Resolution of line-transferred power in grids yielded by circuit-laws' symmetry under deductive reasoning of shapley theorem


This study presents a strict technique for resolving line-transferred power (or decomposing line-power flow) into sourcedriven component powers over lines. First, 3 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 3 properties build all conditions or hypothesis in Shapley theorem satisfied. Then the deductive reasoning of Shapley theorem is employed to solve the model, that immediately provides a discrete and non-analytical resolution formula in terms of linetransferred powers caused by excitations of possible combination of sources. Representing the facility by source currents (or electromotive forces), a nonstop and analytical resolution formula in terms of supply currents (or electromotive forces) is then proved mathematically. The resolution formula is invariantly the same for all sources together with the slack supply. It's additionally applicable to search out the supply-driven component powers flowing into masses and out of sources in arbitrarily difficult grids. Simulation results show the options of the proposed method.

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