Harmonic Analysis
Types of Power Quality Problems
Waveform Distortion • Primary Types of Waveform Distortion – DC Offset – Harmonics – Interharmonics – Notching – Noise
Harmonics • One special category of power quality problems • “Harmo “Harmonic nics s are voltag voltages es and/or and/or curren currents ts present in an electrical system at some multiple of the fundamental frequency.” (IEEE Std 399, Brown Book)
Nonlinear Loads • Sinusoidal voltage applied to a simple nonlinear resistor • Increasing the voltage by a few percent may cause current to double
Fourier Representation • Any periodic waveform can be expressed as a sum of sinusoids • The sum of the sinusoids is referred to as Fourier Series (6-pulse) 2 3
I ac
I h cos(h t h
1
1
I d (cos t
5 h
)
cos3
t
1 7
cos 7
t
1 11
cos11
t
1 13
cos13
t
Harmonic Sources • Utilities (Power Grid) – Known as “Background Harmonic” – Pollution from other irresponsible customers – SVC, HVDC, FACTS, … – Usually a voltage source
• Synchronous Generators – Due to Pitch (can be eliminated by fractionalpitch winding) and Saturation – Usually a voltage source
Harmonic Sources (cont’d) • Transformers – Due to magnetizing branch saturation – Only at lightly loaded condition – Usually a current source
• Power Electronic Devices – Charger, Converter, Inverter, UPS, VFD, SVC, HVDC, FACTS, … – Due to switching actions – Either a voltage source or a current source
Harmonic Sources (cont’d) • Other Non-Linear Loads – Arc furnaces, discharge lighting, … – Due to unstable and non-linear process – Either a voltage source or a current source
• In general, any load that is applied to a power system that requires other than a sinusoidal current
Harmonic I and V
Classification of Harmonics • Harmonics may be classified as: – Characteristic Harmonics
Generally produced by power converters
– Non-Characteristic Harmonics
Typically produced by arc furnaces and discharge lighting (from non-periodical waveforms)
Phase Angle Relationship • Fundamental Frequency
Phase Angle Relationship • Third Order
Phase Angle Relationship • Fifth Order
• Seventh Order
Order vs. Sequence
Characteristic Harmonics
Characteristic Harmonics (cont’d)
Harmonic Spectrum
Harmonic-Related Problems • Motors and Generators – Increased heating due to iron and copper losses – Reduced efficiency and torque – Higher audible noise – Cogging or crawling – Mechanical oscillations
Harmonic-Related Problems (cont’d) • Transformers – Parasitic heating – Increased copper, stray flux and iron losses
• Capacitors (var compensators) – Possibility of system resonance – Increased heating and voltage stress – Shortened capacitor life
Harmonic-Related Problems (cont’d) • Power Cables – Involved in system resonance – Voltage stress and corona leading to dielectric failure – Heating and derating
• Neutrals of four-wire systems (480/277V; 120/208V) – Overheating
• Fuses – Blowing
Harmonic-Related Problems (cont’d) • Switchgears – Increased heating and losses – Reduced steady-state current carrying capability – Shortened insulation components life • Relays – Possibility of misoperation • Metering – Affected readings
Harmonic-Related Problems (cont’d) • Communication Systems – Interference by higher frequency electromagnetic field
• Electronic Equipment (computers, PLC) – Misoperation
• System – Resonance (serial and parallel) – Poor power factor
Parallel Resonance • Total impedance at resonance frequency increases • High circulating current will flow in the capacitance-inductance loop
Parallel Resonance
Capacitor Banks
Capacitor Banks
Capacitor Banks
Say, Seventh Harmonic Current = 5% of 1100A = 55 A
Capacitor Banks
Resistance = 1% including cable and transformer CAF = X/R = 7*0.0069/0.0012 =40.25 Resonant Current = 55*40.25 = 2214 A
Parallel Resonance (cont’d) Cause:
Source inductance resonates with capacitor bank at a frequency excited by the facilities harmonic sources
Impacts: 1. Excessive capacitor fuse operation 2. Capacitor failures 3. Incorrect relay tripping 4. Telephone interference 5. Overheating of equipment
Harmonic Distortion Measurements • Total Harmonic Distortion (THD) – Also known as Harmonic Distortion Factor (HDF), is the most popular index to measure the level of harmonic distortion to voltage and current – Ratio of the RMS of all harmonics to the fundamental component – For an ideal system THD = 0% – Potential heating value of the harmonics relative to the fundamental
Harmonic Distortion Measurements (cont’d) – Good indicator of additional losses due to current flowing through a conductor – Not a good indicator of voltage stress in a capacitor (related to peak value of voltage waveform, not its heating value) F i TH D
2
2
F 1
Where F i is the amplitude of the i th harmonic, and F 1 is that for the fundamental component.
Harmonic Distortion Example Find THD for this waveform
Harmonic Example • Find THD for this Harmonic Spectrum
Adjustable Speed Drive – Current Distortion
Adjustable Speed Drive – Voltage Distortion
Harmonic Distortion Measurements (cont’d) • Individual Harmonic Distortion (IHD) - Ratio of a given harmonic to fundamental - To track magnitude of individual harmonic I H D
F i F 1
• Root Mean Square (RMS) - Total - Root Mean Square of fundamental plus all harmonics - Equal to fundamental RMS if Harmonics are zero RM S
F i 1
2
Harmonic Distortion Measurements (cont’d) • Arithmetic Summation (ASUM) – Arithmetic summation of magnitudes of all components (fundamental and all harmonics) – Directly adds magnitudes of all components to estimate crest value of voltage and current – Evaluation of the maximum withstanding ratings of a device ASUM
F i 1
Harmonic Distortion Measurements (cont’d) • Telephone Influence Factor (TIF) – Weighted THD – Weights based on interference to an audio signal in the same frequency range – Current TIF shows impact on adjacent communication systems 2
W i F i T I F
1 2
F i 1
Harmonic Distortion Measurements (cont’d) • I*T Product (I*T) – A product current components (fundamental
and harmonics) and weighting factors H
I
( I h
T h
where
T h )
2
1
= current component T h= weighting factor h = harmonic order (h=1 for fundamental) H = maximum harmonic order to account
I h
Triplen Harmonics • Odd multiples of the third harmonic (h = 3, 9, 15, 21, …) • Important issue for grounded-wye systems with neutral current • Overloading and TIF problems • Misoperation of devices due to presence of harmonics on the neutral
Triplen Harmonics
Winding Connections •
Delta winding provides ampere turn balance
•
Triplen Harmonics cannot flow
•
When currents are balanced Triplens behave as Zero Sequence currents
•
Used in Utility Distribution Substations
•
Delta winding connected to Transmission
•
Balanced Triplens can flow
•
Present in equal proportions on both sides
•
Many loads are served in this fashion
Implications • Neutral connections are susceptible to overheating when serving single-phase loads on the Y side that have high 3rd Harmonic • Measuring current on delta side will not show the triplens and therefore do not give a true idea of the heating the transformer is subjected to • The flow of triplens can be interrupted by appropriate isolation transformer connection • Removing the neutral connection in one or both Y windings blocks the flow of Triplen harmonic current • Three legged core transformers behave as if they have a “phantom” delta tertiary winding
Modeling in Harmonic Analysis • Motors and Machines – Represented by their equivalent negative sequence reactance
• Lines and Cables – Series impedance for low frequencies – Long line correction including transposition and distributed capacitance
Modeling in Harmonic Analysis (cont’d) • Transformers – Leakage impedance – Magnetizing impedance
• Loads – Static loads reduce peak resonant impedance – Motor loads shift resonant frequency due to motor inductance
Reducing System Harmonics • Add Passive Filters – Shunt or Single Tuned Filters – Broadband Filters or Band Pass Filters – Provide low impedance path for harmonic current – Least expensive
Reducing System Harmonics (cont’d) • Increase Pulse Numbers – Increasing pulse number of convert circuits – Limited by practical control problems
Reducing System Harmonics (cont’d) • Apply Transformer Phase Shifting – Using Phase Shifting Transformers – Achieve higher pulse operation of the total converter installation
• In ETAP – Phase shift is specified in the tab page of the transformer editor
Reducing System Harmonics (cont’d) • Either standard phase shift or special phase shift can be used
Reducing System Harmonics (cont’d) • Add Active Filters – Instantly adapts to changing source and load conditions – Costly – MVA Limitation
Voltage Distortion Limits Recommended Practices for Utilities (IEEE 519): Bus Voltage Individual Total Voltage Distortion
Distortion
(%)
THD (%)
69 kV and below
3.0
5.0
69.001 kV through 161kV
1.5
2.5
161.001 and above
1.0
1.5
At PCC
In ETAP: Specify Harmonic Distortion Limits in Harmonic Page of Bus Editor:
