Research On The Calculation Method Of Magnetic Characteristics Of Power Transformers Under Subsynchronous Components Excitation

With the increase in the capacity of new energy power generation such as wind power and the wide application of various power electronic converters,the risk of subsynchronous oscillation in the power system is increased.In order to suppress the spread of the oscillation risk,various subsynchronous oscillation suppressors have also been used.The above conditions will cause subsynchronous components injecting into the power system.Therefore,the transformer is operated under the condition of periodic asymmetrical bias magnetization,resulting in core saturation,current harmonic/interharmonic distortion,higher core loss and temperature rise,increase in reactive power,etc,which will affect the steady-state magnetic characteristics of the transformer core.However,the existing researches on transformer bias magnetization are all focused on the DC bias conditions,and the problem of subsynchronous component injection is more complicated in terms of component categories,nonlinear electromagnetic field steady-state calculation methods and operating parameters.This paper focuses on the efficient calculation method of field-circuit coupling finite element method of transformer and the simulation method of steady-state magnetic characteristics under the condition of asymmetric bias magnetization.The main work and achievements are as follows:(1)Aiming at the fast simulation of the nonlinear magnetic field of power transformers under the condition of bias magnetization,the 2D fixed-point field-circuit coupling finite element equations are deduced,and two efficient solving algorithms are proposed from the perspectives of parallel computing and model order reduction.In terms of time parallel computing,an improved Parareal(parallel-in-time)algorithm for nonlinear coefficients matrices and input vectors is proposed,and the convergence of improved Parareal algorithm is analyzed.The numerical cases show that the overall iterative efficiency is improved while retaining the original accuracy.In terms of model order reduction,a reduced order finite element model based on Proper Orthogonal Decomposition and Discrete Empirical Interpolation Method(POD-DEIM)is proposed to deal with double nonlinear components.The numerical cases show that the solution efficiency of POD-DEIM is greatly improved by retaining a lower degree of freedom,and this model order reduction method is still guaranteed the high accuracy.(2)For the problem that the 2D model can only calculate the magnetic field of the central plane and cannot reflect the global magnetic field,which leads to the reduction of the accuracy when the saturation degree of the three-phase iron core is different,this paper derives and establishes the 3D fixed-point field-circuit coupling time domain finite element model.Firstly,the Galerkin finite element iterative scheme is established considering the Coulomb gauge and two types of boundary conditions.Secondly,for solving the model,the direction vectors of winding current density are established in the preprocessing stage to process the scalar-vector conversion relationship,the appropriate locally convergent fixed-point reluctivity is selected in the anisotropic core region,the steady-state solution of the winding current calculated by the two-dimensional time-periodic finite element method is used as the initial current value of the three-dimensional field-circuit coupling calculation to reduce total iteration time,and the iterative error can be reduced by means of differential permeability and shortening the step size when the local magnetic density is too large.The simulation results show that the subsynchronous component causes the distribution of the magnetic flux of the transformer core to change and the leakage diffusion area of the spatial leakage magnetic field to increase.And the influence on the transformer is related to the amplitude,frequency,phase sequence and three-phase distribution of the subsynchronous components.(3)In order to analyze influence of the core loss with subsynchronous components,a calculation model based on the loss separation theory and the Parareal algorithm is established.The loss separation theory is used to deal with the core loss calculation problem under non-sinusoidal excitation.According to the causes and characteristics in loss separation theory,different time scales need to be used for different loss components.The Parareal algorithm is introduced to solve the model by time parallelism,and the sub-time-interval division deals with the problem that the instantaneous value of the residual loss has no practical physical meaning.The comparison of simulation and experimental results verifies the accuracy of the loss calculation.(4)Aiming at the problem that the subsynchronous components causes the iron core to saturate and causes the non-active power of transformer core to increase,the fundamental reactive power and the full frequency domain non-active power are analyzed respectively.For the fundamental reactive power,the three-phase maximum fundamental period reactive power and the steady-state calculation period average reactive power are analyzed.The results show that the fundamental reactive power fluctuates significantly at each moment when the subsynchronous component is applied,and the reactive power varies between different phases at the same time,but the three-phase reactive power in total calculation period is approximately equal.Due to the injection of subsynchronous components,new frequency components are introduced with the operation of the transformer.Therefore,based on the Clifford’s theory,a multi-vector power theory considering interharmonics is established and the non-active power components are divided.The results show that the variation trend of each power component with the subsynchronous frequency components is different,and the harmonic/interharmonic distortion power is the most significant component of non-active power.(5)In order to explore the influence of the subsynchronous components on the transformers in the practical power system,two typical transformers operating in the 220kV system,the parallel power transformer and the series power flow control transformer,are taken as examples for simulation.Considering the morphological differences of the two types of transformers subjected to the subsynchronous components from the system,the simulation models are established respectively.Based on the field-circuit coupled finite element model,the influence of the subsynchronous components on the steady-state electromagnetic characteristics such as magnetic field,magnetizing current,core loss,and non-active power are analyzed.According to the above electromagnetic characteristics,relevant operation indicators including core saturation,temperature rise,non-active power and harmonics are formulated,and the situation that the transformer can withstand subsynchronous components under the limited indicators is explored.This paper provides guidance for the operation control of subsynchronous oscillation suppressors and other devices that provide subsynchronous components appropriately.