Research On Convergence Of Cartesian Coordinates Newton Power Flow Algorithm With Small Impedance Branch

As a very important calculation in power system,Power flow calculation is often used to study various problems encountered in system planning and operation.Power flow calculation is essentially a problem of solving nonlinear equations by using the idea of iteration in mathematics.Since the iterative calculation of numerical values is used in the process of power flow calculation,its convergence is very important when performing power flow calculations.With the continuous expansion of the scale of modern power networks,the ill-conditioned phenomena during power system operation have also increased.This phenomenon often causes the results of power flow calculations to fail to converge.Therefore,the research on the convergence of illconditioned power flows has important practical significance.Based on the theoretical analysis of Newton power flow algorithm,this paper applies Kantorovich theory in mathematics to Newton power flow algorithm,and obtains a method to judge the convergence and divergence of Newton power flow algorithm.This method can be used to evaluate whether the selected initial value can guarantee the convergence of Newton power flow algorithm.Through the simulation analysis of IEEE14,IEEE30 bus system and northeast power grid,the feasibility and rationality of the theory are verified,and the practicability of NR method in power flow calculation is improved.Based on this method,it is found that the deterioration of the numerical conditions of the Jacobian matrix is the main reason that the power flow calculation fails to converge in the low impedance branch system.Therefore,by further analyzing the influence of small impedance branch on Newton power flow algorithm,an improved Newton power flow algorithm is obtained by modifying the initial value of Jacobian matrix on the basis of traditional Newton power flow algorithm: In the first iteration,use the active and reactive power given by the system for the PQ bus to replace the bus’ s calculated power,so as to find the real and imaginary parts of the bus injected current,and then obtain the corresponding Jacobian matrix elements.For PV bus,the real part and imaginary part of the bus injection current are ignored to calculate the Jacobian matrix elements,which reduces the uncertainty of using the bus injection current to replace the calculation current,and minimizes the influence of small impedance parameters on the real part and imaginary part of the bus current.For the second iteration and subsequent iterations,the Jacobian matrix elements are calculated using bus calculation current.It is proved by theoretical derivation that this method can make the power flow of the system with small impedance branch converge.The improved algorithm is simulated in IEEE14,IEEE30 bus system and 445 bus power grid.The results show that the improved algorithm has good convergence reliability in power flow calculation of systems with small impedance branches.Compared with the existing injection method,it needs fewer iterations on the basis of ensuring the convergence reliability,has better convergence and adaptability,and has a certain practical value in engineering.