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Implement four types of three-phase harmonic filters using RLC components
Three-phase 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 power system. The resulting distorted currents flowing through system impedance produce harmonic voltage distortion. Harmonic filters reduce distortion by diverting harmonic currents in low impedance paths. Harmonic filters are designed to be capacitive at fundamental frequency, so that they are also used for producing reactive power required by converters and for power factor correction.
In order to achieve an acceptable distortion, several banks of filters of different types are usually connected in parallel. The most commonly used filter types are
Band-pass filters, which are used to filter lowest order harmonics such as 5th, 7th, 11th, 13th, etc. Band-pass filters can be tuned at a single frequency (single-tuned filter) or at two frequencies (double-tuned filter).
High-pass filters, which are used to filter high-order harmonics and cover a wide range of frequencies. A special type of high-pass filter, the C-type high-pass filter, is used to provide reactive power and avoid parallel resonances. It also allows filtering low order harmonics (such as 3rd), while keeping zero losses at fundamental frequency.
The Three-Phase 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 Three-Phase Harmonic Filter block are shown below:
The simplest filter type is the single-tuned 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} | P ≈ (Q_{C}/Q)·n/(n^{2} – 1) | V = nominal line-line voltage | |
X_{L} = inductor
reactance at | |||
X_{C} = capacitor
reactance at |
The double-tuned filter performs the same function as two single-tuned 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 double-tuned 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 double-tuned 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 high-pass filter is a single-tuned filter where the L and R elements are connected in parallel instead of series. This connection results in a wide-band filter having an impedance at high frequencies limited by the resistance R.
The quality factor of the high-pass filter is the quality factor of the parallel RL circuit at the tuning frequency: Q = R / ( L · 2πf_{n} ).
The C-type high-pass filter is a variation of the high-pass 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 C-type 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 60 Hz network. Each filter is rated 315 kV, 49 Mvar.
Single-Tuned, 315 kV, 49 Mvar, 5th Harmonic Filter; Q = 30
Double-Tuned, 315 kV, 49 Mvar, 11th and 13th Harmonics Filter; Q = 16
High-Pass, 315 kV, 49 Mvar, 24th Harmonic Filter; Q = 10
C-Type High-Pass, 315 kV, 49 Mvar, 3rdHharmonic Filter; Q = 1.75
Select one of the four filter types: Single-tuned, Double-tuned, High-pass or C-type high-pass.
Select the connection of the three filter branches.
Y(grounded) | Neutral is grounded. |
Y(floating) | Neutral is not accessible. |
Y(neutral) | Neutral is made accessible through a fourth connector. |
Delta | Three phases connected in delta. |
The nominal phase-to-phase voltage of the filter, in volts RMS (Vrms) and the nominal frequency, in hertz (Hz).
The three-phase capacitive reactive power Q_{C}, in vars. Specify a positive value.
The tuning frequency of the single frequency filter (single-tuned, high-pass or C-type high-pass), or the two frequencies of the double-tuned filter, in hertz (Hz).
The quality factor Q of the filter defined as explained in the above Description section. Dimensionless positive number.
Select Branch voltages to measure the three voltages across each phase of the Three-Phase Harmonic Filter block terminals. For a Y connection, these voltages are the phase-to-ground or phase-to-neutral voltages. For a delta connection, these voltages are the phase-to-phase 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 Three-Phase Harmonic Filter block.
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): Uag, Ubg, Ucg | Uag: , Ubg: , Ucg: |
Y(floating): Uan, Ubn, Ucn | Uan: , Ubn: , Ucn: | |
Y(neutral): Uan, Ubn, Ucn | Uan: , Ubn: , Ucn: | |
Delta: Uab, Ubc, Uca | Uab: , Ubc: , Uca: | |
Branch currents | Y(grounded): Ia, Ib, Ic | Iag: , Ibg: , Icg: |
Y(floating): Ia, Ib, Ic | Ian: , Ibn: , Icn: | |
Y(neutral): Ia, Ib, Ic | Ian: , Ibn: , Icn: | |
Delta: Iab, Ibc, Ica | Iab: , Ibc: , Ica: |
The power_harmonicfilterpower_harmonicfilter example illustrates the use of the Three-Phase Harmonic Filter block to filter harmonic currents generated by a 12-pulse, 1000 MW, AC/DC converter in a 500 kV, 60 Hz system. The filter set is made of the following four components providing a total of 600 Mvar:
One 150 Mvar C-type high-pass filter tuned to the 3rd harmonic (F1)
One 150 Mvar double-tuned filter tuned to the 11/13th (F2)
One 150 Mvar high-pass filter tuned to the 24th (F3)
One 150 Mvar capacitor bank
Time-domain simulation
Run the simulation with an alpha firing angle of 19 degrees. You should get a DC voltage level of 500 kV. Now, look inside Scope1. Compare the currents flowing into Bus B1 (Iabc_B1, axis 2) with those flowing into Bus B2 (Iabc_B2, axis 3). You can see that the harmonic filters almost eliminate the harmonics generated by the converter. If you use the FFT tool of the Powergui, you will find that the harmonic filters reduce the THD of the current injected in the system from 9% to 0.7%.
Frequency-Domain Response
You will now plot the impedance vs. frequency of the harmonic filters:
Disconnect the filters from the AC bus. To do so, double-click on the breaker Brk1, select open for initial status of breakers, and click OK.
Open the Powergui and select Impedance vs Frequency Measurement.
Click the Display/Save button. The software computes and displays the filter's frequency response.
Double-click the block Show filters impedance vs frequency. A second figure appears, showing the precomputed filters frequency response. The impedance data of the two figures should be identical to the one shown below.
If you zoom the figure (using the Tool menu), you should find an impedance of 417 ohms capacitive (−90deg.) at 60 Hz. This value confirms that the total reactive power of the filters at 60 Hz is:
$${Q}_{c}=\frac{{V}^{2}}{{X}_{c}}=\frac{{\left(500\cdot {10}^{3}\right)}^{2}}{417}=600\text{Mvar}\text{.}$$