The interaction between grid-connected inverters and the grid may cause stability issues, and compromise the reliable operation of the inverters. This study investigates the stability of a three-level neutral point clamped (NPC) inverter connected to the grid using impedance-based methods. Because the impedance model of a three-phase three-level NPC inverter has not yet been reported, this study fills the literature gap by analyzing the influence of three-level DC-side neutral point control on the impedance characteristics. By fully considering the DC bus dynamics and DC voltage control loop, and the current loop and phase-locked loop (PLL), the admittance model of a three-phase three-level NPC inverter is established and verified by simulation. Additionally, in the stability analysis of a three-level NPC inverter grid-connected system, the frequency coupling introduced by the PLL and DC bus dynamics is included with the help of an established admittance model. The stability of the grid-connected system under different grid short circuit ratios (SCR) and operating power levels is analyzed according to the Nyquist stability criterion. The experimental results revealed that the established impedance model of the three-phase three-level NPC inverter can properly represent the stability of this system.

Impedance modeling and stability analysis of a three-phase three-level NPC inverter connected to the grid

In near future, power converters will be introduced into transmission grids on a large scale due to increase of renewable energy sources. The control schemes of grid-connected inverters currently assume that there are sufficient synchronous generators (SGs) in the grid for synchronization and integration of electric power. However, when grid-connected inverters significantly outnumber SGs, there is a need for the grid-forming capability to operate the transmission grid autonomously. These inverters should generate AC voltages and are called "grid-forming" inverters. They behave as voltage sources and the cascaded PI controller has been often used. However, it is difficult to tune the control gains because of system couplings and the controller’s bandwidths. This paper proposes a new controller based on the linear quadratic regulator (LQR) for voltage regulation and shows comparisons of the performances between them. It is also well known that the instability due to interactions between inverters and a grid is sometimes observed. This paper utilizes the impedance-based method in dq frame to analyze the stability of the grid-forming inverters with both the LQR and the cascaded PI controller. The stability is also investigated using eigenvalue analysis and the results are validated by numerical simulations.

Stability Analysis of Grid-Forming Inverter in DQ Frequency Domain

Multi-terminal modular multilevel converter (MMC) power transmission is the current development trend in DC transmission. However, owing to its fast control and dynamic characteristics, it may interact with the other inductive devices or the grid and cause stability issues. This paper describes the use of the impedance analysis method in the frequency domain to analyze system stability. First, the multi-harmonic linearization method is used to model the impedance of a three-terminal MMC system. To make the model more accurate, the modeling considers the effect of frequency coupling caused by an asymmetric controller and the AC sampling site position. This paper then proposes an equivalent method of the grid impedance for the three-terminal system that can accurately judge the stability of the grid-connected system when the AC side is coupled. This work provides a theoretical basis for the prediction and suppression of the oscillation of MMC grid-connected system with coupling on the AC side. Finally, a three-terminal MMC model is built in Matlab/Simulink and the Nyquist stability criterion is used to verify the correctness of the analysis. 

Stability Modeling of a Three-Terminal MMC-HVDC Transmission System

This paper presents a theoretical discussion on a combined-compensation control and its stability on harmonic resonance for grid-connected converters. The interaction between the gird impedance and the grid-connected converter potentially brings harmonic resonance. The compensation control with a digital filter and a virtual impedance is an effective approach of impedance shaping. Theoretical analysis reveals that the proper use of the two effectively enhances system stability. The theoretical design considering a compensation limit can minimize the effect of phase lag on the virtual impedance. Moreover, the trade-off issue between stability and transient response always comes up in impedance shaping. The disturbance observer with a dead band restores transient response only during faults and make up for the low sensitivity due to the digital filter. Finally, simulated results on a typical converter system verify this analysis. 

A Combined-Compensation Control on Harmonic Resonance for Grid-Connected Converters

High voltage direct current (HVDC) transmission system with modular multilevel converter (MMC) as converter station has been widely used in engineering. However, when MMC is connected with weak power grid or new energy station, it may induce broadband oscillation events. It is necessary to understand the propagation of broadband oscillations in the system in order to monitor the oscillation events in MMC-HVDC system. In this paper, firstly, the mechanism of oscillation propagation in MMC is analyzed qualitatively, and then the 3x3 admittance matrix which describe oscillation propagation quantitatively is derived. Finally, the method of quantitative analysis of oscillation propagation in MMC-HVDC system is introduced with a case in Matlab/Simulink. 

Quantitative Analysis of Oscillation Propagation in MMC-HVDC System

A grid-connected inverter must be designed to assure stable operation. Stability analysis of the system is one of the most important design processes and it is calculated mainly by four types of analysis methods both in time and frequency domains. This paper investigates and compares these stability analysis methods. In frequency domain, according to the impedance method, frequency characteristics of an output impedance or admittance are calculated and investigated. Three frequency analysis methods, the analytical derivation method, the numerical frequency analysis method that is based on an automatic and numerical formulation and solution algorithm, and the simulator-based frequency scan method, are often used and useful. According to the impedance method, it is sufficient when the real part of the admittance of the inverter is positive and passive to ensure stability. Three types of passivity-based design examples are shown. In time domain, a unique analysis method which is based on the eigenvalue analysis of the Poincare map or the sensitivity matrix of state-variables for perturbations along an operating trajectory, has been developed and it is also useful. These four methods are investigated for their features. Application example cases for grid-connected inverters are investigated and compared between the methods by simulation and experiment.

Stability Analysis Methods of a Grid-Connected Inverter in Time and Frequency Domains

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Stability Analysis Methods of a Grid-Connected Inverter in Time and Frequency Domains