A fixed topology Thevenin equivalent integral model for modular multilevel converters

摘要

The Thevenin equivalent model for half-bridge modular multilevel converters on electromagnetic transient simulation, applying 2-state resistances to represent switches and adopting Dommel's algorithm to get a discretized capacitance in each submodule, achieves good central processing unit time saving while maintaining the identity of every submodule. But the large number of changeable resistances still brings a computational challenge for simulation efficiency, because the admittance matrix gets an equaled size to the amount of nodes, and inverts (re-triangularizes) each time when a switch performs. This paper presents a novel fixed topology Thevenin equivalent half-bridge modular multilevel converter integral model and simplifies its mathematical expression markedly. The choice of integration methods is also performed by discussion of the stability, and backward Euler algorithm is selected for further speedup. Basically, it achieves speedup by (1) the use of novel Thevenin equivalent model to achieve unchangeable admittance matrix while regarding the switches as excitations; (2) merging the elements (inductances, resistances, and submodules) in the arm of modular multilevel converter by Thevenin equivalent to reduce the order of admittance matrix; (3) simplifying the mathematica expression of sub module by Thevenin equivalent and omitting the small resistance; and (4) the use of backward Euler algorithm to discretize all the elements (capacitances, inductances, resistances, and submodules) in the circuit for a better convergence speed and larger speedup factor. The model is implemented in a 3-phase grid-connected modular multilevel converter circuit; the results show that the proposed Thevenin equivalent integral model makes a good accuracy on simulating the performances of the half-bridge modular multilevel converter with drastically reduced computational time.