Design and Specification of Harmonic Filters for Variable Frequency Drives PDF

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An-Najah National University Faculty of Graduate Studies Design and Specification of Harmonic Filters for Variable Frequency Drives (Simulation and Analysis) Prepared by: Tareq Foqha Prepared to: Dr. Moien Omar Nablus, Palestine 2022 Abstract The widespread use of variable frequency drives (VFD) in ...

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An-Najah National University Faculty of Graduate Studies

Design and Specification of Harmonic Filters for Variable Frequency Drives (Simulation and Analysis)

Prepared by:

Tareq Foqha

Prepared to:

Dr. Moien Omar

Nablus, Palestine 2022

Abstract The widespread use of variable frequency drives (VFD) in industry has raised serious concerns about power quality in electrical distribution systems. VFDs are nonlinear loads that cause harmonic voltages across the system impedance by injecting harmonic currents into the power system. The performance of other sensitive loads in the system may be harmed as a result of this harmonic distortion. This study presents a method for designing and specifying low voltage harmonic filters for VFDs. An electrical distribution system feeding a group of variable frequency drives is analyzed using the proposed methodology. To carry out this research Matlab coding will be used. The minimum value of the filter's var and its specifications are determined using an iterative technique. To validate the proposed method, a number of case studies are presented. The results demonstrate that the method is effective.

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I.

Introduction

Variable Frequency Drives have become increasingly popular in a variety of applications in recent years. The generation of harmonic distortion in the power system is one of the undesirable side effects of using a VFD. These harmonics flow through the power system, causing a variety of issues such as supply voltage distortion, overloading of electrical distribution equipment such as transformers, a reduction in system efficiency, and other issues. Several methods can be used to improve the performance of a VFD, including (appropriate motor and design selection), application of a suitable control method, and improvement of the converter's (input and output waveforms) [1]. Harmonics reduction can be accomplished through a variety of methods. In cases where the preventive actions, such as installation modifications and special devices in the supply system, are insufficient, filtering systems must be installed. Because of its mature technology, reliable operation, and lower installation and maintenance costs, the passive filter, which is an LC circuit tuned to each harmonic order to be filtered and installed in parallel with the non-linear load, is widely used in industries [2]. The filters are made up of combination sets of inductance (L) and capacitance (C), each resonantly tuned to a specific frequency. A small amount of resistance (R) is also included to act as a harmonic current limiter (damper). Because filtering is imperfect over a wide frequency range, the harmonic problem is not completely solved, but it is greatly reduced [3]. The inductor (L) and capacitor (C) are connected in series or parallel in a passive filter. The filter circuit can be tuned to a specific frequency by making the inductor's impedance equal to the capacitor's impedance. Changes in electrical network impedance determine the effectiveness of filters, so thorough research is required before filter installation [4]. This study discusses how to design harmonic filters for an electrical system that will feed variable frequency drives using a simple methodology. The proposed methodology calculates the filter's harmonic voltage attenuation factor. The attenuation factor is then used to calculate voltage harmonic distortion and harmonic currents injected into the system at the point of connection. A Matlab coding was developed to simulate system performance. This program is also used to analyze an electrical distribution system that feeds a group of VFDs.

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II.

Performance Guideline

The total harmonic distortion (THD) of voltage at the point of common connection (PCC) for low voltage and medium voltage systems is limited by IEEE Std. 519-1992, "IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems," as shown in Table 1 below [5]. Table 1: Limits of the THD_V. System nominal voltage (V) THD, % General systems 120-600 5 69kV and below 5 69-161kV 2.5 161kV and above 1.5 The THD limits listed in the table above refer to the THD at the source-to-distribution system interface.

Harmonic Currents Drawn by The VFD’S

III.

Information about the harmonic currents drawn by the VFD’s is the key to any harmonic analysis. Characteristic harmonics are related to the pulse number by the following equation: h=p x n + 1 Where: h: the harmonic order p: the pulse number of the converter n: an integer having values of 1, 2, 3, …. This means that a 6-pulse converter at the front end of a VFD draws harmonic currents of orders 5, 7, 11, 13, 17, 19, 23, 25, .. etc. The harmonic current magnitudes for the 6-pulse, VFD are given in Table 2. Table 2: harmonic current magnitudes for the 6-pulse VFD. Harmonic order Harmonic current A Harmonic order Harmonic current A 5 364.8 25 15.2 7 11.8 29 8.7 11 79.8 31 9.7 13 37.9 35 6.5 17 37.9 37 5.4 19 22.7 41 4.3 23 17.3 43 3.2

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IV.

Harmonic Filters And Tuning

Harmonic filters are preferably connected to the system on the source side of the VFD isolation transformer or line reactors. The series L-C circuit has the lowest impedance at its resonant frequency, as is well known. The circuit acts as a capacitor below the resonant frequency and as an inductor above the resonant frequency. The filter should ideally be tuned to the characteristic harmonic it is meant to suppress. The 5th and 7th harmonic filters, for example, are most effective when tuned to 300 Hz and 420 Hz for a 3-phase 6-pulse VFD. However, in practice, the filters are tuned to a frequency slightly lower than the nominal resonant frequency to avoid parallel resonance if the filter component parameters change due to temperature and aging. The nominal resonant frequency of most low and medium voltage harmonic filters is about 0.95 times that of the nominal resonant frequency. Attenuation of the harmonic voltages produced by the filter reduces as the ratio of the actual resonant frequency to the nominal resonant frequency departs from 1.0. For single tuned filters the equation of detuning factor is as follows [5]:

V.

Attenuation Of Harmonic Voltages By The Filter

At the point of connection, a harmonic filter reduces all harmonic voltages. The voltage whose frequency is equal to or close to the filter's resonant frequency experiences the greatest attenuation [6], we will define the attenuation factor as [7]:

where an(h) = attenuation factor due to the nth-order filter of the hth-order harmonic voltage. V(h) = the hth harmonic voltage without the filter at the point of connection Vf(h) = the hth harmonic voltage with the filter at the point the point of connection

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A high value of the attenuation factor an(h) is desirable. A value of 1.0 indicates that the filter has caused no attenuation. A value less than 1.0 indicates that the harmonic voltage is amplified rather than attenuated. At any frequency, a positive attenuation factor indicates that the filter circuit's impedance is inductive at that harmonic frequency. A negative value indicates that the impedance at that frequency is capacitive [5].

VI.

Design of Harmonic Filters

The following procedure is suggested for the design of the filters using the equations and graphs given in this study [5]: 1. Obtain the harmonic signature of the VFD from & manufacturer. 2. Calculate the voltage THD at the point of connection of the VFD and decide whether harmonic filtering is necessary. 3. If harmonic filtering is required calculate the percent harmonic voltages without the filter. 4. Begin with a 5th harmonic filter. Select a kvar for the filter. Calculate the attenuation factors for h = 5, 7, 11, 13, … 5. Calculate the harmonic voltages with the filter. 6. Calculate %THD with the filter. Some iterations are required at this stage to select the minimum rating of the filter such that the THD is just below the desired value (5.0% or less). 7. If the THD cannot be reduced below the desired value, add a seventh harmonic filter and repeat the design.

VII. Methodology Figure 1 shows a one-line diagram of an electrical distribution system feeding a Variable Frequency Drive (VFD). The harmonic filter consists of a capacitor and an inductor connected in series.

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Figure 1: One-line diagram of the electrical distribution system feeding the VFD The n-th harmonic filter impedance at the harmonic frequency (h) can be expressed in terms of the filter (kVAn) and its tuning frequency (hn) as:

The attenuation factor an(h) is obtained as:

where:

When more than one filter is used, the attenuation factor of the h-th harmonic voltage is given by:

Harmonic currents flowing into the tuned filters and into the system (utility) with the connected filter(s) can be calculated as follows:

Once these currents have been calculated, it is possible to get filter’s specifications using Matlab coding. Figure 2 shows the flowchart for the proposed methodology.

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Figure 2: Flowchart for the proposed methodology.

A.

System Specifications

The system consists of utility, transformer and group of VFDs, the specifications of each component is shown in Table 3. Component Utility Transformer VFD

Ratings 13.8kV, 50MVAsc 1000kVA, 13.8/0.48kV, Z= 5.75% 6 pulse, PWM VFD with isolation XFMR 900kVA, DPF= 0.9

To calculate the short circuit kVA of the transformer, the following equation will be used: kVAsc= kVA/Z = 1000/5.75% = 17391.3 kVAsc

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The short circuit kVA at the terminals of the VFD is calculated as follows: kVAscdrive= Suti*Str / Suti+Str

The specifications of the filter are obtained as follows: 

The reactance of the capacitor



The size of the reactor that is necessary to trap the hi harmonic



The filter size

B.

Matlab Coding

The code that performs the methodology consists of the following parts: Part (I): Input data of the system %Utility & Transformer Specifications fprintf(2,'Utility & Transformer Specifications.\n') fprintf(2,'Enter the value of the source rms voltage, frequency, and short circuit VA.\n') vrms=input('Enter the value of the rms voltage of the source in V ='); f=input('Enter the value of the system frequency ='); SCu= input('Enter the value of short circuit VA ='); %Transformer Specifications fprintf(2,'Enter the value of the transformer VA, and PU impedance.\n') vatr= input('Enter the value of the rated VA of the transformer ='); Ztr= input('Enter the value of the impedance of the transformer as percentage % ='); SCt=vatr/(Ztr/100); %Harmonic Analysis fprintf(2,'Drive Specifications.\n') Vlv= input('Enter the value of bus voltage in V ='); vad= input('Enter the value of the rated VA of the drive ='); DPF= input('Enter the value of the Displacement Power Factor ='); Scs= ((SCu*SCt))/((SCu+SCt));

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Part (II): Filter Specifications This code is built for filtration of 5th and 7th harmonics only, as mentioned previously the filter should ideally be tuned to the characteristic harmonic it is meant to suppress. The 5 th and 7th harmonic filters are most effective for a 3-phase 6-pulse VFD. %Filter Specifications fprintf(2,'Filter Specifications.\n') hn5= input('Enter the value of the tuning frequency for 5th harmonic (recommended to choose detuning factor of 0.9) ='); Qmax5= input('Enter the value of the max var rating of the filter ='); first5= input('Enter the value of the starting value of the filter Var ='); step5= input('Enter the step size ='); hn7= input('Enter the value of the tuning frequency for 7th harmonic(recommended to choose detuning factor of 0.9) ='); Qmax7= input('Enter the value of the max var rating of the filter ='); first7= input('Enter the value of the starting value of the filter Var ='); step7= input('Enter the step size ='); Vrated= input('Enter the value of the rated voltage of the filter =');

Part (III): Calculation of THDI and THDV In this code: 1. The fundamental current based on the bus voltage and VFD rating is calculated. 2. The harmonic orders and current magnitudes is defined. 3. The harmonic voltages is calculated using this equation:

4. Calculate total harmonic distortion of current and voltage. %Calculation of Harmonic current I1=(vad)/((sqrt(3))*(Vlv)); % fundamental current (I1) h=[5 7 11 13 17 19 23 25 29 31 35 37 41 43]; Ih=[364.8 11.8 79.8 37.9 37.9 22.7 17.3 15.2 8.7 9.7 6.5 5.4 4.3 3.2]; fprintf(2,'%IH/I1.\n') IH=(Ih./I1)*100; Vh = (IH)*(vad/Scs).*h; Vhz=Vh.^2; Itot=[I1 Ih]; summ= sum(Vhz); Ihy=Ih.^2; Ihar= sqrt(sum(Ihy)); Harmonics_currents_voltages=[IH;,Vh;].' fprintf(2,'Total Harmonic Distortion.\n') THD_V= sqrt(summ) THD_I= (Ihar/I1)*100

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Part (IV): Iterative method to determine the minimum value of the filter’s kVar. In this code: 1. If the calculated THDV value is greater than 5%, the program indicates that a filter is required. 2. An iterative method used to determine the minimum value filter’s kVar. - Firstly 5th harmonic filter will be used and if the THD of voltage cannot be reduced below the desired value, 7th harmonic filter will be added. 3. The filters Kvar is obtained. 4. The THDI, THDV, harmonic voltages, source currents and attenuation factor are calculated for each value of the filter’s kVar. %Iterative method to determine the minimum value of the filter’s kvar if THD_V>=5 f2=false; fprintf(2,'harmonic filtering is necessary.\n') THD_V2=THD_V; varf1=first5:step5:Qmax5; j=1; while THD_V2>=5 h2=[1 5 7 11 13 17 19 23 25 29 31 35 37 41 43]; Ih2=[0 364.8 11.8 79.8 37.9 37.9 22.7 17.3 15.2 8.7 9.7 6.5 5.4 4.3 3.2]; VH=[0 Vh]; for i=1:length(h2) delta (i)=((hn5^2)*(h2(i)^2))/((h2(i)^2) -(hn5)^2); atten(i)= 1+ ((delta(i) *(varf1(j)))/Scs); Vf(i)=VH(i)/atten(i); Vhz2(i)=Vf(i)^2; Zn5(i)= (1/(varf1(j)*1e-3))*(((h2(i))/((hn5)^2)- (1/h2(i)))); In5(i)=VH(i)/Zn5(i); Is5(i)=Ih2(i)/atten(i); end fprintf('Filter 5 with value= %2.0f kvar \n' ,varf1(j)*1e-3) summm= sum(Vhz2); THD_V2= sqrt(summm) Ihb=Is5.^2; Ihar_with_filter= sqrt(sum(Ihb)); THD_I_after_filtering= (Ihar_with_filter/I1)*100 source_currents_before_and_after_filtering =[Itot(2:14); Is5(2:14)].' attenuation_and_Voltage_after_attenuation=[atten(2:14);Vf(2:14)].' if j==length(varf1) f2=true; break end j=j+1; end if f2==true varf1=first5:step5:Qmax5; varf2=first7:step7:Qmax7;

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z=0; p=0; while THD_V2>=5 p=length(varf1) ; if z==length(varf2) z=length(varf2); else z=z+1; end for l=1:length(h2) delta1 (l)=((hn5^2)*(h2(l)^2))/((h2(l)^2) -(hn5)^2); delta2(l)=((hn7^2)*(h2(l)^2))/((h2(l)^2) -(hn7)^2); attenn(l)= 1+ ((delta1(l)*(varf1(p)))/Scs)+((delta2(l) *(varf2(z)))/Scs) ; Vf2(l)=VH(l)/attenn(l); Vhz22(l)=Vf2(l)^2; Zn5(l)= (1/(varf1(p)*1e-3))*(((h2(l))/((hn5)^2)- (1/h2(l)))); Zn7(l)= (1/(varf1(z)*1e-3))*(((h2(l))/((hn7)^2)- (1/h2(l)))); In5(l)=VH(l)/Zn5(l); Is5(l)=Ih2(l)/attenn(l); In7(l)=Vf(l)/Zn7(l); end fprintf('Filter 5 with value= %2.0f kvar \n' ,varf1(p)*1e-3) fprintf('Filter 7 with value= %2.0f kvar \n' ,varf2(z)*1e-3) summm= sum(Vhz22); THD_V2= sqrt(summm) source_currents_before_and_after_filtering =[Itot(2:14); Is5(2:14)].' attenuation_factor_and_Voltage_after_attenuation=[attenn(2:14); Vf2(2:14);].' I1n=I1*attenn(1); Ihb=Is5.^2; Ihar_with_filter= sqrt(sum(Ihb)); THD_I_after_filtering= (Ihar_with_filter/I1n)*100 end end else fprintf(2,'harmonic filtering is not necessary.\n') end end

Part (V): Calculation of the filter’s specifications. In this code: Rated reactive power, capacitor current, reactance of the capacitor, reactance at tuned frequency of the filter are calculated. %Filter 1 specifications Qrated5=varf1(j)*((Vrated/Vlv)^2).*1e-3; Capacitor_current5=varf1(j)/(sqrt(3)*Vlv);

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Reactance_of_the_capacitor_bank5=Vlv^2./varf1(j); Reactance_at_tuned_frequency5=Reactance_of_the_capacitor_bank5./hn5^2; Filter_Current5=(Vlv/sqrt(3))./(Reactance_of_the_capacitor_bank5+Reactance_ at_tuned_frequency5); Q_supplied_by_the_filter5= sqrt(3)*Vlv.*Filter_Current5; Q_Rating_and_capacitor_current_of_5th_harmonic_filters=[Qrated5; Capacitor_current5;].' Q_Supplied_by_the_5th_harmonic_Filter=[Q_supplied_by_the_filter5;].' Reactances_of_5th_harmonic_filter=[Reactance_of_the_capacitor_bank5; Reactance_at_tuned_frequency5;].' %Filter 2 specifications Qrated7=varf2(z)*((Vrated/Vlv)^2).*1e-3; Capacitor_current7=varf2(z)/(sqrt(3)*Vlv); Reactance_of_the_capacitor_bank7=Vlv^2./varf2(z); Reactance_at_tuned_frequency7=Reactance_of_the_capacitor_bank7./hn7^2; Filter_Current7=(Vlv/sqrt(3))./(Reactance_of_the_capacitor_bank7+Reactance_ at_tuned_frequency7); Q_supplied_by_the_filter7= sqrt(3)*Vlv.*Filter_Current7; Q_Rating_and_capacitor_current_of_7th_harmonic_filters=[Qrated7; Capacitor_current7;].' Q_Supplied_by_the_7th_harmonic_Filter=[Q_supplied_by_the_filter7;].' Reactances_of_7th_harmonic_filter=[Reactance_of_the_capacitor_bank7; Reactance_at_tuned_frequency7;].'

VIII. Case Studies In this section we present a number of case studies to validate the proposed methodology. The aim is to find the minimum value of filter rating and to determine the effect of these harmonic filters on harmonic voltages and currents distortion. A.

Case I

Figure 3 depicts this case. The 5th harmonic filter has a maximum rating of 300kVar with a 50kVar step size, whereas the 7th harmonic filter has a maximum rating of 150kVar with a 50 kVar step size.

Figure 3: Case I. 12

Inputs:

Results: I. Harmonic currents (%IH), voltages (%VH) , THDV and THDI %IH 33.6988 1.0900 7.3716 3.5011 3.5011 2.0969 1.5981 1.4041 0.8037 0.8960 0.6004 0.4988 0.3972 0.2956 %THDI= 35.0268

%VH 11.7524 0.5322 5.6559 3.1746 4.1514 2.7790 2.5638 2.4484 1.6256 1.9375 1.4658 1.2874 1.1359 0.8866 %THDV=15.1748

II.

Decision:

III.

Filter’s Kvar, %THDV, %THDI, Source current before and after filtering, and attenuation factor and voltage after attenuation:

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Filter in operation Filter 1

Results 50 kvar

%THDV

10.7119

%THDI

Filter 1

19.7639 364.8000 192.3326 11.8000 10.1545 79.8000 72.0562 37.9000 34.4264 37.9000 34.6171 22.7000 20.7636 17.3000 15.8523 15.2000 13.9360 8.7000 7.9828 9.7000 8.9029 6.5000 5.9684 5.4000 4.9592 4.3000 3.9500 1.8967 6.1962 1.1620 0.4580 1.1075 5.1070 1.1009 2.8836 1.0948 3.7918 1.0933 2.5419 1.0913 2.3492 1.0907 2.2448 1.0898 1.4916 1.0895 1.7783 1.0891 1.3460 1.0889 1.1823 1.0886 1.0435 100 kvar

%THDV

9.0558

%THDI

14.4288 364.8000 130.5922 11.8000 8.9118 79.8000 65.6824 37.9000 31.5360 37.9000 31.8577 22.7000 19.1316 17.3000 14.6282 15.2000 12.8660 8.7000 7.3749 9.7000 8.2269 6.5000 5.5172 5.4000 4.5849 4.3000 3.6526

Source current before and after filtering

Attenuation factor and voltage after attenuation

Source current before and after filtering

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2.7934 4.2072 1.3241 0.4019 1.2149 4.6553 1.2018 2.6415 1.1897 3.4895 1.1865 2.3421 1.1826 2.1678 1.1814 2.0725 1.1797 1.3780 1.1791 1.6432 1.1781 1.2442 1.1778 1.0930 1.1772 0.9649 150 kvar

Attenuation factor and voltage after attenuation

Filter 1 %THDV

9.0558

%THDI

Filter 1

11.6862 364.8000 98.8579 11.8000 7.9401 79.8000 60.3445 37.9000 29.0934 37.9000 29.5056 22.7000 17.7375 17.3000 13.5796 15.2000 11.9486 8.7000 6.8530 9.7000 7.6463 6.5000 5.1294 5.4000 4.2631 4.3000 3.3969 3.6901 3.1848 1.4861 0.3581 1.3224 4.2769 1.3027 2.4369 1.2845 3.2319 1.2798 2.1714 1.2740 2.0124 1.2721 1.9247 1.2695 1.2805 1.2686 1.5273 1.2672 1.1567 1.2...