The small-signal impedance modeling of a modular multilevel converter (MMC) is the key for analyzing resonance and stability of MMC-based power electronic systems. The MMC is a power converter with a multifrequency response due to its significant steady-state harmonic components in the arm currents and capacitor voltages. These internal harmonic dynamics may have great influence on the terminal characteristics of the MMC, which, therefore, are essential to be considered in the MMC impedance modeling. In this paper, the harmonic state-space (HSS) modeling approach is first introduced to characterize the multiharmonic coupling behavior of the MMC. On this basis, the small-signal impedance models of the MMC are then developed based on the proposed HSS model of the MMC, which are able to include all the internal harmonics within the MMC, leading to accurate impedance models. Besides, different control schemes for the MMC, such as open-loop control, ac voltage closed-loop control, and circulating current closed-loop control, have also been considered during the modeling process, which further reveals the impact of the MMC internal dynamics and control dynamics on the MMC impedance. Furthermore, an impedance-based stability analysis of the MMC-high-voltage direct current connected wind farm has been carried out to show how the HSS-based MMC impedance model can be used in practical system analysis. Finally, the proposed impedance models are validated by both simulation and experimental measurements.

/pdf/harmonic-state-space-based-small-signal-impedance-modeling-2964si2j5k.pdf

Harmonic State-Space Based Small-Signal Impedance Modeling of a Modular Multilevel Converter With Consideration of Internal Harmonic Dynamics

A subsynchronous oscillation (SSO) phenomenon has been observed in a modular multilevel converter-based high-voltage dc (MMC-HVDC) transmission system for wind farm integration in the real world, which is independent of the type of wind turbine generator. This kind of oscillation appears different from those in doubly fed induction generator-based wind farm with series-compensation line or wind farm integration through two-level voltage-source converter-HVDC transmission system, because the internal dynamics of the MMC may have significant impact on the oscillation. By far, however, very few papers have reported it. In this paper, the generation mechanism of the SSO phenomenon in an MMC-HVDC transmission system for wind farm integration is revealed from an impedance point of view. The harmonic state-space modeling method is applied to model the multifrequency behavior of the MMC, based on which, the ac-side small-signal impedance of the MMC is analytically derived according to harmonic linearization theory. As a general rule, the controller parameters of the wind power inverter and the HVDC converter are designed separately, to meet the performance requirements of the single converter under ideal conditions, but this practice does not guarantee the stability of the interconnected system. Therefore, an optimal design method for controller parameters is proposed in this paper in order to guarantee the small-signal stability of the interconnected system from a system point of view. Finally, time-domain simulations validate the effectiveness of the theoretical analysis and the proposed optimal design method.

/pdf/optimal-design-of-controller-parameters-for-improving-the-421xn1pcg8.pdf

Optimal Design of Controller Parameters for Improving the Stability of MMC-HVDC for Wind Farm Integration

Voltage-source converter-high-voltage direct current (VSC-HVDC) systems have become an attractive option for integrating remote and far-from-shore renewable energy resources to main AC grids. The desire for greater power transfer capability and the difficulty in securing right-of-way for new AC lines in many countries is also resulting in the increased use of embedded VSC-HVDC systems operating in parallel with existing AC lines. It has been stated that the control and operation of VSC-HVDC systems are of particular concern for weak grids with fewer large synchronous generation units (a highly probable case for many grids in future). If the anticipated proliferation of VSC-HVDC links continues, several aspects of system stability will be significantly impacted. This study presents an overview of the effects of VSC-HVDC control and operation on power system stability. The structure, control, control tuning, and modelling of VSC-HVDC is briefly summarised to provide context for subsequent discussion of the system dynamics. An extensive critical review of the previous research into mixed AC-DC systems incorporating VSC-HVDC is then provided including voltage stability, small and large-disturbance angle stability, high-frequency interaction, and frequency stability. Finally, recommendations are presented to guide critical future research.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-gtd.2017.1140

Stability and control of mixed AC–DC systems with VSC-HVDC: a review

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 the 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 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 electro-magnetic transient (EMT) simulation model of an MMC with 400 submodules per arm.

/pdf/improving-small-signal-stability-of-an-mmc-with-ccsc-by-47xioc747g.pdf

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

A small signal model of a multi-infeed high-voltage direct current (HVdc) transmission system containing a line commutated converter (LCC) and a voltage source converter (VSC) is developed. This model represents the LCC and VSC converters as operational impedances as seen from the converter ac busbar. This permits the converters to be included in the effective short-circuit ratio (ESCR) calculations. The resulting ESCR is referred to in this paper as the “Impedance based Effective Short Circuit Ratio” (IESCR). It is shown that the maximum power transfer limit (referred to as the maximum available power or MAP) of the converters is better predicted by this index compared to the conventional ESCR which ignores the operational impedances of the converters. The question also arises as to how close to this theoretical maximum power transfer limit can the HVdc system operate. Using the small-signal model, it is shown that with commonly used control strategies, the predicted MAP can only be achieved by reducing the controller gains. The results are validated using detailed electromagnetic transients simulation of the multi-infeed VSC-LCC system.

An Improved Measure of AC System Strength for Performance Analysis of Multi-Infeed HVdc Systems Including VSC and LCC Converters

This paper reveals the existence of poorly damped resonant modes in the modular multilevel converter (MMC) that can result in harmonic instability. A small-signal model based on dynamic phasors is introduced which takes into consideration the dynamics of internal variables, such as circulating arm currents, which have a tendency for a large second harmonic component and module capacitor voltage ripple, which has other harmonic components. The small-signal model is validated by comparison with the electromagnetic transient simulation of a detailed model. It is shown that the use of an active circulating current suppressing scheme can effectively improve the damping of internal harmonic modes in comparison with a passive filter used for the same purpose. The damping of internal harmonic modes has been shown to be significantly impacted by the gains of the MMC's outer-loop controller but is less sensitive to the ac system strength or the gain of the phase-locked loop. A larger arm resistance also increases the damping of these internal modes.

Harmonic Instability in MMC-HVDC Converters Resulting From Internal Dynamics

The modular multilevel converter (MMC) has been rapidly developed and widely applied since it was proposed in 2001, especial in high voltage direct current transmission (HVDC), the MMC has been the primary choice. The reliability of submodule capacitors is a major concern since many practitioners consider it the most vulnerable component in power electronic devices. Therefore, it’s meaningful to put forward an on-line capacitor condition monitoring method to keep its safety operation. This paper presents an on-line monitoring method for capacitance and ESR values of submodule capacitors. In this method, the voltage and current equations are constructed by using MMCs operation characteristics and capacitor equivalent model to obtain the state parameters. Among them, the Cotes rule is used to simplify the calculation and Kalman filter is used to reduce the error. Simulation results verify the feasibility of this method. It shows that the capacitance calculation error is less than 1%, and the ESR calculation error is less than 4.2%.

Tan Li

Papers

Harmonic Instability in MMC-HVDC Converters Resulting From Internal Dynamics

An On-line Capacitance and ESR Monitoring Method of Submodule Capacitors for Nearest Level Modulation Based Modular Multilevel Converters