See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/261944345 A New Design Procedure for Output LC Filter of Single Phase Inverters CONFERENCE PAPER · JANUARY 2010 CITATIONS READS 2 2,149 1 AUTHOR: Ahmad Ale Ahmd Babol Noshirvani University of Technology 14 PUBLICATIONS 59 CITATIONS SEE PROFILE Available from: Ahmad Ale Ahmd Retrieved on: 20 January 2016 Other ones used the same method too. IEEE. INTRODUCTION II. Design of an LC filter for the PWM based inverter is very important issue. the capacitor and inductor value are designed [4]. but the ripple current of inductor. The simulations run either linear or nonlinear full loads.5 0. and ω=2πf.3%. f is the input voltage frequency. the high frequency distortion is only included switching or PWM frequency. then calculating the L and C value to minimize this cost function. Abstract. In [4-6]. stand-alone application based on renewable energy. 1). According to the standard this distortion should be limited under 0. the cut off frequency of LC filter is designed based on the Fourier series of the inverter output voltage. Also. H(ω). bandwidth of inverter controller is limited by the cut off frequency of the filter [3]. LC filter. This filter should reduce the high frequency distortion of output voltage and control the switching current. Then by using the relation between the filter capacitor and the system time constant. LC FILTER ANALYSIS Today. The switching devices generate this distortion. there is a trade off between the bandwidth of the controller and filter attenuation. So. The design steps and their considerations are discussed comprehensively. the filter should be studied in two situations. 5KVA inverter. Considering the switches current ripple. active filter. IEEE. determining the L and C values is very important issue. The IEEE Std. and the load (RL) can be varied from the minimum load (RL=∞) to maximum load (RL= RLm). respectively. So. uninterruptible power supply (UPS) and dynamic voltage restorers [1-3]. 86 PEITS2010 .This paper presents a new design procedure for output LC filter of single phase inverter. and the bandwidth of the controller have to be wide for fast response to step or nonlinear load. 1547 requirement for maximum harmonic voltage distortion is shown in table 1. IEEE STD. 3rd.0 1. the inductance and capacitance value are calculated.6 0. So. 1547 requirements for attenuating the harmonics distortion. Also. This procedure is verified with simulation results for a 220V. Two main goals of the procedure are to meet the IEEE Std. Member. The specifications and design criteria’s are illustrated in this paper. efficiency [4-5]. L and C. Adib Abrishamifar. switching frequency and its relation to the cut off frequency of filter is not well considered. For the medium power inverters whose PWM frequency is higher than 3 KHz. 1547 requirements for attenuating of harmonics distortion and to limit the high frequency current of switches in acceptable value.2010 3rd International Conference on Power Electronics and Intelligent Transportation System A New Design Procedure for Output LC Filter of Single Phase Inverters Ahmad Ale Ahmad.Inverter. TABLE 1.3 5.0 The LC filter and its input and output voltage are shown in Fig1. This filter consists of two unknown components. the L and C are selected to minimize the filter reactive power. Authors of [6] defined a cost function based on reactive power where the reactive power of inductor is weighted two times higher than the reactive power of capacitor. I. In [5]. Mohammad Farzi. THD. the low frequency harmonics (2nd. 5th . This paper analyses the characteristics of the output LC filter for PWM inverter. transient response [3] and also the cost of the inverter. inverter with an output LC filter has an especial application such as distributed generation. none of them were presented a straight forward method or relation to calculate the L and C values. The attenuation of switching frequency voltage at the output node is depended on the cut off frequency of filter. the inverter output impedance [4]. Student Member. The cut off frequency of filter and its relation to the modulation factor and switching frequency are determined to meet the IEEE Std. Two main duties of the output LC filter are to attenuate the output voltage ripple and to limit the high frequency ripple current of inverter switches. This procedure is verified with simulation results. inductor current ripple. After selecting the cut off frequency of filter. The cut off frequency of the filter have to be selected small for perfect voltage ripple attenuation.0 11≤h<17 17≤h<23 23≤h<35 35≤h Harmonic Distortion 2. and 7th) are usually rejected by controller perfectly. cut off frequency. The transfer function from Vi to Vo (Fig. Keyword. is shown in (1): X C (ω)||R L Vo(ω) H(ω)= = (1) Vi(ω) X C (ω)||R L +X L (ω) Where XC(ω) and XL(ω) are impedance of capacitor and inductor. IRIEE. minimum and maximum load. because they affect on ripple current of inverter switches. 1547 REQUIREMENTS FOR MAXIMUM HARMONIC VOLTAGE DISTORTION Individual Harmonic order h<11 Total Percent (%) 4. On the other hand. A. the cut off frequency of the LC filter (fr) must be less than fs/15 to satisfy the standard limitation. B. Filter attenuation at the fundamental frequency in minimum load situation. the attenuation of the LC filter at the switching frequency should satisfy following inequality: ω2r = Fig 2.3 = H NL (ωs ) Vo (ω1 ) Vi (ω1 ) H NL (ω1 ) πm 100 (6) So to meet the IEEE Std. It can obtain as: Vi (ω1 ) =mVDC (5) where ω1=2πf1 and f1 and m are fundamental frequency and modulation factor.2010 3rd International Conference on Power Electronics and Intelligent Transportation System 3πm (7) 2000 If the inequality (7) is solved for m=0.95. 1547 requirements. H NL (ωs ) Fig 1. the amplitude of input voltage at fundamental frequency depends on DC voltage and modulation factor. (1) can be summarized as: ω2 H NL (ω)= 2 r 2 (2) ω r -ω 1 (3) LC where ωr=2πfr and fr is the cut off frequency of the LC filter. at the fundamental frequency. So: 4 V (4) Vi (ωs ) max = DC π 2 where ωs=2πfs and fs is the switching frequency. The reactive power of filter at the 87 PEITS2010 . we can write: Vo (ωs ) max Vi (ωs ) max H NL (ωs ) 2 0. It means that the attenuation of the LC filter at the fundamental frequency is approximately 0dB. load value and also capacitor or inductor value. The amplitude of input voltage at the switching frequency depends on DC input voltage and duty ratio of PWM signal. we calculated the L and C value to minimize the filter reactive power. The transfer function of the LC filter at the maximum load condition is: ω 2r H FL (ω)= (10) ω ω 2r -ω2 +j R Lm C Then: ω2r H FL (ω) = (11) ω 2 2 2 2 (ω r -ω ) +( ) R Lm C (11) shows that the attenuation amplitude depends on the cut off frequency. It will be maximum when the duty ratio is 50%. Minimum Load condition In minimum load condition (RL=∞). Maximum Load condition At the maximum load condition (RL= RLm) the filter attenuation at the switching frequency is more than minimum load condition. In the first approach. a) Output LC filer connected to a load. so according to the standard limitation for output voltage distortion. This is suitable to increase the inverter efficiency. we neglect this voltage drop by the first assumption. So: 1 (8) ωr ωs and k 15 k Really. the attenuation due to the filter at the fundamental frequency obtains as follow: ω2 H NL (ω1 ) = 2 s 2 (9) ωs -(kω1 ) Fig 2 shows the |HNL(ω1)| as a function of fs and k where the k factor and switching frequency have been changed from 15 to 20 and 3KHz to 10KHz. These curves reveal that our first assumption about the attenuation of the filter at the fundamental frequency is not far from our expectation. the voltage drop across the filter can not be estimated before the L and C values are specified. b) input voltage and c) output voltage of the filter. respectively. But the filter attenuation at the fundamental frequency should be studied. There are several methods to determine the inductor and capacitor value. Because. respectively. it provides a very large inductor value. The large inductor value increases the output impedance of inverter too. the maximum acceptable ripple current and the switching frequency of the inverter can determine the minimum inductor value. and it can be considered as a fraction of output voltage: VL (ω1 ) =α Vo (ω1 ) (21) Selection of α depends on the switching frequency and maximum acceptable ripple current. Q. With KCL at the output node: 1 (22) I L (ω1 )=IC (ω1 )+IO (ω1 )=(jω1C )Vo (ω1 ) RL 1 )Vo (ω1 ) (23) RL At the maximum load condition. as follow: Lω ω ω3 Q= 21 . So. Fig 3. by using (21) and (25): VL (ω1 )=jω1LI L (ω1 )=jω1 L(jω1C 1 ) Vo (ω1 ) (24) R 2Lm Now. the inductor value can be determined as follow: Q=0 (13) So: R L= Lm ω 2r ω12 (14) ω2r If the ωr is at least 3 times larger than ω1 then the inductor value can be approximated by: R (15) L Lm ωr Also.12 + 1 4 VO2 (12) R L Lωr Lωr To minimize the filter reactive power at the maximum load. and dividing by inductor fundamental current: I L mω1 VDC -Vomsin(ω1 t) sin(ω1 t) = IL fs IL Lω1 (20) mω1 VDC -Vom sin(ω1 t) sin(ω1t) fs VL (ω1 ) Where the VL(ω1) is the inductor voltage at the fundamental frequency. All of these evidences indicate that other criteria should be selected to calculate the inductor value. Although. Replacing (18) and (19) in (17). Fig 4. If equations (20) and (21) are solved for α. the inductor and capacitor values are: VL (ω1 ) =α Vo (ω1 ) =ω1L (ω12 C2 + 88 PEITS2010 . Fig 3 shows the ripple of inductor current in two conditions. The ripple can be estimated as: V (17) I L = L t L According to Fig 1. the cut off frequency of filter should be selected as large as possible (greater than the fundamental frequency of the inverter). the Δt is obtained as follow: D m sin(ω1 t) Δt= = (19) fs fs Where m is modulation index and 0<m<1.2010 3rd International Conference on Power Electronics and Intelligent Transportation System fundamental frequency. The maximum ripple occurs at ω1t=nπ±π/2. It also causes a large over or under-shoot voltage in the step load condition. cut off frequency of filter. The main duty of inductor is the control of the switching frequency of inverter ripple current. The equation (16) shows that to decrease the filter reactive power at the minimum load. However. can be obtained as a function of inductor value. If α is selected then the inductor value can be calculated. The ripple of the inductor current at half of the fundamental period. the reactive power at the minimum load is calculated as: ω Q(R L = ) PLm 1 (16) ωr where the PLm is the output power at the maximum load. When the inverter switches are on. So. this approach improves the inverter efficiency. Usually. when the inverter switches are on: (18) VL =VDC -Vo =VDC -Vomsin(ω1 t) Where Vom is the amplitude of output voltage. it increases the cost and the size of filter. the quantity of α is obtained for specified maximum ripple current at different switching frequencies (Fig 4). The quantity of α as a function of switching frequency for maximum ripple current of 20% and 40%. output voltage and the load. the ripple current between 20% to 40% is acceptable. So. 3) Selecting α factor. if k=15. if the cut off frequency of the filter is decreased below the 200Hz. α completely depends on the switching frequency and acceptable inductor ripple current. If it is not maintained. Another important result of these figures is that. VDC VO Sout fs f1 360V 220VRMS 5KVA 20KHz 50Hz According to DC input and AC output voltage of the inverter. If the modulation factor is less than 0. the filter can amplify the fundamental frequency. 2) Selecting k factor. this aims to optimize the size of inductor and capacitor .2. respectively. Also. IV.95 is appropriate for modulation factor. High switching frequency aims to reduce the filter size. Now at the full load condition.95. but lager k factor causes more attenuation at switching frequency and little amplification at the fundamental frequency.2010 3rd International Conference on Power Electronics and Intelligent Transportation System L= R Lm ω1 α2 - ω14 ω4r (25) ω12 1 (26) R Lm α 2 ωr4 -ω14 To obtain real answer for the equations (25) and (26). A DESIGN EXAMPLE To verify the algorithm. 20% to 40% is an acceptable range for ripple current. This is sometimes useful. but the maximum frequency of solid state switches and their dynamic losses limit the switching frequency. Fig 5. the following condition must be satisfied: ω (27) ωr > 1 α or k (28) fs > f1 α C Fig 6. The filter attenuation at the fundamental frequency in maximum load for fs =3KHz.02 to 0. this factor can be selected. So using the equation (20) or Fig 4. INVERTER CHARACTERISTICS. The filter attenuation at the fundamental frequency in maximum load for fs =20KHz. the 0. the maximum attenuation of filter will only be 3%. The standard requirement will be meet. The inequalities (27) and (28) should be satisfied. And at fundamental frequency: ωr H FL (ω1 ) = (30) 2 (1+α )ωr2 -2ω12 Fig 6 and 7 show the |HFL(ω1)| as function of ωr and α for fs equal to 3KHz and 20KHz. so k=15. TABLE 2. then the k and α factor should be renewed and selected again. but the filter size will be increased. the stability of the system will be very critical. because the phase margin of system decreases when the cut off frequency is decreased. It is usually chosen between 3KHz to 15KHz for IGBT based inverter and 10KHz to 100KHz for MOSFET based inverter. the necessary L and C can be calculated. PROPOSED LC FILTER DESIGN PROCEDURE The LC filter of an inverter can be designed in the following mentioned 4 steps: 1) Selecting the switching frequency. The figures 5 and 6 imply that if α is varied from 0. To limit the inductor ripple current below the 89 PEITS2010 . the minimum of k should be calculated by equations (7) and (8). an LC filter is designed for an inverter whose main characteristics are mentioned in table 2. 4) Now using equations (8). the magnitude of transfer function from Vi to Vo can be written as: ω 2r H FL (ω) = (29) ω 2 2 4 4 2 2 2 (ω r -ω ) +( ) (α ω r -ω1 ) ω1 III. (25) and (26). the gains of voltage and current loop are easily obtained. The current crest factor is 3. As we have designed. 3rd. α factor should be more than 0. Also. a) a) b) b) Fig 10. The THD is below the standard limitation. The capacitor current loop is employed to guarantee the stability of the inverter. it meets the standard requirements for harmonics distortion. a) The inductor current and its ripple.5% and also the switching frequency distortion is below 0. respectively. the ripple is below 40% and the maximum ripple is occured about 45 degree.2010 3rd International Conference on Power Electronics and Intelligent Transportation System 40%. a) The output voltage and current and b) The spectrum of output voltage in maximum nonlinear load with CF=3. Also. To reject the main low frequency harmonics (2nd. the inner loop make the inverter to present a fast response to nonlinear loads. Fig 8. The inverter with designed output filter has been simulated with Simulink Toolbox in MATLAB. Fig 10 a) shows the inductor current. This aims us the filter specification which is listed in table3. fig 10 b) shows the ripple of inductor current in one-fourth of a period. The THD of the output voltage is below 0. 90 PEITS2010 . The fig 9 (a) and (b) show the output voltage and its spectrum at maximum nonlinear load. TABLE 3. 5th. b) Fig 9. The controller of single phase inverter. Fig 8 a and b show the output voltage and its spectrum at maximum linear load.1%. a) The output voltage and current and b) The spectrum of output voltage in maximum linear load. T HE LC FILTER CHARACTERISTICS . So. Using the sliding mode control theory. L C fr 770μH 18μF 1330Hz a) The control loop is illustrated in Fig 7.025 at fs=20KHz. 7th) of output voltage the bandwidth of control loop should be at least 350Hz. Fig 7. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS.D.. Dewan. A. [3] 3. IEEE. To meet the IEEE Std. 6. José Rodríguez. and M. respectively. IPEMC2009. Analysis on Output LC Filter for PWM Inveter. 1(1). VI. 56(6): p.1% at linear and nonlinear full load.G. An LC Filter Degign Method for single Phase PWM Inverter. H.2010 3rd International Conference on Power Electronics and Intelligent Transportation System V. [2] 2. [4] 4.K. IA-21(3): p. Senior Member. J. 1995: p. 2007. Output LC Filter Design of Voltage Source Inverter Considering the Performance of Controller. Juan I. Hong. This algorithm is verified with simulation results for a 220V. In both simulations. [5] 5. Kim. REFERENCES [1] 1. S.V. 14. S. M. and Leopoldo G. Model Predictive Control of an Inverter With Output LC Filter for UPS Applications.. 6. Gabriel Ortiz.4% and 1. 5KVA inverter. L. S. Fellow. 6. [6] 6.. Member.D. IEEE Transaction on Industrial Application.M...P. 2009: p. Student Member. P. Member.15%. Qamaruzzaman. CONCLUSION A complete algorithm to design output LC filter of a single phase inverter is developed in this paper. Yuz. The inductor value is designed to limit the high frequency ripple of switches current. Optimum Filter Design for a Single Phase Solid State UPS System. 2009. Pekik A. 1975. a relation between cut off frequency of the filter and switching frequency is calculated. and JAVIER UCEDA. IEEE. Hyosung Kim . Dahono. B. J. IEEE. The THD of output voltage is less than 0.S. IEEE. 1547 requirements for attenuating of harmonics distortion. Sergio Vazquez.. GUERRERO. Franquelo.Z. Uninterruptible power supply systems provide protection. 6. 2000: p. Patricio Cortés. Choi. IEEE. 91 PEITS2010 . the HD of switching frequency is lower than 0. IEEE. IEEE. IEEE Industrial Electronics Magazine. JOSEP M. IEEE.