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A problem based on transient thermal circuit equation and modified thermal limits was studied in this paper, which was involved in mathematic model of optimal power flow(OPF) about available transfer capability ( ATC ) .The weakest lines were found applying modal analysis,then we estimated whether the transmitting capacity was conditioned by the temperature variation of the lines by using constraints of temperature substitute for the thermal limits of the weakest lines. The new model was constructed in order to overcome conservatism of judgement by current capacity, and the latent transmitting capacity will be fully excavated.Then, increased the conductor allowable temperature from 70℃ that specified by the present specifications to 80℃, a great number of both foreign and domestic test datas showed that it will make great profit in the long run. The solution of the optimal power flow problem by a nonlinear primal-dual interior point method is considered. A case study of IEEE-30 bus system demonstrated the rationality and validity of strategies proposed in this paper.Index Terms-Available transfer capability, thermal limits, temperature of the lines, optimal power flow, weakest lines.Guoqing Li was born in china,1963. He received Ph.D degrees in electrical engineering from Tianjin University ,China ,in 1998. He was promoted exceptionally to associate professor in 1993, then he was promoted exceptionally to professor in 1996. His research interests are in the areas of power system operation and optimization, stability and security assessment and power system planning. Yinfeng Sun was born inJilin of china, on september 8, 1983. He obtained B.Eng.in Electrical Engineering from Northeast Dianli University in 2006. He studied in the same university for master degree since 2006. His research interests include power system stability analysis and security analysis .Xiaojun Li was born in China in 1978. He graduated from Xi'an Jiao Tong University in 2002, and received his master degree from Northeast Dianli University in 2008. Now he is working at power system operation as a employee of Northwest Power Grid Co., Ltd. His interests are in the area of power system operation and voltage stability etc.

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Flexible direct current (DC) grid can realize large-scale renewable energy, wide-area coordinated complementation, and reliable power transmission. It is an important development that can be used to support high-voltage and large-capacity flexible DC transmission in the future. The short-circuit current of the DC line is one of the important bases for the selection of key main equipment parameters such as converter valves, DC circuit breakers, and reactors in the flexible DC grid. In this paper, a flexible DC grid equivalent circuit network model with alternating current (AC) feed-in is established. Aiming at the monopolar ground fault of the flexible DC grid grounded through the metal loop, an optimized traditional matrix calculation method is proposed to obtain the accurate line fault current value. On this basis, with an actual engineering background, the equivalent circuit model of the four-terminal bipolar flexible DC power grid is established, and the influence of grounding position, grounding parameters, and current-limiting reactor on the fault current of the DC line is analyzed. Finally, simulation using the PSCAD software verifies the effectiveness and accuracy of the proposed method. The method proposed in this paper can provide the necessary bases and references for the selection of flexible DC grid equipment.