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This article reviews the design and evaluation of different DC-DC converter topologies for Battery Electric Vehicles (BEVs) and Plug-in Hybrid Electric Vehicles (PHEVs). The design and evaluation of these converter topologies are presented, analyzed and compared in terms of output power, component count, switching frequency, electromagnetic interference (EMI), losses, effectiveness, reliability and cost. This paper also evaluates the architecture, merits and demerits of converter topologies (AC-DC and DC-DC) for Fast Charging Stations (FCHARs). On the basis of this analysis, it has found that the Multidevice Interleaved DC-DC Bidirectional Converter (MDIBC) is the most suitable topology for high-power BEVs and PHEVs (> 10kW), thanks to its low input current ripples, low output voltage ripples, low electromagnetic interference, bidirectionality, high efficiency and high reliability. In contrast, for low-power electric vehicles (<10 kW), it is tough to recommend a single candidate that is the best in all possible aspects. However, the Sinusoidal Amplitude Converter, the Z-Source DC-DC converter and the boost DC-DC converter with resonant circuit are more suitable for low-power BEVs and PHEVs because of their soft switching, noise-free operation, low switching loss and high efficiency. Finally, this paper explores the opportunity of using wide band gap semiconductors (WBGSs) in DC-DC converters for BEVs, PHEVs and converters for FCHARs. Specifically, the future roadmap of research for WBGSs, modeling of emerging topologies and design techniques of the control system for BEV and PHEV powertrains are also presented in detail, which will certainly help researchers and solution engineers of automotive industries to select the suitable converter topology to achieve the growth of projected power density.