Power factor correction

Training module I01

1
Introduction

 Power factor correction allows to increase the available power on the

secondary of the transformer.

Division - RPB – Mar07 - EN 2

 Introduction

RIGHT

The capacitors supply reactive energy.

So the transformer does not have to supply it.

Division - RPB – Mar07 - EN 3

Introduction

 Reactive power is useless in the network.

Division - RPB – Mar07 - EN 4

Introduction

WRONG

This energy allows to magnetize the magnetic circuits of the

motors and transformers although it products no work.

Division - RPB – Mar07 - EN 5

Introduction

 Compensate reactive power consists in increasing the cos phi of the

installation.

Division - RPB – Mar07 - EN 6

Introduction

RIGHT

The cos phi represents the efficiency of the network.

More it is close to 1, and better is the efficiency of the network

Division - RPB – Mar07 - EN 7

Electric energy

 Essential notions

 Cos , tan , power factor,

 Active power, reactive power, apparent power,

 Fundamental magnitudes, RMS magnitudes,

 Difference between cos  and power factor.

Division - RPB – Mar07 - EN 8

Electric energy
Agreement
 By agreement, an inductive load consumes reactive energy. We
speak about inductive cos .

 A capacitive load produces reactive energy. We speak about

capacitive cos .

 Most of loads are inductive loads (motors, transformers, …).

They consume reactive energy.

 Because of the inductive nature of the loads connected on the

network, displacement factor is inductive in most cases.

Division - RPB – Mar07 - EN 9

Electric energy
Recalls

 Any electric system (cable, line, transformer, engine, lighting,…) using the
AC current needs two forms of energy:

 Consumed active energy (kWh)

It results from the use of the active power P (kW) of the loads.

It is converted into mechanical power (work) or heat (losses,…).

It is the “useful” energy

 Consumed reactive power (kvarh)

It is used for magnetizing of the motors and the transformers.
It corresponds to the reactive power Q (kvar) of the loads.
It depends on the displacement between the tension and the current.

It is a “necessary energy” but it produces no work”

Division - RPB – Mar07 - EN 10

Electric energy
Definitions
 Reactive power used by the loads is supplied by the electric network. This
power has to be supplied added to active power.

 Reactive power in the electric network causes:

 Transformers overload,
 Cables and lines heating,
 …so losses.

 For these reasons, reactive energy must be produced as close as possible

to the loads, to prevent the unnecessary circulation of current in the
network.

This is what is known as “power factor correction”

Division - RPB – Mar07 - EN 11

Electric energy
Definitions

 Cos  : It depends on the displacement between current and voltage

fundamental magnitudes.
U1


I1
FRESNEL diagram

P1
cos  1 
S1

P1 : active power of the fundamental component.

S1: apparent power of the fundamental component.

Division - RPB – Mar07 - EN 12

Electric energy
Definitions

 Power factor

active power (kW) P

PF  
apparent power (kVA) S

 If currents and voltages are perfectly sinusoidal, power factor is

equal to cos .

Division - RPB – Mar07 - EN 13

Electric energy
Definitions

 tan  is often used instead of cos .

 tan 

reactive power (kvar) Q

tan   
active power (kW) P
Without harmonics only

Division - RPB – Mar07 - EN 14

Why compensate reactive power?
Graphical illustration

 Before power factor correction

P(kW)

Q(kvar)
S(kVA)

S>P
Cos  < 1

Division - RPB – Mar07 - EN 15

Why compensate reactive power?
Graphical illustration

 After power factor correction

P(kW)

S(kVA)

S=P
Cos  = 1

Division - RPB – Mar07 - EN 16

Why compensate reactive power?
Users advantages

Without power factor correction With power factor correction

P Q P Q

loads M M loads M M
Qc
Capacitor bank

 Important Joule losses in cables.  Decrease of consumed reactive energy.

 Important voltage drops in cables.  No distributor penalties.
 Penalties by the utilities (in France  Increase of available power on the secondary
for example). of the transformers.

Division - RPB – Mar07 - EN 17

Why compensate reactive power?
Consumer or no consumer?

Motor ○

Rectifiers ○ ○ Consumer

AC variable speed drive ○

Welding machine ○

Transformers ○

Arc furnace ○ ○ No consumer

Halogen lamps ○

Division - RPB – Mar07 - EN 18

How to correct power factor?
Generalities

 By producing reactive power as close as possible to the loads.

 By installing capacitors on the network. Capacitors generate reactive

power on the network.
It is the easiest and the most common way.

 Capacitors are put in parallel on the network loads by optimizing their

position according to economic criteria.

 On all voltage levels.

Division - RPB – Mar07 - EN 19

How to correct power factor?
Modes of correction

 Individual correction
The capacitor bank is connected closest to the loads

ADVANTAGES
The reactive power is done where it is consumed.
It is the best way to reduce the apparent power,
losses and voltage drops into the conductors.

Loads M M

DRAWBACKS
The cost because small capacitors are more
expansive than big ones.

Division - RPB – Mar07 - EN 20

How to correct power factor?
Motor and individual correction
 A motor still turns when power supply is stopped.

 Rotor magnetic inertia induces an electromotive force in stator

windings since a short time.

 If there is no capacitor bank => electromotive force disappear in few

periods.

Division - RPB – Mar07 - EN 21

How to correct power factor?
Motor and individual correction
 If the motor is compensated:

Increase of motor voltage

Capacitive current circulation in the stator windings

Magnetic field in the rotor

Increase of magnetic flux in the rotor

M
Increase of statoric currents

»self-excitation » phenomena

Division - RPB – Mar07 - EN 22

How to correct power factor?
Motor and individual correction: solutions
 Solution 1: Limit the capacitor bank power

Qc  0,9  I0  Un  3

 Qc: capacitor bank power

 I0: no load current of the motor
 Un: rated motor voltage

Division - RPB – Mar07 - EN 23

How to correct power factor?
Motor and individual correction: solutions
 Solution 2: Disconnect the capacitor bank when the motor stops.

 A contactor is installed on the capacitor bank which allows an

automatic disconnection when the motor stops.

Division - RPB – Mar07 - EN 24

How to correct power factor?
Modes of correction

 Sector correction
The capacitor bank is connected at the supply end of the
installation sector and supplies reactive energy by sector.

ADVANTAGES
Investments are less expansive than individual
correction.
The sector correction is advised for installations
where many loads are used in same time.

M M M M DRAWBACKS
The connection cables of the loads are not
compensated.

Division - RPB – Mar07 - EN 25

How to correct power factor?
Modes of correction

 Global correction
Capacitor bank is connected to busbars of the main LV distribution
board.

ADVANTAGES
It is an interesting economical solution
if the loads are stable and continuous.

DRAWBACKS
Reactive power circulates everywhere
Loads M M in the installation

Lighting, ...

Division - RPB – Mar07 - EN 26

Exercise: Advantages of power factor correction

630 kVA
400V

M M

250 kW 250 kW
Cos   0,75 Cos   0,75

Data

 2 motors P=250kW cos  = 0,75

 Target cos =0,93
5’
Pb: WhichPcapacitor bank do you install?
S= = 665power?
kVA
1
cos -Reactive
-Type? Fixe or automatic?

Division - RPB – Mar07 - EN 27

Exercise: Advantages of power factor correction

630 kVA
400V

M M

250 kW 250 kW
Cos   0,75 Cos   0,75

Installation without capacitor bank Installation with capacitor bank

 Apparent power demand 667 kVA  Apparent power demand 537 kVA
 Cos  = 0,75  Cos  = 0,93
P bill
S Electricity  No electricity bill
= = 665 kVA
cos 1
 Overloaded transformer  No overloaded transformer
 93 kVA available

Division - RPB – Mar07 - EN 28

 Harmonics

Division - RPB – Mar07 - EN 29

Harmonics
Introduction

 Motors generate harmonic currents

Division - RPB – Mar07 - EN 30

Harmonics
Introduction

WRONG

Installing loads using electronic power like variable speed

drive for motors increase harmonic pollution on electric
networks.

Division - RPB – Mar07 - EN 31

Harmonics
Introduction

 Harmonic currents have no effects on the network and on

capacitor bank

Division - RPB – Mar07 - EN 32

Harmonics
Introduction

WRONG

The effects are very important on the network (overheating

of the transformer, …) and on capacitor banks (overload
and risk of destruction)

Division - RPB – Mar07 - EN 33

Harmonics
Introduction

 Capacitor banks do not generate harmonic currents.

Division - RPB – Mar07 - EN 34

Harmonics
Introduction

RIGHT

Capacitor banks do not generate but they can amplify them

in certain cases.

Division - RPB – Mar07 - EN 35

Harmonics
Introduction
 Installing loads using electronic power like variable speed drive for
motors increase harmonic pollution on electric networks.

 No linear loads distort voltage waveform due to the propagation of

harmonic currents throw network impedance. The network is said
« polluted ».

 Harmonic effects are bad for the network components and especially
for capacitor banks.
The network behavior has to be studied.

Division - RPB – Mar07 - EN 36

Harmonics
Harmonic origin
 Most electric networks supply alternative sinusoidal voltage with a
frequency of 50 or 60 Hz depending on countries.

 A motor, when it is connected on the network, absorbs a current

which has the same waveform as the supply voltage and the same
frequency.
This load is said « linear ».
Linear load
A load is said to be "linear" when the
U
current it draws has the same waveform
as the supply voltage. Such a current
I has no harmonic components.
Examples : resistors in electric heaters,

inductive loads under steady-state
conditions (motors, transformers, etc.)

Division - RPB – Mar07 - EN 37

Harmonics
Harmonic origin
 It exists some loads which current waveform is different as the supply
voltage waveform.
These loads are said « no linear ».

No linear load
I
A load is said to be "non-linear" when the
U current it draws does not have the same
waveform as the supply voltage. The
current then has a high harmonic content.
The harmonic spectrum depends on the
type of load.
Examples: variable speed drives,
rectifiers, switch-mode power supplies,
motors during startup, transformers
during switch-on

Division - RPB – Mar07 - EN 38

Harmonics
Harmonic origin
 Waveform deformation is due to sinusoidal waveforms whose
the frequency is multiple of the fundamental frequency which
add to the fundamental waveform. That are « harmonics »

 To conclude, no linear loads which absorb no sinusoidal currents

which are harmonics current generators.

 Generally, all components which use “rectifier” function of the

alternative waveform with diode or thyristor bridge, generate
harmonics currents.

 In industry, the most common harmonic generator is the variable

speed drive which allows a high flexibility for the motor control.

Division - RPB – Mar07 - EN 39

Harmonics
Definitions
 Any periodic signal of frequency "f", whatever its waveform, can be
represented as the sum below:
50
s(t )  S 0   Sn 2 sin nwt  n 
n 1

with S0, DC component, generally equal to zero,

Sn, the rms value of the fundamental signal with a « n »
frequency equal to « n » times the fundamental one.

 The signal is a sum of fundamental component and harmonics

components.

Division - RPB – Mar07 - EN 40

Harmonics
Definitions

 The fundamental component : The

fundamental is the sinusoidal component of
frequency f equal to the power supply one.

 The harmonics components : The harmonic

component of « n » rank is the sinusoid with a
fn frequency equal to « n » times the f power
supply network one.

 Harmonic rank : Integer number equal to the

ratio between fn harmonic frequency and f
fundamental frequency.

Division - RPB – Mar07 - EN 41

Harmonics
Definitions
 Example :

Signal

Division - RPB – Mar07 - EN 42

Harmonics
Definitions
 It is the sum of the fundamental…

Fundamental

Only the fundamental (f=50Hz or 60Hz) provides energy

Division - RPB – Mar07 - EN 43

Harmonics
Definitions
We
We
We add
add
add H11...
H5...
H7...
Distortion
Distortion So
of thethe
of the result is... by by
fundamental
fundamental H5H5
& H7

t
t

Division - RPB – Mar07 - EN 44

Harmonics
Representations
 TEMPORAL representation

 FREQUENTIAL representation Spectrum

Harmonic spectrum in % of fundamental The spectrum of a signal is the
graph representing the amplitudes
100 of the various harmonics as a
function of their respective
50
frequencies.
0 f (ex : rank 5 = 250Hz (if f=50Hz)
1 2 3 4 5 6 7 8 9 10 11

Division - RPB – Mar07 - EN 45

Harmonics
The rms value
 The RMS VALUE of a current or a voltage, is the DC current or
voltage value which causes the same heating in a resistor (for
periodic signals).

 Mathematically, the rms value of an harmonics deformed signal is

defined by:

rms value  H1²  H2²  H3²  ...  H50²

H1 is the fundamental value
H2, H3… correspond to the rms of each harmonic component.
Example : Rms current calculation by a single phase computer load
I1=56.2A, I3=27.2A, I5=2.7A, I7=9.2A and I9=7.8A

I rms  56.2²  27.2²  2.7²  9.2²  7.8²  63.6 A

Division - RPB – Mar07 - EN 46

Harmonics
Harmonic distortion
 The TOTAL HARMONIC DISTORTION (THD) represents the
deformation of the fundamental sinusoidal signal by harmonics.

 Mathematically, current or voltage total harmonic distortion is

calculated by:

n  50
 Hn ²
n2
THD  100
H1
 This is the ratio of the rms value of the harmonics to the rms value
of the fundamental. It is a percent value (%).

 Standards define total harmonic distortion differently. The

denominator is Hrms instead of H1.

Division - RPB – Mar07 - EN 47

Harmonic generators
Generalities
 ELECTRONIC POWER EQUIPMENTS
 Variable speed drives
 Thyristor controlled equipments
 Static converters (UPS)

 Loads using electric arc

 Arc furnaces
 welding machines
 Lighting

 Equipment with magnetic circuits

 Alternators
 Transformers

Division - RPB – Mar07 - EN 48

Harmonics generators
Variable speed drive • DIAGRAM

Is
 3-phase loads
M
 Draws high harmonic currents of e1
orders 5, 7, 11, 13 e2

e3

 CURRENT DRAWN Is  HARMONIC SPECTRUM

THDI=44% 35% H5, 15% H7, 8% H11, ...
A
%
100

t
50

0
1 5 7 11 13

Division - RPB – Mar07 - EN 49

Harmonics generators
Rectifiers / chargers
 DIAGRAM
 3-phase loads
 Controlled Graëtz bridge L1 iIIs
e1
 Draws high harmonic currents of L2 C
orders 5, 7, 11, 13 e2 Z
L3
e3

 CURRENT DRAWN Is
 HARMONIC SPECTRUM
S=122KVA THDI=30%
19% H5, 11% H7, 6% H11, ...
A %
100

50
t

0
1 5 7 11 13

Division - RPB – Mar07 - EN 50

Harmonic generators
Welding machines
 Single-phase loads
 Current with a high harmonic
content
 Lasts between 20 and 50 cycles

 CURRENT DRAWN Is  HARMONIC SPECTRUM

Is=341A THDI=58% 56% H3, 9% H5, 9% H7
A
100

50
t

0
1 3 5 7 9

Division - RPB – Mar07 - EN 51

Harmonic generators
Lighting
 DIAGRAM

 Single-phase loads Ph Is
 H3 harmonic current FL

 CURRENT DRAWN Is  HARMONIC SPECTRUM

S=22KVA THDI=53% 51% H3, 11% H5, 8% H9...

A %
100

50
t

0
1 3 5 7 9

Division - RPB – Mar07 - EN 52

Harmonics effects on electric equipments
Generalities
 The most known harmonics effects are destruction of capacitor
banks or circuit-breakers due to the high harmonic level amplified
by resonances.

 They are seen on internal factory networks.

 Another effect is transformers and neutral conductors heating due

to 3rd harmonic current.

 Three main effects:

 Immediate effects are instantaneous on the equipments as for
example measure instruments of precision and TV screens,
 Short-term effects (from few seconds to few hours) are for example
circuit-breaker disconnection and dysfunction of sensible
applications,
 Long-term effects (more than few hours) are over heating of
conductors, transformers, alternators and capacitor banks.

Division - RPB – Mar07 - EN 53

Harmonics effects on electric equipments
In other words, immediate effects are…
 The disturbance of electronic systems
 Bad commutation of the thyristors because of the deformation of the
voltage waveform,
 Disturbance of the remote control systems of the energy distributors.

 Noises and vibrations

 Pulsatory torques due to the harmonic rotating field in machines
inducing vibrations.
 Electrodynamic strains inducing vibrations and noises in
electromagnetic instruments (transformer).

 Difference between potential and mass. The flow of harmonic

currents in conductors induces a voltage drop. In the case of the
TNC neutral mode, the equipment masses are not with the same
potential, which can disturb the systems of exchanges of
information.

Division - RPB – Mar07 - EN 54

Harmonics effects on electric equipments
In other words, immediate effects are…
 Iron losses and eddy current losses in transformers and
machines.

 Losses in conductors

 Harmonic resonance due to the use of capacitor banks on

the electrical network.

 Increase of total harmonic distortion on the network

 Accelerated ageing of capacitors

Division - RPB – Mar07 - EN 55

Capacitors on polluted networks
What are the problems?

 On the networks, the existence of capacitive elements can cause

series and parallel resonances with the lines reactors, the
transformers and the loads.

 The presence of resonances within an electrical supply network

involves a certain number of risks due to the harmonic
disturbances.

Division - RPB – Mar07 - EN 56

Capacitors on polluted networks
Basis concept: characteristic impedance
 Capacitor
Zh

1
Zh  
Ch

Division - RPB – Mar07 - EN 57

Capacitors on polluted networks
Basis concept: characteristic impedance
 Reactor
Zh

Zh  Lh 

Examples: transformers, motors, upstream network...

Division - RPB – Mar07 - EN 58

Capacitors on polluted networks
Basis concept: characteristic impedance
 Reactor + capacitor in series

Zh

C
LC ² h²  1 
Zh 
Ch

Examples: capacitor banks with detuned reactor or passive filter

Division - RPB – Mar07 - EN 59

Capacitors on polluted networks
Basis concept: characteristic impedance
 Reactor + capacitor in parallel

L C

L
Z  
1  LC ²

Examples: capacitor banks connected on network

Division - RPB – Mar07 - EN 60

Capacitors on polluted networks
Basis concept: characteristic impedance
 Reactor in parallel with capacitor and reactor in series

L’
L
C

Lh(1  L' C ² h²)

Zh  
1  ( L  L' )C ² h²

Examples: capacitor banks with detuned reactor connected on network

Division - RPB – Mar07 - EN 61

Capacitors on polluted networks
Basis concept: characteristic impedance
 Example

Scc Equivalent diagram (at point A)

jL

A L’
L
C
L’

R
(By neglecting R)
C

Division - RPB – Mar07 - EN 62

Capacitors on polluted networks
Basis concept: characteristic impedance
 Example

Zh
A

L’
L
C

Lh(1  L' C ² h²)

Zh 
1  ( L  L' )C ² h²   2  f
far fr
1 1
far  fr 
2    ( L' L)C 2    L' C

Division - RPB – Mar07 - EN 63

Capacitors on polluted networks
Basis concept: Resonance
 For each harmonic rank h, there is an equivalent diagram.

 For each harmonic rank you can write the following Ohm rule:

Vh  Zh  Ih
Vh is the h rank harmonic voltage
Ih is the h rank harmonic current
Zh is the h rank harmonic impedance

 If Zh is high but Ih=0 => Vh=0 no problem of resonance

 If Zh is high and Ih≠0 => Vh is high risk of resonance

Division - RPB – Mar07 - EN 64

Capacitors on polluted networks
Basis concept: Resonance
 Example 1: Compensation without harmonic currents

Ssc

Division - RPB – Mar07 - EN 65

Capacitors on polluted networks
Basic concept: Resonance
Zh

Z5=0,3Ω
Network only
Network + capacitor bank

Z5=0,06Ω

Without capacitor bank V5  Z5 I5  0,06  0  0V

Resonance but no risk
because no harmonic
With capacitor bank V5  Z5 I5  0,3  0  0V
currents

Division - RPB – Mar07 - EN 66

Capacitors on polluted networks
Basis concept: Resonance
 Example 2: Compensation with harmonic currents

Ssc

Harmonic generator (VFD)

I5=30A
I7=15A
I11=7A
I13=3A

Division - RPB – Mar07 - EN 67

Capacitors on polluted networks
Basis concept: Resonance
Zh

Z5=0,3Ω
Network only
Network + capacitor bank

30A

Z5=0,06Ω 15A
7A
3A

Without capacitor bank V5  Z5 I5  0,06  30  1,8V

Resonance on rank 5
With capacitor bank V5  Z5 I5  0,3  30  9V BAD SOLUTION

Division - RPB – Mar07 - EN 68

Capacitors on polluted networks
Basis concept: Resonance

Inside capacitor bank

High value of the RMS current => overload and big
risk of destruction.

On the network
Increasing of the pollution on the network => big
value of THD (U) and risk of disturbance of electronic
device for example.

Division - RPB – Mar07 - EN 69

Capacitors on polluted networks
Consequences of resonance

 Several consequences

 Increasing of harmonic voltage distortion on the busbar where

the capacitor bank is connected.

 Overload of the capacitor bank so big risk of destruction.

 Increasing of risk of disturbance of sensible loads (electronic

device,…).

 …

Division - RPB – Mar07 - EN 70

Capacitors on polluted networks
Important concept

 Capacitors do not generate harmonics.

 They can amplified harmonics.

Division - RPB – Mar07 - EN 71

Capacitors on polluted networks
Solutions
 To limit the emission of the harmonic currents injected by
disturbing equipment

 by limiting their power,,

 by admitting the injection of harmonics of currents of higher

frequencies.

– Examples :
• use of 12-pulse rectifier instead of 6-pulse ones,
• use of line reactor with variable speed drives,
• …

Division - RPB – Mar07 - EN 72

Capacitors on polluted networks
Solutions

 Detuned reactor

 A reactor is added in series with the capacitors to tune the unit

before the first current injection frequency.

 Generally, the unit detuned reactor + capacitors is tuned near 215

Hz. (fn=50Hz, tuning rank 4,3)

 Capacitors are thus protected against harmonic overloads.

Division - RPB – Mar07 - EN 73

Capacitors on polluted networks
Solutions
 Example 3: Compensation with harmonic currents

Ssc

Harmonic generator (VFD)

I5=30A
I7=15A
I11=7A
L
I13=3A

M C

Division - RPB – Mar07 - EN 74

Capacitors on polluted networks
Solution with detuned reactor
Network + capacitors

Network only
z
Network + detuned
reactor + capacitors

fr 250 350 550 f (Hz)

harmonic spectrum present on the network

Resonance frequency
1
fr 
2 LC

Division - RPB – Mar07 - EN 75

Capacitors on polluted networks
Solution with detuned reactor

Network only
Network + capacitor bank with detuned reactor

30A
Z5=0,06Ω
15A
7A
Z5=0,02Ω 3A

Without capacitor bank V5  Z5 I5  0,06  30  1,8V

No resonance on rank 5
With capacitor bank V5  Z5 I5  0,02  30  0,6V GOOD SOLUTION

Division - RPB – Mar07 - EN 76

Capacitors on polluted networks
Passive filtering solutions

 When detuned reactors are not enough to decrease harmonic

pollution, a filtering solution is needed.

 Principle: A short-circuit is created at an accurate frequency in

order to trap the harmonic current generated at this frequency.

Division - RPB – Mar07 - EN 77

Capacitors on polluted networks
Passive filtering solutions

HT

Transformers
HV/LV
Iharmonics

~ ~
M
= = 5 7
Harmonic generators(Gh) Harmonic filters

Division - RPB – Mar07 - EN 78

Capacitors on polluted networks
Passive filtering solutions

With filter
V5  Z5  I5  0,01 30  0,3V
V7  Z7  I7  0,0115  0,15V

30A

15A
7A
3A

1
fr 
2    LC
H5 H7
fr=250Hz fr=350Hz fr: tuning frequency of the passive
filter

Division - RPB – Mar07 - EN 79

 Capacitors on polluted networks
Active filtering solutions

 PRINCIPLE

 Active Harmonic Filter injects anti-phase harmonic current which

cancels the existing harmonic currents.

 Provides Harmonic current or reactive current or any combination of

both

100% 100% 100%

LOAD ACTIVE FILTER

1 5 7 11 13
1 5 7 11 13 1 5 7 11 13

Division - RPB – Mar07 - EN 80

Capacitors and polluted networks
Filtering solutions: Advantages and drawbacks

Passive filter Active filter

Advantages  high power  wide spectrum

 simultaneous power  easy commissionning
factor correction  flexibility

Drawbacks  study by a specialist is  high price

necessary
 filter adapted to only a
few orders of
harmonics

Division - RPB – Mar07 - EN 81

Bibliography

 Technical book n°199: Power quality

 Guide design of the industrial electrical supply networks vol 1&2

 Expert guides low tension N°6

Division - RPB – Mar07 - EN 82