Limit cycle bifurcations in resonant LC power inverters under zero current switching strategy. (English) Zbl 1391.94891
Summary: The dynamics of a DC-AC self-oscillating LC resonant inverter with a zero current switching strategy is considered in this paper. A model that includes both the series and the parallel topologies and accounts for parasitic resistances in the energy storage components is used. It is found that only two reduced parameters are needed to unfold the bifurcation set of this extended system: one is related to the quality factor of the LC resonant tank, and the other accounts for the balance between serial and parallel losses. Through a rigorous mathematical study, a complete description of the bifurcation set is obtained and the parameter regions where the inverter can work properly is emphasized.
MSC:
| 94C05 | Analytic circuit theory |
| 37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |
| 34C37 | Homoclinic and heteroclinic solutions to ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
References:
| [1] | Suryawanshi, HM; Tarnekar, SG, Resonant converter in high power factor, high voltage DC applications, IEE Proc.- Electr. Power Appl., 145, 307-314, (1998) · doi:10.1049/ip-epa:19981933 |
| [2] | Schwarz, FC, An improved method of resonant current pulse modulation for power converters, IEEE Trans. Ind. Electron. Control Instrum., 23, 133-141, (1976) · doi:10.1109/TIECI.1976.351365 |
| [3] | Steigerwald, R.L., Ngo, K.D.T.: Full bridge lossless switching converter. U.S. Patent 4,864,479 (1989) · Zbl 1198.34059 |
| [4] | Samanta, S; Rathore, AK, A new current-fed CLC transmitter and LC receiver topology for inductive wireless power transfer application: analysis, design, and experimental results, IEEE Trans. Transp. Electrif., 1, 357-368, (2015) · doi:10.1109/TTE.2015.2480536 |
| [5] | Fernandes, R.C, de Oliveira, A.A.: Theoretical bifurcation boundaries for wireless power transfer converters. IEEE 13th Brazilian Power Electron. Conf. and 1st Southern Power Electron. Conf. (COBEP/SPEC). 1-4., Fortaleza (2015) · Zbl 1330.34030 |
| [6] | Bonache-Samaniego, R., Olalla, C., Martínez-Salamero, L., Maksimovic, D.: 6.78 MHz self-oscillating parallel resonant converter based on GaN technology. 2017 IEEE Applied Power Electron. Conf. and Expos. (APEC). 1594-1599, Tampa, FL (2017) · Zbl 1314.37031 |
| [7] | Deng, J; Li, S; Hu, S; Mi, CC; Ma, R, Design methodology of LLC resonant converters for electric vehicle battery chargers, IEEE Trans. on Veh. Technol., 63, 1581-1592, (2014) · doi:10.1109/TVT.2013.2287379 |
| [8] | Baya, B.: Simplified model of resonant inverters for the modelisation of induction heating of billet. IECON 40th Annual Conference of the IEEE Ind. Electron. Soc. 3270-3276, Dallas (2014) · Zbl 1079.34029 |
| [9] | Schnell, R.W., Zane, R.A., Azcondo, F.J.: HID lamp driver with phase controlled resonant-mode ignition detection and fast transition to LFSW warm-up mode. IEEE 12th Workshop on Control and Model. for Power Electron. (COMPEL). 1-8, Boulder, CO (2010) |
| [10] | Erickson, R.W., Maksimovic, D.: Fundamentals of Power Electronics. Lluwer, Springuer (2001) · doi:10.1007/b100747 |
| [11] | Bonache-Samaniego, R; Olalla, C; Martínez-Salamero, L, Design of self-oscillating resonant converters based on a variable structure systems approach, IET Power Electron., 57, 111-119, (2015) |
| [12] | Ehsani, M.: Power conversion using zero current soft switching. U.S. Patent 5,287,261 (1994) · Zbl 1003.34009 |
| [13] | Andronov, A.A., Vitt, A., Khaikin, S.E.: Theory of Oscillators. Pergamon Press, Oxford (1966) · Zbl 0188.56304 |
| [14] | di Bernardo, M., Budd, C.J., Champneys, A.R., Kowalczyk, P.: Piecewise-Smooth Dynamical Systems: Theory and Applications. Appl. Math. Sci. 163, Springer-Verlag London Ltd., London (2008) · Zbl 1146.37003 |
| [15] | Filippov, A.F., Arscott, F.M.: Differential Equations with Discontinuous Right-Hand Sides. Kluwer Academic, Dordrecht (1988) · Zbl 0664.34001 · doi:10.1007/978-94-015-7793-9 |
| [16] | Kuznetsov, YuA; Rinaldi, S; Gragnani, A, One-parameter bifurcations in planar Filippov systems, Int. J. Bifurc. Chaos, 13, 2157-2188, (2003) · Zbl 1079.34029 · doi:10.1142/S0218127403007874 |
| [17] | Freire, E; Ponce, E; Torres, F, Canonical discontinuous planar piecewise linear systems, SIAM J. Appl. Dyn. Syst., 20, 181-211, (2012) · Zbl 1242.34020 · doi:10.1137/11083928X |
| [18] | Freire, E; Ponce, E; Torres, F, A general mechanism to generate three limit cycles in planar Filippov systems with two zones, Nonlinear Dyn., 78, 251-263, (2014) · Zbl 1314.37031 · doi:10.1007/s11071-014-1437-7 |
| [19] | Freire, E; Ponce, E; Torres, F, On the critical crossing cycle bifurcation in planar Filippov systems, J. Differ. Eq., 259, 7086-7107, (2015) · Zbl 1330.34030 · doi:10.1016/j.jde.2015.08.013 |
| [20] | Coll, B; Gasull, A; Prohens, R, Degenerated Hopf bifurcation in discontinuous planar systems, J. Math. Anal. Appl., 253, 671-690, (2001) · Zbl 0973.34033 · doi:10.1006/jmaa.2000.7188 |
| [21] | Han, M; Zhang, W, On Hopf bifurcation in non-smooth planar systems, J. Differ. Eq., 248, 2399-2416, (2010) · Zbl 1198.34059 · doi:10.1016/j.jde.2009.10.002 |
| [22] | Chen, X; Romanovski, V; Zhang, W, Degenerate Hopf bifurcations in a family of FF-type switching systems, J. Math. Anal. Appl., 432, 1058-1076, (2015) · Zbl 1327.34023 · doi:10.1016/j.jmaa.2015.07.036 |
| [23] | Chen, X; Llibre, J; Zhang, W, Averaging approach to cyclicity of Hopf bifurcations in planar linear-quadratic polynomials discontinuous differential systems, Disc. Cont. Dyn. Syst., 22, 3953-3965, (2017) · Zbl 1371.37101 · doi:10.3934/dcdsb.2017203 |
| [24] | Giannakopoulos, F; Pliete, K, Planar systems of piecewise linear differential equations with a line of discontinuity, Nonlinearity, 14, 1611-1632, (2001) · Zbl 1003.34009 · doi:10.1088/0951-7715/14/6/311 |
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