Resolution of line-transferred power in grids yielded by circuit-laws' symmetry under deductive reasoning of shapley theorem
Resolution of line-transferred power in grids yielded by circuit-laws' symmetry under deductive reasoning of shapley theorem
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DOI：
10.1049/iet-gtd.2011.0536
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发表时间：
2012-07
影响因子：
2.5
通讯作者：
Jianchun Peng;Y. Zeng;H. Jiang
中科院分区：
文献类型：
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作者：
Jianchun Peng;Y. Zeng;H. Jiang
该研究提出了一种严格的方法，将线路传输功率（或将线路潮流分解）分解为线路上的源驱动分量功率。首先，推导了电路定律的守恒性、对称性和可加性。将其与电路定律方程相结合，建立了求解线路传输功率的模型。这三个性质使沙普利定理中的所有条件或假设都得到满足。然后利用Shapley定理的演绎推理对模型进行求解，该模型立即给出了由可能的组合源激励引起的线传递功率的离散非解析解析公式。用源电流（或电动势）表示功率，然后用数学方法证明了源电流（或电动势）的连续解析解析公式。对于包括松弛源在内的所有源，解析公式都是不变的。该方法也适用于求解任意复杂电网中流入负载和流出源的源驱动分量功率。仿真结果表明了该方法的特点。
This study presents a strict method for resolving line-transferred power (or decomposing line-power flow) into source-driven component powers over lines. First, three properties of conservation and symmetry and additivity inherent in circuit laws are derived. Incorporating them with circuit-laws' equation, a model for resolving line-transferred power is built. The three properties make all conditions or hypothesis in Shapley theorem satisfied. Then the deductive reasoning of Shapley theorem is used to solve the model, which immediately gives a discrete and non-analytical resolution formula in terms of line-transferred powers caused by excitations of possible combination of sources. Representing the power by source currents (or electromotive forces), a continuous and analytical resolution formula in terms of source currents (or electromotive forces) is then proved mathematically. The resolution formula is invariantly the same for all sources including the slack source. It is also applicable to find the source-driven component powers flowing into loads and out of sources in arbitrarily complicated grids. Simulation results show the features of the proposed method.