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20120140506014
1. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 6, June (2014), pp. 89-98 © IAEME 89 SINUSOIDAL FRONT END CONVERSION WITH HIGHER ORDER INPUT FILTER Renjith Kumar D Assistant Professor, Department of Electrical and Electronics Engineering, College of Engineering Adoor, Kerala, India ABSTRACT The fast development of consumer electronics and increase in growth of power electronic devices resulted in a plethora of nonlinear loads which invariably uses mains rectification circuits using line commutated devices at the front end, acting as the dominant cause of current harmonic distortion. The non sinusoidal currents drawn from the supply at the various harmonic frequencies produce individual voltage drops creating voltage distortions and consequent losses. To reduce those issues, Pulse Width Modulation (PWM) based Voltage Source Converters (VSC) employed as Sinusoidal Front End Converters (SFECs) interfacing the grid and the load are being used. Their main characteristics are the generation of reduced low frequency line current harmonics, better overall input power factor, substantially smaller filter requirements, consistent dc bus voltage and inherent regeneration capability. Compared with an L filter at the input side of SFEC, an LCL filter is preferred for the grid tied voltage source converter to limit the switching current ripple emitted into the grid. The advantages of using LCL filter include better attenuation of harmonics, reduction in filter inductance value and high dynamic performance. This paper analyzes how LCL filter acts as a better alternative to conventional L filter for improving the input spectral quality at the input of Pulse Width Modulated Voltage Source Converter based Front End Conversion, thereby meeting the prescribed harmonic standards. Passive damping techniques are utilized to settle down the resonance issues that are caused due to interaction of energy storage elements present. Successful simulations are also carried out with designed values for establishing the merits of using the higher order filter at the input. Keywords: EMI (Electro Magnetic Interference), FFT (Fast Fourier Transform), LCL Filter, PI Control, PWM (Pulse Width Modulation), SFEC (Sinusoidal Front End Converter), THD (Total Harmonic Distortion), VSC (Voltage Source Converter). INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING AND TECHNOLOGY (IJARET) ISSN 0976 - 6480 (Print) ISSN 0976 - 6499 (Online) Volume 5, Issue 6, June (2014), pp. 89-98 © IAEME: http://www.iaeme.com/IJARET.asp Journal Impact Factor (2014): 7.8273 (Calculated by GISI) www.jifactor.com IJARET © I A E M E
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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 6, June (2014), pp. 89-98 © IAEME 90 1. INTRODUCTION Conventional diode and thyristor rectifiers employed as front end converters for the ever increasing number of power electronic loads draw highly distorted current and have a poor overall input power factor. A large number of these devices distributed in a grid may severely distort the grid voltage in a cumulative way causing mal operation and premature failure of other sensitive loads [1]. This led to the wide acceptance of active power filters and Front End Converters based on force commutated devices. The high frequency components associated with Pulse Width Modulation of the SFEC may cause disruption to other Electro Magnetic Interference (EMI) sensitive loads connected on the grid. To mitigate this effect in high power systems, the input filter inductance value of the SFEC has to be increased which can cause unstable operation of the system. Also, the dynamics of the response becomes poorer causing long time responses, more losses and cost [2]. Using LCL filter at the input side reduces the filter size, cost etc. and improves the harmonic performance [3]. The shunt capacitor in the filter circuit offers more attenuation to the switching ripple present in the input current of the rectifier favoring lower values of inductors. But resonance problems can occur due to the interaction of inductive and capacitive elements giving rise to instability issues [4]. The oscillations due to resonance can be easily damped out by using damping resistors in the circuit. 2. CONFIGURATION AND CONTROL OF PWMVSC WITH LCL FILTER The converter consists of a three phase IGBT bridge converter, a high capacitance on the dc side and three single phase LCL filters on the line side [4]. The Pulse Width Modulated pole voltage consists of a fundamental component at line frequency besides harmonic components around the switching frequency of the converter. Being at high frequencies, these harmonic components are well filtered by the input filter, hence the mains current is nearly sinusoidal. The fundamental component of pole voltage controls the flow of real and reactive power. High capacitance at the dc side maintains a stable dc bus voltage. Input power factor is normally kept at unity. Besides inverter current sensor, an additional current sensor which senses either line current or capacitor current is used for current detection. The use of line current feedback is justifiable since line current phase angle can be directly adjusted to control the power factor at the point of grid connection. Based on the feedback variables and input commands, proper control signals are derived from the controller for sinusoidal PWM switching of the converter as shown in Fig. 1. Fig. 1: Basic configuration of Voltage Source Converter with LCL filter and its control
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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 6, June (2014), pp. 89-98 © IAEME 91 Presence of capacitor in the filter can lead to undesirable resonance oscillations due to zero impedance at resonance frequency causing both dynamic and steady state input current distortions and instability problems [1]. Proper damping will move the unstable poles more inside the stability region and absorbs a part of the switching frequency ripple to avoid the resonance, making the attenuation effective. As parasitic losses of the filter elements yield only slight damping at resonance which is not sufficient, passive damping has to be achieved by introducing an element like resistance in the filter circuit. The guidelines to select the appropriate seat of damping resistor are minimum losses and size, minimum effect on switching ripple attenuation, effective damping at resonance etc. Considering all these guide lines, based on frequency response analysis, a resistor in series with the capacitor is considered for passive damping analysis [5]. 3. MATHEMATICAL MODELING OF DAMPED LCL FILTERS Let vg be the grid voltage, ig be the grid current, vi be the inverter ac side voltage, ii be the inverter ac side current, vc be the capacitor voltage, Lg be the grid side inductance, Li be the inverter side inductance, Cf be the filter capacitance, Rd be the damping resistance, ic be the filter capacitance current, C be the dc bus capacitance, Idc be the dc current from the rectifier, Io be the load current and Vdc be the dc bus voltage. The single phase representation of the converter with LCL filter using passive damping is shown in Fig. 2. Fig. 2: Single phase representation of SFEC with LCL filters using passive damping Fig. 3: Block diagram of the transfer function of the LCL filter using passive damping Fig. 3 shows the block diagram of the transfer function of the LCL filters with damping resistor where the parasitic resistors in the filter elements are ignored [2]. Corresponding open loop transfer function connecting converter voltage and grid current can be written as ܑሺܛሻ ܞܑሺܛሻ ൌ ܀܌۱ܛା ൫ۺܑାۺ൯ܛቈ ۺܑۺ۱ܛ ۺܑశۺ ା۱܀܌ܛା (1)
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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 6, June (2014), pp. 89-98 © IAEME 92 In the grid connected system with L filter alone, the relationship between grid current (ig = ii) and converter voltage is ܑሺܛሻ ܞܑሺܛሻ ൌ ۺܛ (2) The LCL filter transfer function relating converter voltage and grid current with no damping is given by ܑሺܛሻ ܞܑሺܛሻ ൌ ۺܑۺ۱ܛା൫ۺܑାۺ൯ܛ (3) 4. DESIGN CONSIDERATIONS Usually the converter side reactor attenuates most of the switching ripple generated by the converter and hence should be normally bigger than that at the grid side. The higher the ratio Li/Lg is chosen, the better the attenuation of switching frequency components. However if Lg is very small, the dependency on grid stiffness is highly increased such that the influence of line impedance variations on the resonance frequency is increased causing stability problems, especially in weak grids. The total inductance Li+Lg can be up to 10% of base inductance so that voltage drop can be limited [2]. Capacitors are selected based on power factor, reactive power, resonant frequency, bandwidth of closed loop system etc. Larger capacitor results in good damping of high frequency switching current components and leads to smaller size of magnetic components, lesser filter volume, losses and cost [3]. However it can result in high inrush current, too low resonance frequency, grid side resonance, stability problems, increased reactive power consumption, dependence of grid impedance on overall harmonic attenuation and a higher harmonic current through the capacitor and inductor. Small filter capacitance causes resonance at higher frequency and thus the controller design becomes more difficult. Thus an optimal design of capacitor is appreciated. The best seat of resonant frequency is in a range between ten times the supply line frequency and one half of the switching frequency to avoid resonance problems in the lower and higher parts of the harmonic spectrum [2]. Damping resistor must be a compromise between reduction of oscillations and increased power losses. The filter capacitor value is referred in % of the following base values Base impedance value, ܈܊ ൌ ܄ ۾ (4) Base capacitance value, ۱܊ ൌ મ܈܊ (5) where P is the rated active power of the system, Vg is the RMS value of grid line voltage and f is the frequency of grid voltage. Generally, the fundamental reactive power absorbed by filter capacitors should be less than 5% of rated power of VSC to avoid excess power factor decrease. Hence it is considered that the maximum power factor variation seen by the grid is 5%. Thus, ۱ ൌ . ۱܊ (6)
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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 6, June (2014), pp. 89-98 © IAEME 93 As in SFEC with L filters, assuming current ripple to be largest for a duty cycle of 50% ۺܑ ൌ ܄܋܌ ૡ√∆۷ܟܛ (7) where ∆I is the permitted rms current ripple and fsw is the switching frequency. The relation between the harmonic current generated by the inverter and the current injected in the grid is explained by the following transfer function ܑሺܛሻ ܑܑሺܛሻ ൎ ାܛۺ۱ (8) Considering a suitable ripple attenuation factor on the grid side with respect to the current ripple on the inverter side, the ratio ‘r’ between the inductance at the grid side and the one at the inverter side can be computed such that ۺ ൌ ۺܚܑ (9) To avoid resonance, the resonance frequency (fres) should be such that ܛ܍ܚ . ܟܛ (10) ܛ܍ܚ ൌ મ ට ۺܑାۺ ۺܑۺ۱ (11) The value of the damping resistor should be at least one third of the impedance of the filter capacitor at the resonant frequency. Hence ܀܌ ૈܛ܍ܚ۱ (12) The allowable ripple component on the dc bus voltage decides the value of the required capacitor. The dc bus capacitance is given by ۱ ൌ ۾ܑܖઢܜ ܄܋܌ઢ܄ (13) where Pin is the input power at rated condition, ∆t is the discharge period (to load) and ∆V is the ripple voltage allowed at the dc bus. 5. CONTROL STRATEGY The control scheme modulates the inverter to regulate the magnitude and phase angle of the grid supply current, so that the real and reactive power entering the network can be controlled. The transient operating conditions resulting from change of load and load voltage reference will be taken care of by the charge or discharge process of the capacitor. The outer dc bus voltage control loop keeps a constant value of the dc link voltage and provides the d axis reference current for the current loop which influences the active power flow. The q axis reference current is set to zero so as to make input power factor unity. Synchronous reference frame based PI controls have been adopted that has
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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 6, June (2014), pp. 89-98 © IAEME 94 the d axis oriented on the grid voltage [2]. The parameters involved, transformations and control topology are applicable to both d axis parameters and q axis parameters. The single phase model of the current control loop representing the system without damping is shown in Fig. 4. Bode analysis are used to assess the stability of the system. Fig. 4: Single phase representation of the control strategy without damping The corresponding closed loop transfer function without damping is given by ܑሺܛሻ ܑ܍ܚሺܛሻ ൌ ۹ܘܛା۹ܑ ۺܑۺ۱ܛା൫ۺܑାۺ൯ܛା۹ܘܛା۹ܑ (14) Obviously the system is unstable. The system can be made stable by inserting a proper resistor in series with the capacitor filter indicating passive damping as shown in Fig. 5. Fig. 5: Single phase representation of the control strategy with passive damping The closed loop transfer function for the current control loop with passive damping is then ܑሺܛሻ ܑ܍ܚሺܛሻ ൌ ۹ܘ܀܌۱ܛା൫۹ܘା۹ܑ܀܌۱൯ܛା۹ܑ ۺܑۺ۱ܛା൫܀܌۱ۺܑା܀܌۱ۺ൯ܛା൫ۺܑାۺା۹ܘ܀܌۱൯ܛା൫۹ܘା۹ܑ܀܌۱൯ܛା۹ܑ (15) 6. STABILITY ANALYSIS AND SIMULATION RESULTS The system parameters taken for the calculation of the filter components of the SFEC using both L and LCL filters are P = 7 kW, Vg = 415 V, f = 50 Hz, fsw = 10 kHz, Vdc = 700 V. Current controller time constant, Ti = 150 µs and voltage controller time constant, Tv = 20 ms. Assuming unity input power factor and an efficiency of 95% for the SFEC, rated input grid current, I ൌ 10.26 A From Eqn. (4), (5) and (6), filter capacitance, C ؆ 7 µF From Eqn. (7), inductance on the converter side for 10% rms current ripple, L୧ ؆ 5 mH
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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 6, June (2014), pp. 89-98 © IAEME 95 Considering a ripple attenuation factor of 5%, from the sinusoidal transfer function of Eqn. (8) and from Eqn. (9), r = 0.14 and grid side inductance, L ؆ 700 µH From Eqn. (11), resonant frequency, f୰ୣୱ ؆ 2450 Hz this satisfies Eqn. (10). Consequently resonant angular frequency, ω୰ୣୱ ؆ 15300 rad/sec From Eqn. (12) damping resistor, Rୢ 3.3 For 2% dc voltage ripple and a discharge period of 1 ms, from Eqn. (13), C ൌ 700 µF For the simulation of SFEC, the inductance of the L filter has been chosen as the sum of the inductances in LCL filter for an easy comparison of harmonic performance. The frequency response plots of the SFEC with different filters and control loops are given in Fig. 6 to Fig. 9. Designed values of filter elements are taken for the analysis. Fig. 6: Frequency response of ig(s)/vi(s) for L and LCL filters without damping In the lower part of the spectrum, the LCL type filter behaves like an L type filter as the effect of filter capacitance can be neglected. If no damping is applied, resonance occurs at the resonant frequency (15300 rad/sec) causing very high gain, promoting instability. In the higher part of the spectrum, LCL filtering effectiveness is highly improved by attenuating high-frequency harmonics. Thus to obtain a given attenuation of switching frequency ripple, lower values of inductances are sufficient in case of LCL filter. This reduces the size of filter components and also the cost. Fig. 7: Frequency response of ig(s)/vi(s) for LCL filter with different Rd -100 -50 0 50 100 150 Magnitude(dB) System: sys Frequency (rad/sec): 1.53e+004 Magnitude (dB): 104 10 2 10 3 10 4 10 5 -540 -360 -180 0 Phase(deg) Bode Diagram Frequency (rad/sec) L LCL -80 -60 -40 -20 0 20 40 Magnitude(dB) 10 2 10 3 10 4 10 5 -225 -180 -135 -90 Phase(deg) Bode Diagram Frequency (rad/sec) Rd=5 ohm Rd=20 ohm
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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 6, June (2014), pp. 89-98 © IAEME 96 Fig. 8: Open loop frequency response of current control loop without damping Fig. 9: Open loop frequency response of current control loop with passive damping The simulation results using PSIM for the SFEC with LCL filter at full load and Iqref = 0 A are given in Fig. 10 and Fig. 11. Designed values of filter elements and controller time constants are taken for the simulation analysis. Fig. 10: Grid current when no damping is applied 10 2 10 3 10 4 10 5 -675 -630 -585 -540 -495 -450 Phase(deg) Bode Diagram Frequency (rad/sec) -100 0 100 200 300 400 Magnitude(dB) System: sys Frequency (rad/sec): 1.53e+004 Magnitude (dB): 309 No damping -60 -40 -20 0 20 40 Magnitude(dB) System: sys Frequency (rad/sec): 1.81e+004 Magnitude (dB): -4.77 10 2 10 3 10 4 10 5 -225 -180 -135 -90 Phase(deg) System: sys Frequency (rad/sec): 1.81e+004 Phase (deg): -180 Bode Diagram Frequency (rad/sec) Passive damping
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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 6, June (2014), pp. 89-98 © IAEME 97 Fig. 11: Grid voltage, grid current (scaled by 10), inverter current and capacitor current on passive damping Fig. 12 shows the effect of damping on the FFT (Fast Fourier Transform) of the grid current drawn by the SFEC. Fig. 12: FFT of grid current The THD of the input current (THDi) measured after connecting each of the input filters to the front end converter is indicated in the Table 1.
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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 6, June (2014), pp. 89-98 © IAEME 98 Table 1: THD comparison Input filter THDi at full load THDi at half load L filter 6 mH 3.59% 7.02% LCL filter 5 mH, 7 µF, 1 mH 2.13% 4.29% 7. CONCLUSION Improved harmonic performance is obtained from SFEC when L filter is replaced with LCL filter. The size of filter inductors in the case of the LCL filters can be made smaller than that of L filters for the same filtering effect of harmonic components. This topology provides a better decoupling between filter and grid impedance and the ripple current stress is lower across the grid inductor. The simulation results proved that the high frequency grid current ripple due to PWM switching is considerably reduced using properly damped LCL filter, improving the input spectral quality and harmonic performance. Passive damping technique has been effectively utilized for limiting the resonance issues associated with LCL filters. 8. ACKNOWLEDGEMENT The author would like to thank CDAC Trivandrum and Faculty Members of Department of EEE, NIT Calicut for their immense help and support extended for completing the task. REFERENCES [1] I. C. Evans and A. H. Hoevenaars, “ Meeting harmonic limits on marine vessels”, Electric Ship Technologies Symposium, ESTS’07, IEEE, May 2007, pp. 115-121. [2] M. Liserre, F. Blaabjerg and S. Hansen, “Design and control of an LCL filter based three phase active rectifier”, IEEE Transactions on Industry Applications, vol.41, Sep/Oct 2005, pp.299-307. [3] H R Karshenas and H Saghafi, “Performance investigation of LCL filters in grid connected inverters”, IEEE PES Transmission and Distribution Conference and Exposition Latin America, Venezuela 2006, pp. 1-6. [4] Fei Liu et al. “Design and research on parameter of LCL filter in three phase grid connected inverter”, IPEMC 2009, pp. 2174-2177. [5] Wenqiang Zhao et al. “A double-loop current control strategy for shunt active power filter with LCL filter”, IEEE International Symposium on Industrial Electronics (ISlE 2009), Seoul Olympic Parktel, Seoul, Korea, July 5-8, 2009, pp. 1841-1845. [6] Narayan G. Apte and Dr. Vishram N. Bapat, “Indirect Current Controlled Single Phase Shunt Active Filter”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 4, 2013, pp. 264 - 273, ISSN Print : 0976-6545, ISSN Online: 0976-6553. [7] Mihail Antchev, Ivailo Pandiev, Mariya Petkova, Eltimir Stoimenov, Angelina Tomova and Hristo Antchev, “PLL for Single Phase Grid Connected Inverters”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 5, 2013, pp. 56 - 77, ISSN Print: 0976-6545, ISSN Online: 0976-6553. [8] Dr. Leena G, Bharti Thakur, Vinod Kumar and Aasha Chauhan, “Fuzzy Controller Based Current Harmonics Suppression using Shunt Active Filter with PWM Technique”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 1, 2013, pp. 162 - 170, ISSN Print : 0976-6545, ISSN Online: 0976-6553.
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