Triple Take Holographics Dinesh Padiyar Aberrations in Holography ISDH 2012
HARMONICS AND FILTERS - · PDF fileHARMONICS AND FILTERS Book Referred by : 1. HVDC Power...
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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
โข HVDC converters introduce both AC and DC harmonics which are injected into the ACsystem .
โข There are several problems associated with the injection of harmonics are listed below:
โข Telephone interference
โข Extra power losses and consequent heating in machines & capacitors connected in the S/Y
โข Overvoltage's due to resonances
โข Instability of converter controls, primarily with Individual Phase Control (IPC) scheme of firing pulse generation
โข Interference with ripple control systems used in load management
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GENERATION OF HARMONICS
โข Characteristics Harmonics
โข Non Characteristics Harmonics
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CHARACTERISTICS HARMONICS
โข The characteristic harmonics are harmonics which are always present even underideal operation - balanced AC voltages, symmetric three phase network andequidistant pulses.
โข In the converter, the DC current is assumed to be constant.
โข In this case, there are Harmonics in AC current of the order
โ = ๐๐ ยฑ 1 -------------------------- (1)
Where, p is the pulse number
n is any integer
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โข There are Harmonics in converter DC voltage of the order
โ = ๐๐ -------------------------- (2)
โข 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
โข Consider a 12 pulse converter
โข From fig, Neglect over lap, waveform for ๐๐ด1and ๐๐ด2are shown
โข For convenience, the ordinate axis is chosen that the waveform have even symmetry [๐๐ก = 0]
โข The waveform has half wave symmetry so that even harmonics are zero
โข Hence we can express ๐๐ด1 ๐๐ ,
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โข we can express current ๐๐ด2 ๐๐ ,
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โข 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
โข The harmonics of the order other than the characteristic harmonics are termed as non-characteristic.
โข 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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โข The harmonics produced due to the first cause are termed as residual harmonics.
โข 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.
โข The unequal leakage impedances of the two converter transformers feeding the two bridges also lead to residual harmonics.
โข 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
โข It is convenient to neglect overlap in the analysis.
โข The errors in the firing angles can be due to nature of the control system.
โข The equidistant pulse control scheme ideally, has inherent errors except due to thejitter.
โข 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,
โข We consider the error ํ๐ 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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โข There is no loss of generality in assuming the firing error for valve 1 is zero as theanalysis
โข applies to steady state conditions, where it is assumed that the waveform isperiodic with the
โข Fundamental frequency of ๐. Thus, there are five independent parameters ยฃ2, ยฃ3,ยฃ4. ยฃ5, and ยฃ6
โข To illustrate the analysis. we will consider an example with following data:
ํ3 = ํ5 = 0,ํ2 = ํ4 = ํ6 = ํ
The waveform of the phase similar to the waveform of ๐๐ด1,to analyze the waveform consider the sum of two waveform and the other represents the effect of firing errors
๐๐ ๐ก = ๐๐๐ ๐ก + โ๐๐(๐ก)๐๐ ๐ก = ๐๐๐ ๐ก + โ๐๐(๐ก)๐๐ ๐ก = ๐๐๐ ๐ก + โ๐๐(๐ก)
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By Neglecting Firing angle errors. For the delta given the waveform of โ๐๐ , โ๐๐ and โ๐๐
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Effect of unbalanced voltages
โข The presence of the negative sequence component in the AC voltage shifts thezero crossing of the commutation voltages
โข With individual phase control (IPC) system. this introduces firing angledissymmetry and results in non-characteristic harmonics.
โข 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
โข The major design objective of AC filters is to reduce the telephone interference.
โข This can be measured by any of the following performance indices.
Criteria of Design
Harmonic Distortion
This can be measured in two ways:
๐ผ๐,๐๐ ๐๐๐ ๐ธ1= 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
โข This is an index of possible telephone interference and is defined as
Where
๐๐ 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)
โข This is analogous to TIF except that
โข Where ๐๐ is the psophometric weight at the harmonic order n, as defined as thecumulative commission on telephone and telegraph system(CCITT)
โข While TIF is used in USA ,THFF is popular in Europe.
โข The maximum values of๐๐ =1.0 at the frequency of 800Hz.
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IT product
โข In BTS-EEI system, there is another index called IT product and is defined by
๐ผ๐ = [
๐=1
๐
(๐ผ๐๐น๐)2]1/2
โข KIT Product is defined as
๐พ๐ผ๐ = ๐ผ๐ 100
โข 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
โข The are basically two types of filter used.
โข They are
Passive Filter
Damped filters โ Low Q Filters Tuned filters โ High Q Filters
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Active Filter
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Resonant frequency
๐๐ =1
๐ฟ๐ถ
Reactance of the Inductor or capacitor at the resonant frequency
๐๐ = ๐๐๐ฟ =1
๐๐๐ถ=๐ฟ
๐ถ
โข The reactance of the inductor or capacitor at the resonance frequency.
โข Note that both filter become identical when R = G = 0. In this case the impedance of the filter is purely reactive becomes zero at โ = โ๐ ,.. where โ๐. is the order of the harmonic for which the filter is designed.
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โข We express the sharpness of tuning in terms of the quality factor (Q) defined as,
๐ =๐0๐ ๐๐๐ ๐กโ๐ ๐ก๐ข๐๐๐ ๐๐๐๐ก๐๐
๐ =1
๐บ๐0for 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
โข The impedance (๐๐โ) of the single tuned filter
at the harmonic order โhโ is given by
โข Where ๐ is the fundamental frequency of which can vary with the power system operating conditions.
โข A tuned is designed to filter a single harmonics.
โข If โ๐๐ = ๐๐, then obviously
๐๐นโ = ๐ =๐0๐๐๐๐ ๐๐ ๐๐๐๐๐๐ข๐.
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โข It is necessary to compute the impedance of the tuned filter as a function of the detuning parameter (del) defined by,
โข Considering variations in the frequency (/), inductance (L) and capacitance (C), we can express as
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โข It is to be noted that โ๐ฟ can be treated as the error in setting the value of L.
โข The variation in C can be due to
โข error in the initial setting of C and
โข the variation in C due to the temperature dependence of the dieiectric constant.
โข We can express ๐๐โ,
โข 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
๐๐โ = ๐ + ๐๐02๐ฟ
= ๐0((๐๐๐ฃ)๐ + ๐2๐ฟ)
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IMPEDANCE OF DAMPED FILTER
โข The impedance in a damped filter is not critical, hence we will ignorethe effects variations in the system frequency ,impedance andcapacitance.
โข We can express the impedance of the filter as,
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โข The variation in the (normalized) magnitude of the damped filter๐๐โ
๐0
as the function ofโ๐
โ0for 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
โข Single tuned filter are designed to filter out characteristics harmonics of single frequency
โข The harmonics current in filter are given by
๐ผ๐นโ =๐ผโ|๐๐ โ|
|๐๐ โ + ๐๐นโ|
โข The harmonics voltages are given by
๐โ = ๐ผ๐นโ ๐๐นโ =๐ผโ
|๐พ๐นโ + ๐พ๐โ|=๐ผโ|๐พโ|
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โข Basic objective in designing the filter is to select the filter admittance in order to minimize voltage in the harmonics.
โข They are two possible representation of system impedance in the complex plane.
โข Impedance angle is limited.
โข Impedance is limited both in angle and impedance
โข The impedance is assumed to lie in the region shown in which R1 and R2 and ๐๐Obtained in the system characteristics.
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๐๐๐๐ก =cot ๐๐ 2
2๐ฟ๐
=1 + cos ๐๐2๐ฟ๐ sin ๐๐
The corresponding Harmonics voltage ๐โ is
๐โ =๐ผโ
|๐๐โ + ๐๐ โ|
=4๐ฟ๐๐0๐ผโ1 + cos ๐๐
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Minimum Cost Tuned filter
โข The cost of the reactor and the capacitor which make up the tunedfilter are dependent on their respective ratings.
โข The rating of the capacitor is given by
๐๐ = (๐๐12 + ๐๐โ
2)๐1๐ถ
โข The rating of the reactor is given by
๐๐ฟ = ๐ผ๐12 + ๐ผ๐โ
2 ๐1๐ฟ
Where
๐ผ๐1 =โ
โ2 โ 1
๐1๐0; ๐ผ๐โ = ๐ฅ๐ผโ
๐๐1 =โ2
โ2โ1๐1 ; ๐๐โ = ๐ฅ๐ผโ๐0
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โข The reactive power generated by the filter branch at the frequency is
๐๐ = ๐1๐ผ๐1 =โ
โ2 โ 1
๐12
๐0Eliminating ๐0 in the above equation and sub in the ๐๐ , ๐๐ฟ equation we get
The cost of filter is
๐พ = ๐ด๐๐ + ๐ต1
๐๐
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
๐๐โ =
๐ต
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Design of High Pass Filter
โข For Harmonics frequencies of order equal to or higher than 17, acommon second order high pass filter is usually provided.
โข By defining the following parameters
โ0๐1 = 1 ๐ฟ๐ถ
๐0 = ๐ฟ/๐ถ
๐ = ๐ ๐0
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โข The following values can be chosen
0.5 < < 2
โ0 โค 2โ๐๐๐Where โ๐๐๐ is the smallest value of h to be handled by the filter.
The filter impedance is given by
๐๐ =๐0[๐ + ๐ โ0 โ . (๐
2 โ 1 โ๐โ0โ
2
]
1 + (๐โ0โ)2
The reactive power supplied by the filter is
๐๐ =โ0
โ02โ1. (๐12
๐0)
If Filtering is improved If Q1
increase So choose โ0 is high Its
advantage then six pulse
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Protection of Filters
โข The filter is exposed to an overvoltage during switching in and the magnitude.
โข The overvoltage is a function of the short circuit ratio (higher with low values of SCR) and the saturation characteristics of the converter transformer.
โข 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.
โข The lower values are for tuned filters and higher values are applicable to high pass fillers.
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โข These overcurrent must be taken into consideration in the mechanical design of reactor coils.
โข When filters are disconnected, their capacitor remain charged to the voltage at the instant of switching.
โข 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 โข The harmonics in the DC voltage across the converter contain both characteristic and
non-characteristic orders.
โข These harmonics result in current harmonies in DC lines and cause noise in telephone circuits.
โข 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.
โข 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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โข The second criterion is widely used and involvesthe computation of harmonic currents and themutual impedance which depends upon factorssuch as
โข Earth resistivity
โข Mono polar or bipolar operation
โข Grounder metallic returns.
โข Typically INV of 18-20 m\/[km for mono polaroperation is allowed.
โข 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.
โข 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
โข HVDC converter stations can produce high levels of electrical noise in the Carrier frequency band from 20 KHz to 490 KHZ.
โข They also generate radio interference noise in the mega Hertz range of frequencies.
โข However, converters are usually located in buildings which are effectively shielded against electromagnetic radiation.
โข PLC- RI filter can be reduced and minimized the impact of noise and elimination of interference with power line carrier communication
โข The attenuation requirements of the filters must above the curve shown below
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