THE voltage-source converter (VSC) may be used as an

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1 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 5, SEPTEMBER/OCTOBER Design and Control of an LCL-Filter-Based Three-Phase Active Rectifier Marco Liserre, Member, IEEE, Frede Blaabjerg, Fellow, IEEE, and Steffan Hansen, Member, IEEE Abstract This paper proposes a step-by-step procedure for designing the LCL filter of a front-end three-phase active rectifier. The primary goal is to reduce the switching frequency ripple at a reasonable cost, while at the same time achieving a high-performance front-end rectifier (as characterized by a rapid dynamic response and good stability margin). An example LCL filter design is reported and a filter has been built and tested using the values obtained from this design. The experimental results demonstrate the performance of the design procedure both for the LCL filter and for the rectifier controller. The system is stable and the grid current harmonic content is low both in the low- and high-frequency ranges. Moreover, the good agreement that was obtained between simulation and experimental results validates the proposed approach. Hence, the design procedure and the simulation model provide a powerful tool to design an LCL-filter-based active rectifier while avoiding trial-and-error procedures that can result in having to build several filter prototypes. Index Terms Cascade control, LCL filter, rectifier, stability, voltage-source converter (VSC). I. INTRODUCTION THE voltage-source converter (VSC) may be used as an active rectifier, with the advantages of its potential for full control of both dc-link voltage and power factor, and its ability to work in rectifying and regenerating mode [1]. Moreover, the use of pulsewdith modulation (PWM) in conjunction with closed-loop current control allows a sinusoidal input current to be achieved with a total harmonic distortion (THD) below 5%, even if grid voltage or current sensors are not used [2] [5]. However, typical power device switching frequencies of between 2 15 khz can cause high-order harmonics that can disturb other sensitive loads/equipment on the grid, and can also produce losses [6]. To reduce the current harmonics around the switching frequency a high value of input inductance should be used. However, for applications above several kilowatts, it becomes quite expensive to realize higher value filter reactors. Moreover, the system dynamic response may become poorer. Paper IPCSD , presented at the 2001 Industry Applications Society Annual Meeting, Chicago, IL, September 30 October 5, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial Power Converter Committee of the IEEE Industry Applications Society. Manuscript submitted for review July 1, 2003 and released for publication June 2, M. Liserre is with the Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari, Bari, Italy ( liserre@ieee.org; liserre@poliba.it). F. Blaabjerg is with the Institute of Energy Technology, Aalborg University, DK-9220 Aalborg East, Denmark ( fbl@iet.auc.dk). S. Hansen is with Danfoss Drives A/S, DK-6300 Graasten, Denmark ( s_hansen@danfoss.com). Digital Object Identifier /TIA An alternative and attractive solution to this problem is to use an LCL filter as shown in Fig. 1. With this solution, optimum results can be obtained in the range of power levels up to hundreds of kilovoltamperes, still using quite small values of inductors and capacitors [6], [7]. A further issue for a VSC is high-frequency electromagnetic interference (EMI) (differential mode and common mode) [8], which needs specific filters (passive [9], [10] or active [11]) in frequency ranges above 150 khz and rated at lower power levels. Of course, an LCL filter that is effective in the reduction of switching frequency harmonics may also be effective for differential mode EMI if the filter inductors are built using chokes that can mitigate high frequency (using ferrite cores, for example). Similarly, for common-mode EMI, a commonmode inductor could be included in the differential-mode filter as suggested in [12]. However, conducted EMI is a very complex problem: depending on the frequency range it needs different solutions and specifically designed filters. Hence, even if filter integration is feasible in some cases, the use of one filter over a wide frequency range is often too expensive since the same reactive element must be designed to work over different frequency ranges and at different power levels. It should be noted that European standards in the frequency range khz are incomplete and still under discussion and, hence, grid filters are often designed to work at frequencies higher than 150 khz [13]. However, IEEE recommends that harmonics higher than the 35th should be limited and switching current ripple reduction is also explicitly required for equipment with high safety issues (such as cranes and elevators). Hence, the design of an LCL filter to limit switching frequency ripple injection into the grid in the range of khz is often specifically required. A good criterion to choose LCL filter parameters is to limit the size of the installed reactive elements (these can result in a poor power factor [14]) and the LCL filter power losses (due to the passive damping required to avoid resonance). Some issues have been explored in the literature: criteria for parameter choices [15], [16], active damping of the filter [7], [17], and state feedback control using state observers [15], [16], [18] [21]. Techniques for current control have also been compared taking into account the LCL filter design [22]. However, the design of an LCL filter, and how it might be optimized, has not been analytically studied to date. This paper presents a design procedure for an LCL filter together with consideration of the control of an active rectifier employing an LCL filter using proportional-plus-integral (PI)- based control strategies for the dc voltage and the ac current. These current regulators are typically designed in a rotating /$ IEEE

2 1282 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 5, SEPTEMBER/OCTOBER 2005 Fig. 1. Three-phase active rectifier with LCL filter. Fig. 2. Single-phase equivalent of the active rectifier with LCL filter. frame but the use of the LCL filter requires additional investigation to determine correct orientation of the frame [23]. Furthermore, stability problems should be correctly addressed by considering zero/pole placements in the -plane. Finally, the dynamic performance of the controlled system should be verified. All these topics are addressed in this paper, to provide a detailed and practical guideline both for the design and for the control of an LCL-filter-based three-phase active rectifier. II. MODEL AND CONTROL OF THE SYSTEM The LCL-filter-based active rectifier has been previously modeled in the rotating frame [7] and state feedback controls have been presented to guarantee the stability of the system. However, these approaches require either an increased number of sensors or increased complexity in the control algorithm [15], [16], [18] [21]. The purpose of this paper is to present a simple and low-cost (both in hardware and in software) LCL-filter-based active rectifier. The system is shown in Fig. 2. The VSC is connected to the grid through an LCL filter and an isolation transformer (used in the test setup for security purposes). Note that the transformer inductance and resistance have to be taken into account in the design of the filter and the controllers. The LCL filter is made up of three reactors with resistance and inductance on the converter side, three reactors with resistance and inductance on the grid side, and three capacitors (each of them damped with a resistor ). Fig. 2 also shows a common-mode filter that may or may not be included in the LCL filter [12]. The design of this filter is not treated in this paper. The system proposed has no additional sensors compared to a conventional L filter configuration. It should be noted that the current sensors are on the converter side because in an industrial inverter they are also used to protect the power converter and are, therefore, integrated in it. The main aim is to achieve decreased switching ripple with only a small increase in filter hardware, and by only adapting the parameters of the PI-based controller that is already used for the L filter configuration. This is expected because the LC part of the LCL filter aims to primarily reduce the high-frequency current ripple, and the capacitor s influence can be neglected in the current controller design if its value is low. In fact, current control, because of its bandwidth, primarily influences only the low-order current harmonics. Thus, the upgrade to an LCL filter is easy and effective with a little increase in overall system cost and no new sensors required. Overall, a designer needs to model the system in the rotating frame of the L-filter-based active rectifier (for the control), and consider the transfer function of the overall filter with damping for stability and dynamic purposes. A. Controller Design From Fig. 2, the system can be defined using the following equation, neglecting the filter capacitor : where,, is the grid voltage space vector, is the converter current space vector, and is the converter-side voltage space vector. Current control is developed in a frame that rotates at an angular speed (note that can be zero). In this frame, two (1)

3 LISERRE et al.: DESIGN AND CONTROL OF AN LCL-FILTER-BASED THREE-PHASE ACTIVE RECTIFIER 1283 Fig. 3. Vector diagram for the active rectifier. voltage equations can be written to identify the and current components Fig. 4. Input filter model for active rectifier. These currents are controlled by the correct choice of the voltages generated by the converter. Two PI regulators command a space-vector modulator to generate the voltages that should control these currents. The design of the PI controllers is done using zero/pole placement in the -domain, where as a design criterion the technical optimum is used with both plants for the current control having the same time constant [7]. All processing and modulation delays should be taken into account [23], [24]. For dc voltage control, once the dc load current, the dc load voltage, and the converter-side current are defined, the following equation can be written: The dc voltage is controlled using the converter-side dc current. The PI controller is synthesized using zero/pole placement in the -domain with the objective of obtaining the best possible compromise between rapid dynamic control of the dc output voltage and reduction of the ac current overshoot. All processing and filtering delays must be considered. B. Rotating Frame Orientation A rotating frame is often chosen in order to obtain current control with rapid dynamic response [2]. However, similar results can be obtained using resonant controllers in the stationary frame [2], [25]. For the active rectifier, the frequency of rotation of the frame is the line frequency. If the axis is oriented on the grid voltage vector, the grid current vector should have a zero component to obtain unity power factor while the component regulates the dc voltage (Fig. 3). However, problems can arise from wrong orientation of the frame: firstly it can be difficult to obtain unity power factor, and then the efficiency of the control loops may be compromised. Two issues must be considered. 1) Since current control is performed on the converter current rather than the grid current, it should be controlled with the goal of zero displacement between the grid current and the grid voltage. This implies a nonzero -com- (2) (3) ponent reference for the converter current, to take the filter capacitor into account [24]. 2) The voltage used for the -frame orientation is not the grid voltage, if a transformer is present (such as the isolation transformer used in this setup) or if the capacitor voltage is sensed instead of the grid voltage for active damping purposes [7]. Thus, the voltage drop between the grid voltage and the sensed voltage creates an angle displacement that should be taken into account. This also results in a nonzero -reference current. Thus the component of the reference current is used for dc voltage control and the component of the reference is used for correct orientation of the frame. C. LC Filter Influence The selection of the parameters of the filter will be explained in the next section, but the configuration of the filter should be taken into account when the stability of the system is investigated. So far, the current controller design has neglected the zero and poles introduced by the capacitor presence. If the whole LCL filter is considered as in Fig. 4, its transfer function becomes in case where and. Hence, the LCL filter has two more zeros and two more poles compared to a simple L filter. If the transfer function expressed by (4) is discretized, and the closed-loop root locus is considered with the PI controller tuned using the previously identified criteria (i.e., considering only the inductance ), these additional zeros and poles can make the system unstable without proper damping. Damping is achieved by connecting a resistor in series with the filter capacitor, as shown in Fig. 1, Fig. 2, and the model of the input filter of Fig. 4. This moves the unstable poles more inside the stability region, as will be shown by analyzing the -domain zeros and poles of the closed-loop system in Section VI. III. CONSTRAINTS ON THE LCL FILTER DESIGN The LCL filter aims to reduce high-order harmonics on the grid side, but a poor filter design can cause lower attenuation (4)

4 1284 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 5, SEPTEMBER/OCTOBER 2005 Fig. 5. Equivalent single-phase LCL filter at the h harmonic. where,, ( is the switching frequency), and is the switching frequency harmonic order. The attenuation introduced by the LCL filter is effective only if the filter is properly damped. Otherwise, the resonance of the filter produces a higher ripple. One damping method is to connect a resistor in series with the filter capacitor. The plant of the current-controlled system as expressed by (4) then becomes compared to what is expected, or can even cause a distortion increase because of oscillation effects. In fact, the rectifier current harmonics may cause saturation of the inductors or filter resonance. Therefore, the inductors should be correctly designed considering current ripple, and the filter should be damped to avoid resonances. However, the damping level is limited by cost, the value of the inductors, losses, and degradation of the filter performance. The procedure for choosing the LCL filter parameters uses the power rating of the converter, the line frequency, and the switching frequency as inputs. The process to calculate the switching ripple attenuation is based on a frequency-domain approach rather than on a time-domain approach. In the following development, the filter values are reported as a percentage of the base values, given by where is the line-to-line rms voltage, is the grid frequency, and is the active power absorbed by the converter in rated conditions. The resonant frequency is referred to the switching frequency value by where the factor expresses how far the switching frequency is from the resonant frequency. The equivalent single-phase LCL filter configuration for the harmonic is shown in Fig. 5, neglecting the resistors,, and (Fig. 2). and indicate the harmonic of the current and of the voltage, while is the order of the switching frequency harmonic. The current ripple attenuation is computed by considering that at high frequencies, the converter is a harmonic generator, while the grid can be considered as a short circuit. Therefore, the converter voltage harmonic, at the switching frequency, is and the grid voltage harmonic, at the switching frequency, is. The ripple attenuation, passing from the converter side to the grid side, can be calculated with the following steps: (5) (6) (7) (8) (9) (10) and the losses can be calculated as (11) (12) where the skin effect is neglected. The main terms of the sum in (12) are for the index near (previously defined) and its multiples. In fact, damping absorbs a part of the switching frequency ripple to avoid the resonance. The losses decrease as the damping resistor value increases but at the same time this reduces its effectiveness (11). Furthermore, the required damping cannot be calculated without considering the current control strategy because the LCL filter is connected to a closed-loop-controlled rectifier. Also, a disturbance can trigger a reaction from the closed-loop current controller (e.g., caused by a PWM modulator with a wide spectrum spread between the fundamental and the switching frequency harmonics, by an A/D characterized by poor resolution, by inadequate filters on the measured grid voltage [14], [26], or by an external disturbance such as a load connected to the same point of common coupling (PCC) [17]). If the closed-loop control is not properly damped, a resonance can occur. Having established (10) and (12) to design the filter, some limits on the parameter values should be introduced. a) The capacitor value is limited by the decrease of the power factor at rated power (generally less than 5%). The power factor decrease can also be a function of the ac sensor position as discussed in [14]. b) The total value of inductance should be less than 0.1 pu to limit the ac voltage drop during operation. Otherwise a higher dc-link voltage will be required to guarantee current controllability, which will result in higher switching losses [14]. Moreover, the maximum overall inductance of the LCL filter is strongly dependent on the power level and on the application. A standard mass-produced product (low power) should integrate the LCL filter into its hardware and, as a consequence, a more stringent overall inductance limit (perhaps less than 5%) should be adopted to avoid packaging problems. On the other hand, for higher power levels (at present power levels of interest by industry for active rectifier applications are above tens of kilowatts) and in the absence of clearly defined standards on the switching ripple, the LCL filter will probably not be integrated in the converter. In this case the main aim is to avoid saturation in the inductors, with consequent higher losses.

5 LISERRE et al.: DESIGN AND CONTROL OF AN LCL-FILTER-BASED THREE-PHASE ACTIVE RECTIFIER 1285 c) The resonant frequency should be in a range between ten times the line frequency and one-half of the switching frequency, to avoid resonance problems in the lower and upper parts of the harmonic spectrum. d) Passive damping must be sufficient to avoid oscillation, but losses cannot be so high as to reduce efficiency [7]. Finally, depending on the desired application, the designer should impose some constraints: on the filter efficiency at low frequency (first 50 harmonics) and high frequency (around the switching frequency), and on the current tracking capability (which can be compromised by the reactive power absorbed by the input capacitors). The following performance factors are used to verify the filter effectiveness (the first three are low-frequency indicators and the last two are high-frequency indicators): THD of the current power factor ; average of the absolute dc voltage error ; largest of the sideband current harmonics around the switching frequency (this is because of the frequency-domain approach used to study the switching ripple reduction); rms value of the high-frequency ( khz) harmonic content of the current as a percentage of the fundamental harmonic ; where is the overall rms value of the current and is the rms value of the current harmonic and is the angle between the fundamental current and fundamental voltage. IV. LCL FILTER DESIGN PROCEDURE The LCL filter can be designed using the following step-bystep procedure. 1) Select the required current ripple on the converter side design the inner inductor. The outer inductor value can then be determined as a function of, using the index for the relation between the two inductances (13) 2) Select the reactive power absorbed at rated conditions determine the capacitor value. Take as a percentage of the reactive power absorbed under rated conditions (14) The capacitor value is limited by condition a) above. 3) Select the desired current ripple reduction knowledge of and then design the outer inductor. The ripple attenuation, calculated neglecting losses and damping of the filter, is defined by (10) and can be rewritten, considering (13) and (14), as (15) where is a constant. Before using (15) to calculate, the desired attenuation should be multiplied by a factor that takes into account the losses and the damping. If the sum of the two inductances does not respect condition (b), another attenuation level should be chosen, or another value for the absorbed reactive power should be selected as per step 2). 4) Verify the resonant frequency obtained (16) which can be written, considering (7), (13), and (14), as (17) where is a constant. The resonant frequency is limited by condition (c). If this is not correct the absorbed reactive power returned in step 2) or the attenuation returned in step 3) should be changed. 5) Set the damping according to condition d) above. At the resonant frequency the impedance of the filter is zero. The aim of the damping is to insert an impedance at this frequency to avoid oscillation. Hence, the damping value is set to a similar order of magnitude as the series capacitor impedance at the resonant frequency [26]. If the filter attenuation is not adequate, the design procedure returns to step 3) to increase the multiplication coefficient that takes into account the decrease of the filtering action due to losses. If this is not sufficient the design procedure should go back to step 2) and select a higher value of the reactive power. 6) Verify the filter attenuation under other load conditions and with other switching frequencies. V. LCL FILTER DESIGN EXAMPLE The step-by-step procedure has been applied to a system with a rated voltage of 380 V (line to line) and rated power of 4.1 kw (maximum test power for the laboratory prototype). The base impedance is approximately 35, and the base capacitance is 90 F, taking V and W in (5) and (6). The lower rectifier switching frequency was chosen as 5 khz, but tests were also done up to 8 khz because these frequencies are suitable for the chosen power level. The procedure of Section IV is as follows. 1) Adopting a 2.7% impedance for the converter side, a 10% current ripple is obtained. Adding the LC part the aim is selected to reduce the current ripple to 2%. 2) The maximum capacitor value is 4.7 F under the limits of condition 1. However, if too low a capacitor value is selected, too high a value of inductance could be necessary. Hence, it is better to start with about one-half of this value (2.2 F) and then, if some of the constraints cannot be respected, increase it up to the maximum limit. 3) Selecting a current ripple attenuation of 20% with respect to the ripple on the converter side, a value of is calculated using (15) (see Fig. 6). The isolation transformer

6 1286 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 5, SEPTEMBER/OCTOBER 2005 Fig. 6. Relation between the harmonic attenuation at the switching frequency and the ratio r between grid and converter inductors. TABLE I LCL FILTER PARAMETERS for the experimental setup provides a 2.7% inductance. With a 1.8% inductor, the resultant 4.6% grid inductance gives an value of 1.6, which takes into account the reduction in filter effectiveness caused by damping. It is commented also that to obtain a ripple attenuation of less than 20%, the value of increases too much (as shown in Fig. 6) and the filter may become too expensive. 4) The consequent resonant frequency is 2.5 khz, which is exactly one-half of the switching frequency. 5) The impedance of the filter capacitor at the resonant frequency is 29. The damping value is chosen as one-third, i.e., 10. The losses are 0.8% of rated power (under rated conditions). Even with this damping the filter gives good results and the objective of a ripple reduction to 20% is fulfilled. 6) Simulation and experimental tests, using the designed LCL filter (Table I), show the ripple reduction achieved over a wide range of working conditions. VI. ANALYSIS AND SIMULATION OF THE SYSTEM Simulation models have been built using Matlab and Simulink. The rated rms line-to-line voltage is 380 V and the rated power of the system is 4.1 kw, the switching frequency of the rectifier is in the range 5 8 khz, and the modulation strategy adopted is the sinusoidal modulation with centered pulses, with the sampling frequency equal to the switching frequency. The dc-voltage reference is 700 V and the rated load current is 5.5 A. The stability and dynamic response of the system will now be analyzed, and then the designed filter effectiveness will be evaluated to validate the reported procedure. A. Stability and Dynamic Response The stability and dynamic response of the overall system is analyzed in the plane using the poles of the closed-loop current controller. It should be noted that there is one sample delay in the system for the digital processing, plus one-half sample delay caused by the double-edge PWM because the modulator cannot Fig. 7. Zeros and poles of the closed-loop current control 1 without and 2 with damping (5-kHz sampling frequency). respond for this period after the duty cycle has been determined by the control algorithm [7]. This half-period delay is implicitly introduced by discretization of the system plant using a zerothorder hold, as is commonly used to describe continuous systems controlled by PWM. From the analysis of the left side of the plane it is clear that the system is close to the border of the stability region without damping (zeros and poles numbered with 1 in Fig. 7). If a 10- damping resistor is used then the system becomes more stable (zeros and poles numbered with 2 in Fig. 7). It is commented that stability analysis relating to resonance dynamics becomes less reliable as the sampling frequency approaches twice the resonant frequency [26]. For this example, the resonant frequency is just below 2.5 khz and, hence, a stability analysis at a 5-kHz sampling frequency is still possible. From the analysis of the right side of the plane in Fig. 7, it is clear that the dynamic response remains unchanged with the introduction of damping, because the two complex poles shift only slightly. Further proof comes from frequency analysis of the filter using the Bode diagram shown in Fig. 8, where it can be seen that at low frequency the damped LCL filter behaves like an L filter of value. It is also useful to study the evolution of the zeros and poles as the sampling frequency changes (with the consequent change of the parameters in the current controller) but with the same damping. With respect to stability, as the sampling frequency increases the poles move toward the stability borders and so the

7 LISERRE et al.: DESIGN AND CONTROL OF AN LCL-FILTER-BASED THREE-PHASE ACTIVE RECTIFIER 1287 Fig. 10. Simulation of d-axis reference and feedback currents for a step change from 33% to 100% rated load (5-kHz sampling and switching frequency). Fig. 8. Bode plot of the transfer function of the L filter and of the damped LCL filter (bold). Fig. 9. Zeros and poles of the closed-loop current varying the sampling frequency from 5 to 8 khz with 1-kHz step variation (the arrows show the evolution of the zeros and poles). damping becomes less effective (Fig. 9). In particular, for an 8-kHz switching frequency, the poles cross the border of the stability region. However, around the resonant frequency the passive elements of the system have extra resistance due to skin effect and iron losses, and this does offer some extra damping. As the sampling frequency increases, the bandwidth of the current controller varies from 200 to 400 Hz. Its dynamic response can be tested in simulation with a step load change. Using a step from 33% to 100% of rated load it is possible to confirm whether the active rectifier with LCL filter is stable and if the controllers have been well tuned. The result of this test is shown in Fig. 10 and it is satisfactory. It should be noted that this result has been obtained simply by adjusting the parameters of the PI controllers without any change in their structure. B. Filter Effectiveness Fig. 11 shows the simulated converter and grid currents and their associated high-frequency spectra obtained with the Fig. 11. (a) Simulated steady-state converter current, (b) grid current, and (c) their spectra (black for the grid current and white for the converter one) at high frequency with LCL filter (rated conditions). LCL filter, operating under rated conditions. The largest near switching frequency current harmonic component is 0.48 A on the converter side and 0.07 A on the grid side. Thus, it has been reduced to 15%. Table II compares the performance factors identified in Section III, for the filter configuration and the LCL filter. The results show that the high-frequency current ripple has been reduced by one-half using the filter capacitors, while at low frequency the two filters have an equivalent performance.

8 1288 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 5, SEPTEMBER/OCTOBER 2005 L TABLE II FILTER VERSUS LCL FILTER TABLE III ELECTRICAL PARAMETERS OF THE VSC Fig. 13. Measured grid voltage (86 V/div), grid current, converter current, and input filter capacitor current (5 A/div) at rated conditions (5-kHz switching frequency). Fig. 12. Controller setup for active rectifier with LCL filter. VII. EXPERIMENTAL RESULTS The experimental setup used in the laboratory of the Institute of Energy Technology at Aalborg University, Aalborg, Denmark, consists of a three-phase 30-kVA programmable power supply, a commercial Danfoss inverter VLT 3008 (ratings shown in Table III), with the control card removed and a resistor used to load the dc link. The control is implemented using an Analog Devices ADSP SHARC floating-point digital signal processor, while the timing of the system and the PWM generation is managed by a Siemens microcontroller SAB80C167 [27], as shown in Fig. 12. A. Validation of the Model The first use of the experimental system was to validate the simulation model for both the low- and the high-frequency ranges. In the low-frequency range, the simulated grid current fed from a sinusoidal grid voltage had a THD of 1.4%. In contrast, the experimental system had a grid current THD of 3%, but the grid voltage had a THD of 1%, (waveforms are shown in Fig. 13). However, the measured grid current has some low-frequency harmonics, with about a 1% amplitude relative to the fundamental. The odd harmonics come from system unbalances that also cause slight even harmonics in the dc-link voltage as Fig. 14. Measured grid currents (5 A/div) and dc voltage (14 V/div, only ac component) at rated conditions (5-kHz switching frequency). shown in Fig. 14 [28]. The even harmonics come from dead time, some delays, suppression of pulses, and the fact that the grid voltage is measured after a dominant reactance [23].These harmonics have less influence as the switching and sampling frequency increase (Fig. 15 shows the grid currents and the dc voltage in the case of 8 khz). The high-frequency range is more effective to verify the filter s performance. It has already been shown in simulation that with a ripple-free grid voltage, the largest near switching frequency harmonic currents are 0.48 A on the converter side and 0.07 A on the grid side. The comparable experimental results are, respectively, 0.41 A and 0.07 A.

9 LISERRE et al.: DESIGN AND CONTROL OF AN LCL-FILTER-BASED THREE-PHASE ACTIVE RECTIFIER 1289 TABLE V GRID CURRENT HIGH-FREQUENCY HARMONIC CONTENT VARYING THE LOAD AND THE SAMPLING/SWITCHING FREQUENCY TABLE VI DAMPING LOSSES VARYING THE SAMPLING/SWITCHING FREQUENCY Fig. 15. Measured grid currents (5 A/div) and dc voltage (14 V/div only ac component) at rated conditions (8-kHz switching frequency). TABLE IV GRID CURRENT THD VARYING THE LOAD AND THE SAMPLING/SWITCHINGFREQUENCY Also, the total rms high-frequency harmonic current ripple (as defined in Section III) is 16% of the fundamental on the converter side and 1.2% on the grid side. B. Performance Evaluation of the Overall System A performance analysis of the system on the grid side, shows that the low-frequency distortion is well below 5% at rated load and the high-frequency ripple is properly reduced. However, it is useful to analyze the system performance under different load conditions and for different switching frequencies as stated in step 6) of the design procedure. In the low-frequency range, grid current THD (defined in Section III) is the significant parameter. Table IV shows this parameter for different switching frequencies and for three different load conditions. The high THD at low power occurs because the harmonics caused by the system unbalance have more weight when the fundamental current value is low. In the high-frequency range, the harmonic content of the current (defined in Section III) is the significant parameter: Table V shows that, as would be expected, higher switching frequencies lead to a more effective filter. The next step in the system performance analysis is to consider the damping losses. Since load variation has little effect Fig. 16. Measured grid currents (5 A/div) and dc voltage (28 V/div, only ac component) for a step change from 33% to 100% rated load (5-kHz switching frequency). on the damping losses, Table VI shows the effect of varying switching frequency for the same value of damping resistor (10 ). It can be seen that damping losses decrease as the switching frequency increases. However, as identified in Section VI-A the system is also less damped, and at 8 khz reaches the limit of the stability region. Finally, the dynamic response of the system has been tested by step changing the load from 33% to 100% of rated power, as shown in Fig. 16. It can be seen that the dc voltage dynamic response is slowed down compared to simulation because of the dc filter that is used to reduce measurement ripple to avoid problems in the control loops [14]. VIII. CONCLUSION This paper has analyzed both the design and control of an active rectifier employing an LCL filter to reduce the switching

10 1290 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 5, SEPTEMBER/OCTOBER 2005 frequency current ripple. The main aim is to provide a design procedure for the filter and study the stability and the dynamic response of the overall system. The design procedure has been tested in simulation and with an experimental system, and the desired current ripple attenuation has been achieved for the test system parameters. In fact, compared to a simple L filter with an inductance equal to the sum of all inductances in the LCL filter, the current ripple magnitude has been halved. Stability and a rapid dynamic response have also been confirmed. Moreover, all the results have been obtained using a simple control method and no additional sensors. Thus, the system can be implemented using a standard industrial inverter. A further research topic in this field is the development of a more embedded design procedure taking into account conducted EMI disturbances. However, this will be strongly dependent on the ongoing standards in the field and on the limits they will impose on the switching ripple injection in the grid, and is left for future investigations. REFERENCES [1] R. Wu, S. B. Dewan, and G. R. Slemon, Analysis of an ac-to-dc voltage source converter using PWM with phase and amplitude control, IEEE Trans. Ind. Appl., vol. 27, no. 3, pp , Mar./Apr [2] M. P. Kazmierkowski, R. Krishnan, and F. Blaabjerg, Control in Power Electronics. New York: Academic, [3] M. Malinowksi, M. P. Kazmierkowski, S. Hansen, F. Blaabjerg, and G. Marques, Virtual flux based direct power control of three-phase PWM rectifiers, IEEE Trans. Ind. Appl., vol. 37, no. 4, pp , Jul./Aug [4] C. Cecati, A. Dell Aquila, M. Liserre, and A. Ometto, A fuzzy-logicbased controller for active rectifier, IEEE Trans. Ind. Appl., vol. 39, no. 1, pp , Jan./Feb [5] C. Cecati, A. Dell Aquila, A. Lecci, and M. Liserre, Implementation issues of a fuzzy-logic-based three-phase active rectifier employing only voltage sensors, IEEE Trans. Ind. Electron., vol. 52, no. 2, pp , Apr [6] W. A. Hill and S. C. Kapoor, Effect of two-level PWM sources on plant power system harmonics, in Conf. Rec. IEEE-IAS Annu. Meeting, 1998, pp [7] V. Blasko and V. Kaura, A novel control to actively damp resonance in input lc filter of a three-phase voltage source converter, IEEE Trans. Ind. Appl., vol. 33, no. 2, pp , Mar./Apr [8] G. L. Skibinski, R. J. Kerkman, and D. Schlegel, EMI emissions of modern PWM AC driver, IEEE Ind. Appl. Mag., vol. 5, no. 6, pp , Nov./Dec [9] W. Khan-ngern and Y. Prempaneerach, Reduction of conducted emission for UPS s using passive EMI filters, in Proc. APCCAS 98, 1998, pp [10] S. Fu-Yuan, D. Y. Chen, W. Yan-Pei, and C. Yie-Tone, A procedure for designing EMI filters for AC line applications, IEEE Trans. Power Electron., vol. 11, no. 1, pp , Jan [11] T. Farkas and M. F. Schlecht, Viability of active EMI filters for utility applications, IEEE Trans. Power Electron., vol. 9, no. 3, pp , May [12] H. Akagi, H. Hasegawa, and T. Doumoto, Design and performance of a passive EMI filter for use with a voltage-source PWM inverter having sinusoidal output voltage and zero common-mode voltage, IEEE Trans. Power Electron., vol. 19, no. 4, pp , Jul [13] A. Nagel and R. W. De Doncker, Systematic design of EMI-filters for power converters, in Conf. Rec. IEEE-IAS Annu. Meeting, 2000, pp [14] M. Liserre, F. Blaabjerg, and A. Dell Aquila, Step-by-step design procedure for a grid-connected three-phase PWM Voltage Source Converter, Int. J. Electron., vol. 91, no. 8, pp , Aug [15] M. Bojrup, Advanced control of active filters in a battery charger application, Ph.D. dissertation, Lund Univ. Technol., Lund, Sweden, [16] M. Lindgren, Modeling and control of voltage source converters connected to the grid, Ph.D. dissertation, Chalmers Univ. Technol., Göteborg, Sweden, [17] M. Liserre, A. Dell Aquila, and F. Blaabjerg, Genetic algorithm based design of the active damping for a LCL-filter three-phase active rectifier, IEEE Trans. Power Electron., vol. 19, no. 1, pp , Jan [18] A. Draou, Y. Sato, and T. Kataoka, A new state feedback based transient control of PWM AC to DC voltage type converters, IEEE Trans. Power Electron., vol. 10, no. 6, pp , Nov [19] M. Lindgren and J. Svensson, Control of a voltage-source converter connected to the grid through an LCL-filter-application to active filtering, in Proc. IEEE PESC 98, vol. 1, 1998, pp [20] J. R. Espinoza, G. Joos, E. Araya, L. A. Moran, and D. Sbarbaro, Decoupled control of PWM active-front rectifiers using only dc bus sensing, in Conf. Rec. IEEE-IAS Annu. Meeting, vol. 4, 2000, pp [21] E. J. Bueno, F. Espinosa, F. J. Rodríguez, and J. U. S. Cobreces, Current control of voltage source converters connected to the grid through an LCL-filter, in Proc. IEEE PESC 04, vol. 1, 2004, pp [22] A. M. Hava, T. A. Lipo, and W. L. Erdman, Utility interface issues for line connected PWM voltage source converters: a comparative study, in Proc. IEEE APEC 95, vol. 1, 1995, pp [23] M. Liserre, A. Dell Aquila, and F. Blaabjerg, Design and control of a three-phase active rectifier under nonideal operating conditions, in Conf. Rec. IEEE-IAS Annu. Meeting, vol. 2, 2002, pp [24] D. Y. Ohm and R. J. Oleksuk, On pratical digital current regulator design for PM synchronous motor drives, in Proc. IEEE APEC 98, Feb. 1998, pp [25] S. Hiti, V. Vlatkovic, D. Borojevic, and F. C. Y. Lee, A new control algorithm for three-phase PWM buck rectifier with input displacement factor compensation, IEEE Trans. Power Electron., vol. 9, no. 2, pp , Mar [26] E. Twining and D. G. Holmes, Grid current regulation of a three-phase voltage source inverter with an LCL input filter, in Proc. IEEE PESC 02, vol. 3, Jun. 2002, pp [27] M. Liserre, A. Dell Aquila, and F. Blaabjerg, Stability improvements of an LCL-filter based three-phase active rectifier, in Proc. IEEE PESC 02, Jun. 2002, pp [28] F. Abrahamsen, F. Blaabjerg, and J. K. Pedersen, Digital signal processing in power electronics and drives, in Proc. DSP 96, 1996, pp [29] L. Moran, P. D. Ziogas, and G. Joos, Design aspects of synchronous PWM rectifier-inverter system under unbalanced input voltage conditions, IEEE Trans. Ind. Appl., vol. 28, no. 6, pp , Nov./Dec Marco Liserre (S 00-M 03) received the M.Sc. and Ph.D. degrees in electrical engineering from the Politecnico di Bari, Bari, Italy, in 1998 and 2002, respectively. He is currently an Assistant Professor at the Politecnico di Bari. He spent one year as an Invited Researcher and two months as an Invited Associate Professor at the Institute of Energy Technology, Aalborg University, in 2001 and 2004, respectively. Since 1999, he has been carrying out a collaboration with the Università dell Aquila. His research interests are in power converters and drives, namely, in the control of converters, in power quality, and in distributed generation. He has coauthored more than 70 technical papers, ten of them published in IEEE TRANSACTIONS. Dr. Liserre is a Member of the IEEE Industry Applications, IEEE Industrial Electronics, and IEEE Power Electronics Societies. In the IEEE Industrial Electronics Society, he has been an AdCom Member for the period , Chair for Student Activities for the period , Chair for Region 8 Membership Activities since 2004, and Newsletter Editor since He has served as a Student Forum Co-Chair of ISIE 2002, ISIE 2003, ISIE 2004, ISIE 2005, Mechatronics and Robotics 2004, and ICIT 2004.

11 LISERRE et al.: DESIGN AND CONTROL OF AN LCL-FILTER-BASED THREE-PHASE ACTIVE RECTIFIER 1291 Frede Blaabjerg (S 86 M 88 SM 97 F 03) was born in Erslev, Denmark, in He received the M.Sc.E.E. degree from Aalborg University, Aalborg East, Denmark, in 1987, and the Ph.D. degree from the Institute of Energy Technology, Aalborg University, in He was with ABB-Scandia, Randers, Denmark, from 1987 to During he was a Ph.D. student at Aalborg University. He became an Assistant Professor in 1992, an Associate Professor in 1996, and a Full Professor of power electronics and drives in 1998 at Aalborg University. In 2000, he was a Visiting Professor at the University of Padova, Padova, Italy, as well as becoming a part-time Programme Research Leader at the Research Center Risoe, working with wind turbines. In 2002, he was a Visiting Professor at Curtin University of Technology, Perth, Australia. His research areas are power electronics, static power converters, ac drives, switched reluctance drives, modeling, characterization of power semiconductor devices and simulation, wind turbines, and green power inverters. He is involved in more than ten research projects with industry. Among them is the Danfoss Professor Programme in Power Electronics and Drives. He is the author or coauthor of more than 300 publications in his research fields including the book including the book Control in Power Electronics (New York: Academic, 2002). Dr. Blaabjerg is a Member of the European Power Electronics and Drives Association and of the Industrial Drives, Industrial Power Converter, and Power Electronics Devices and Components Committee Committees of the IEEE Industry Applications Society. He is an Associate Editor of the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, IEEE TRANSACTIONS ON POWER ELECTRONICS, Journal of Power Electronics, and the Danish journal Elteknik. He has been active in the Danish Research Policy for many years. He became a member of the Danish Academy of Technical Science in He served as a Member of the Danish Technical Research Council during , and from he was its Chairman. He received the 1995 Angelos Award for his contribution to modulation technique and control of electric drives and an Annual Teacher Prize from Aalborg University, also in In 1998, he received the Outstanding Young Power Electronics Engineer Award from the IEEE Power Electronics Society. He has received four IEEE Prize Paper Awards during the last five years. In 2002, he received the C. Y. O Connor Fellowship from Perth, Australia, and in 2003, the Statoil Prize for his contributions to power electronics. He also received the Grundfos Prize in Steffan Hansen (S 95 A 96 M 99) was born in Sonderborg, Denmark, in He recieved the M.Sc.E.E. and the Ph.D. degrees through an industrial fellowship supported by Danfoss Drives A/S and the Danish Academy of Technical Sciences from Aalborg University, Aalborg East, Denmark, in 1996 and 2001, respectively. Since 1996, he has been with Danfoss Drives A/S, Graasten, Denmark, where his main research activities are focused on solutions to reduce line-side harmonics from adjustable-speed drives. He is currently Product Manager responsible for high-performance drives and products reducing secondary effects.