Time Domain Analysis of Three-Phase Single-Stage AC/DC Resonant Converter Using Numerical Calculation

Abstract

Since <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> converter is capable of naturally creating the soft-switching condition to improve the overall efficiency, it is widely used in dc–dc applications. Using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> resonant tank to realize soft switching for three-phase ac–dc converters would be a very promising solution to high efficiency and low cost ac–dc conversion, an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> -based three-phase single-stage ac–dc converter was configured by taking advantage of three-phase voltage feature <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ u_{\mathrm a}$</tex-math></inline-formula> + <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ u_{\mathrm b}$</tex-math></inline-formula> + <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ u_{\mathrm c}$</tex-math></inline-formula> = 0 and incorporating three bidirectional switches. Because of time-varying feature of three-phase voltages, the input voltage of the converter to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> resonant tank is no longer a symmetrical square wave, but a time-varying and asymmetrical three-level waveform, which makes the analysis of the resonant circuit behavior much complicated. Some traditional analysis methods, such as fundamental harmonic approximation and its variants, are impossible to deal with. To overcome this analysis obstacle, this article proposes a numerical analysis method to analyze the time-varying three-level <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> resonant tank for this converter. According to the monotonous change of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> input voltage in one fundamental cycle, it calculates and determines the time durations of three phases and the corresponding operation modes in each switching cycle. And this numerical analysis method is used to calculate the numerical relationship between the two control variables (switching frequency <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ f_{\mathrm s}$</tex-math></inline-formula> and duty cycle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ D_{\mathrm M}$</tex-math></inline-formula> ) of this converter and the voltage gain and power level, which is a guideline for the design of the resonant tank parameters and control strategy of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> -based three-phase single-stage ac–dc converter. Finally, the time-varying waveforms of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ f_{\mathrm s}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ D_{\mathrm M}$</tex-math></inline-formula> obtained by numerical calculation well match the PSIM simulation results, and a 3.3-kW three-phase 220Vac input and 48Vdc output prototype was built to verify the effectiveness of the proposed numerical analysis method and the feasibility of the control strategy.