Electrical Power System Essentials

  29. Phasor/Vector Calculus Real/imaginairy part: Addition/substraction Length/angle: Multiplication/division Electrical Power System Essentials

  30. Network Elements Electrical Power System Essentials

  31. Time  Phasor Current in phase U = IR Current lagging U = jLI Current leading I = jCU Electrical Power System Essentials

  32. Per-Unit Normalization • 156150 V  1.041 pu (150000 V = 1 pu) • Advantageous to calculating with percentages • 100% * 100% = 10000/100 = 100% • 1 pu * 1 pu = 1 pu • Define 2 base quantities  Example: Electrical Power System Essentials

  33. Power System Structure Electrical Power System Essentials

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