The dc-side admittance of a modular multilevel converter can be used in assessing the stability of the dc system by means of impedance-based stability criteria. An accurate mathematical representation of the small-signal admittance can be given using harmonic linearization. To this end, the effect of the internal dynamics of the converter, e.g., the circulating current, the converter control scheme, and the controller parameters on the admittance of the converter should be analyzed. In this paper, a linear analytical model for the dc-side admittance of the converter is derived based on a combination of harmonic linearization and frequency-domain representation which incorporates different control schemes. Moreover, an admittance model is given for the closed-loop voltage control mode of the converter, where the ideal insertion indices are applied. To this end, the impact of an arm-balancing controller and its parameters on the dc-side admittance of the converter is investigated. Finally, experiments are carried out on a down-scaled prototype to validate the accuracy of the analytical model.

The stability of a power electronics system can be assessed by means of the impedance-based stability criterion. Impedance modeling is a useful tool to analyze the effect of different circuit parameters and control schemes on the behavior of a converter. Modeling the input impedance of a power electronics converter is often successful when having full knowledge of the converter topology, the circuit parameters, and the parameters and implementation of the control system. However, due to the proprietary nature of voltage source converter-based high voltage direct current systems, their exact control structure is often concealed. This complicates the calculation of the impedance of a modular multilevel converter, known for its complex internal dynamics. This paper proposes a method to estimate the impedance of a modular multilevel converter with partially black-boxed converter control. A discussion on partitioning the control system into open and closed parts is made, and the results are verified with simulations in time and frequency domains.

Grid-forming converters can emulate the behavior of a synchronous generator through frequency droop control. The stability of grid-forming modular multilevel converters can be studied via the impedance-based stability criterion. This paper presents an ac-side impedance model of a grid-forming modular multilevel converter which includes a complete grid-forming control structure. The impact of different control schemes and parameters on the closed-loop output impedance of the converter is thoroughly analyzed and the learnings have been used in mitigating undesired control interactions with the grid. The results are verified through simulations in time- and frequency-domains along with experiments on a down-scaled laboratory prototype.

High voltage direct current (HVDC) grids are envisioned for large-scale grid integration of renewable energy sources. Upon realization, components from multiple vendors have to be coordinated and interoperability problems can occur. To address these problems, a multi-vendor HVDC system can benefit from a partially open control and protection system. Unwanted interactions can be investigated and solved more easily in partially open software compared to when applying black-boxed and vendor-specific software. Although a partially open approach offers these advantages, practical aspects, such as the implementation in a real station architecture, have to be addressed carefully. This paper covers this important topic, first by reviewing the required control and protection functions and second by discussing the choice for certain open and closed software parts, their implementation in physical units as well as the required communication and interfaces. The result from this discussion is a first proposal of a station architecture for a multi-vendor HVDC system using partially open control and protection. This architecture will be a helpful starting point to industry and academia working with research and harmonization on this topic as ad-hoc solutions in terms of practical aspects can be avoided.

In this paper, harmonic stability of a back-to-back modular multilevel converter based voltage source converter high voltage direct current system is analyzed. These systems are prone to ac- and dc-side resonances and interactions between the converter and its interconnected systems. The stability of the system can be predicted by the impedance based stability criterion, which requires the modeled or measured converter impedance. The analysis in this paper focuses on interoperability when the converters employ different control schemes in order to utilize the inherent damping properties of the sum capacitor voltage balancing control loops.

Incorporation of inverter-based resources is progressively increasing in modern power systems. The absence of inherent physical inertia in converter-based systems has resulted in a decrease in the total inertia of the grid. Grid-forming control of voltage source converters emulates the workings of a conventional synchronous generator through frequency droop control, allowing the converter to provide inertial support while contributing to the support of grid voltage. This paper presents a dc-side impedance model of a grid-forming modular multilevel converter. A control interaction between a grid-forming and a grid-following converter in a back-to-back structure is investigated and a stabilizing compensator is proposed.