中文摘要：

传统潮流追踪在节点计算线路分摊时使用了比例分摊假设。所建立的模型一般为代数模型。以有功网络流为对象建立了有功潮流追踪数学优化模型。模型放松了比例分摊假设，从潮流追踪求解空间角度，建立了潮流追踪物理属性约束和决策约束．拓展了有功潮流追踪的范围。具有广泛的应用前景。通过负荷节点电价和电价竞争力2个应用案例进行了说明。应用于负荷节点电价计算时．以方差最小．体现公平地共享输电网，并使用简单算例进行了验证。应用于电价竞争力计算时．探索了各负荷电价竞争力的关系。提供了负荷电价竞争力更多的信息．最后使用实例验证潮流追踪对负荷之间电价竞争力的影响。

英文摘要：

Conventional power flow tracing uses proportional sharing assumption in calculating nodal sharing, and its models are generally algebra equations. In order to promote the application of power flow tracing, a real power flow tracing optimal modeling is established in this paper based on a real power network flow. This model establishes attributive constrains and decision-making objectives front nlathematical optimization perspective. The attributive constrains make the power flow tracing satisfy the real power balance of network, and the deeision-making objective can be established according to the real application. The method ibr establishing the deeision-making objective is demonstrated through two application examples, including load nodal power price and power price competitions. When applied to calculation of load nodal power price, the model can better refleet the fair sharing principles of transmission networks. When applied to calculation of power price competitions, the model can give the maximum and minimum power price competition result of power flow lracing. This work is supported by State Key Program of National Natural Science Foundation of China （No. 51337005） and Science ＆ Technology Project of State Grid Energy Research Institution （No. Sgeri01 kj（2015） 137）.