1
Course
Power Quality - 2
Ljubljana, Slovenia2013/14
Prof. dr. Igor Papič[email protected]
Harmonics – definitions
Content
1st day 2nd day 3rd day 4th day 5th day
Session 1
Introduction to Power Quality • what is PQ • economic value • responsibilities
Harmonics – definitions • calculations • non-linear loads • harmonic
sequences
Harmonics - design of power factor correction devices • resonance points • filter design
Flicker case study • calculation of
flicker spreading in radial network
• variation of network parameters
Interruptions • definitions • reliability indices • improving
reliability
Session 2
Basic terms and definitions • voltage quality • continuity of
supply • commercial
quality
Propagation of harmonics • sources • consequences • cancellation
Flicker - basic terms • voltage variation • flicker frequency • sources • flickermeter
Voltage sags – definitions • characteristics • types • causes
Consequences of inadequate power quality • voltage quality • interruptions • costs
Session 3
PQ standards • EN 50 160 • other standards • limit values
Harmonics - resonances in network • parallel
resonance • series resonance
Flicker spreading • radial network • mashed network • simulation • examples
Propagation of voltage sags • transformer
connections • equipment
sensitivity • mitigation
Modern compensation devices • active and hybrid
compensators • series and shunt
compensators
Session 4
PQ monitoring • measurements • PQ analyzers • data analyses
Harmonics case study • calculation of
frequency impedance characteristics
Flicker mitigation • system solutions
– network enforcement
• compensation
Other voltage variations • unbalance • voltage
transients • overvoltages
Conclusions • PQ improvement
and costs • definition of
optimal solutions
Power Quality, Ljubljana, 2013/14 3
2
Harmonics - definitions
– harmonics are sinusoidal voltages or currents having frequencies that are integer multiples of the frequency at which the supply system is designed to operate (fundamental frequency -50 Hz or 60 Hz)
Power Quality, Ljubljana, 2013/14 4
Harmonics - definitions
• harmonic distortion – steady-state deviation from an ideal sine wave
• harmonic distortion is caused by nonlinear loads • current is not proportional to the applied voltage
Power Quality, Ljubljana, 2013/14 5
Harmonics - definitions
• some load equipment does not draw a sinusoidal current from a perfectly sinusoidal voltage source
• the relationship between voltage and current at every instant of time is not constant, i.e., the load is non-linear
• harmonic currents flowing through the system impedance results in harmonic voltages at the load
Power Quality, Ljubljana, 2013/14 6
3
Harmonics - definitions
• current vs. voltage distortion
Power Quality, Ljubljana, 2013/14 7
Current vs. voltage distortion
• three-phase electronic load
Power Quality, Ljubljana, 2013/14 8
Current vs. voltage distortion
• three-phase electronic load –increased current
Power Quality, Ljubljana, 2013/14 9
4
Current vs. voltage distortion
• example of distorted voltage and current– supply voltage and current – Faculty of EE, Ljubljana
Power Quality, Ljubljana, 2013/14 10
Fourier series
• well established methods for circuit analysis with sinusoidal voltage and current sources
• Fourier series-framework for circuit analysis with periodic non-sinusoidal voltage and current sources– decomposition into harmonic components.– each periodic function can be expressed as a sum of
pure sine waves– frequency of each sinusoid is an integer multiple of the
fundamental frequency
Power Quality, Ljubljana, 2013/14 11
Fourier series
( )
∫
∫
∫
∑
−
−
−
∞
=
⋅⎟⎠⎞
⎜⎝⎛ ⋅⋅⋅=
⋅⎟⎠⎞
⎜⎝⎛ ⋅⋅⋅=
→=
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ ⋅⋅⋅+⎟
⎠⎞
⎜⎝⎛ ⋅⋅⋅+⋅=
2/
2/
2/
2/
2/
2/0
10
2sin)(2
2cos)(2
component dc)(2
2sin2cos21
T
Th
T
Th
T
T
hhh
dttT
htfT
b
dttT
htfT
a
dttfT
a
tT
hbtT
haatf
π
π
ππ
Power Quality, Ljubljana, 2013/14 12
5
Fourier series
( )
( ) ∑
∑
∞
=
∞
=
⎟⎠⎞
⎜⎝⎛ +⋅⋅⋅+⋅=
=
+=
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ ⋅⋅⋅+⎟
⎠⎞
⎜⎝⎛ ⋅⋅⋅+⋅=
10
22
10
2sin21
tan
2sin2cos21
hhh
h
hh
hhh
hhh
tT
hAatf
babaA
tT
hbtT
haatf
ϕπ
ϕ
ππ
Power Quality, Ljubljana, 2013/14 13
Fourier series
• odd symmetry
• even symmetry
∫ ⋅⎟⎠⎞
⎜⎝⎛ ⋅⋅⋅=
=−−=
2/
0
2sin)(4
0)()(
T
h
h
dttT
htfT
b
atftf
π
0
2cos)(4
)()(2/
0
=
⋅⎟⎠⎞
⎜⎝⎛ ⋅⋅⋅=
−=
∫h
T
h
b
dttT
htfT
a
tftf
π
Power Quality, Ljubljana, 2013/14 14
Fourier series
• odd harmonics in the system
– positive and negative half-cycles of a waveform have identical shapes
• even harmonics in the system
– something wrong– voltage fluctuation
(flicker)
Power Quality, Ljubljana, 2013/14 15
6
Fourier series
• convergence– square wave– 4. components
Power Quality, Ljubljana, 2013/14 16
Fourier series
• convergence– triangle– 2. components
Power Quality, Ljubljana, 2013/14 17
Fourier series
• decomposition of a distorted waveform into harmonic components
Power Quality, Ljubljana, 2013/14 18
7
Decomposition into harmonic components
• triangle wave
Power Quality, Ljubljana, 2013/14 19
Decomposition into harmonic components
• three-phase bridge rectifier
Power Quality, Ljubljana, 2013/14 20
Decomposition into harmonic components
• notched voltage
Power Quality, Ljubljana, 2013/14 21
8
Decomposition into harmonic components
• flat-top voltage
Power Quality, Ljubljana, 2013/14 22
Total harmonic distortion – THD
• THD – measure of the effective (rms) value of harmonic distortion (this may show high relative distortion even though the magnitude of the current may be low)
• h – order of harmonic• M – rms value of h-th harmonic
1
2
2max
M
MTHD
h
hh∑
==
Power Quality, Ljubljana, 2013/14 23
Total demand distortion – TDD
• Ih – magnitude of the individual harmonic components• IL – maximum demand load current (rms amps) at the
fundamental frequency at the point of common coupling –PCC (annual average)
• fundamental harmonic of the sample may change over time
L
h
hh
I
ITDD
∑==
max
2
2
Power Quality, Ljubljana, 2013/14 24
9
Power and distortion
• apparent power– represents required
system capacity
• active power– represents energy
consumption
rmsrms IUS ⋅=
hh
hhIUP ϕ∑∞
=
=1
cos
∑∞
=
=1
2
hhrms UU ∑
∞
=
=1
2
hhrms II
Power Quality, Ljubljana, 2013/14 25
Power and distortion
• reactive power
• distortion VA– is not a conservative
quantity
hh
hhIUQ ϕ∑∞
=
=1
sin
222 QPSD −−=
Power Quality, Ljubljana, 2013/14 26
Power factor and distortion
• displacement power factor
• true power factor
1
1
SPDPF =
S
IU
SPTPF h
hhh∑∞
=== 1
cosϕ
Power Quality, Ljubljana, 2013/14 27
10
Harmonics in balanced 3-phase system
– harmonics of order h = 3, 9, 15, 21, 27, ... are purely zero sequence
– harmonics of order h = 5, 11, 17, 23, ... are purely negative sequence
– harmonics of order h = 7, 13, 19, 25, ... are purely positive sequence
– will be harmonics of order h = 3, 9, 15, ... always compensated in delta winding of a transformer
– neutral line!
Power Quality, Ljubljana, 2013/14 28
Harmonic sequences
– 3. harmonic – zero sequence
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Harmonic sequences
– 3. harmonic – positive sequence
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Harmonic sequences
– 3. harmonic – negative sequence
Power Quality, Ljubljana, 2013/14 31
Harmonic sequences
– 5. harmonic – zero sequence
Power Quality, Ljubljana, 2013/14 32
Harmonic sequences
– 5. harmonic – positive sequence
Power Quality, Ljubljana, 2013/14 33
12
Harmonic sequences
– 5. harmonic – negative sequence
Power Quality, Ljubljana, 2013/14 34
Harmonic sequences
– 7. harmonic – zero sequence
Power Quality, Ljubljana, 2013/14 35
Harmonic sequences
– 7. harmonic – positive sequence
Power Quality, Ljubljana, 2013/14 36
13
Harmonic sequences
– 7. harmonic – negative sequence
Power Quality, Ljubljana, 2013/14 37
Propagation of harmonics
Content
1st day 2nd day 3rd day 4th day 5th day
Session 1
Introduction to Power Quality • what is PQ • economic value • responsibilities
Harmonics – definitions • calculations • non-linear loads • harmonic
sequences
Harmonics - design of power factor correction devices • resonance points • filter design
Flicker case study • calculation of
flicker spreading in radial network
• variation of network parameters
Interruptions • definitions • reliability indices • improving
reliability
Session 2
Basic terms and definitions • voltage quality • continuity of
supply • commercial
quality
Propagation of harmonics • sources • consequences • cancellation
Flicker - basic terms • voltage variation • flicker frequency • sources • flickermeter
Voltage sags – definitions • characteristics • types • causes
Consequences of inadequate power quality • voltage quality • interruptions • costs
Session 3
PQ standards • EN 50 160 • other standards • limit values
Harmonics - resonances in network • parallel
resonance • series resonance
Flicker spreading • radial network • mashed network • simulation • examples
Propagation of voltage sags • transformer
connections • equipment
sensitivity • mitigation
Modern compensation devices • active and hybrid
compensators • series and shunt
compensators
Session 4
PQ monitoring • measurements • PQ analyzers • data analyses
Harmonics case study • calculation of
frequency impedance characteristics
Flicker mitigation • system solutions
– network enforcement
• compensation
Other voltage variations • unbalance • voltage
transients • overvoltages
Conclusions • PQ improvement
and costs • definition of
optimal solutions
Power Quality, Ljubljana, 2013/14 39
14
Sources of harmonic distortion
• saturable devices – electromagnetic devices with a steel core– nonlinear magnetizing characteristics of the steel– transformers, rotating machines, non-linear reactors
• power electronics based converters– VSD, DC motor drives, electronic power supplies,
rectifiers, inverters, SVCs, HVDC transmission
• arcing devices – induction and arc furnaces, welding machines, ...– fluorescent lighting
Power Quality, Ljubljana, 2013/14 40
Sources of harmonic distortion
• transformer saturation – non-sinusoidal exciting current though less then 1% of
rated full load current – odd harmonics and triplens– due to dc component of this current even harmonics are
also possible• rotating machines
– varying magnetic field reluctance– THDV typically less then 3%
• arc furnaces – non-linear V/I characteristic of the arc – 2nd, 4th harmonic
Power Quality, Ljubljana, 2013/14 41
Sources of harmonic distortion
• arc welding – non-linear V/I characteristic of the arc
• fluorescent lighting – non-linear V/I characteristic of the arc
• power electronics– electronic power supply– battery chargers– Variable Speed Drives – VSD– DC motor drives– rectifier/inverter applications
Power Quality, Ljubljana, 2013/14 42
15
Sources of harmonic distortion
• elements of power system– transformers– compensators (resonances)
• industrial loads– power electronics– arc furnaces
• households and commercial buildings– lighting– switch mode power supplies
Power Quality, Ljubljana, 2013/14 43
Examples of nonlinear loads
• single-phase power supplies
• current and harmonic spectrum for switch mode power supply (SMPS)– triplen
harmonics
Power Quality, Ljubljana, 2013/14 44
Examples of nonlinear loads
• fluorescent lamp current and spectrum– magnetic ballast
Power Quality, Ljubljana, 2013/14 45
16
Examples of nonlinear loads
• fluorescent lamp current and spectrum– electronic ballast
Power Quality, Ljubljana, 2013/14 46
Examples of nonlinear loads
• three-phase power converters
• current and harmonic spectrum for adjustable speed drive(ASD)
Power Quality, Ljubljana, 2013/14 47
Examples of nonlinear loads
• transformer magnetizing current and harmonic spectrum
Power Quality, Ljubljana, 2013/14 48
17
Examples of nonlinear loads
• semiconductor devices– rectifiers, inverters, frequency converters– most frequent source of voltage distortion
Type of load Typical waveform Current distortion THD
Single PhasePower Supply
80 % (high 3rd)
Semiconverter
high 2nd, 3rd, 4th at partial loads
Power Quality, Ljubljana, 2013/14 49
Examples of nonlinear loads
• semiconductor devicesType of load Typical waveform Current distortion THD
6-Pulse Converter, capacitive smoothing, no series inductance
80 %
6-Pulse Converter, capacitive smoothing with series
inductance > 3%, or dc drive
40 %
AC VoltageRegulator
varies with firing angle
Power Quality, Ljubljana, 2013/14 50
Examples of nonlinear loads
• semiconductor devices
Type of load Typical waveform Current distortion THD
12-Pulse Converter
15 %
AC VoltageRegulator
varies with firing angle
Power Quality, Ljubljana, 2013/14 51
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Propagation of harmonics
• representation of a nonlinear load
Power Quality, Ljubljana, 2013/14 52
Propagation of harmonics
• harmonic sources in the network– equivalent
schemes
Power Quality, Ljubljana, 2013/14 53
Consequences of harmonic distortion
– additional losses – accelerated insulation ageing
• thermal stress – through increasing copper, iron and dielectric losses
• harmonic distortion generates high current crest factor (the ratio of peak current and RMS current)
• insulation stress – through the increase of peak voltage (voltage crest factor)
• dielectric breakdown of insulated cables
– harmless for heating bodies
Power Quality, Ljubljana, 2013/14 54
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Consequences of harmonic distortion
– motors and generators• overheating• decreased efficiency• vibrations• high-pitched noises
– interference in communication circuits
Power Quality, Ljubljana, 2013/14 55
Consequences of harmonic distortion
– high neutral currents (triplen harmonics)
Power Quality, Ljubljana, 2013/14 56
Consequences of harmonic distortion
– high neutral currents• transformer connection• neutral to earth voltages
create common mode noise problems
• circulating currents flowing in transformers
• high voltage drop at loads
• failure of neutral conductor
Power Quality, Ljubljana, 2013/14 57
20
Consequences of harmonic distortion
– resonance – reactive power compensation• capacitor or transformer failure• capacitor fuse blowing• transformer overheating at less than full load and
decreased efficiency– unstable operation of zero-crossing firing
circuits• semiconductors devices
Power Quality, Ljubljana, 2013/14 58
Consequences of harmonic distortion
– protection• nuisance tripping• fuses malfunction (both, due to higher harmonics and
spikes)• failure of ground fault relaying (due to excessive third
harmonic currents in the neutral 20-25% of the fundamental current)
– interference with power meters – induction disk W-meters
• the error can be as high as 35%• biggest error in measuring demand (no account of D)• measured demand is less than actual in particular
when THD>10% (customer pays less!?)– ...
Power Quality, Ljubljana, 2013/14 59
Harmonic cancellation
• modification of system frequency response– system impedance - resonances– reactive power compensation– detuned filters
• passive compensation– passive elements (capacitors, inductors)– resonance
Power Quality, Ljubljana, 2013/14 60
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Harmonic cancellation
• active compensation– source of harmonic current or voltage– universal solution– price
• system measures• equipment manufacturer measures
Power Quality, Ljubljana, 2013/14 61
Harmonic cancellation
– modification of system frequency response• real case• classical reactive power compensation
– load-side frequency characteristics– resonance at 5th in 7th harmonic
• compensation with detuned filters– load-side frequency characteristics– partial renovation of compensators
Power Quality, Ljubljana, 2013/14 62
Harmonic cancellation
– modification of system frequency response• real case
Power Quality, Ljubljana, 2013/14 63
22
Harmonic cancellation
– modification of system frequency response• classical reactive power compensation - load-side
frequency characteristics
Abs
(Z2)
/ Ohm
Power Quality, Ljubljana, 2013/14 64
Harmonic cancellation
– modification of system frequency response• compensation with detuned filters - load-side
frequency characteristics
Abs
(Z2)
/ O
hm
Power Quality, Ljubljana, 2013/14 65
Harmonic cancellation
– modification of system frequency response• resonance could be caused by current or voltage
harmonics, which are under “normal” operating conditions well below limit values (EN 50160)
• modification of system frequency response eliminates resonance
– eliminated amplification– no harmonic cancellation
Power Quality, Ljubljana, 2013/14 66
23
Harmonic cancellation
– passive compensation –passive filters
• resonance problem– constant short-circuit power– close to a harmonic source
• parallel and series resonance circuit
• different configurations– single-tuned filter– double-tuned filter– ...
Power Quality, Ljubljana, 2013/14 67
Harmonic cancellation
– active compensation• based on voltage sourced converter - VSC
– IGBTs– pulse width modulation - PWM
S1
S4
L1
S3
S6
S5
S2
L2L3
CUdc
+
-
Power Quality, Ljubljana, 2013/14 68
Harmonic cancellation
– active compensation• parallel connected active filter
U s
L s
Is
Lp
I L
I p
CUdc
Load
voltagesourced
converter
Power Quality, Ljubljana, 2013/14 69
24
Harmonic cancellation
– active compensation• series connected active filter
U s
L s
I s I LUp
CUdc
Load
voltagesourced
converter
Power Quality, Ljubljana, 2013/14 70
Harmonic cancellation
– active compensation• Unified Power Quality Conditioner - UPQC
U s
Ls
I s I L
U p
Load
series AF parallel AF
Power Quality, Ljubljana, 2013/14 71
Harmonic cancellation
– active compensation• hybrid filter
U s
Ls
I s
voltage sourced
converter
Lp
IL
I p
CUdc
Load
passivefilter
Power Quality, Ljubljana, 2013/14 72
25
Harmonic cancellation
– active compensation• general application
Power Quality, Ljubljana, 2013/14 73
Harmonic cancellation
– active compensation
• simulation of parallel active filter operation
Power Quality, Ljubljana, 2013/14 74
Harmonic cancellation
– active compensation• simulation of parallel hybrid filter operation
Power Quality, Ljubljana, 2013/14 75
26
Harmonic cancellation
– active compensation– no influence on system impedance– on-line adaptation– series harmonic compensation possible only with active
filter– dynamic (quick response) compensation– compensation of other disturbances
» flicker» voltage dips» unbalance
– price!!
Power Quality, Ljubljana, 2013/14 76
Harmonic cancellation
– system measures• electrical separation of disturbing loads• increased short-circuit power
– equipment manufacturer measures• compensation within devices• use of converters with efficient smoothing• use of multi-pulse converters• use of PWM with high switching frequency
Power Quality, Ljubljana, 2013/14 77
Harmonic cancellation
– equipment manufacturer measures• example of non-compensated and compensated
compact fluorescent lamp
Power Quality, Ljubljana, 2013/14 78
27
Harmonics – resonances in network
Content
1st day 2nd day 3rd day 4th day 5th day
Session 1
Introduction to Power Quality • what is PQ • economic value • responsibilities
Harmonics – definitions • calculations • non-linear loads • harmonic
sequences
Harmonics - design of power factor correction devices • resonance points • filter design
Flicker case study • calculation of
flicker spreading in radial network
• variation of network parameters
Interruptions • definitions • reliability indices • improving
reliability
Session 2
Basic terms and definitions • voltage quality • continuity of
supply • commercial
quality
Propagation of harmonics • sources • consequences • cancellation
Flicker - basic terms • voltage variation • flicker frequency • sources • flickermeter
Voltage sags – definitions • characteristics • types • causes
Consequences of inadequate power quality • voltage quality • interruptions • costs
Session 3
PQ standards • EN 50 160 • other standards • limit values
Harmonics - resonances in network • parallel
resonance • series resonance
Flicker spreading • radial network • mashed network • simulation • examples
Propagation of voltage sags • transformer
connections • equipment
sensitivity • mitigation
Modern compensation devices • active and hybrid
compensators • series and shunt
compensators
Session 4
PQ monitoring • measurements • PQ analyzers • data analyses
Harmonics case study • calculation of
frequency impedance characteristics
Flicker mitigation • system solutions
– network enforcement
• compensation
Other voltage variations • unbalance • voltage
transients • overvoltages
Conclusions • PQ improvement
and costs • definition of
optimal solutions
Power Quality, Ljubljana, 2013/14 80
Resonances in network
• possible resonance between reactive power compensator and network impedance– series resonance– parallel resonance
• procedure of determination of potential resonance problems– resonance frequencies close to characteristic harmonics– actual presence of harmonics
• analysis of two practical cases
Power Quality, Ljubljana, 2013/14 81
28
Resonances in network
• frequency impedance characteristics– possible resonance – connection of capacitance
(capacitor banks) and inductance (lines, transformers,...)
CfCX
LfLX
C
L
πω
πω
211
2
==
==
Power Quality, Ljubljana, 2013/14 82
Resonances in network
• frequency impedance characteristics– resonance – inductive reactance equals capacitive
reactance
CfLf
LCf
CL
XX
rr
r
CL
ππ
πωω
212
211
=
=⇒=
=
Power Quality, Ljubljana, 2013/14 83
Resonances in network
• frequency impedance characteristics– series resonance
• series connection of capacitor and inductor
∞→→
=→
→→
+=
)()(
0)(2
12)(
rr
r
ffjXUffI
ffjXCfj
LfjfjXπ
π
U
I
L
C
Power Quality, Ljubljana, 2013/14 84
29
Resonances in network
• frequency impedance characteristics– parallel resonance
• parallel connection of capacitor and inductor
∞→→
=→
→→
+=
)()(
0)(
22
1)(
rr
r
ffjBIffU
ffjB
CfjLfj
fjB ππ
UI L C
Power Quality, Ljubljana, 2013/14 85
Resonances in network – case 1
• frequency impedance characteristics– example of supply network
Power Quality, Ljubljana, 2013/14 86
Resonances in network – case 1
• frequency impedance characteristics– example of supply network – equivalent circuit
Power Quality, Ljubljana, 2013/14 87
30
Resonances in network – case 1
• frequency impedance characteristics– voltage harmonic source is on the network side
Power Quality, Ljubljana, 2013/14 88
Resonances in network – case 1
• frequency impedance characteristics– voltage harmonic source is on the network side
• impedance from the network side• series resonance
)(Z1
)(Z1
1)(Z)(Z)(Z1
ωω
ωωω
jj
jjj
CL
TRSC+
++=
Power Quality, Ljubljana, 2013/14 89
Resonances in network – case 1
• frequency impedance characteristics– harmonic source
is on the network side
• impedance characteristics as a function of frequency
Power Quality, Ljubljana, 2013/14 90
31
Resonances in network – case 1
• frequency impedance characteristics– harmonic source
is on the network side
• impedance characteristics as a function of number of used compensation stages
Power Quality, Ljubljana, 2013/14 91
Resonances in network – case 1
• frequency impedance characteristics– current harmonic source is on the load side
Power Quality, Ljubljana, 2013/14 92
Resonances in network – case 1
• frequency impedance characteristics– current harmonic source is on the load side
• impedance from the load side• parallel resonance
)(Z)(Z1
)(Z1
)(Z1
1)(Z2
ωωωω
ω
jjjj
j
TRSCCL +++
=
Power Quality, Ljubljana, 2013/14 93
32
Resonances in network – case 1
• frequency impedance characteristics– harmonic source
is on the load side
• impedance characteristics as a function of frequency
Power Quality, Ljubljana, 2013/14 94
Resonances in network – case 1
• frequency impedance characteristics– harmonic source
is on the load side
• impedance characteristics as a function of number of used compensation stages
Power Quality, Ljubljana, 2013/14 95
Resonances in network – case 1
• frequency impedance characteristics– example of supply network – conclusions based on
performed analysis• possible series resonance at 11th harmonic if 4, 5 or 6
compensation stages are used • possible series resonance at 13th harmonic if 3, 4 or 5
compensation stages are used • possible parallel resonance at 11th harmonic if 5
compensation stages are used • possible parallel resonance at 13th harmonic if 3
compensation stages are used
Power Quality, Ljubljana, 2013/14 96
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Resonances in network – case 2
– frequency impedance characteristics• real case 2
Power Quality, Ljubljana, 2013/14 97
Resonances in network – case 2
– frequency impedance characteristics• classical reactive power compensation• network-side equivalent circuit
Power Quality, Ljubljana, 2013/14 98
Resonances in network – case 2
– frequency impedance characteristics• classical reactive power compensation• network-side frequency characteristics
Power Quality, Ljubljana, 2013/14 99
34
Resonances in network – case 2
– frequency impedance characteristics• classical reactive power compensation• load-side equivalent circuit
Power Quality, Ljubljana, 2013/14 100
Resonances in network – case 2
– frequency impedance characteristics• classical reactive power compensation• load-side frequency characteristics
Abs
(Z2)
/ Ohm
Power Quality, Ljubljana, 2013/14 101
Resonances in network – case 2
– frequency impedance characteristics• problem
– resonance at 5th and 7th harmonic– renovation of first 4 stages (K1, K2, K3 and K4)
• solution– renovated stages as detuned filters– solution for operation with 2 old stages – classical
compensators (K5 in K6)
Power Quality, Ljubljana, 2013/14 102
35
Resonances in network – case 2
– frequency impedance characteristics• compensation with detuned filters• network-side frequency characteristics
Power Quality, Ljubljana, 2013/14 103
Resonances in network – case 2
– frequency impedance characteristics• compensation with detuned filters• load-side frequency characteristics
Abs
(Z2)
/ O
hm
Power Quality, Ljubljana, 2013/14 104
Resonances in network – case 2
– frequency impedance characteristics• measurements results
• determination of harmonic sources– harmonic current vector method– network and load side
Power Quality, Ljubljana, 2013/14 105
36
Resonances in network – case 2
– frequency impedance characteristics• simulation results
– classical reactive power compensation– 5th harmonic
Power Quality, Ljubljana, 2013/14 106
Resonances in network – case 2
– frequency impedance characteristics• simulation results
– compensation with detuned filters– 5th harmonic
Power Quality, Ljubljana, 2013/14 107
Harmonics case study
37
Content
1st day 2nd day 3rd day 4th day 5th day
Session 1
Introduction to Power Quality • what is PQ • economic value • responsibilities
Harmonics – definitions • calculations • non-linear loads • harmonic
sequences
Harmonics - design of power factor correction devices • resonance points • filter design
Flicker case study • calculation of
flicker spreading in radial network
• variation of network parameters
Interruptions • definitions • reliability indices • improving
reliability
Session 2
Basic terms and definitions • voltage quality • continuity of
supply • commercial
quality
Propagation of harmonics • sources • consequences • cancellation
Flicker - basic terms • voltage variation • flicker frequency • sources • flickermeter
Voltage sags – definitions • characteristics • types • causes
Consequences of inadequate power quality • voltage quality • interruptions • costs
Session 3
PQ standards • EN 50 160 • other standards • limit values
Harmonics - resonances in network • parallel
resonance • series resonance
Flicker spreading • radial network • mashed network • simulation • examples
Propagation of voltage sags • transformer
connections • equipment
sensitivity • mitigation
Modern compensation devices • active and hybrid
compensators • series and shunt
compensators
Session 4
PQ monitoring • measurements • PQ analyzers • data analyses
Harmonics case study • calculation of
frequency impedance characteristics
Flicker mitigation • system solutions
– network enforcement
• compensation
Other voltage variations • unbalance • voltage
transients • overvoltages
Conclusions • PQ improvement
and costs • definition of
optimal solutions
Power Quality, Ljubljana, 2013/14 109
Case study – frequency response
• frequency impedance characteristics– example of supply network
Power Quality, Ljubljana, 2013/14 110
Case study – frequency response
• frequency impedance characteristics– example of supply network – data for calculation
• network equivalent– short-circuit power
– rated voltage
– ratio R/X
MVA 80=scS
kV 20=MVU
10/1)/( =SCXR
Power Quality, Ljubljana, 2013/14 111
38
Case study – frequency response
• frequency impedance characteristics– example of supply network – data for calculation
• 2 x transformer 20/0,4 kV– short-circuit voltage
– rated power
– rated voltage
– ratio R/X
% 13,4=scu
kV 4,0kV; 20 == LVMV UU
4/1)/( =TRXR
MVA 63,0 x 2=nS
Power Quality, Ljubljana, 2013/14 112
Case study – frequency response
• frequency impedance characteristics– example of supply network – data for calculation
• load– rated voltage
– active power
– reactive power
kV 4,0=LVU
MW 54,0=LP
MVAr 46,0=LQ
Power Quality, Ljubljana, 2013/14 113
Case study – frequency response
• frequency impedance characteristics– example of supply network – data for calculation
• compensator– rated voltage
– reactive power
– ratio R/X
MVAr 40,0=CQ
kV 4,0=LVU
50/1)/( =CXR
Power Quality, Ljubljana, 2013/14 114
39
Case study – frequency response
• frequency impedance characteristics– example of supply network – equivalent circuit
Power Quality, Ljubljana, 2013/14 115
Case study – frequency response
• frequency impedance characteristics– example of supply network – calculation of parameters in
equivalent circuit (the same voltage level ULV)• network equivalent
SCSCSC
SC
SC
sc
LVSC
SCsc
LVSC
LfjRfjZXR
XRSUR
XRSUL
ππ
π
2)2(
m 199,0)/(1
)/(
μH 33,6)/(1
1100
2
2
2
2
+=
Ω=+
=
=+
=
Power Quality, Ljubljana, 2013/14 116
Case study – frequency response
• frequency impedance characteristics– example of supply network – calculation of parameters in
equivalent circuit (the same voltage level ULV)• transformer
TRTRTR
TR
TRsc
n
NNTR
TR
sc
n
LVTR
LfjRfjZXR
XRuSUR
XR
uS
UL
ππ
π
2)2(
m 27,1)/(1
)/(100
μH 2,16)/(1
1100100
2
2
2
2
+=
Ω=+
=
=+
=
Power Quality, Ljubljana, 2013/14 117
40
Case study – frequency response
• frequency impedance characteristics– example of supply network – calculation of parameters in
equivalent circuit (the same voltage level ULV)• load
LLL
LL
LVLL
LL
LVLL
LfjRfjZQP
UPR
QPUQL
ππ
π
2)2(
m 172
mH 466,0502
1
22
2
22
2
+=
Ω=+
=
=+
=
Power Quality, Ljubljana, 2013/14 118
Case study – frequency response
• frequency impedance characteristics– example of supply network – calculation of parameters in
equivalent circuit (the same voltage level ULV)• compensator
CC
CCC
C
C
C
LVC
CLV
CC
CfjR
CfjRfjZ
XR
XRQUR
XRU
QC
πππ
π
221)2(
m 8)/(1
)/(
mF 96,7)/(1100
2
2
22
−=+=
Ω=+
=
=+=
Power Quality, Ljubljana, 2013/14 119
Case study – frequency response
• frequency impedance characteristics– voltage harmonic source is on the network side
Power Quality, Ljubljana, 2013/14 120
41
Case study – frequency response
• frequency impedance characteristics– harmonic source is on the network side
• impedance from the network side• series resonance
)2(Z)(Z valueabsolute
)(Z1
)(Z1
1)(Z)(Z)(Z
11
1
fjj
jj
jjj
CL
TRSC
πω
ωω
ωωω
=→
+++=
Power Quality, Ljubljana, 2013/14 121
Case study – frequency response
• frequency impedance characteristics– harmonic source
is on the network side
• impedance characteristics as a function of frequency
Power Quality, Ljubljana, 2013/14 122
Case study – frequency response
• frequency impedance characteristics– current harmonic source is on the load side
Power Quality, Ljubljana, 2013/14 123
42
Case study – frequency response
• frequency impedance characteristics– harmonic source is on the load side
• impedance from the load side• parallel resonance
)2(Z)(Z valueabsolute
)(Z)(Z1
)(Z1
)(Z1
1)(Z
22
2
fjj
jjjj
j
TRSCCL
πω
ωωωω
ω
=→
+++
=
Power Quality, Ljubljana, 2013/14 124
Case study – frequency response
• frequency impedance characteristics– harmonic source
is on the load side
• impedance characteristics as a function of frequency
Power Quality, Ljubljana, 2013/14 125