- 1. Design and Specification of Harmonic Filters for Variable Frequency Drives Jesús A. Baez Moreno ITESM (Departamento de Ingeniería Eléctrica) Monterrey, NL. CP. 64849 ABSTRACT This paper presents a method that can be applied to design and specify low voltage harmonic filters for variable frequency drives. The proposed methodology is used to analyze an electrical distribution system feeding a group of variable frequency drives. 1. INTRODUCTION Generalized use of Variable Frequency Drives has increased harmonic distortion at electrical distribution systems. Some pieces of equipment, such as personal computers, programmable controllers and microprocessor-based instrumentation are very sensitive to harmonic distortion. Proper application of harmonic filters can help to keep harmonic distortion within acceptable limits. This paper describes a simple methodology that can be applied to design harmonic filters for an electrical system that will feed variable frequency drives. The proposed methodology calculates the harmonic voltage attenuation factor produced by filters [1]. Attenuation factor is then used to estimate voltage harmonic distortion at the point of connection and also the harmonic currents injected into the system. A computer program (EXCEL Macro) was developed using Visual Basic for Application language to simulate system performance. The application of this program to the analysis of a electrical distribution system feeding a group of VFDs is also presented. 2. SOLUTION METHODOLOGY Figure 1 shows a one-line diagram of a electrical distribution system feeding a Variable Frequency Drive (VFD). The harmonic filter consists of a capacitor and an inductor connected in series. ~ Utility Nonlinear Load (VFD) Filter Low Voltage Bus Figure 1. One-line diagram of the electrical distribution system feeding the VFD A harmonic filter modifies all harmonic voltages at the point of connection(Low Voltage Bus). Maximum attenuation occurs for the voltage whose frequency is equal or close to the resonant frequency of the filter. In order to quantify how harmonic voltages are affected, we will define the attenuation factor[1] as ( ) a h V h Vf h n = ( ) ( ) Where: V(h): Harmonic voltage without the filter at the low voltage bus. Vf(h): The h-th Harmonic voltage with the filter at the low voltage bus an(h) : Attenuation factor of the harmonic voltage(h) due to the (n-th) tuned filter.
- 2. Figure 2 illustrates the basic circuit used to calculate the h-th harmonic attenuation factor produced by the n-th harmonic filter. In this diagram, I(h) represents the h-th harmonic injected by the variable frequency drive, Zs(h) accounts for the system impedance and Zn(h) represents the n-th harmonic filter impedance at the h-th harmonic. I(h) Zn(h) Zs(h) jh SCKVA − j h KVAn j h h KVAn n 2 Figure 2. Circuit used for harmonic voltage calculation. The n-th harmonic filter impedance at the harmonic frequency (h) can be expressed in terms of the filter kVAR(kVAn) and its tuning frequency (hn) as: Z h j kVAn h h h j kVAn h h h h n n ( ) ( ) = − = − 2 2 2 2 1 n n The distribution system impedance seen by the low voltage bus at the harmonic frequency (h) is related to the low voltage bus short circuit kVA as follows: Zs h j h SCkVA ( ) = In order to simplify the calculation, the filter and the system are represented by their admittance values. Yn h kVAn j h h h h Ys h SCKVA jh ( ) ( ) = − = n 2 n 2 2 The equivalent admittance seen by the VFD is calculated by adding Yn(h) and Ys(h) Yeq h kVAn j h h h h h SCKVA jh ( ) = − + 2 2 n 2 n 2 [ ] Yeq h jh kVAn SCKVA ( ) = + 1 δ where: δ = − h h h h 2 2 n 2 n 2 The attenuation factor an(h) is then obtained as [1]: [ ] an h V h Vf h Yeq h Ys h jh kVAn SCKVA SCKVA jh an h kVAn SCKVA ( ) ( ) ( ) ( ) ( ) ( ) = = = + = + 1 1 δ δ When more than one filter is used, the attenuation factor of the h-th harmonic voltage is given by ( ) ( ) an h kVA SCKVA kVA SCKVA h h h h n n N n k n k N k ( ) ( ) ( ) ( ) ( ) = + + + = − 1 1 2 2 2 2 1 δ δ δ L where: Harmonic currents flowing into the tuned filters and into the system(utility) with the connected filter(s) can be calculated as follows: In h V h Zn h ( ) ( ) ( ) = ; Is h I h an h ( ) ( ) ( ) =
- 3. I(h) Zn(h) Zs(h) Is(h) If(h) + V(h) - Figure 3. Harmonic filter and system current calculation Once these currents have been calculated, it is possible to get filter’s specifications with the aid of the worksheet filter.xls [3] The above procedure is summarized in the flowchart shown in Figure 4. Read system data UtilitySCMVA,XFMR(ZandkVA) Drive KVA, Harmonic Spectra (%I(h)), Displacement power factor Filter(s) kVAr, Detuning Factors(α) MaximumallowedTHDV(THDVmax) Evaluate harmonic Voltages and THDV without filters V h I h h DrivekVA SCKVA ( ) [% ( )][ ] = Calculate attenuation factors an(h), resulting harmonic voltages and THDV ( ) Vf h V h a h n ( ) ( ) = [ ] THDV Vf h h = = ∑ ( ) 2 5 43 [ ] THDV V h h = = ∑ ( ) 2 5 43 THDV<THDVmax? Modify filter(s) kVAr Calculate harmonic filter loading and harmonics flowing into the system Calculate filter specs using spredasheet filters.xls NO YES In h V h Zn h ( ) ( ) ( ) = SCMVA 13.8 kV 50 5.75% 1000 kVA 12903.2 SCKVA 480 V THDV 3.58% 472.50 233.62 0.031911 Ω Ω A RMS 0.03256 Ω Ω A RMS 500kVAr 250kVAr @ 600V @ 600V 5-th 7-th 900 kVA 6-pulse 250 HP 480-V CSI VFD(measured) ~ Generate Report *Voltage/current distortion * Filter sepecifications) I s h I h an h ( ) ( ) ( ) = ; an h kVA SCKVA kVA SCKVA n n N N ( ) ( ) ( ) = + + + 1 1 1 δ δ L Figure 4. Flowchart for the proposed solution methodology
- 4. 3. COMPUTER PROGRAM The computer program was developed in an Excel Workbook (VFD.XLS), using Visual Basic for Applications Language[2]. Harmonic Spectra of Variable Frequency Drives is stored in one worksheet within the same workbook. To add harmonic spectra of a non listed VFD(or group of VFDs), the user types in this worksheet a name for this load and its harmonic spectra. Simulation results are stored into the following Worksheets: 1) SUMMARY : Summary of the results obtained in the simulation (THDV, Filter specs) 2) VOLTAGES: Harmonic voltages in the low voltage bus without filters, with filters and with plain capacitors(no tuning reactor) 3) CURRENTS: Harmonic currents flowing into the system with and without filters, and filter currents 4) FILTER-5: 5th harmonic filter design specifications 5) FILTER-7: 7th harmonic filter design specifications The program was written under the following assumptions: 1)This application was developed for VFDs operating at 240V and 480 V systems. For applications at 240V, 480 V capacitor banks are used, and the total KVAR rating is adjusted to the next multiple of 25 kVAR For applications at 480V , 600 V capacitor banks are used and the total KVAR rating is adjusted to the next multiple of 50 kVAR For example, if the user chooses a 300 kVAR bank at 480 V, the required kVAR rating at 600 V is 300(600/480) ^2 = 468.75 kVAR. The bank kVAr rating is adjusted to 500 kVAR. 2) Load at the low voltage bus consists only of VFDs and the resistive effect is neglected 3) 5th and 7th harmonic voltage distortion at the high voltage side is given a as 2%. (This value can be modified in Worksheets FILTER-5 and FILTER-7 4) Voltage at the low voltage bus is assumed constant (1.0 pu). 4. SIMULATION RESULTS The proposed methodology and the computer program (VFD.XLS) were used to simulate the sample electrical distribution system depicted in figure 5. UTILITY 5th 7th SCMVA=50 ~ Z (%) = 5.75 1000 KVA 150-HP PWM VFDs TOTAL LOAD =900 KVA 300 kVAR 150 kVAR α=0.95 α=0.95 . . . 13.8 kV 480 V Figure 5. One-line diagram of the electrical system This system feeds a group of PWM variable frequency drives with a total load of 900 kVA operating at 0.9(-) displacement power factor. This loading condition results in a very high harmonic current and voltage distortion. The proposed methodology was used to analyze the effect of connecting two harmonic filters on low voltage bus harmonic distortion levels. Filter 1: 300 kVAR, 5-th harmonic filter tuned at hn=4.75 Filter 2: 150 kVAR, 7-th harmonic filter tuned at hn=6.65 The computer program calculates harmonic voltage and current distortion with and without filters and also calculates harmonic filter loading. A summary of the simulation results is presented in figure 6 (actual program output). The effect of these harmonic filters on harmonic voltages and currents distortion is presented in Tables 1 and 2. Total harmonic current distortion (THDI) is reduced from 35% to 7.5% and total harmonic voltage distortion is reduced from 15.76 to 4.56 %. Figure 7 shows the 5-th harmonic filter spec sheet.
- 5. Figure 6. Simulation Results (summary) Table 1. Voltage at the low voltage bus with and without filters connected NO FILTERS FILTERS h %I(h) % V(h) a(h) % Vf(h) 5 33.7 11.753 6.03 1.9504 7 1.09 0.5322 7.66 0.0695 11 7.37 5.6546 2.55 2.2158 13 3.5 3.1736 2.39 1.3287 17 3.5 4.1501 2.25 1.8409 19 2.1 2.783 2.22 1.2526 23 1.6 2.5668 2.18 1.1759 25 1.4 2.4413 2.17 1.1247 29 0.8 1.6182 2.15 0.7513 31 0.9 1.946 2.15 0.906 35 0.6 1.4648 2.14 0.6848 37 0.5 1.2904 2.14 0.6042 41 0.4 1.1439 2.13 0.537 43 0.3 0.8998 2.13 0.4228 THDV(%) 15.176 4.5581
- 6. Table 2 . Harmonic currents flowing into the system and harmonic filters loading XFMR(NO FILTERS) XFMR(FILTERS) 5TH FILTER 7TH FILTER I(AMPS) I(AMPS) I(AMPS) I(AMPS) FUNDAMENTAL 1082.5 982.62 402.75 196.90 5 364.8 60.54 347.45 43.18 7 11.8 1.54 1.60 8.66 11 79.8 31.26 21.50 27.02 13 37.9 15.86 10.24 11.78 17 37.9 16.81 10.20 10.88 19 22.7 10.23 6.11 6.39 23 17.3 7.93 4.64 4.75 25 15.2 6.98 4.05 4.12 29 8.7 4.02 2.31 2.33 31 9.7 4.54 2.60 2.61 35 6.5 3.04 1.73 1.73 37 5.4 2.53 1.44 1.44 41 4.3 2.03 1.15 1.14 43 3.2 1.53 0.86 0.86 HARM. CURRENT 379.2 73.85 348.55 55.01 RMS CURRENT 1147.0 985.39 532.63 204.44 THDI (%) 35.0% 7.52%
- 7. Low Voltage Filter Calculations: Example Filter Design Spreadsheet SYSTEM INFORMATION: Filter Specification: 5 th Power System Frequency: 60 Hz Capacitor Bank Rating(Available) 500 kVAr Capacitor Rating: 600 Volts Rated Bank Current: 481 Amps 60 Hz Nominal Bus Voltage: 480 Derated Capacitor: 320 kVAr Capacitor Current (actual): 384.9 Amps Total Harmonic Load: 900 kVA Filter Tuning Harmonic: 4.75 Filter Tuning Frequency: 285 Hz Cap Impedance (wye equivalent): 0.7200 Ω Ω Cap Value (wye equivalent): 3684.1 uF Reactor Impedance: 0.0319 Ω Ω Reactor Rating: 0.0846 mH Filter Full Load Current (actual): 402.8 Amps Supplied Compensation: 335 kVAr Filter Full Load Current (rated): 503.4 Amps Transformer Nameplate: 1000 Utility Side Vh: 2.00 % T H D (Rating and Impedance) 5.75 (Utility Harmonic Voltage Source) Load Harmonic Current: 86.54 % Fund Load Harmonic Current: 348.6 Amps Utility Harmonic Current: 67.8 Amps Max Total Harm. Current: 416.4 Amps CAPACITOR DUTY CALCULATIONS: Filter RMS Current: 579.3 Amps Fundamental Cap Voltage: 502.3 Volts Harmonic Cap Voltage: 103.9 Volts Maximum Peak Voltage: 606.1 Volts RMS Capacitor Voltage: 512.9 Volts Maximum Peak Current: 819.1 Amps CAPACITOR LIMITS: (IEEE Std 18-1980) FILTER CONFIGURATION: Peak Voltage: 120% <−−−−−−> 101% Current: 180% <−−−−−−> 120% XL => 0.0319 Ω Ω KVAr: 135% <−−−−−−> 103% RMS Voltage: 110% <−−−−−−> 85% 500 kVAR 600 V F I L T E R R E A C T O R D E S I G N S P E C I F I C A T I O N S : Reactor Impedance: 0.0319 Ω Ω Reactor Rating: 0.0846 mH Fundamental Current: 402.8 Amps Harmonic Current: 416.4 Amps Figure7. 5th Harmonic filter specifications
- 8. 5. CONCLUSIONS The filter design iterative procedure can be greatly simplified using the equations presented in this paper along with the program developed. Using the proposed methodology, it is possible to determine the required rating of the filters to keep harmonic distortion (voltage and current) within acceptable limits and also define filters specifications. ACKNOWLEDGEMENT The author wishes to acknowledge the support received from Electrotek Concepts Inc., which allowed me to develop this project. REFERENCES [1] Peeran S.M. and Cascadden C. “Application, Design and Specification of harmonic filters for Variable Frequency Drives”, IEEE Trans. Ind. Applicat., vol. 31, pp. 841-847, July/August 1995 [2] Boonin Elisabeth, Using Excel Visual Basic for Applications, QUE, 1995 [3] ELECTROTEK, Harmflo+ Tech Notes, Issue # 93- 2, September, 1993 Jesus Baez. Received his BSEE in 1987, his Master of Engineering degree in Electric Power Engineering in 1990 and his Master of Sciences Degree in Control Engineering in 1995 from ITESM, Campus Monterrey. He is professor of the Electrical Engineering Department at ITESM since 1992. His research interest is simulation and analysis of distribution and industrial power systems.