Generalized Dynamic Phasor Modeling of the MMC for Small-Signal Stability Analysis

© 2018 IEEE. This paper introduces a dynamic phasor model of a half-bridge modular multilevel converter based on variables in the stationary ABC frame. The application of the dynamic phasor theory makes it possible to use converter eigenvalues to study the effect of steady-state harmonics present in the modular multilevel converter (MMC) on its small-signal stability, since the model is inherently time invariant. Relying on a linear transformation, this paper uses a new set of variables with a modified frequency content, which results in lower order dynamic phasor models. A nonlinear dynamic phasor model is developed and linearized. The linear model is compared with a nonlinear averaged MMC model in time domain. Stability analysis by means of eigenvalues and participation factors is carried out for dynamic phasor models that include different frequency content, and the effect of the circulating current suppression controller is analyzed.status: publishe

Impact of PLL Dynamics on the Small-Signal Stability of the MMC using Dynamic Phasor Modeling in the ABC Frame

status: Published onlin

Equivalent Multiple dq-Frame Model of the MMC using Dynamic Phasor Theory in the αβz-Frame

This paper introduces an equivalent multiple dq-frame model of the modular multilevel converter (MMC) that is derived from a dynamic phasor based small-signal state-space MMC model in the stationary αβz frame. When compared to a model in the stationary ABC frame, the order of the model in the αβz frame can be reduced for balanced operation, during which some voltage and current harmonics are inherently separated in an αβz representation. The proposed method enables further model-order reduction through a generalized transformation towards multiple dq frames. The development of the model and the generalized transformation are explained in detail, and the obtained equivalent multiple dq-frame models are verified against a nonlinear averaged model in MATLAB®/Simulink. An eigenvalue-based small-signal stability analysis highlights the effect of higher-order harmonics in system-level small-signal stability studies, and two case studies of active harmonic suppression illustrate how the presented model allows an in-depth investigation of the impact of extended control functionalities on the small-signal stability.status: Published onlin

Input Admittance Calculation of the Modular Multilevel Converter using a Linearized Dynamic Phasor Model

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How do demand response and electrical energy storage affect (the need for) a capacity market?

To ensure security of supply and incentivize reliable investment in generation capacity, capacity markets (CMs) have been implemented or are being considered. However, demand response (DR) and electrical energy storage (EES) also contribute to system adequacy. In this paper, we analyse the change in the need for a CM if DR and EES are available, in the presence of a growing portfolio share of intermittent renewable energy sources electricity (RES-E). We present a novel hybrid electricity market model of the transition to a low-carbon electricity system which uses optimization for short-term market operations and agent-based simulation of long-term decisions. DR and EES may significantly reduce the risk of shortages in an energy-only market, even if investment decisions are myopic, like in our model, as compared to an energy-only market without flexibility options. We also present a novel mechanism for contribution of EES to the CM. This reduces the cost of the CM and improves the business case for EES. In our model, DR and EES achieve almost the same improvement of security of supply as a CM, but they do so at a lower cost. Therefore, the case for a centralized CM is weakened in a system with even a limited share of DR and medium-term EES, as presented in our model. These results depend on the duration of scarcity events and the cost of EES and DR. Refinement of the model representation will be required to extrapolate these conclusions to real markets with other types of DR, EES and CMs.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Energy & Industr