Generalized Electromagnetic Transient Equivalent Modeling Algorithm And Its Implementation Method For MMC

Modular multilevel converter(MMC)has been widely used in the world to build the high-voltage direct current(HVDC)grid with renewable power integration.The number of sub-modules(SMs)in the modular multilevel converter(MMC)based HVDC converters are increasing nowadays and new SM structures with specified functions are emerging.With the increasing requirement for the functions of MMCs.multi-port sub-modules with more complex structures and more complex structures are constantly appearing.Although the existing MMC modeling methods can greatly improve the simulation efficiency,they are mostly focusing on the half-and full-bridge SMs based MMCs.As for the multi-port sub-module based MMCs.the existing modeling method is only focused on two-port sub-module based MMC.So the existing MMC modeling methods are poorly behaved in terms of versatility.Therefore,there is an urgent need to establish a high-efficiency,high-precision and generalized electromagnetic transient(EMT)model to accommodate the emerging single-port or multi-port sub-module based MMCs to meet simulation speed and accuracy requirements.Aiming at the problems above,firstly,the single-port SM based MMCs are studied due to its relatively simple structure.And then a generalized electromagnetic transient equivalent modeling approach on single-port MMCs with arbitrary SM structures is proposed based on Thevenin equivalent model and the nested fast and simultaneous solution algorithm.The proposed method automatically transfers the internal node information of the SMs into the interface nodes,then the reduced-order Thevenin equivalent model of each SM is obtained without losing any accuracy.Further all the SMs are cascaded into one ultimate arm Norton or Thevenin equivalents.After each time step solution,the previously eliminated internal capacitor currents and voltages are updated,making the proposed algorithm capable of providing accurate external as well as internal steady and transient behaviors.The proposed method unifies the parameter solving process of the Thevenin equivalent circuit and has strong versatility for all single-port SM based MMCs.The applicability of the proposed algorithm is validated by modeling the proposed enhanced double half-bridge sub-module(D-HBSM)based MMC topology and the EMT simulations on PSCAD/EMTDC verified the accuracy and efficiency of the proposed generalized modeling approach.Secondly,according to the proposed generalized electromagnetic transient equivalent modeling approach on single-port SM based MMCs and the existing modeling method for two-port SM based MMCs,the generalized modeling method and implementation for arbitrary multi-port SM based MMCs is proposed,which is suitable for both single-port SM based MMCs and two-port SM based MMCs.Due to the theory the proposed method used,all the internal information should be preserved.The sub-module topology identification method is proposed to minimize the efforts of the model users when they have specific MMC topologies at hand.In addition,the model codes can be inherited to a large extent.In the electromagnetic transient simulation of MMC,most of the existing models including the proposed model are simplified only for the converter system(primary system).But as the complexity of the primary system model decreases and the number of SMs increases,the sorting algorithm has become the main factor affecting the efficiency of MMC electromagnetic transient simulation.The efficiency of the existing MMC equivalent models is still low in simulating the MMCs with high voltage levels-based DC grids due to the sorting algorithm.Previous research proposed the linear sorting algorithm for full-bridge sub-module(FBSM)based MMC by representing the turn-off resistance of the IGBT switches using ideal zero conductance and using backward Euler method to discretize the capacitor voltage.The calculation complexity of the linear ranking algorithm shows a linear relationship with the change of the number of the sub-modules(SMs).This paper will theoretically prove that under different integration methods,the linear ranking algorithm is also valid with the typical two-value switches used in the FBSM based MMC models on the basis of nested fast and simultaneous solution.Therefore,the internal switching failures can be accurately reproduced by the enhanced high-speed models.In addition,this paper also analyzes the essential principle of the linear ranking algorithm and points out the grouping principle of the algorithm.Then,the advantages and disadvantages as well as the applicability of the ranking algorithm are analyzed.