Introduction to Power System Analysis

22 April 2023

DelftUniversity ofTechnology

Electrical Power System Essentials

ET2105 Electrical Power System EssentialsProf. Lou van der Sluis

Introduction to Power System Analysis

21. Introduction to Power System Analysis | 33

Electrical Power System Essentials ET2105

Test (1)

• The average power of the instantaneous power dissipated in an AC circuit is called

A. Complex power SB. Apparent power |S|C. Active power PD. Reactive power Q



Test (2)

• An inductive currentA. leadsB. lagsthe voltage

• A capacitive loadA. suppliesB. consumesreactive power



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



The energy is stored in the Electromagnetic Field



Why…?

• Why AC and not DC ?

• Why a sinusoidal alternating voltage ?

• Why 50 Hz (or 60 HZ) ?

• Why three-phase systems ?



Why AC and not DC ?Break-even distance for HVDC



Why a Sinusoidal Alternating Voltage ?

Triangular, sinusoidal and block



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



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

1.5 2.5:: hysP f

2 2::eddyP f



Three Phase Systems (1)Phase voltages in a balanced three-phase system (50 Hz)



Three Phase Systems (2)The magnetic field generated by a three-phase system is a rotating field



Some basics

• 3 phase systems

• Power

• Voltage levels

• Phasors

• Per unit calculation

• Power system structure



Three Single Phase Systems One Three Phase System



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

Va

Vb

Vc

Ia

Ic

Ib



Balanced Three Phase System (2)

Va

Vb

Vc

Ia

Ic

Ib

0 n a b cI I I I

IaIc

Ib

0



Balanced system Single Phase calculation

Va

Ia

Vb

Ib

120º

Vc Ic

120º



Line-to-Line Voltage



Three Phase Complex Power

• 3 x 1-phase complex power



Power (1)

P: Active power (average value viR)Q: Reactive power (average value viX)



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*

PositivePositive

NegativeNegative



Power (3)

S Complex power VA

|S| Apparent power VA

P Active power

Average power

W

Q Reactive power var



Series / Parallel



Power Factor

Power factor That part of the apparent power that is related to the mean energy flow



System Voltage Levels



Steady State Analysis: f = 50 Hz

• f = 50Hz = v/f = 3e8/50 = 6000km

• Modelling with R, G, L and C

6000 km

L

C/2C/2



Steady State Analysis (1)

Example:

86.686.6

100100

3030°°

5500 VV



Steady State Analysis (2)

PowerPowerSystemSystem



Phasor/Vector Calculus

Real/imaginairy part:Addition/substraction

Length/angle:Multiplication/division



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



Time PhasorCurrent in phase

Current lagging

Current leading

U = IR

U = jLI

I = jCU



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



Power System Structure

Documents

Introduction to Power System Analysis