02 July 2015 Delft University of Technology Electrical Power System Essentials ET2105 Electrical Power System Essentials Prof. Lou van der Sluis Introduction to Power System Analysis

2 1. Introduction to Power System Analysis | 33 ET2105 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

3 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Test (2) An inductive current A.leads B.lags the voltage A capacitive load A.supplies B.consumes reactive power

4 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials 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 Outline

5 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials The energy is stored in the Electromagnetic Field

6 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Why…? Why AC and not DC ? Why a sinusoidal alternating voltage ? Why 50 Hz (or 60 HZ) ? Why three-phase systems ?

7 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Why AC and not DC ? Break-even distance for HVDC

8 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Why a Sinusoidal Alternating Voltage ? Triangular, sinusoidal and block

9 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials The choice of Frequency (1) 50 Hz and 60 Hz Between 1885 and 1890 in the U.S.A.: 140, 133 ⅓, 125, 83 ⅓, 66 ⅔, 50, 40, 33 ⅓, 30, 25 en 16 ⅔ Hz Nowadays: 60 Hz in North America, Brazil and Japan (has also 50 Hz!) 50 Hz in most other countries 25 Hz Railways (Amtrak) 16 ⅔ Hz Railways 400 Hz Oil rigs, ships and airplanes

10 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials 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

11 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Three Phase Systems (1) Phase voltages in a balanced three-phase system (50 Hz)

12 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Three Phase Systems (2) The magnetic field generated by a three-phase system is a rotating field

13 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Some basics 3 phase systems Power Voltage levels Phasors Per unit calculation Power system structure

14 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Three Single Phase Systems  One Three Phase System

15 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Balanced Three Phase System (1) Voltages in the 3 phases have the same amplitude, but differ 120 electrical degrees in phase Equal impedances in the 3 phases VaVa VbVb VcVc Ia Ic Ib

16 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Balanced Three Phase System (2) VaVa VbVb VcVc Ia Ic Ib Ia Ic Ib 0

17 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Balanced system  Single Phase calculation VaVa Ia VbVb Ib 120º VcVcIc 120º

18 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Line-to-Line Voltage

19 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Three Phase Complex Power 3 x 1-phase complex power

20 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Power (1) P:Active power (average value vi R ) Q: Reactive power (average value vi X )

21 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Power (2) Inductive load consumes reactive power (Q>0) Current lags the supply voltage Capacitive load generates reactive power (Q<0) Current leads the supply voltage How to calculate P and Q from the voltage and current phasor ?  V I I*I*PositiveNegative

22 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Power (3) SComplex powerVA |S||S|Apparent powerVA P Active power Average power W QReactive powervar

23 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Series / Parallel

24 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Power Factor  Power factor  That part of the apparent power that is related to the mean energy flow

25 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials System Voltage Levels

26 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Steady State Analysis: f = 50 Hz f = 50Hz  = v/f = 3e8/50 = 6000km Modelling with R, G, L and C 6000 km L C/2

27 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Steady State Analysis (1) Example: ° V

28 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Steady State Analysis (2) PowerSystem

29 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Phasor/Vector Calculus Real/imaginairy part: Addition/substraction Length/angle: Multiplication/division

30 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Network Elements ElementTime domainPhasor domain Resistancev = iRV = IR Reactorv = L (di/dt) V = j  LI = jXI Capacitori = C (dv/dt) I = j  CV = jBV

31 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Time  Phasor Current in phase Current lagging Current leading U = IR U = j  LI I = j  CU

32 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Per-Unit Normalization V  pu ( 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 quantityValue Voltage (apparent) Power Current Impedance

33 1. Introduction to Power System Analysis | 33 ET2105 Electrical Power System Essentials Power System Structure