“…Considering perturbations, the transformation angle for PT and IPT is θ = θ 0 + Δθ. The PT process for the variable x = x 0 + Δx in the ABC frame can be written as (6), while the IPT process for the variable x dq = x 0,dq +Δx dq in the dq frame is given by (7) (detailed derivations of ( 6) and ( 7) can be found in Appendix A). Transformations used in CCSC, whose transformation angle is −2θ, can be deduced by substituting θ 0 and Δθ with −2θ 0 and −2Δθ in ( 6) and (7).…”
Section: Modelling Of Reference Frame Transformationsmentioning
confidence: 99%
“…By converting (6) into HSS form and subtracting the steadystate term, we have the d-/q-axis perturbation terms generated by the PT in HSS, whose expressions are…”
Section: Modelling Of Reference Frame Transformationsmentioning
confidence: 99%
“…In response to the increasing penetration of power electronics, grid-forming control schemes which enable converters to behave as voltage sources have become a research hotspot for industry and academia [4,5]. Besides the conventional use in the offshore rectifier station, grid-forming MMCs are also in high demand in the upcoming projects and are considered to play an important role in the modern power system [6,7].…”
With the increasing penetration of power electronics, grid-forming modular multilevel converters (MMCs) have attracted great attention in the upcoming MMC-based high-voltage direct current transmission (HVDC) projects. Power synchronization control (PSC) and direct power control (DPC) are two typical grid-forming control schemes for MMCs. This paper sets out to investigate the impedance-based stability characteristics of PSC-MMC and DPC-MMC. Utilizing the harmonic state space (HSS), equivalent impedance models of PSC-MMC and DPC-MMC are developed with the consideration of complete controllers and MMC internal dynamic characteristics. Impedance shaping effects of the major controllers are further analyzed to identify the frequency bands where the MMCs have negative resistive impedance characteristics. Finally, potential instability phenomena of the interconnected system are shown through the case studies, and the virtual impedance method is introduced as the stabilization control scheme. The electromagnetic transient simulation results based on PSCAD/EMTDC verify the accuracy of the impedance models and the effectivity of the stabilization control scheme.
“…Considering perturbations, the transformation angle for PT and IPT is θ = θ 0 + Δθ. The PT process for the variable x = x 0 + Δx in the ABC frame can be written as (6), while the IPT process for the variable x dq = x 0,dq +Δx dq in the dq frame is given by (7) (detailed derivations of ( 6) and ( 7) can be found in Appendix A). Transformations used in CCSC, whose transformation angle is −2θ, can be deduced by substituting θ 0 and Δθ with −2θ 0 and −2Δθ in ( 6) and (7).…”
Section: Modelling Of Reference Frame Transformationsmentioning
confidence: 99%
“…By converting (6) into HSS form and subtracting the steadystate term, we have the d-/q-axis perturbation terms generated by the PT in HSS, whose expressions are…”
Section: Modelling Of Reference Frame Transformationsmentioning
confidence: 99%
“…In response to the increasing penetration of power electronics, grid-forming control schemes which enable converters to behave as voltage sources have become a research hotspot for industry and academia [4,5]. Besides the conventional use in the offshore rectifier station, grid-forming MMCs are also in high demand in the upcoming projects and are considered to play an important role in the modern power system [6,7].…”
With the increasing penetration of power electronics, grid-forming modular multilevel converters (MMCs) have attracted great attention in the upcoming MMC-based high-voltage direct current transmission (HVDC) projects. Power synchronization control (PSC) and direct power control (DPC) are two typical grid-forming control schemes for MMCs. This paper sets out to investigate the impedance-based stability characteristics of PSC-MMC and DPC-MMC. Utilizing the harmonic state space (HSS), equivalent impedance models of PSC-MMC and DPC-MMC are developed with the consideration of complete controllers and MMC internal dynamic characteristics. Impedance shaping effects of the major controllers are further analyzed to identify the frequency bands where the MMCs have negative resistive impedance characteristics. Finally, potential instability phenomena of the interconnected system are shown through the case studies, and the virtual impedance method is introduced as the stabilization control scheme. The electromagnetic transient simulation results based on PSCAD/EMTDC verify the accuracy of the impedance models and the effectivity of the stabilization control scheme.
“…2) MMC internal dynamics and control: As exhaustively discussed in [32], [33], including the overall internal energy dynamics requires an extensive mathematical manipulation. Thereby, a simplified model that considers only the total energy dynamics of the MMC [34] will be used in the present study (14). Assuming that the horizontal and vertical energy balancing controllers are properly tuned, that model effectively captures the overall ac/dc dynamics.…”
Section: Small-signal Model Of the Systemmentioning
confidence: 99%
“…Despite using MMC models in both articles, they focus on the ac voltage and frequency control, with no discussion about the internal energy control. In [14], a dynamic protection integrated model predictive control concept is developed and applied to the MMC for grid restoration purposes, focusing on avoiding MMC overcurrents. An ac fault analysis of islanded grid including MMCs operating in grid-forming mode is presented in [15], also focusing on the ac side control structure.…”
With an increasing number of renewable energy resources being integrated into the power system through power electronics, conventional power plants based on large synchronous machines tend to be reduced in the upcoming future. With the Modular Multilevel Converter as the state-of-the-art power electronics solution for power systems, it will be necessary to operate some of these converters in grid-forming mode, in order to either preserve the stability and robustness of the ac grid or as the only solution to generate the ac grid in cases with no available synchronous generation. This paper aims to understand how the internal energy control of the MMC can be used to effectively mitigate the propagation of ac power disturbances to the dc side, thanks to its buffering capability. Different energy control structures are explored, and a comprehensive discussion and comparison among them is provided, including stability analysis, transient performance and tuning guidelines. Simplified and linear models are used to address the analysis, whereas detailed non-linear models implemented in MATLAB Simulink are used to verify the results via time-domain simulations.
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