Analytical solutions for power flow equations based on the multivariate quotient-difference method

This paper proposes a method of obtaining the approximate analytical solutions for power flow equations based on the multivariate quotient-difference method. The power flow solutions for different operating conditions can be directly obtained by scaling multiple symbolic variables in the analytical solutions, such that the power injections or consumptions of selected buses or groups of buses can be independently adjusted. This method first uses the multi-dimensional holomorphic embedding method to derive the power flow solutions in the form of multivariate power series. Then, the multivariate quotient-difference method is applied to transform multivariate power series (MPS) to multivariate Padé approximants (MPA) to expand the radius of convergence (ROC), so that the accuracy of the derived analytical solutions can be significantly increased. This method can adapt to many online applications, since the analytical solution can be derived offline and evaluated online by only plugging values into the system symbolic variables according to actual operating conditions. This proposed method is validated in detail on the IEEE 39-bus New England power system considering independent load variations in multiple regions.