Implement four types of threephase harmonic filters using RLC components
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Threephase harmonic filters are shunt elements that are used in power systems for decreasing voltage distortion and for power factor correction. Nonlinear elements such as power electronic converters generate harmonic currents or harmonic voltages, which are injected into the power system. The resulting distorted currents flowing through the system impedance produce harmonic voltage distortion. Harmonic filters reduce distortion by diverting harmonic currents in low impedance paths. Harmonic filters are capacitive at the fundamental frequency, so they are also used for producing reactive power required by converters and for power factor correction.
To achieve an acceptable distortion, several banks of filters of different types are connected in parallel. The most commonly used filter types are:
Bandpass filters, which are used to filter lowest order harmonics such as 5th, 7th, 11th, 13th. Bandpass filters can be tuned at a single frequency (singletuned filter) or at two frequencies (doubletuned filter).
Highpass filters, which are used to filter highorder harmonics and cover a wide range of frequencies. A special type of highpass filter, the Ctype highpass filter, is used to provide reactive power and avoid parallel resonances. It also allows filtering loworder harmonics (such as 3rd), while keeping zero losses at the fundamental frequency.
The ThreePhase Harmonic Filter is built of RLC elements. The resistance, inductance, and capacitance values are determined from the filter type and from the following parameters:
Reactive power at nominal voltage
Tuning frequencies
Quality factor. The quality factor is a measure of the sharpness of the tuning frequency. It is determined by the resistance value.
The four types of filters that can be modeled with the ThreePhase Harmonic Filter block are shown below:
The simplest filter type is the singletuned filter. The following figure gives the definition of the quality factor Q and practical formulae for computing the reactive power Q_{C} and losses (active power P). The quality factor Q of the filter is the quality factor of the reactance at the tuning frequency Q = (nX_{L})/R. The quality factor determines the bandwidth B, which is a measure of the sharpness of the tuning frequency as shown in the figure.
Tuned harmonic order  n = f_{n}/f_{1} = $$\sqrt{{X}_{C}/{X}_{L}}$$  f_{1} = fundamental frequency  
Quality factor  Q = nX_{L}/R = X_{C}/(nR)  ω = 2πf_{1} = angular frequency  
Bandwidth  B = f_{n}/Q  where  f_{n} = tuning frequency 
Reactive power at f_{1}  Q_{C} = (V^{2}/X_{C})·n^{2}/(n^{2} – 1)  n = harmonic order = (f_{n}/f_{1})  
Active power at f_{1}(losses)  P ≈ (Q_{C}/Q)·n/(n^{2} – 1)  V = nominal lineline voltage  
X_{L} = inductor reactance at  
X_{C} = capacitor reactance at 
The doubletuned filter performs the same function as two singletuned filters although it has certain advantages: its losses are much lower and the impedance magnitude at the frequency of the parallel resonance that arises between the two tuning frequencies is lower.
The doubletuned filter consists of a series LC circuit and a parallel RLC circuit. If f_{1} and f_{2} are the two tuning frequencies, both the series circuit and the parallel circuit are tuned to approximately the mean geometric frequency $${f}_{m}=\sqrt{{f}_{1}{f}_{2}}$$.
The quality factor Q of the doubletuned filter is defined as the quality factor of the parallel L, R elements at the mean frequency f_{m}: Q= R /(L · 2πf_{m}).
The highpass filter is a singletuned filter where the L and R elements are connected in parallel instead of series. This connection results in a wideband filter having an impedance at high frequencies limited by the resistance R.
The quality factor of the highpass filter is the quality factor of the parallel RL circuit at the tuning frequency: Q= R /(L · 2πf_{n}).
The Ctype highpass filter is a variation of the highpass filter, where the inductance L is replaced with a series LC circuit tuned at the fundamental frequency. At fundamental frequency, the resistance is, therefore, bypassed by the resonant LC circuit and losses are null.
The quality factor of the Ctype filter is still given by the ratio: Q =R / (L · 2πf_{n}).
The following figures give R, L, C values, and typical impedance versus frequency curves obtained for the four types of filters applied on a 60Hz network. Each filter is rated 315 kV, 49 Mvar.
SingleTuned, 315 kV, 49 Mvar, 5th Harmonic Filter; Q = 30
DoubleTuned, 315 kV, 49 Mvar, 11th and 13th Harmonics Filter; Q = 16
HighPass, 315 kV, 49 Mvar, 24th Harmonic Filter; Q = 10
CType HighPass, 315 kV, 49 Mvar, 3rd Harmonic Filter; Q = 1.75
Select one of the four filter types: Singletuned
, Doubletuned
(default), Highpass
, or Ctype highpass
.
Select the connection of the three filter branches.
 Neutral is grounded. 
 Neutral is not accessible. 
 Neutral is made accessible through a fourth connector. Default. 
 Three phases connected in delta. 
The nominal phasetophase voltage of the filter, in volts RMS (Vrms) and the nominal frequency, in hertz (Hz). Default is [315e3 60]
.
The threephase capacitive reactive power Q_{C}, in vars. Specify a positive value. Default is 49e6
.
The tuning frequency of the single frequency filter (singletuned, highpass or Ctype highpass), or the two frequencies of the doubletuned filter, in hertz (Hz). Default is [11*60 13*60]
when Type of filter is Doubletuned
and [5*60]
when Type of filter is Singletuned
, Highpass
, or Ctype highpass
.
The quality factor Q of the filter defined as explained in the above Description section. Dimensionless positive number. Default is 16
.
Select Branch voltages
to measure the three voltages across each phase of the ThreePhase Harmonic Filter block terminals. For a Y connection, these voltages are the phasetoground or phasetoneutral voltages. For a delta connection, these voltages are the phasetophase voltages.
Select Branch currents
to measure the three currents flowing through each phase of the filter. For a delta connection, these currents are the currents flowing in each branch of the delta.
Select Branch voltages and currents
to measure the three voltages and the three currents of the ThreePhase Harmonic Filter block.
Default is None
.
Place a Multimeter block in your model to display the selected measurements during the simulation. In the Available Measurements list box of the Multimeter block, the measurements are identified by a label followed by the block name.
Measurement  Label  

Branch voltages  Y(grounded) 

Y(floating) 
 
Y(neutral) 
 
Delta 
 
Branch currents  Y(grounded) 

Y(floating) 
 
Y(neutral) 
 
Delta 

The power_harmonicfilter
example illustrates the use of the ThreePhase Harmonic Filter block.