A NOVEL DEAD-BEAT CURRENT CONTROL FOR SHUNT ACTIVE POWER FILTERS

Transcription

1 A NOVEL DEAD-BEAT CURRENT CONTROL FOR SHUNT ACTIVE POWER FILTERS A. Dell'Aquila, P. Zanchetta, M. Liserre, L. Manelli, M. Marinelli Politecnico di Bari Dipartimento di Elettrotecnica ed Elettronica Via E.Orabona 4, Bari, Italy Tel Fax Abstract. This summary proposes a simple and novel dead-beat control for a 3-phase PWM inverters used as shunt active power filter. A modified mathematical model has been developed to suitably improve the dead-beat control to this particular applications. The design and the test of the controller have been carried out by means of a powerful tool, built in LabVIEW environment. The final simulation results show an excellent behaviour of the system with a low and constant switching frequency in the case of non-linear leads with both inductive and capacitive dc-link.

2 A NOVEL DEAD-BEAT CURRENT CONTROL FOR SHUNT ACTIVE POWER FILTERS I. INTRODUCTION Traditional compensating systems, i.e. passive filters, are quite a lot used in a lot of different applications, but they present a great numbers of well-known drawbacks. Innovative and more effective solutions for harmonic distortion problems are active power filters, deeply studied and tested in the last years. Among them the most effective and simplest configuration is the shunt active filter which employs an inverter parallel connected to the grid (fig. 1). Hence this type of configuration has been largely studied and a lot of different types of controls, standard and innovative like fuzzy logic, have been investigated [1],[2],[3], [4],[5]. possibility of changing parameters configurations or control strategies in a very immediate way [6],[7]. Among the standard control techniques, dead-beat control [8], [9] is a very exact, simple and easy-to-use method. This summary proposed a modified dead-beat control suitably designed for shunt active power filters. This control has been simulated in LabVIEW and tested by means on the above mentioned instrument on two different network feeding respectively a phase-controlled rectifier and an induction motor drive. This dead-beat method, modified with a line voltage measure and a current prediction, result a very simple and effective technique to compensate highly distorted currents presenting very steep slopes using a very low switching frequency. The shunt active filter configuration used has the common circuital structure shown in Fig.2. Fig. 1. Shunt active filter. The first step in the design of a compensating system is to deeply analyse the behaviour of the network to which it will be applied by monitoring its impedance versus frequency, the electrical quantities and their harmonic characteristics. All these informations are of a basic importance to choose the suitable compensating system, that represents the best solution for the examined case, or to design or adapt particular structures or existing solution to the considered case. For this reason a special monitoring system has been developed in LabVIEW environment. It is able to measure and show all the characteristics of the network, but, at the same time, can test via software on-line the effectiveness of different compensating systems on the acquired distorted current waveforms using a portable instrument. Our effort was to provide such a tool with a great library of the most diffuse active, passive or hybrid compensating systems with the Fig. 2. Active filter circuit. II. DEAD-BEAT MATHEMATICAL MODEL The following mathematical model is based on a simplified dead-beat control design, in which it is supposed that there are no unstable poles and zeros and the transfer function of the closed loop system can therefore be written as: (1) where k is the delay of the close loop control system. The mathematical model of the controller results:

3 (2) where Gp(z) is the plant transfer function. The system mathematical model is based on the simple circuit of Fig. 3, in which the load can be neglected if it presents an high impedance compared to the line one. This is certainly verified if the non-linear load is a rectifier with an inductive load. In the case of an induction motor drive with a capacitive dc link, to verify the previous approximation we need a value of L 2 sufficiently higher than L 1. + (8) from which, with a Z-transformation: (9) Therefore: (10) so the plant transfer function is deduced: Gp(z)= (11) The controller transfer function results as: Fig.3. System circuit model. The circuit mathematical model is: D(z) (12) that is: (3) where is the single phase filter current, Vp is the inverter voltage, V is the line voltage and L T =L f +L 1. The solution results: If we denote: - (4) (5) (6) u(kts)= (7) the following equation is derived: D(z) (13) In the end it results: D(z) (14) III. MODIFIED DEAD-BEAT MATHEMATICAL MODEL The drawbacks of the dead-beat control for this application are two: the first is the sample delay due to the signal acquisition, the second is the presence of the line voltage, that is not included in a simple non- accurate mathematical model, but it produces interference in the control signals. In scientific literature the first problem has been solved in a fast and simple way by a current prediction [10]. In this summary we propose a new interesting and simple method to solve the second draw back based on an instantaneous voltage measurement. The presence of line voltage must be considered (Fig. 4) to characterise the system closed loop:

4 (15) I( z ) (16) I( z ) (17) and being: (18) it results: (19) which does not respect the system purpose. IV.DEAD-BEATCONTROLLER DESIGN To implement the system in LabVIEW environment the Z-equation must be transformed as follows: (24) (25) (26) Therefore considering a sampled data system, the fundamental equation of the controlis: Fig. 4. Dead-beat control scheme. The line voltage must be measured and taken into consideration in the mathematical model (Fig. 5). So we have: (20) It can be noted that the filter current follows the referent current. In fact: (21) I( z ) (22) Therefore it results: (23) V. SIMULATION RESULTS (27) Reference current calculation for the active filter is performed with a classical p-q method combined to a simple PI control on the dc side of the inverter. R-L parameters at the output of the inverter, are chosen to reduce the harmonics produced by PWM switches. The fundamental due is assumed by inductance L, that must damp fast variations; on the other side the resistance must not be too small because of stability reasons. A simulated active filter implementing the proposed control has been applied to compensate the on-line acquired distorted currents, measured by our portable instrument, produced by a high power phase-controlled rectifier and a 7.5Kw induction motor drive. Figs. 6 to 10 report load and line current waveforms, their harmonic spectra and the instantaneous switching frequency in the case 1 of compensation of the phase-controlled rectifier working with a firing angle of 60. The design of the active filter for this application has given the following parameters: Lf(mH) Rf(Ω) C(mF) Switching Frequency (Hz) Vdc(V) 2,5 1, Fig. 5. New dead-beat control scheme.

5 The reduction of current harmonic distortion is remarkable in terms of THD: we reach a value of 2.56% starting from a value of 29%. The design of the active filter when applied to compensate our induction motor drive (case 2) has given, on the contrary, the following parameters: Lf(mH) Rf(Ω) C(mF) Switching Frequency (Hz) Vdc(V) 2, Fig. 9. Line current spectrum for α=60 (case 1) Also in this case the current THD decrease from a value of about 130% to a value of 4.7% that is under the standard limits. This control action is shown in Figs 11 to 16. Fig. 10. Instantaneous switching frequency for α=60 (case 1) Fig. 6. Load current waveform for α=60 (case 1) Fig. 11. Load current waveform (case 2) Fig. 7. Load current spectrum for α=60 (case 1) Fig. 12. Load current spectrum (case 2) Fig. 8. Line current waveform for α=60 (case 1) Fig. 13. Line current waveform (case 2)

6 Fig. 14. Line current spectrum (case 2) Fig. 15. Voltage control waveform (case 2) Fig. 16. Instantaneous switching frequency (case 2) VI. CONCLUSIONS In this summary a simple and novel dead-beat control for a 3-phase PWM inverters used as shunt active power filter has been proposed and discussed. A modified mathematical model has been developed to suitably improve the dead-beat control to this particular applications. Its advantages are the simplicity and the extreme precision of the compensation (using a low and almost constant switching frequency) even when the reference current to track present very steeply slopes. The design and the test of the controller have been carried out by means of a powerful tool, built in LabVIEW environment. It is able to measure and show all the characteristics of the network, but, at the same time, can test via software online the effectiveness of different compensating systems on the acquired distorted current waveforms using a portable instrument. The presented simulation results show, at the end, an excellent behaviour of the designed system when it is applied to compensate both a phase-controlled rectifier and an induction motor drive. VII. REFERENCES H. Akagi: New Trends in Active Filters for Power Conditioning, IEEE Transaction on Industry Applications, vol. 32, Nov./Dec. 1996, pp ; F. Z. Peng: Application Iussues of Active Power Filters, IEEE Industry Applications Magazine, Sept./Oct. 1998, pp.21-37; H. Akagi: Control Strategy and Site Selection of a Shunt Active Filter for Damping of Harmonic Propagation in Power Distribution Systems, IEEE Transaction on Power Delivery, vol.12, No. 1, January 1997, pp ; Dell'Aquila, M. Liserre, P Zanchetta: A New Low Cost CC-PWM Inverter Based on Fuzzy Logic, Proc. of International Conference PEVD 00, London, United Kingdom, September Dell Aquila, A. Lecci, M. Liserre, P. Zanchetta: Design of the Optimum Duty Cycle for a Fuzzy Controlled Active Filter, Proc. of International Conference ISIE 00, Puebla, Mexico, December Dell'Aquila, G. Carbone, F. Loiudice, P. Zanchetta: A Powerful System for Low Frequency EMI Monitoring and Power Filter Design - Proc. of International Conference SPEEDAM 98, Sorrento, Italy, June Dell'Aquila, F. Loiudice, M. Liserre, M. Marinelli P. Zanchetta: Performances evaluation of different active filters for compensation of distorted line currents produced by induction motor drives Proc. of International Conference ELECTRIMACS 99, Lisboa, Portugal, September Kawabata, Miyashita, Yamamoto: Dead Beat Control of Three Phase PWM Inverter IEEE Transaction on Power Electronics, vol. 5, No. 1, January 1990; Buso, Malesani, Mattavelli, Veronese: Robust Dead-Beat Current Control PWM Rectifiers and Active Filters, IEEE Transaction on Industry Applications, vol. 35, No. 3, May/June 1999; Takahashi, Nunokawa: Prediction Control for a Cycloconverter of a Power Distortion Compensation System, IEEE Transaction on Industry Applications, vol. 25, No. 2, March/April 1989;