AVERAGE CURRENT MODE CONTROL OF A VOLTAGE SOURCE INVERTER CONNECTED TO THE GRID: APPLICATION TO DIFFERENT FILTER CELLS

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1 Journal of ELECTRICAL ENGINEERING, VOL. 55, NO. 3-4, 24, AVERAGE CURRENT MODE CONTROL OF A VOLTAGE SOURCE INVERTER CONNECTED TO THE GRID: APPLICATION TO DIFFERENT FILTER CELLS Mustapha Raoufi Moulay Tahar Lamchich In this paper the average current moe control of a gri connecte inverter is investigate. Two control loops are use: the outer one controls the power flow from the source generator to the gri an the inner one controls the gri currents. This control metho is applie to two system configurations with ifferent filter cells, L- an LCL-filter. The comparison shows the effectiveness of the last configuration in terms of harmonics rejection. Simulations of the propose metho show performances in both transient an steay state. K e y w o r s: gri connecte inverter (VSI), passive filter esign, LCL filter, average current moe control (ACMC) 1 INTRODUCTION The contribution of a renewable power source to the total power generation becomes more an more important. A full-brige inverter is practically always use for interfacing this Green Power Source to the utility-gri. The control of the energy flowing from the DC source, which is corresponing to an arbitrary renewable power source (win turbine, photovoltaic cell, fuel cell, etc), to the gri must be one in orer to track the maximum power point an to maintain a sinusoial gri current with low harmonic istortion an a high power factor. In orer to lower the transmitte high frequency current ripple, ue to the operation of the inverter, a passive filter consisting of inuctors or combination of capacitors an inuctors can be inserte between the inverter operating as a stiff voltage source an the gri that operates also as a stiff voltage source. One of the aims of this paper is to aress some comparisons for ifferent filter types: two cases are consiere L-filter an LCL-filter. Also the esign of these filters will be presente. We can note that the simplest an most common gri filter is the L-filter, which has three inuctors connecte in series, one in each phase. The secon part of this paper eals with the control of the system. The control loops inclues a controller for the gri current an the DC link voltage. As the DC source is a current source, it is necessary to inclue a link capacitor between the renewable power source an the gri inverter, to maintain a voltage source in the input of the last one. The regulation of the system is performe by the DC voltage control loop, which permits to maintain the DC voltage as constant as possible. Then it is necessary to esign a PI control because of the non-linearity between DC-link voltage an gri current that hols a constant DC voltage. The aim of this slower regulator is to keep the DC link capacitor voltage to its reference value by properly regulating the current injecte into the mains. On the other han, the technique use in this paper is the Average Current Moe Control (ACMC) which permits to control the inuctor current an to regulate the three phase inverter output. This metho eliminates some problems observe when using the Current Moe Control such as noise immunity, the nee for a slope compensator, instability at uty ratios exceeing.5,... [4, 6]. ACMC is a current control technique that has an almost constant frequency an prouces a user-efine current waveform. It has a fast response time an is capable of supporting a wie range of power circuit topologies. ACMC is base on a compensator circuit which compensate the poles of an integrating filter transfer function. It uses this integrating filter to prouce an average current error signal that is compare to a triangular waveform to prouce the require pulse with moulation signal [2]. 2 SYSTEM DESCRIPTION, FILTER TOPOLOGY AND DESIGN 2.1. System escription The system is compose, as seen in Fig. 1, of a voltage source inverter (VSI) an a line filter. As mentione above, the source coul be an array of PV panels, a win turbine or a fuel cell source. Generally, a conversion process of the source generator output is use to aapt it to the DC-link voltage of the inverter. Université Cai Ayya, Faculté es Sciences Sémlalia Département e Physique, Laboratoire Electronique et Instrumentation B. Prince My Abellah B.P. 239, Marrakech (Morocco) ISSN c 24 FEI STU

2 78 M. Raoufi M.T. Lamchich: AVERAGE CURRENT MODE CONTROL OF A VOLTAGE SOURCE INVERTER CONNECTED... DC-link voltag Inverter Gri i 1 L 1 L 2 i g From source Line filter Converter sie u c C u g Gri sie Fig. 1. Connecting DC source to gri via a VSI an a line filter. Fig. 2. LCL-filter: single-phase case. gain (B) C FP i L C FZ R i R F V U -8 S R S f (Hz) V ref V tr Fig. 3. Frequency responses, L-filter (ashe) an LCL-filter (soli) from output voltage to line current. Fig. 4. ACMC implementation. Thus, when analyzing the system, the source generator is moele as an ieal current source Filter topology The line filter reuces the high frequency harmonic content of the line current cause by the switche operation of the VSI. Usually, the line filter consists of filter inuctors but other combinations of capacitors an inuctors such as LC- or LCL-filters can be use. The L-filter is a first-orer filter. Its attenuation is 2 B/ecae over the whole range of frequency. Using this filter, the switching frequency of the converter has to be high to obtain sufficient attenuation of the harmonics cause by the PWM converter. The LC-filter is investigate especially in systems using UPS where the loas are resistors in most cases [8]. However, when connecting systems with this filter to a public gri, the resonance frequency varies over time like the inuctance value of the gri. For the reason above, the LC-filter is not investigate in this paper. Using LCL-filter, seen in Fig. 2, the resonance frequency, given by equation (1), epens only to values of the filter components. fres = 1 L1 + L 2 2π L 1 L 2 C (1) The most avantages of LCL-filter are: a) low gri current istortion an reactive power prouction, b) attenuation of 6 B/ecae for frequencies over the resonance frequency, c) possibility of using a relatively low switching frequency. The frequency responses of L- an LCL-filters [1, 5] are given in Fig. 3. It is shown that the two filters have the same attenuation below the resonance frequency. For this range of frequencies, the LCL-filter can be regare as an L-filter with an inuctance of L 1 +L 2. However, the ifference in the attenuation inicates that the sum L 1 +L 2 is smaller than the L-filter inuctance L. Consequently, the voltage rop across the LCL-filter, cause by the injecte current harmonics, is lower compare to the L-filter case. 2.3 Filter esign The passive filter esign epens on the attenuation neee in orer to reuce the high frequency component of the line current. Stanars, such as IEC regulation on current harmonic emissions into the power gri, must be use to rate this attenuation. The IEC regulation states that current harmonics above the 33 r shoul be less than.6 % of the nominal current. The transfer function of the LCL-filter efine by the output voltage to the input current is: G αβ (s) = 1 L 1 L 2 C s ( s 2 + L1+L2 L 1L 2C ) (2) where the series resistance of inuctors are neglecte for simplicity. The corresponing Fourier transform gain

3 Journal of ELECTRICAL ENGINEERING VOL. 55, NO. 3-4, V c I S i inv C L Inverter L 1 L 2 i g V g C Fig. 5. System to be controlle: the VSI sie inuctors are equal, the same for the gri sie inuctors an capacitors. V c ref + - I g 2 3 V g I S + 1 C L.s V c is a two-loop technique that uses an integrator in the inner loop to average the sense current. ACMC escription an its stanar esign are presente in [2]. A circuit scheme that coul be use to implement ACMC is shown in Fig. 4. The current to be controlle is sense through R S an average. The voltage reference V ref is elivere by the outer loop. The integrator output is compare to a triangular waveform, the switch control is then generate. The transfer function of the integrator circuit [4] is escribe by equation (6). sr F C F Z + 1 V = V ref +(V ref V i ) sr i (sr F C F P F Z +C F P + C F Z ) (6) where V i = R S i L. 4 CONTROL SYSTEM Fig. 6. DC-link voltage regulation. function for each harmonic component (n) is: G αβ (jnω) 1 = L 1 L 2 C nω ( ) n 2 ω 2. (3) + L1+L2 L 1 L 2 C With this equation an other statements, like resonance frequency an low ripple current in the inner inuctor, inuctors values are etermine. In aition the capacitor value is rate with the accepte reactive power prouction in the level of the capacitor. In fact, from reference [1], aitional requirements are given by: L 1 = 2 L 2 C =.5C base (4) where C base is the base value of capacitance in the p.u system. Substituting (4) into (3) an solving for the outer inuctor L 2 finally gives a esign expression for the LCLfilter: ( L 2 = max n 3 4Cn 2 ω 2 + ( 3 ) 2+ V ) g,rms 4Cn 2 ω 2. (5) nωi n The same proceure use above can be applie to esign the L-filter. 3 AVERAGE CURRENT MODE CONTROL A wie range of power conversion applications use the current control technique. This technique controls the peak inuctor current to regulate the converter output. The most rawbacks of current control are a poor noise immunity an instability at uty ratios exceeing.5. The Average Current Moe Control (ACMC) is a control technique that overcomes problems liste above. ACMC The system to be controlle is a three phase VSI connecting a source generator to the gri. An L- or LCL-filter is applie to eliminate harmonics generate in VSI. The basic scheme with an LCL-filter is shown in Fig. 5. The main goal of the control is to transfer all source generator prouce energy to the gri. The propose system control is a two loop base. The outer loop is the DC-link voltage. The inner one is aroun ACMC compensators an controls inuctors currents. 4.1 DC-link voltage regulator To esign the DC-link voltage regulator, the following assumptions are consiere: The gri voltage amplitue is constant; Using rotary axes q, the gri voltage v g coincies with -axis; The unity power factor is require, then the isplacement between the gri voltage an current is zero. Their q-axis components are also zeros. The gri power is expresse as follows [7]: P gri = 3 V g I g = 3 2 V g I g. (7) The generate power an the link capacitor power are expresse by equations (8) an (9) respectively P source = V c I S, (8) P capacitor = C L V c V c t. (9) The VSI losses is assume to be omitte, the following relationship is verifie: P gri = P source P capacitor. (1)

4 8 M. Raoufi M.T. Lamchich: AVERAGE CURRENT MODE CONTROL OF A VOLTAGE SOURCE INVERTER CONNECTED... I g (From c voltage control) (t) V Sene gri currents iga,igb, igc q/abc transform iga igb igc iga ref igb ref igc ref Current control loop ACMC ACMC ACMC Switches control 2 n orer filter PI Freq. Variable frequency main value V q abc to q transform Sene gri voltages V ga,v gb,v gc Transfert function Sin_Cos function PLL iagram bloc Fig. 7. Average Current Moe Control scheme. Following equations (7) to (1), the relation between DClink voltage an the gri current expresse in rotary axis is obtaine: V c = 1 Is C L s( 3 Vg I ) g. (11) 2 V c A PI regulator must be esigne to hol a constant DClink voltage [3]. The DC-link voltage control loop is presente in Fig Current control As mentione above, the current control is base on the Average Current Moe Control (ACMC). The propose moel scheme is shown in Fig. 7. The gri currents are sense an compare with references currents. The errors are integrate by ACMC compensators. The outputs are compare with a saw tooth waveform an switch controls are then generate. Ig is the output of PI control in DC-link voltage regulator. θ(t) is obtaine from a Phase-Looke Loop (PLL) which is require to perform the synchronization. In fact, since the reference currents are generate using the q to abc transformation, a sine wave an cosine wave neee to be generate must be synchronize to the utility gri voltage. Figure 7 shows also a block iagram of the improve PLL. The compensator use is base on the PI regulator which must rive the component value of the utility gri voltage in the -axis (V ) to zero performing then the esire value of θ(t). 5 SIMULATION RESULTS The rate power, AC voltage level, filters parameters an frequencies switching use in this simulation are liste below. Rate power: 1 KW Voltage (RMS): 22 V L-filter: Inuctance (L, r ): 1 mh, 1 Ω Frequency switching: 1 KHz LCL-filter: Converter sie inuctance (L1, r1): 2 mh,.2 Ω Gri sie inuctance (L2, r2): 1 mh,.1 Ω Capacitor (C, r): 5 µf, 5 Ω Frequency switching: 2.5 KHz 5.1. DC-link Voltage regulation Figure 8 shows the DC-link voltage result. It is regulate an reaches closely the voltage reference after a small rise time compare to the gri perio. Furthermore, in actual case, the DC-link capacitor shoul be charge before starting the system VSI an Gri currents The gri current is generate using two filter cells mentione earlier (L an LCL ones), Figs. 9 an 1(b). It can be seen that the result are enhance using an LCLfilter.

5 Journal of ELECTRICAL ENGINEERING VOL. 55, NO. 3-4, DC - link voltage gri current (A) Fig. 8. DC-link voltage. Fig. 9. Gri currents: L-filter case. VSI current (A) a) gri current (A) b) Fig. 1. Generate current: a):before an b):after filtering with LCL-filter case. gri current (A) gri voltage an current (V,A) Fig. 11. Transient response: effect in step change (lower an upper) in source current. Fig. 12. Phase isplacement between gri voltage an current (current is multiplie by a factor of 5). LCL-filter case. 5.3 Transient Response A 5 % step (lower an upper) change in the source current s simulate. Figure 11 shows that the gri current follows this change with a fast time. 5.4 Power factor Figure 12 shows one phase isplacement (the same for other phases) between the gri voltage an current. A near unity power factor can be reache as require.

6 82 M. Raoufi M.T. Lamchich: AVERAGE CURRENT MODE CONTROL OF A VOLTAGE SOURCE INVERTER CONNECTED... magnitue magnitue THD = 13.23% 4 THD = 4.91% 4 2 a) 2 b) frequency (Hz) frequency (Hz) Fig. 13. The frequency response an the value of the THD for L-filter (a) an LCL-filter (b). 5.5 Total harmonic istortion The effectiveness of each configuration, corresponing to a type of the filter cell inserte between the VSI an the utility gri, in term of harmonic rejection, was quantitatively etermine by calculating the total Harmonic Distortion (THD) of the resulting supply current. An expression for THD is given in equation (12) bellow, where I n(rms) is the root-mean-square current of the n th harmonic. T HD = 2 I2 n(rms) I l(rms) 1 % (12) Figure 13 shows the frequency response an the value of the THD for each type of filter cell. 6 CONCLUSION This paper presents the Average Current Moe Control (ACMC) technique applie to a three phase fullbrige inverter inserte between an arbitrary renewable power source (fuel cell, photovoltaic cell, win turbine, etc) an the utility-gri. This metho, base on a compensator circuit use as an integrating filter, prouces a user-efine current waveform. By using the Concoria (alpha, beta) transformation, we reuce the compensator blocks to two circuits. In the future, most investigations will be one in the object to control the currents in the mains by using minimum sensors. Another interesting point presente in this paper concerns the choice of the filter type inserte between the inverter an the gri in orer to lower the transmitte high frequency current ripple. The comparison one between two filter configurations shows the effectiveness of the LCL-filter in terms of harmonic rejection versus the most common L-filter. References [1] BOJRUP, M. : Avance Control of Active Filters in a Battery Charger Application, Licenciete thesis, Lun Institute of Technology, Sween, [2] DIXON, L. : Average Current Moe Control of Switching Power Supplies, Unitroe Switching Regulate Power Design Seminar Manual, SEM-7, 199. [3] DOMINGUEZ, J. A. LORENZO, S. DePABLO, S. CACE- RES, S. : Global Control for Two PV Applications: Pumping an Connecting to the Gri Systems, EPE 97. 7th European Conference on Power Electronics an Applications. Tronheim, Noruega. Septiembre [4] ERICSON, R. W. MAKSIMOVIC, D. : Funamentals of Power Electronics, Kluwer Acaemic Publishers, 2n eition 21. [5] KJAER, S. B. ANDERSEN, G. K. KLUMPNER, C. BLAADJERG, F. : Control Aspects of a LCL Gri-Connecte Green Power Inverter, NORPIE 22, August 22. [6] MIDDLEBROOK, R. D. : Moeling Current Programme Buck an Boost Regulators, IEEE Transactions on Power Electronics 4 No. 1 (1989). [7] SUN, Q. : Control of PWM VSI with LCL-Filter in WTG Application, Master thesis. [8] SVENSSON, J. Gri-Connecte Voltage Source Converter Control Principles an Win Energy Applications : PhD thesis, Chalmers Unversity of Technologie, Göteborg, Sweeen, March Receive 9 September 23 Mustapha Raoufi was born in 1965 in Ben Ahme (Settat), Morocco. He has presente his thesis in electronics in September 1992 an receive his thir cycle egree from the Faculty of Sciences Semlalia at Marrakech. He is presently Professor-assistant at the same faculty, at the Department of Physics. His research interests have inclue active power filters an static converters. Moulay Tahar Lamchich was born in 1965 in Marrakech, Morocco. He has presente his thesis in electrotechnics in September 1991 an receive his thir cycle egree from the Faculty of Sciences Semlalia at Marrakech. He receive his PhD from the same university in July 2. He is presently Professor-ability at the same Faculty, at the Department of Physics. His main activity is base on short-circuit mechanical effects in substation structures an his research interests have inclue active power filters, machine rivers, static converters, an publishe several technical paper in this fiel.