Comparative Study of Dynamic Phasor and Harmonic State-Space Modeling for Small-Signal Stability Analysis

Rua, Philippe De; Sakinci, Özgür Can; Beerten, Jef

doi:10.1016/j.epsr.2020.106626

Cited by 24 publications

(7 citation statements)

References 12 publications

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“…Spurious eigenvalues, i.e. those that are not aligned with a vertical set of eigenvalues, are a consequence of truncation: they have no physical meaning and may be disregarded [35].…”

Section: ) Eigenvalues and Participation Factors Analysismentioning

confidence: 99%

Generalization of Harmonic State-Space Framework to Delayed Periodic Systems for Stability Analysis of the Modular Multilevel Converter

Rua

Beerten

2022

IEEE Trans. Power Delivery

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Stability analysis of the modular multilevel converter (MMC) requires accurate models over wide frequency ranges, accounting for both the time-periodic nature of internal dynamics and non-passive behavior resulting from time delays. Frequency-lifting techniques such as harmonic state-space (HSS) can be used to tackle the time-periodicity and obtain linear time-invariant models on which classical stability analysis techniques can be applied. However, exact time delays are generally approximated by rational polynomial functions to study the eigenvalues of ordinary differential equations (ODEs), which leads to inaccuracies at higher frequencies. Such approximations can be avoided by preserving delays in their exact form and studying eigenvalues of delay differential equations (DDEs).To that end, this paper presents the generalization of the original ODE-based HSS framework to DDEs, accounting for both time-delay and time-periodic behaviors of the MMC. The generalized HSS framework benefits from the insights of eigenvalues and participation factors analysis while at the same time guaranteeing the derivation of accurate frequency-response models. Using the developed HSS-DDE framework, AC and DCside admittances of the MMC are obtained and validated against frequency scans. Lastly, the stability of a test system is studied in both time and frequency domains to show the advantages of the developed framework.

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“…Spurious eigenvalues, i.e. those that are not aligned with a vertical set of eigenvalues, are a consequence of truncation: they have no physical meaning and may be disregarded [35].…”

Section: ) Eigenvalues and Participation Factors Analysismentioning

confidence: 99%

Generalization of Harmonic State-Space Framework to Delayed Periodic Systems for Stability Analysis of the Modular Multilevel Converter

Rua

Beerten

2022

IEEE Trans. Power Delivery

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“…Each major harmonic's magnitude and phase is individually compared between the two models to obtain the error. Mathematically, for each major harmonic, Fx, the relative error is magnitude can be calculated as in (15), whereas the error in phase can be calculated as in (16).…”

Section: A Mathematical Development Of Hssmentioning

confidence: 99%

“…Some modeling works have tried to circumvent the modulator inclusion within HSS by just including a gain and delay [14]- [15], but as highlighted earlier, such simplification cannot always be justified. Some other great efforts have also been made to develop a modulator for frequency-based modeling but fall short due to the absence of some key considerations.…”

Section: Introductionmentioning

confidence: 99%

Modeling of Power Electronics Systems and PWM Modulators in Harmonic-State Space

Motwani

Xue

Nazari

et al. 2022

IEEE Open J. Power Electron.

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Modeling and simulation of the converter dominated systems have recently emerged as a monumental challenge. These simulations are useful for predicting instability and system's harmonic content, consequently assisting in developing better control and filters. But, as more and more converters are incorporated into the system, time-domain simulation models have a tradeoff of either limited accuracy or fewer simulated converters. On the contrary, frequency-domain modeling methods like linear timeinvariant models cannot capture the system's time-varying nature and complex converter interactions. The recently developed harmonic state space (HSS) modeling approach has emerged to provide an alternate avenue to model and simulate these converterdominated systems. HSS models, while accurate, until recently have not been able to reliably model the non-linear pulse width modulator. This paper solves this challenge and develops a new modulator model for harmonic domain models, including HSS. The proposed large-signal modulator is computationally less demanding and can reliably capture the harmonic spectrum of complex multi-converter systems till converter switching frequencies. Several optimization methods are introduced to utilize the unique multi-harmonic nature of HSS, making simulations faster than conventional time-domain methods. Results are verified with extensive simulations and experiments. The application, challenges, and future scope for this method are also highlighted.

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“…Frequency and harmonic stability analysis has been performed in the literature with small-signal models. The review performed by [77] investigated the concept and history of harmonic stability analysis and the use of linearized models identified in [25], [81]- [84] to capture harmonics. A harmonic state-space small-signal average model was used in [71] to examine the harmonic interaction between inverters and the grid voltage, and it was validated for the time and frequency domain.…”

Section: B Average Modelsmentioning

confidence: 99%

Review of Dynamic and Transient Modeling of Power Electronic Converters for Converter Dominated Power Systems

et al. 2021

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In response to national and international carbon reduction goals, renewable energy resources like photovoltaics (PV) and wind, and energy storage technologies like fuel-cells are being extensively integrated in electric grids. All these energy resources require power electronic converters (PECs) to interconnect to the electric grid. These PECs have different response characteristics to dynamic stability issues compared to conventional synchronous generators. As a result, the demand for validated models to study and control these stability issues of PECs has increased drastically. This paper provides a review of the existing PEC model types and their applicable uses. The paper provides a description of the suitable model types based on the relevant dynamic stability issues. Challenges and benefits of using the appropriate PEC model type for studying each type of stability issue are also presented.

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Comparative Study of Dynamic Phasor and Harmonic State-Space Modeling for Small-Signal Stability Analysis

Cited by 24 publications

References 12 publications

Generalization of Harmonic State-Space Framework to Delayed Periodic Systems for Stability Analysis of the Modular Multilevel Converter

Generalization of Harmonic State-Space Framework to Delayed Periodic Systems for Stability Analysis of the Modular Multilevel Converter

Modeling of Power Electronics Systems and PWM Modulators in Harmonic-State Space

Review of Dynamic and Transient Modeling of Power Electronic Converters for Converter Dominated Power Systems

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