An Approach for Calculating the Power Distribution of Electrical Circuits Based on the Nodal Power

Since the discovery of Kirchhoff's law in 1847, almost all the research of electric circuits has been based on it, for the variables of circuits can be worked out by solving a set of Kirchhoff equations. For small scale circuits, this method is accurate and convenient, but for large-scale circuits, it is not an easy task to solve the equations. Enlightened by the movement of water flows, we found, in a parallel circuit, Kirchhoff's current law can be converted into 2 current distribution rule: at each node, the total incoming current will be distributed to each outgoing branch in proportion to the branch gradient of electric potential. Calculating according to this, we designed a distributed algorithm, Power Gradient Algorithm (PGA), to calculate the power distribution of electric circuits based on the Nodal Power. Having been validated on various circuits, PGA is proved to be simpler, more efficient and without astringency problem comparing with the classical algorithms based on Kirchhoff's law. In addition, we found its accuracy is related with the topological structure of circuits. That is, along with the increment of the circuit size or the small-world characteristic becoming more and more outstanding, the accuracy of PGA is better and better. Therefore, PGA is more suitable for the real-time calculations of large-scale power grids.