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Transcript
Introduction to Power System Analysis ET2105 Electrical Power System Essentials Prof. Lou van der Sluis 30 April 2017 Delft University of Technology Electrical Power System Essentials Test (1) • The average power of the instantaneous power dissipated in an AC circuit is called A. Complex power S B. Apparent power |S| C. Active power P D. Reactive power Q 1. Introduction to Power System Analysis Electrical Power System Essentials 2 | 33 ET2105 Test (2) • An inductive current A. leads B. lags the voltage • A capacitive load A. supplies B. consumes reactive power 1. Introduction to Power System Analysis Electrical Power System Essentials 3 | 33 ET2105 Electrical Power System Essentials Outline 1. Introduction to Power System Analysis 2. The Generation of Electric Energy 3. The Transmission of Electric Energy 4. The Utilization of Electric Energy 5. Power System Control 6. Energy Management Systems 7. Electricity Markets 8. Future Power Systems 1. Introduction to Power System Analysis Electrical Power System Essentials 4 | 33 ET2105 The energy is stored in the Electromagnetic Field 1. Introduction to Power System Analysis Electrical Power System Essentials 5 | 33 ET2105 Why…? • Why AC and not DC ? • Why a sinusoidal alternating voltage ? • Why 50 Hz (or 60 HZ) ? • Why three-phase systems ? 1. Introduction to Power System Analysis Electrical Power System Essentials 6 | 33 ET2105 Why AC and not DC ? Break-even distance for HVDC 1. Introduction to Power System Analysis Electrical Power System Essentials 7 | 33 ET2105 Why a Sinusoidal Alternating Voltage ? Triangular, sinusoidal and block 1. Introduction to Power System Analysis Electrical Power System Essentials 8 | 33 ET2105 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 1. Introduction to Power System Analysis Electrical Power System Essentials 9 | 33 ET2105 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: Phys :: f 1.52.5 • Increases the eddy current losses: Peddy :: f 2 2 • Increases the cable and line impedance 1. Introduction to Power System Analysis Electrical Power System Essentials 10 | 33 ET2105 Three Phase Systems (1) Phase voltages in a balanced three-phase system (50 Hz) 1. Introduction to Power System Analysis Electrical Power System Essentials 11 | 33 ET2105 Three Phase Systems (2) The magnetic field generated by a three-phase system is a rotating field 1. Introduction to Power System Analysis Electrical Power System Essentials 12 | 33 ET2105 Some basics • 3 phase systems • Power • Voltage levels • Phasors • Per unit calculation • Power system structure 1. Introduction to Power System Analysis Electrical Power System Essentials 13 | 33 ET2105 Three Single Phase Systems One Three Phase System 1. Introduction to Power System Analysis Electrical Power System Essentials 14 | 33 ET2105 Balanced Three Phase System (1) Vc Ic • Voltages in the 3 phases have the same amplitude, but differ 120 electrical degrees in phase • Equal impedances in the 3 phases Va Ib Ia Vb 1. Introduction to Power System Analysis Electrical Power System Essentials 15 | 33 ET2105 Balanced Three Phase System (2) Vc Ic 0 I n I a Ib I c 0 Va Ic Ib Vb Ia Ia Ib 1. Introduction to Power System Analysis Electrical Power System Essentials 16 | 33 ET2105 Balanced system Single Phase calculation Vc Ic 120º Va Ib Vb Ia 120º 1. Introduction to Power System Analysis Electrical Power System Essentials 17 | 33 ET2105 Line-to-Line Voltage 1. Introduction to Power System Analysis Electrical Power System Essentials 18 | 33 ET2105 Three Phase Complex Power • 3 x 1-phase complex power 1. Introduction to Power System Analysis Electrical Power System Essentials 19 | 33 ET2105 Power (1) P: Active power (average value viR) Q: Reactive power (average value viX) 1. Introduction to Power System Analysis Electrical Power System Essentials 20 | 33 ET2105 Power (2) How to calculate P and Q from the voltage and current phasor ? I* V I • Inductive load consumes reactive power (Q>0) • Current lags the supply voltage Positive • Capacitive load generates reactive power (Q<0) • Current leads the supply voltage Negative 1. Introduction to Power System Analysis Electrical Power System Essentials 21 | 33 ET2105 Power (3) S Complex power VA |S| Apparent power VA P Active power W Average power Q Reactive power var 1. Introduction to Power System Analysis Electrical Power System Essentials 22 | 33 ET2105 Series / Parallel 1. Introduction to Power System Analysis Electrical Power System Essentials 23 | 33 ET2105 Power Factor Power factor That part of the apparent power that is related to the mean energy flow 1. Introduction to Power System Analysis Electrical Power System Essentials 24 | 33 ET2105 System Voltage Levels 1. Introduction to Power System Analysis Electrical Power System Essentials 25 | 33 ET2105 Steady State Analysis: f = 50 Hz • f = 50Hz = v/f = 3e8/50 = 6000km 6000 km • Modelling with R, G, L and C L C/2 C/2 1. Introduction to Power System Analysis Electrical Power System Essentials 26 | 33 ET2105 Steady State Analysis (1) 50 V 100 30° 86.6 Example: 1. Introduction to Power System Analysis Electrical Power System Essentials 27 | 33 ET2105 Steady State Analysis (2) Power System 1. Introduction to Power System Analysis Electrical Power System Essentials 28 | 33 ET2105 Phasor/Vector Calculus Real/imaginairy part: Addition/substraction Length/angle: Multiplication/division 1. Introduction to Power System Analysis Electrical Power System Essentials 29 | 33 ET2105 Network Elements Element Time domain Phasor domain Resistance v = iR V = IR Reactor v = L (di/dt) V = jLI = jXI Capacitor i = C (dv/dt) I = jCV = jBV 1. Introduction to Power System Analysis Electrical Power System Essentials 30 | 33 ET2105 Time Phasor Current in phase U = IR Current lagging U = jLI Current leading I = jCU 1. Introduction to Power System Analysis Electrical Power System Essentials 31 | 33 ET2105 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: Base quantity Value Voltage (apparent) Power Current Impedance 1. Introduction to Power System Analysis Electrical Power System Essentials 32 | 33 ET2105 Power System Structure 1. Introduction to Power System Analysis Electrical Power System Essentials 33 | 33 ET2105