Large-scale photovoltaic (PV) power plants connected to the grid leads to the complex calculations in modeling and simulation of the power system, especially in the electromagnetic transient progress. Common averaging methods are studied for modeling a grid-connected converter to simplify the calculation and balance accuracy and efficiency in the simulation. The piecewise technique is applied to the generalized state space averaging model of converters, which combine time segment with similar operating characteristic. In addition, a new piecewise generalized state space averaging (P-GSSA) model is derived and a multi time scale modeling is achieved for the grid-connected converters in PV systems. The model error and accuracy of the P-GSSA model are analyzed, the physical significance and the influence factors in the model error of P-GSSA model are discussed. The proposed P-GSSA model is flexible to be used in a PVs system simulation, and it can accurately reflect the steady-state and transient characteristics of a converter. The research shows that P-GSSA model improved the simulation efficiency over 20% by the index of consumed time, meanwhile, the model error analysis is under 5%. The analysis of the P-GSSA model is verified by simulating a DC/AC converter and a photovoltaic system. INDEX TERMS Converters, efficient simulation, electromagnetic transient model, multi time scale, piecewise generalized state space averaging.

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This study systematically investigated the effects of phytoestrogen glabrene on postmenopausal osteoporosis in an ovariectomy (OVX) rat model. Glabrene administration (25, 50, and 100 mg/kg) for 13 weeks can significantly slow down the body weight gain and slightly increase the uterus weight of OVX rats. The increased levels of U‐Ca, U‐P levels, urine DPD/creatinine, serum ALP, OCN, triglycerides, and total cholesterol induced by OVX were dramatically inhibited in rats, whereas no difference occurred for S‐Ca and S‐P in all groups. Furthermore, glabrene can enhance bone mineral density of the right femur, fourth‐lumbar vertebra and tibia and improve biomechanical parameters, such as femoral neck loading force, three‐point bending of the tibia, and vertebral compression in OVX rats. Moreover, glabrene greatly suppressed the expression of TRAP protein but increased OPG and BGP protein expression in tibia tissue of OVX rats. In addition, OVX‐induced reduction of Lrp‐5, β‐catenin, Runx2, and Osx protein expression was all restored by glabrene treatment. The present study indicated that glabrene might be a potential alternative medicine for the prevention and treatment of postmenopausal osteoporosis via activation of the Wnt/β‐catenin signaling pathway.

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