A modified sequence domain impedance definition and its equivalence to the dq-domain impedance definition for the stability analysis of AC power electronic systems (1605.00526v1)

Abstract: Representations of AC power systems by frequency dependent impedance equivalents is an emerging technique in the dynamic analysis of power systems including power electronic converters. The technique has been applied for decades in DC-power systems, and it was recently adopted to map the impedances in AC systems. Most of the work on AC systems can be categorized in two approaches. One is the analysis of the system in the \textit{dq}-domain, whereas the other applies harmonic linearization in the phase domain through symmetric components. Impedance models based on analytical calculations, numerical simulation and experimental studies have been previously developed and verified in both domains independently. The authors of previous studies discuss the advantages and disadvantages of each domain separately, but neither a rigorous comparison nor an attempt to bridge them has been conducted. The present paper attempts to close this gap by deriving the mathematical formulation that shows the equivalence between the \textit{dq}-domain and the sequence domain impedances. A modified form of the sequence domain impedance matrix is proposed, and with this definition the stability estimates obtained with the Generalized Nyquist Criterion (GNC) become equivalent in both domains. The second contribution of the paper is the definition of a \textit{Mirror Frequency Decoupled} (MFD) system. The analysis of MFD systems is less complex than that of non-MFD systems because the positive and negative sequences are decoupled. This paper shows that if a system is incorrectly assumed to be MFD, this will lead to an erroneous or ambiguous estimation of the equivalent impedance.

• The paper proves that stability assessments via dq-domain and modified sequence domain impedance are equivalent under a unified analytical framework.
• It introduces Mirror Frequency Decoupled (MFD) systems, simplifying analysis by decoupling positive and negative sequence responses.
• The work supports improved design insights by reconciling measurement techniques and enhancing stability predictions for power electronic converters.

Impedance Analysis and Stability in AC Power Electronic Systems

The paper presented explores the equivalency between the dq-domain and sequence domain impedance definitions in the context of analyzing AC power electronic systems. It provides an in-depth mathematical derivation, which bridges the applicability of these approaches for stability analysis, especially employing the Generalized Nyquist Criterion (GNC). The authors propose a modified sequence domain impedance definition which underscores the equivalence between the two domains, thereby enhancing the applicability and accuracy of stability assessments.

Impedance-based methods have long been utilized in the analysis of electrical systems, notably DC systems, but their extension to AC power electronics has proven complex given the intricacies of non-linearities and high dynamism introduced by power electronics converters. These dynamics necessitate robust analytical frameworks enabling stability determinations without exhaustive knowledge of internal system parameters—a requirement well-served by black-box impedance modeling techniques.

The primary contributions of the paper lie within two realms:

1. Equivalence Proof: The authors mathematically demonstrate that stability assessments obtained through the GNC are congruent when utilizing the dq or sequence domain impedance definitions, provided their proposed modifications are applied. This involves a sequence domain impedance matrix where positive and negative sequences are shifted with twice the fundamental frequency, a strategy that elegantly encompasses both components within a unified analytical framework.
2. Mirror Frequency Decoupled (MFD) Systems: A novel concept delineated here, MFD systems, possess decoupled positive and negative impedance sequences, thus evading the "mirror frequency effect" whereby harmonic disturbances provoke responses at frequencies distorted from the original perturbation. This condition maintains the integrity of linearity in dynamic responses, greatly simplifying stability analysis. It is established that assuming a system is MFD when it is not can result in substantial inaccuracies.

The numerical simulations substantiate these theoretical assertions. Case studies examine scenarios where source and load converters with varying degrees of MFD characteristics highlight disparities in impedance measurements and analyses, particularly when contrasting shunt versus series measurements in non-MFD systems.

Practically, these contributions afford significant advancements:

• Enhanced Stability Predictions: By providing a method to reconcile dq- and sequence-domain analyses, systems engineers have a robust toolkit to evaluate stability.
• Simplified Measurements: Through establishing equivalencies, particularly under MFD conditions, the burden of complex measurements is alleviated, favoring sequence domain approaches when possible.
• Design Insights: Understanding impedance behaviors under different conditions aids in tailoring power electronic devices and their control mechanisms, potentially guiding designs towards inherently more stable architectures through MFD-enabling strategies.

The implications of these findings extend into further theoretical considerations, suggesting potential development paths such as broadening stability criteria analyses to different converter configurations or extending these definitions to incorporate even broader classes of perturbations and system types. In exploring these avenues, future research can refine and expand the operational frameworks currently available to AC power electronics system designers, helping to navigate the balancing act between dynamic performance and stability—a critical concern in modern power systems increasingly populated by sophisticated electronic converters. The MFD paradigm notably offers an intriguing avenue for these explorations, signaling a frontier in impedance analysis and system stability assessment.