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HARMONICS AND FILTERS Book Referred by : 1. HVDC Power Transmission by K.R Padiyar UNIT 4 www.eeecube.com www.eeecube.com
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HARMONICS AND FILTERS
Book Referred by :
1. HVDC Power Transmission by K.R Padiyar
UNIT 4
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INTRODUCTION
• HVDC converters introduce both AC and DC harmonics which are injected into the ACsystem .
• There are several problems associated with the injection of harmonics are listed below:
• Telephone interference
• Extra power losses and consequent heating in machines & capacitors connected in the S/Y
• Overvoltage's due to resonances
• Instability of converter controls, primarily with Individual Phase Control (IPC) scheme of firing pulse generation
• Interference with ripple control systems used in load management
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GENERATION OF HARMONICS
• Characteristics Harmonics
• Non Characteristics Harmonics
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CHARACTERISTICS HARMONICS
• The characteristic harmonics are harmonics which are always present even underideal operation - balanced AC voltages, symmetric three phase network andequidistant pulses.
• In the converter, the DC current is assumed to be constant.
• In this case, there are Harmonics in AC current of the order
ℎ = 𝑛𝑝 ± 1 -------------------------- (1)
Where, p is the pulse number
n is any integer
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• There are Harmonics in converter DC voltage of the order
ℎ = 𝑛𝑝 -------------------------- (2)
• When reactor smoothing is used then harmonics in the dc current also of the order given by equation 2
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CALCULATION OF CHARACTERISTICS AC HARMONICS
• Consider a 12 pulse converter
• From fig, Neglect over lap, waveform for 𝑖𝐴1and 𝑖𝐴2are shown
• For convenience, the ordinate axis is chosen that the waveform have even symmetry [𝜔𝑡 = 0]
• The waveform has half wave symmetry so that even harmonics are zero
• Hence we can express 𝑖𝐴1 𝑎𝑠,
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• we can express current 𝑖𝐴2 𝑎𝑠,
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• So the magnitude of the characteristics harmonics are shown below
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From the Fourier series analysis of DC voltage waveform, We can obtain
DC VOLTAGE HARMONICS
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NON CHARACTERISTICS HARMONICS
• The harmonics of the order other than the characteristic harmonics are termed as non-characteristic.
• These are due to
(i) Imbalance in the operation of two bridges forming a 12 pulse converter
(ii) Firing angle errors
(iii) Unbalance and distortion in AC voltages and
(iv) unequal transformer leakage impedances.
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• The harmonics produced due to the first cause are termed as residual harmonics.
• These mainly due to the difference in the firing angles in the two bridges which lead to unequal cancellation of the harmonics of order 5. 7, 17, 19, etc.
• The unequal leakage impedances of the two converter transformers feeding the two bridges also lead to residual harmonics.
• The last three causes can lead to the generation of triplen and even harmonics and their analysis is complex
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Effect of Firing Angle Errors
• It is convenient to neglect overlap in the analysis.
• The errors in the firing angles can be due to nature of the control system.
• The equidistant pulse control scheme ideally, has inherent errors except due to thejitter.
• To study the effect of firing angle errors, we will simplify the analysis byconsidering a single Graetz bridge fed from a star/star connected transformer,
• We consider the error 휀𝑗 as the delay in the firing of valve j from the instant
corresponding to the desired value of the firing angle
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• There is no loss of generality in assuming the firing error for valve 1 is zero as theanalysis
• applies to steady state conditions, where it is assumed that the waveform isperiodic with the
• Fundamental frequency of 𝜔. Thus, there are five independent parameters £2, £3,£4. £5, and £6
• To illustrate the analysis. we will consider an example with following data:
휀3 = 휀5 = 0,휀2 = 휀4 = 휀6 = 휀
The waveform of the phase similar to the waveform of 𝑖𝐴1,to analyze the waveform consider the sum of two waveform and the other represents the effect of firing errors
𝑖𝑎 𝑡 = 𝑖𝑎𝑜 𝑡 + ∆𝑖𝑎(𝑡)𝑖𝑏 𝑡 = 𝑖𝑏𝑜 𝑡 + ∆𝑖𝑏(𝑡)𝑖𝑐 𝑡 = 𝑖𝑐𝑜 𝑡 + ∆𝑖𝑐(𝑡)
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By Neglecting Firing angle errors. For the delta given the waveform of ∆𝑖𝑎 , ∆𝑖𝑏 and ∆𝑖𝑐
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Effect of unbalanced voltages
• The presence of the negative sequence component in the AC voltage shifts thezero crossing of the commutation voltages
• With individual phase control (IPC) system. this introduces firing angledissymmetry and results in non-characteristic harmonics.
• With a 5% negative sequence voltage, the third harmonic current generated can beas large as 5% of the fundamental component.
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DESIGN OF AC FILTERS
• The major design objective of AC filters is to reduce the telephone interference.
• This can be measured by any of the following performance indices.
Criteria of Design
Harmonic Distortion
This can be measured in two ways:
𝐼𝑛,𝑍𝑛 𝑎𝑛𝑑 𝐸1= Harmonics Current injectedwww.eeecube.com
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The second derivation is
In some cases Harmonics distortion can be defined individual for the single harmonic as
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TELEPHONE INFLUENCE FACTOR
• This is an index of possible telephone interference and is defined as
Where
𝑝𝑛 is the C message weighting used by Bell
Telephone Systems (BTS) and Edison
Electric Institute (EEI) in USA. The
weighting reflects the frequency depends
sensitivity of the human ear and has a
maximum value 1.0 at the frequency of
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Telephone Harmonic Form Factor(THFF)
• This is analogous to TIF except that
• Where 𝑊𝑛 is the psophometric weight at the harmonic order n, as defined as thecumulative commission on telephone and telegraph system(CCITT)
• While TIF is used in USA ,THFF is popular in Europe.
• The maximum values of𝑊𝑛 =1.0 at the frequency of 800Hz.
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IT product
• In BTS-EEI system, there is another index called IT product and is defined by
𝐼𝑇 = [
𝑛=1
𝑚
(𝐼𝑛𝐹𝑛)2]1/2
• KIT Product is defined as
𝐾𝐼𝑇 = 𝐼𝑇 100
• Although there are no specific standards in the performance requirements thesuggested values of the above mentioned indices are
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TYPES OF FILTER
• The are basically two types of filter used.
• They are
Passive Filter
Damped filters – Low Q Filters Tuned filters – High Q Filters
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Active Filter
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Resonant frequency
𝜔𝑟 =1
𝐿𝐶
Reactance of the Inductor or capacitor at the resonant frequency
𝑋𝑜 = 𝜔𝑟𝐿 =1
𝜔𝑟𝐶=𝐿
𝐶
• The reactance of the inductor or capacitor at the resonance frequency.
• Note that both filter become identical when R = G = 0. In this case the impedance of the filter is purely reactive becomes zero at ℎ = ℎ𝑟 ,.. where ℎ𝑟. is the order of the harmonic for which the filter is designed.
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• We express the sharpness of tuning in terms of the quality factor (Q) defined as,
𝑄 =𝑋0𝑅𝑓𝑜𝑟 𝑡ℎ𝑒 𝑡𝑢𝑛𝑒𝑑 𝑓𝑖𝑙𝑡𝑒𝑟
𝑄 =1
𝐺𝑋0for the Damped filter
Note that G is the conductance of the resistor in parallel with the inductor do the damped resistor
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Impedance of single tuned filter
• The impedance (𝑍𝑓ℎ) of the single tuned filter
at the harmonic order ‘h’ is given by
• Where 𝜔 is the fundamental frequency of which can vary with the power system operating conditions.
• A tuned is designed to filter a single harmonics.
• If ℎ𝑟𝜔 = 𝜔𝑟, then obviously
𝑍𝐹ℎ = 𝑅 =𝑋0𝑄𝑎𝑛𝑑 𝑖𝑠 𝑚𝑖𝑛𝑖𝑚𝑢𝑚.
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• It is necessary to compute the impedance of the tuned filter as a function of the detuning parameter (del) defined by,
• Considering variations in the frequency (/), inductance (L) and capacitance (C), we can express as
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• It is to be noted that ∆𝐿 can be treated as the error in setting the value of L.
• The variation in C can be due to
• error in the initial setting of C and
• the variation in C due to the temperature dependence of the dieiectric constant.
• We can express 𝑍𝑝ℎ,
• The quantity of inside the brackets in the RHS of ,
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From the above derived value RHS is equal to 2. Thus, We can finally derive
𝑍𝑝ℎ = 𝑅 + 𝑗𝑋02𝛿
= 𝑋0((𝑖𝑛𝑣)𝑄 + 𝑗2𝛿)
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IMPEDANCE OF DAMPED FILTER
• The impedance in a damped filter is not critical, hence we will ignorethe effects variations in the system frequency ,impedance andcapacitance.
• We can express the impedance of the filter as,
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• The variation in the (normalized) magnitude of the damped filter𝑍𝑝ℎ
𝑋0
as the function ofℎ𝑖
ℎ0for three different values of the quality factor Q It
is observed impedance remains practically constant at higherfrequencies.
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Design of Single tuned filter
• Single tuned filter are designed to filter out characteristics harmonics of single frequency
• The harmonics current in filter are given by
𝐼𝐹ℎ =𝐼ℎ|𝑍𝑠ℎ|
|𝑍𝑠ℎ + 𝑍𝐹ℎ|
• The harmonics voltages are given by
𝑉ℎ = 𝐼𝐹ℎ 𝑍𝐹ℎ =𝐼ℎ
|𝛾𝐹ℎ + 𝛾𝑆ℎ|=𝐼ℎ|𝛾ℎ|
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• Basic objective in designing the filter is to select the filter admittance in order to minimize voltage in the harmonics.
• They are two possible representation of system impedance in the complex plane.
• Impedance angle is limited.
• Impedance is limited both in angle and impedance
• The impedance is assumed to lie in the region shown in which R1 and R2 and 𝜃𝑚Obtained in the system characteristics.
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𝑄𝑜𝑝𝑡 =cot 𝜃𝑚 2
2𝛿𝑚
=1 + cos 𝜃𝑚2𝛿𝑚 sin 𝜃𝑚
The corresponding Harmonics voltage 𝑉ℎ is
𝑉ℎ =𝐼ℎ
|𝑌𝑓ℎ + 𝑌𝑠ℎ|
=4𝛿𝑚𝑍0𝐼ℎ1 + cos 𝜃𝑚
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Minimum Cost Tuned filter
• The cost of the reactor and the capacitor which make up the tunedfilter are dependent on their respective ratings.
• The rating of the capacitor is given by
𝑆𝑐 = (𝑉𝑐12 + 𝑉𝑐ℎ
2)𝜔1𝐶
• The rating of the reactor is given by
𝑆𝐿 = 𝐼𝑓12 + 𝐼𝑓ℎ
2 𝜔1𝐿
Where
𝐼𝑓1 =ℎ
ℎ2 − 1
𝑉1𝑍0; 𝐼𝑓ℎ = 𝑥𝐼ℎ
𝑉𝑐1 =ℎ2
ℎ2−1𝑉1 ; 𝑉𝑐ℎ = 𝑥𝐼ℎ𝑍0
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• The reactive power generated by the filter branch at the frequency is
𝑄𝑓 = 𝑉1𝐼𝑓1 =ℎ
ℎ2 − 1
𝑉12
𝑍0Eliminating 𝑍0 in the above equation and sub in the 𝑆𝑐 , 𝑆𝐿 equation we get
The cost of filter is
𝐾 = 𝐴𝑄𝑓 + 𝐵1
𝑄𝑓
Where A and B are the Constants.
When cost of filter is minimum ,so reactive power supply by the filter is at an optimum value
𝑄𝑓∗ =
𝐵
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Design of High Pass Filter
• For Harmonics frequencies of order equal to or higher than 17, acommon second order high pass filter is usually provided.
• By defining the following parameters
ℎ0𝜔1 = 1 𝐿𝐶
𝑍0 = 𝐿/𝐶
𝜎 = 𝑅 𝑍0
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• The following values can be chosen
0.5 < < 2
ℎ0 ≤ 2ℎ𝑚𝑖𝑛Where ℎ𝑚𝑖𝑛 is the smallest value of h to be handled by the filter.
The filter impedance is given by
𝑍𝑓 =𝑍0[𝜎 + 𝑗 ℎ0 ℎ . (𝜎
2 − 1 −𝜎ℎ0ℎ
2
]
1 + (𝜎ℎ0ℎ)2
The reactive power supplied by the filter is
𝑄𝑓 =ℎ0
ℎ02−1. (𝑉12
𝑍0)
If Filtering is improved If Q1
increase So choose ℎ0 is high Its
advantage then six pulse
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Protection of Filters
• The filter is exposed to an overvoltage during switching in and the magnitude.
• The overvoltage is a function of the short circuit ratio (higher with low values of SCR) and the saturation characteristics of the converter transformer.
• During switching in, the filter current (at filter frequencies) can have magnitudes ranging from 20 to 100 times the harmonic current in normal (steady-state) operation.
• The lower values are for tuned filters and higher values are applicable to high pass fillers.
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• These overcurrent must be taken into consideration in the mechanical design of reactor coils.
• When filters are disconnected, their capacitor remain charged to the voltage at the instant of switching.
• If the network frequency deviates from the nominal value, higher currents and losses will result in AC filters. li they exceed the limits, the filters have to be disconnected.
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DC FILTERS • The harmonics in the DC voltage across the converter contain both characteristic and
non-characteristic orders.
• These harmonics result in current harmonies in DC lines and cause noise in telephone circuits.
• The harmonic current generated in the line can be computed from the knowledge of harmonic voltage sources at the converters, smoothing reactor, DC filter and line parameters.
• The effectiveness of the DC filter is judged by one of the following criteria:
1. Maximum voltage TIF on DC high voltage bus
2. Maximum induced noise voltage (INV) in milli voltsfkm in a parallel test line one kilometer away from the HVDC line
3. Maximum permissible noise to ground in telephone lines close to HVDC lines.
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• The second criterion is widely used and involvesthe computation of harmonic currents and themutual impedance which depends upon factorssuch as
• Earth resistivity
• Mono polar or bipolar operation
• Grounder metallic returns.
• Typically INV of 18-20 m\/[km for mono polaroperation is allowed.
• The DC filters are also of single or double tunedtype to filter out 6th and 12th harmonics and a highpass filter for higher order harmonics.
• Computer Programmers are generally used inevaluating the performance of filters anddimensioning them.
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CARRIER FREQUENCY AND RI NOISE
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CARRIER FREQUENCY AND RI NOISE
• HVDC converter stations can produce high levels of electrical noise in the Carrier frequency band from 20 KHz to 490 KHZ.
• They also generate radio interference noise in the mega Hertz range of frequencies.
• However, converters are usually located in buildings which are effectively shielded against electromagnetic radiation.
• PLC- RI filter can be reduced and minimized the impact of noise and elimination of interference with power line carrier communication
• The attenuation requirements of the filters must above the curve shown below
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