Harmonic Instability in MMC-HVDC Converters Resulting From Internal Dynamics

IEEE Trans. Power Delivery

Suul

et al. 2018

Abstract-The DC-side dynamics of Modular Multilevel Converters (MMCs) can be prone to poorly damped oscillations or stability problems when the second harmonic components of the arm currents are mitigated by a Circulating Current Suppression Controller (CCSC). This paper demonstrates that the source of these oscillations is the uncontrolled interaction of the DC-side current and the internally stored energy of the MMC, as resulting from the CCSC. Stable operation and improved performance of the MMC control system can be ensured by introducing closed loop control of the energy and the DC-side current. The presented analysis relies on a detailed state-space model of the MMC which is formulated to obtain constant variables in steady state. The resulting state-space equations can be linearized to achieve a Linear Time Invariant (LTI) model, allowing for eigenvalue analysis of the small-signal dynamics of the MMC. Participation factor analysis is utilized to identify the source of the poorly damped DC-side oscillations, and indicates the suitability of introducing control of the internal capacitor voltage or the corresponding stored energy. An MMC connected to a DC power source with an equivalent capacitance, and operated with DC voltage droop in the active power flow control, is used as an example for the presented analysis. The developed small-signal models and the improvement in small-signal dynamics achieved by introducing control of the internally stored energy are verified by time-domain simulations in comparison to an EMT simulation model of an MMC with 400 sub-modules per arm.

Section: Introductionsupporting

confidence: 79%

Improving Small-Signal Stability of an MMC With CCSC by Control of the Internally Stored Energy

Freytes

IEEE Trans. Power Delivery

Suul

et al. 2018

“…Notice that the comparison between the reference and the proposed MMC model with SSTI solution has been done using the SSTP signal v ∆ Cz instead of its equivalent SSTI version v ∆ CZ defined in section III. This is done for simplicity, as the dynamics of the virtual system used to create v ∆ CZ do not directly exist in the reference 21 The dynamics of the circulating currents i Σ dqz are shown in Fig. 9, where the upper sub-figure depicts the dynamics of the dq components while the lower figure shows the zero-sequence components multiplied by three, since this signal corresponds to the dc current i dc flowing into the dc terminals of the MMC.…”

Section: MMCmentioning

confidence: 99%

“…Especially Figure 1: Overview of MMC modelling approaches and their areas of application a power balance between the ac-and dc-sides of the converter is assumed in the same way as for a two-level VSC model, like in [12], [14], the model will only be suitable for representing very slow transients. Therefore, more detailed dynamic state-space models have been proposed in [15]- [21]. These available models have been developed for representing two different cases:…”

Section: Introductionmentioning

confidence: 99%

“…2) The approaches proposed in [17]- [19], [21] consider all the internal variables of the MMC, under the assumption of a control system with a Circulating Current Suppression Controller (CCSC) implemented in a negative sequence double frequency SRRF [22]. Indeed, the methods proposed in [17], [18], [21] model the MMC by representing the internal second harmonic circulating currents and the corresponding second harmonic arm voltage components in a SRRF rotating at twice the fundamental frequency. However, the harmonic superposition principles assumed in the modelling, corresponding to phasor-based representation, 4 could affect the information about the non-linear characteristics of the MMC, and correspondingly limit the applicability of the models in non-linear techniques for analysis and control system design.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalized Voltage-Based State-Space Modeling of Modular Multilevel Converters With Constant Equilibrium in Steady State

IEEE J. Emerg. Sel. Topics Power Electron.

Freytes

Guillaud

et al. 2018

This paper demonstrates that the sum and difference of the upper and lower arm voltages are suitable variables for deriving a generalized state-space model of an MMC which settles at a constant equilibrium in steady-state operation, while including the internal voltage and current dynamics. The presented modelling approach allows for separating the multiple frequency components appearing within the MMC as a first step of the model derivation, to avoid variables containing multiple frequency components in steady-state. On this basis, it is shown that Park transformations at three different frequencies (+ω, −2ω and +3ω) can be applied for deriving a model formulation where all state-variables will settle at constant values in steady-state, corresponding to an equilibrium point of the model. The resulting model is accurately capturing the internal current and voltage dynamics of a three-phase MMC, independently from how the control system is implemented. The main advantage of this model formulation is that it can be linearised, allowing for eigenvalue-based analysis of the MMC dynamics. Furthermore, the model can be utilized for control system design by multi-variable methods requiring any stable equilibrium to be defined by a fixed operating point. Time-domain simulations in comparison to an established average model of the MMC, as well as results from a detailed simulation model of an MMC with 400 sub-modules per arm, are presented as verification of the validity and accuracy of the developed model.

“…The classification presented in the previous section was instrumental in [13], [14] to determine a suitable, multifrequency coordinates transformation that maps the oscillating steady-states of interest to constant quantities, while preserving the original model nonlinear structure and avoiding the dynamic phasor approximation used in [25]. This approach, based on an appropriate combination of Park and rotational transformations, is sketched here for the sake of completeness.…”

Section: A Multi-frequency Coordinates Transformationmentioning

confidence: 99%

PI Passivity-Based Control and Performance Analysis of MMC Multiterminal HVDC Systems

IEEE J. Emerg. Sel. Topics Power Electron.

Zonetti

Sánchez

et al. 2019

In this work, a decentralized PI passivity-based controller (PI-PBC) is applied to Modular Multilevel Converters (MMCs) to ensure global stability of a multi-terminal HVDC system. For the derivation of the controller, an appropriate model with constant steady-state solutions is obtained via a multifrequency orthogonal coordinates transformation. The control design is next completed using passivity arguments and performance guarantees are established by a small-signal analysis. The obtained results are validated by means of detailed timedomain simulations both on a single-terminal and a four-terminal benchmark.