Design Space Analysis and $\rho$– $\eta$ Pareto Optimization of $LC$ Output Filters for Switch-Mode AC Power Sources

Abstract

In this study, the design space (DS) concept is refined and utilized to design the output filter of a ${\rm 10}$ - ${\rm kW}$ , four-quadrant, three-phase, switch-mode controllable AC power source (CPS). The DS concept is based on the simultaneous consideration of multiple criteria that are derived from application-oriented specifications for the CPS regarding quality and transient response of the output voltage, and limited reactive power demand of the output filter. In this paper, the output filter of the studied CPS needs to satisfy six different criteria, which, in the case of a single-stage $LC$ filter, leads to bounds on the values of $L$ and $C$ that can be indicated by boundary curves in an $L\hbox{-}C$ plane. The intersection set of all boundary curves defines the DS, in which all six specifications can be fulfilled. For the considered requirements, it is shown that the DS is empty for a single-stage $LC$ filter, but exists for a two-stage $LC$ filter, which is therefore employed as an output filter of the CPS. To fully exploit the 4D DS of the two-stage $LC$ filter, a multi objective optimization, resulting in the power density–efficiency Pareto front, is performed to determine the most compact and/or most efficient filter design among all possible filter realizations with parameters in the DS. From the outcome of this optimization, the filter design with the highest power density of ${14.6}\, {\rm kW} / {\rm dm}^{3}$ ( ${239}\, {\rm W} /{\rm in}^{3}$ ), for an efficiency of $99.4\%$ , is realized in hardware. Finally, all six specifications for the CPS are successfully verified by experimental measurements.