Exploring Gaussian elimination based solution methods of electric systems using circuit principles

In power system simulation, the mathematical solution methods are typically regarded as pure numerical operations, which are independent of the circuit principles. In this letter, it is demonstrated that the computational procedures in the commonly used numerical solution methods for circuit equations are essentially equivalent to the basic principles of electricity. The computational procedures of the representative Gaussian elimination based solution methods (including GE and pivoting method for sparsity of GE/LU) are comprehensively analyzed and their deep relationships with the circuit principles are revealed: the computation process of these mathematics based numerical solution methods can be completely explained using circuit principles. The interesting findings could help understand the computational process of solution methods from the circuit perspective, which may also guide the design of new circuit solution methods