Dynamic phasor modeling of Modular Multi-level Converters

Deore, S. R.; Darji, Pranav B.; Kulkarni, A. M.

doi:10.1109/iciinfs.2012.6304792

Cited by 37 publications

(23 citation statements)

References 12 publications

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“…It is important to note that unlike (16), equation 17contains a set of 6 th order harmonic terms. However, the amplitudes of the 6 th harmonic terms are all defined by products between d-and q-axis components of the circulating currents and the corresponding voltages.…”

Section: ) Energy Sum Dqz Dynamicsmentioning

confidence: 99%

“…Overview of MMC modelling approaches and their areas of application been recently proposed, with the aim of obtaining linearized models for small-signal power system stability analysis. A first approach has been to apply dynamic phasor modelling to all the internal electrical states of the MMC, as discussed in [16] and [17], resulting in complicated high order models. Another approach has been to neglect parts of the internal dynamics of the MMC, and model mainly the ac-side dynamics in a SRF together with a simplified dc-side representation, as in the models proposed in [18]- [20].…”

Section: Introductionmentioning

confidence: 99%

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Energy-Based State-Space Representation of Modular Multilevel Converters with a Constant Equilibrium Point in Steady-State Operation

Bergna-Diaz

Suul

D’Arco

2018

IEEE Trans. Power Electron.

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The internal currents and voltages of Modular Multilevel Converters (MMCs) contain multiple frequency components in steady state operation and remain time-periodic even when transformed into a synchronously rotating reference frame. This prevents a straightforward state-space representation where a constant equilibrium point is reached and all state variables converge to constant values under steady-state conditions. Such steady-state time-invariant (SSTI) representations are needed for linearization and eigenvaluebased analysis of small-signal stability. This paper presents an energy-based model of an MMC with a modulation strategy where the insertion indices are compensated for the oscillations in the sum arm voltage. The formulation of the model allows for deriving, by the application of Park transformations at three different frequencies, a SSTI representation that accurately captures the internal dynamics of the MMC. This model can be simplified to a reduced order model that maintains accurate reproduction of the external behavior at the ac-and dc-sides while neglecting some of the internal dynamics. The validity and accuracy of these two SSTI MMC models are verified by timedomain simulations and their utilization for eigenvalue-based analysis of MMC dynamics is demonstrated by examples.

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Section: ) Energy Sum Dqz Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Energy-Based State-Space Representation of Modular Multilevel Converters with a Constant Equilibrium Point in Steady-State Operation

Bergna-Diaz

Suul

D’Arco

2018

IEEE Trans. Power Electron.

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“…State-space modeling based on the dynamic phasor [18][19][20][21][22]: this modeling approach is also based on the state-space modeling techniques, but the system is in abc-frame. It is a suitable modeling method for studying the impact of harmonics on the system stability [18].…”

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confidence: 99%

Interaction Assessment and Stability Analysis of the MMC-Based VSC-HVDC Link

et al. 2020

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This paper investigates the dynamic behavior of a modular multi-level converter (MMC)-based HVDC link. An overall state-space model is developed to identify the system critical modes, considering the dynamics of the master MMC and slave MMC, their control systems, and the HVDC cable. Complementary to the state-space model, an impedance-based model is also derived to obtain the minimum phase margin (PM) of the system. In addition, a relative gain array (RGA) analysis is conducted to quantify the level of interactions among the control systems of master and slave MMCs and their impacts on stability. Finally, with the help of the results obtained from the system analysis (eigenvalue, phase margin, sensitivity, and RGA), the system dynamic performance is improved.3 of 19 an eigenvalue and participation factors analysis in Section 6. Moreover, the system minimum PM is calculated through an impedance-based analysis using the Nyquist plot, and the level of interactions among control loops is studied using a frequency-dependent relative gain array (RGA) analysis. Finally, in Section 7, based on the results achieved from the system analyses, the stability of the system is improved by tuning the DC voltage control loop. System DescriptionA typical HVDC link between two AC networks is shown in Figure 1. In such configuration, the master MMC regulates DC voltage while the slave MMC controls active power exchange [27]. Either AC voltage or reactive power can be regulated at both ends. AC network 1 HVDC cable AC network 2 Master Slave V dc control P control

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“…In order to characterize the frequency coupling behavior of the MMC, a few authors have made efforts on the modeling of the MMC. Deore et al [20] introduced dynamic phasor approach to model the MMC in frequency domain, which, however, results in a very large number of variables and equations. Dragan et al…”

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confidence: 99%

Impedance modeling of modular multilevel converter based on harmonic state space

Chen

Lyu

et al. 2016

2016 IEEE 17th Workshop on Control and Modeling for Power Electronics (COMPEL)

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The small-signal impedance modeling of modular multilevel converter (MMC) is the key for analyzing resonance and stability of MMC-based ac power electronics systems. MMC is a converter system with a typical multi-frequency response due to its significant steady-state harmonic components in the arm currents, capacitor voltages, and control signals. Therefore, traditional small-signal modeling methods for 2-level voltage-source converters (VSCs) cannot be directly applied to the MMC. In this paper, the harmonic state-space (HSS) modeling approach is introduced to characterize the harmonic coupling behavior of the MMC. On this basis, the small-signal impedance models of the MMC, which take into account the internal dynamics of MMC, are developed according to the harmonic linearization principle. Furthermore, in order to reveal the impact of the internal dynamics and closed-loop control on the small-signal impedance of the MMC, three cases are considered in this paper, i.e., open-loop control, ac voltage closed-loop control, and circulating current closed-loop control. Finally, the analytical impedance models are verified by both simulation and experimental results. Index Terms-Modular multilevel converter (MMC), impedance modeling, impedance measurement, harmonic state-space (HSS), harmonic coupling. especially for renewable energy integration applications [5]-[7].The impedance-based stability analysis method is one of the preferred methods for stability analysis of power electronics systems, especially for multi-converter interconnected systems [8]- [11]. The impedance modeling of power converters is the prerequisite for applying the impedance-based analytical approach. Most of the research has so far focused on the impedance modeling of 2-level converters [9]- [14]. Sequence impedance models of 2-level grid-connected VSCs with current control and phase-locked loop (PLL) dynamics were developed in [9], [14]. DQ small-signal impedance of 2-level VSCs with closed-loop control was derived in [10]- [13]. However, very few authors have by far reported the impedance modeling of an MMC. The dc-side impedance of an MMC was derived for dc voltage ripple prediction in [15], but there is no mention of ac-side impedances. In the beginning of our previous work [6], [16], the ac-side impedance models of the MMC were developed, where, however, the capacitor voltage harmonics and high-order circulating current harmonics were ignored in the impedance modeling, resulting in imprecise impedance models. Later, the harmonic linearization method and harmonic state-space (HSS) method were introduced by the authors to develop the MMC impedance models in [17], [18], which are able to include all the steady-state harmonics of the state variables. In addition, a similar method to the HSS, so called multi-harmonic linearization method, was also proposed to model the MMC impedance in [19].MMC is a converter system with a typical multi-frequency response due to its significant steady-state harmonic components in the arm currents, capacitor volt...

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Dynamic phasor modeling of Modular Multi-level Converters

Cited by 37 publications

References 12 publications

Energy-Based State-Space Representation of Modular Multilevel Converters with a Constant Equilibrium Point in Steady-State Operation

Energy-Based State-Space Representation of Modular Multilevel Converters with a Constant Equilibrium Point in Steady-State Operation

Interaction Assessment and Stability Analysis of the MMC-Based VSC-HVDC Link

Impedance modeling of modular multilevel converter based on harmonic state space

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