Phase Locked Loop for Distorted Three-Phase Systems tested with a PI, a PID and a Fractional PI

• Autorzy: Minambres V. , Milanés M. , Vinagre B. , Romero E.

Warianty tytułu

PL

Pętla synchronizacji fazowej dla przebiegów odkształconych w systemach trójfazowych testowana z regulatorami PI, PID oraz ułamkowym PI

• Języki publikacji: EN

Abstrakty

EN

This paper proposes a Phase Locked Loop algorithm for three-phase distorted systems. For the Phase Locked Loop it is deduced a mathematical model to design the three different control solutions implemented: a PI, a PID and a novel fractional PI. The damping ratio, the time response and the phase error of the phase tracking system are the criteria to design the controllers. The performance of the three systems is analyzed by connecting inputs with imbalance, harmonics and phase and/or frequency variations. An Autoadjustable Synchronous Reference Frame application is developed to test the Phase Locked Loop by simulation and experimentally through xPCTarget. A comparison of some parameters of the system such as phase margin, settling time, THD and phase error is carried out for each controller.

PL

W artykule zaproponowano algorytm pętli synchronizacji fazy dla odkształconych przebiegów w systemach trójfazowych. Sformułowano model matematyczny pętli fazowej służący opracowaniu rozwiązań z regulatorami PI, PID oraz nowatorskim, ułamkowym PI. Kryteriami projektowymi są poziom tłumienia, czas odpowiedzi i błąd fazowy układu śledzenia. Właściwości trzech systemów zostały zbadane przy zastosowaniu sygnałów niesymetrycznych, odkształconych oraz z wahaniami fazy i częstotliwości. Pętle fazowe testowane były symulacyjnie i doświadczalnie poprzez xPCTarget przy użyciu aplikacji Autoadjustable Synchronous Reference Frame. Przedstawiono porównanie wybranych parametrów takich jak marines fazy, czas synchronizacji, THD i błąd fazowy.

Słowa kluczowe

EN

phase locked loop; modelling; PI control; PID control; fractional control; power systems control

PL

pętla synchronizacji fazy; regulator PI; regulator PID; regulator ułamkowy; sterowanie w układach mocy

• Wydawca: Wydawnictwo SIGMA-NOT
• Czasopismo: Przegląd Elektrotechniczny
• Rocznik: 2009
• Tom: R. 85, nr 10
• Strony: 201--207
• Opis fizyczny: Bibliogr. 22 poz., il., rys., tab.

Twórcy

autor

Minambres V.

autor

Milanés M.

autor

Vinagre B.

autor

Romero E.

• University of Extremadura, School of Industrial Engineering, Avda. Elvas s/n 06006 Badajoz,

Bibliografia

• [1] M. Karimi-Ghatemani, M. Reza Iravani, "A Method for Synchronization of Power Electronic Converters in Polluted and Variable-Frecuency Environments,” IEEE Trans. on Power Systems, Vol. 19, No. 3, pp. 1263-1270. Aug. 2004.
• [2] J.W. Dixon, J.J. García, L. Morán, "Control System for Three-Phase Active Power Filter which Simultaneously Compensates Power Factor and Unbalanced Loads,” IEEE Trans. on Ind. Electronics, Vol.42 (1995), No.6, pp. 636-641,
• [3] S. Luo, Z. Hou, "An Adaptive Detecting Method for Harmonic and Reactive Currents,” IEEE Trans. on Ind. Electronics, Vol. 42 (1995), No. 1, pp. 85-89.
• [4] M. C. Benhabib and S. Saadate, “A New Robust Experimentally Validated Phase Locked Loop for Power Electronic Control,” EPE Journal, Vol.15 (2006), No. 3.
• [5] G.-C. Hsieh, J.C. Hung, "Phase-Locked Loop Techniques - A Survey,” IEEE Trans. on Ind. Electronics, Vol. 43 (1996), No.6, pp. 609-615.
• [6] D Detjen, J. Jacobs, R. W. De Doncker, H.-G. Mall, "A New Hybrid Filter to Dampen Resonances and Compensate Harmonic Currents in Industrial Power Systems With Power Factor Correction Equipment,” IEEE Trans. on Power Electronics, Vol. 16 (2001), No. 6, pp. 821-827.
• [7] V. Kaura, V. Blasko, "Operation of a Phase Locked Loop System Under Distorted Utility Conditions,” IEEE Trans. on Industry Applications, Vol. 33 (1997), No. 1, pp. 58-63..
• [8] S.-K. Chung, "A Phase Tracking System for Three Phase Utility Interface Inverters,” IEEE Trans. on Power Electronics, Vol. 15 (2000), No. 3, pp. 431-438.
• [9] J. Phinney, D.J. Perreault, "Filters With Active Tuning for Power Applications,” IEEE Trans. on Power Electronics, Vol. 18 (2003), No. 2, pp. 636-647.
• [10] P. Jintakosonwit, H. Fujita, H. Akagi, "Control and Performance of a Fully-Digital-Controlled Shunt Active Filter for Installation on a Power Distribution System,” IEEE Trans. on Power Electronics, Vol. 17 (2002), No. 1, pp. 132-140.
• [11] C. Zhan, C. Fitzer, V.K. Ramachandaramurthy, A. Arulampalam, M. Barnes, N. Jenkins, "Software Phase-Locked Loop applied to Dynamic Voltage Restorer (DVR),” IEEE Power Eng. Soc. Winter Meeting. Conf., Vol. 3 (2001), pp. 1033-1038.
• [12] D. Jovcic, "Phase-Locked Loop System for FACTS,” IEEE Trans. on Power Systems, Vol.18, No.3, pp. 1116-1124. 2003.
• [13] M. Karimi-Ghatemani, M.R. Iravani, "A New Phase-Locked Loop (PLL) System,” Proceedings of the 44th IEEE 2001 Midwest Symposium on Circuits and System, pp. 421-424.
• [14] M. Karimi-Ghatemani, H. Moktari, M. Reza Iravani, M. Sedighy, "A Signal Processing System for Extraction of Harmonics and Reactive Current of Single-Phase Systems,” IEEE Trans. on Power Delivery, Vol. 19 (2004), No. 3, pp. 979-986.
• [15] G. Zhou, X. Shi, C. Fu, Y. Wang, "Operation of a Three-phase Soft Phase Locked Loop Under Distorted Voltage Conditions Using Intelligent PI Controller," in Proc. 2006 IEEE Region 10 Conf. TENCON’2006), pp. 315-320.
• [16] M.I. Milanés, E. Romero, A. Rico, V.M. Miñambres, F. Barrero, "Novel method for synchronization to disturbed three-phase and single-phase systems," in Proc. IEEE ISIE’2007, pp. 860-865.
• [17] I. Podlubny, “Fractional-order systems and PID controllers,” IEEE Trans. on Automatic Control, Vol. 44 (1999) No. 1, pp 208-214.
• [18] B. Vinagre, I. Podlubny, L. Dorčá, V. Feliu, (2000), “On fractional PID controllers: A frequency domain approach,” in IFAC workshop on digital control. Past, present and future of PID control, Terrasa, Spain.
• [19] A.J. Calderón, B.M. Vinagre, V. Feliu. "Fractional order control strategies for power electronic buck converters." Signal Processing, 86 (2006) pp. 2803-2819.
• [20] A. Rico, M.I. Milanés, E. Romero, B.M. Vinagre. "PI vs fractional PI for the control of a shunt active power filter," in Proc. of the ASME IDETC/CIE, Las Vegas, 2007.
• [21] C. A. Monje, B. M. Vinagre, V. Feliu, Y. Chen, “Tuning and auto-tuning of fractional order controllers for industry applications,” Control Engineering Practice, Vol. 16 (2008), pp. 798–812.
• [22] D.V. Mata de Oliveira. (2005, Aug.). Ninteger v. 2.3 Fractional control toolbox for MatLab. Instituto Superior Técnico, Universidade Técnica de Lisboa. http://web.ist.utl.pt/duarte.valerio/ninteger/ninteger.htm.