Stability Issues of <formula formulatype="inline"><tex Notation="TeX">$Z + Z$</tex></formula> Type Cascade System in Hybrid Energy Storage System (HESS)

Abstract

Stability issues in hybrid energy storage systems (HESSs) are the major concern, in addition to the control design challenges of individual modules. In this paper, the stability issues of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$Z + Z$</tex></formula> type cascade systems in HESS are focused. The stability issues of cascade systems have been studied for many years. Impedance ratio type criterions in the form of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Z_{S}$ </tex></formula> / <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Z_{L}$</tex></formula> or <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX"> $Z_{L}$</tex></formula> / <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Z_{S}$</tex></formula> have been proposed to solve these stability issues. However, existing ratio type criteria still have problems in some cascade systems. The terminal characteristics of submodule are studied and the different types of cascade system are defined in this paper. The validity of conventional impedance ratio type criterion would be influenced by the right-half-plane zeros (RHZ) in terminal impedance of submodules in the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Z + Z$</tex></formula> type cascade system. Two improved criteria are proposed for the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Z + Z$</tex></formula> type cascade system: one is improved ratio type criterion considering the RHZ in the terminal impedance of the submodule; the other one is sum type criterion which does not need the information about RHZ in terminal impedance of each submodule. Experimental evidences are provided to prove the validity of these two improved criteria.