Steady-State Analysis of the Modular Multilevel Converter

Abstract

This paper focuses on the modeling, dynamic analysis, and simulation of the bidirectional DC-DC boost-buck power converter. The switching sequence applies different duty cycles in the input and output stages, resulting in full regulation of the system variables. By using this strategy, the input stage can be regulated disregarding perturbations in the output leg, as well as the output stage can be controlled independently of the effects of disturbances in the input part; which gives significant robustness to the converter. Based on the switching actions, the state-space average equations are derived, accomplishing the base to obtain the small-signal equations and equivalent small-signal circuits. The open-loop transfer functions are developed, besides the input and output impedance, and the audio susceptibility. Simulation results indicate that the proposed model can predict the dynamic behavior of the system in a wide range of the frequency spectrum, and the results in the time domain are in perfect agreement with the model predictions under disturbances of the control variables, variations of the value of the supply voltage and load changes.

Optimization-Based Methodology to Design the MMC's Sub-Module Capacitors

“…In this step, no optimization algorithm is required. The equilibrium quantities are obtained based on a system of equations describing the MMC's steady-state profile, as the one presented in [22]. The voltages and currents resultant from this equation system are required as the initial conditions of the next step in order to speed up the convergence time and improve its accuracy.…”

“…sin(2ωt + θ k u,l + ϕ k u,l ) As it can be observed from (6), the oscillating energy expression has in total three terms, in which two are related to the first-order frequency and the other one is a second-order frequency term. In order to reduce such equation and ease the derivation of the expression describing the equivalent arm capacitor voltage, the principles presented in [24] are employed. By doing so, the first-order terms can be combined into a single one, consequently, the instantaneous energy expressions can be reduced to…”

Optimal Current Reference Calculation for MMCs Considering Converter Limitations

“…• 80 equations divided in: -11 complex linear AC equations: (5), (6), (7), (25a), (25b) -10 linear DC equations: (25c-25e) -48 non-linear equations: (16)(17)(18)(19), (24), (26) • 39 inequalities: (27a-27d)…”

“…Using 3, the calculation of I k s may result in zero sequence components I 0 s for a generic unbalanced AC voltage condition, which cannot flow due to the three-wire AC connection 1 . To impose this condition in the model, one option is to remove the zero-sequence keeping the positive and negative sequence components [24]. Current I k s will be subsequently used in the following section as an input to solve the steady-state model.…”

Optimization-based reference calculation for Modular Multilevel Converters in balanced and unbalanced network conditions

“…The MMC has additional degrees of freedom that must properly exploited in order to not only improve the converter's performance during AC network voltage sags [2], but also to meet with the grid code requirements (in terms of active and reactive current components to be injected into the AC grid during such faults). Relevant previous works have been done regarding the steady-state analysis of the converter's quantities during normal and faulted scenarios [3][4][5][6], but limited references can be found when the grid operator constraints (for active and reactive current injection during AC grid faults) are considered throughout the steady-state modelling.…”