Modular Multilevel Converter Impedance Computation Based on Periodic Small-Signal Analysis and Vector Fitting

Abstract

Instability and oscillation issues originating in highvoltage direct current (HVDC) systems comprising modular multilevel converters (MMCs) are gaining increasing interest in the research community. To detect such phenomena in advance, considerable effort has been devoted recently to developing MMC models for small-signal analysis. The derivation of such models is a challenging task due to the topology and complex control structure of MMCs, which results in them having a multi-frequency response. To address this issue, scholars developed methods based on dynamic phasors and harmonic state-space modelling, which, however, require extensive pen-and-paper computations. In this paper, the periodic small-signal analysis (PAC) is adopted to determine numerically several MMCs transfer functions. Such functions can be computed between any electrical circuit node or input/output port, without the need to recast the three-phase average MMC model to derive a linear equivalent one, possibly in the DQ-frame. We show how vector fitting allows converting these functions to equivalent algebraic representations, which can be profitably used to design MMCs and study their stability following some parameter changes. To showcase this feature, we exploit one of these transfer functions to detect DC-side instability in a point-to-point HVDC system.

Impact of Passive-Components’ Models on the Stability Assessment of Inverter-Dominated Power Grids

“…In addition, the DC-side voltage reference value of MMC2 (i.e., receiving end) is V dc = 400 kV. The interested reader is referred to Figure 1 of [26] and references therein for a possible MMC control scheme implementation.…”

“…In this paper, we modelled the MMCs of the HVDC system at two very different levels of accuracy: the former, hereafter referred to as accurate, is shown in Figure 1a-c of [26] and derives from [38]. This three-phase model substitutes the SMs in each arm of the MMC with a single equivalent circuit.…”

“…The numeric tool we used to compute admittances is fully described in [26] and implemented in our own simulator PAN [48,49]. In extreme synthesis, a small-signal tone with variable frequency is injected in one of the three phases of the step-up transformer (in our case the "a" phase) of each MMC.…”

Generalized impedance-based AC/DC power system modeling for harmonic stability analysis

“…However, as there is a rapid increase in the deployment of HVDC systems based on modular multilevel converters (MMCs), the stability analysis of hybrid AC/DC systems should account for specific characteristics of the MMC, including frequency couplings as a result of the complicated internal dynamics of the converter. In the recent work [19] the MMC is modeled without simplifications using vector fitting technique for small signal analysis. However, besides a detailed modeling of the MMC, the stability analysis should also account for frequency-dependent characteristics of passive components to lead to accurate results over an extended frequency range.…”