combination of R2 and C2 represents the dielectric dynamics. The ESR of the capacitor in terms of the frequency responses is derived accordingly. For electrolytic capacitors, a rise in temperature causes a decrease in ESR because the resistance R1 is reduced by the increased conductivity of electrolyte. The effect of temperature on R1 is described by [, ]. where R1b represents the value of R1 at the base temperature Tbase (27 oC), T is the capacitor core temperature (oC), and F is a temperature sensitivity factor []. Fig. 2 ESR model of an electrolytic capacitor. Film capacitor A R-L-C series equivalent circuit that includes the equivalent inductance Lc, capacitance Cc and resistance Rc is used to film capacitors. When the operating frequency is higher than 1 kHz, the ESR value can be modeled as a function of frequency based on []. where Rs is the base resistance, f represents the frequency, and As is a given value depending on the capacitor size. K(f) is the predefined function showing the effect of frequency, which is usually given by plots in manufacturer datasheets. In this analysis, K(f) is mathematically expressed as a cubic polynomial function, as shown in (4), in which the coefficients k0-3 can be established by using least square curve fitting. In contrast with the electrolytic capacitor, the ESR value of film capacitors increases with the frequency. Its temperature-sensitivity is less than that of electrolytic capacitors [] because the ESR of film capacitors results mainly from the tabs and contact resistances, but not from the electrolyte [].
of output current amplitude at low , while the corresponding harmonic component reaches as high as 48.8% at the high . Modeling of ESR and self-heating characteristics: the ESR models of electrolytic and film capacitors are derived and experimentally validated. Two dc-link capacitor designs are used for the comparative evaluation. The ESR of scheme II (film capacitor) is always lower than that of scheme I (electrolytic) throughout the frequency spectrum. The ESR value of scheme I decreases with increasing temperature, which is more significant than that of the scheme II. Furthermore, the RMS values and frequency spectra of the dc-link capacitor current are analyzed. The self-heating effect is subsequently considered and numerically evaluated by using the iterative simultaneous solution for core temperature and ESR by electro-thermal coupling method to predict the core temperature. Lifetime estimates are based on core temperature. Experimental evaluation of two design schemes: The applications and performance of electrolytic capacitors (scheme I) and film capacitors (scheme II) were tested and compared and evaluated in terms of power loss, core temperature, lifetime and battery current harmonics based on a practical 80kW permanent-magnet motor drive system. The comparison verifies that the film capacitor application shows significant advantages shown by the improved power density, low power loss, low parasitic inductance, and long lifetime. The capacitor power loss introduced by the scheme II is roughly half of the value of scheme I due to the lower ESR value. The analysis shows that the values of capacitor core temperature are close to each other in both schemes. At the rated ambient temperature of 65 oC, the lifetime of the film capacitors is ten times longer than that of scheme I. Regarding to the battery ripple current, both schemes meet the 10% upper bound limit considering the practical EV system layout. Further, the parasitic inductance is reduced to 34 nH in contrast with the value of 100 nH for scheme I. The power density of 13.3 kW/L was achieved by applying the proposed scheme II, which is compared to the PDV of 2.99 kW/L for scheme I.
Appendix TABLE a-I Specification of the vrla battery (6-DM-150) Parameters Value C20(Ah) 150 Cold Cranking Amperes defined by BCI (A) 300 Rated voltage (V) 12 Weight (kg) 32.5 TABLE A-II Specification of Evox Rifa ALS332QP500and AVX FFVE6K0227K Comparison Items Max ESR(mΩ) at 20 oC/ 100hz Max Impedance (mΩ) at 20oC / 10 khz Ripple current(A) at 85°C & 10 khz Life time Lb at 85°C (hrs) Expected ambient temperature Ta(oC) ALS332QP500 51 32 26.4 4000 65 FFVE6K0227K 1 - 100 30000 65 TABLE A-III Main parameters of AC induction motor Parameters Value Stator resistor (mΩ) 6.8 Stator leakage inductance (mH) 0.071789 Rotor resistor (mΩ) 4.23 Rotor leakage inductance (mH) 0.0921067 Mutual inductance (mH) 2.2857359 of poles 3 Rated speed(rpm) 1860 Reference [1] F. R. Salmasi, "Control Strategies for Hybrid Electric Vehicles: Evolution, Classification, Comparison, and Future Trends," Vehicular Technology, IEEE Transactions on, vol. 56, pp. 2393-2404, 2007. [2] B. Akin, S. B. Ozturk, H. A. Toliyat, and M. Rayner, "DSP-Based Sensorless Electric Motor Fault-Diagnosis Tools for Electric and Hybrid Electric Vehicle Powertrain Applications," Vehicular Technology, IEEE Transactions on, vol. 58, pp. 2679-2688, 2009. [3] C. S. Namuduri and B. V. Murty, "High power density electric drive for an hybrid electric vehicle," in Applied Power Electronics Conference and Exposition, 1998. APEC '98. Conference Proceedings 1998., Thirteenth Annual, 1998, pp. 34-40 vol.1.