In grid-connected inverter systems, frequency-domain passivity theory is increasingly employed to analyze grid-inverter interactions and guide inverter control designs. However, due to difficulties in meeting sufficient passivity-based stability conditions at low frequencies, passivity theory often falls short of achieving stable system specifications. This article introduces an extended frequency-domain passivity theory. By incorporating a weighting matrix, an extended stability condition is derived. Compared to conventional passivity-based stability conditions, the proposed theory significantly reduces conservativeness and is more suited for analyzing grid-inverter interactions and guiding inverter control design. Theoretical analyses, numerical examples, and experimental results are provided to validate the effectiveness of the proposed methods.

This article enhances impedance-based modeling generality and stability assessment flexibility for multi-parallel GFM inverters by proposing a unified perunit scaling method and a configurable decentralized stability condition based on passivity theory.

The rapid integration of renewable energy sources is transforming traditional power systems into converter-dominated networks, characterized by low inertia and complex dynamic behaviors. This shift introduces fundamental challenges to stable system operation, particularly the risk of low-frequency oscillations, where synchronization, power, and voltage-control dynamics exhibit complex couplings. To this end, the thesis investigates low-frequency oscillation risks from three interconnected dimensions: converter-level control design, decentralized stability assessment, and system-level coordination in multi-converter environments.

The first part of the thesis focuses on control design for grid-connected voltage source converters (VSCs). Starting with grid-following (GFL) converters, which traditionally rely on strong grid conditions for stable operation, the work identifies root causes of instability through block diagram modeling. An active damping control strategy (Q-VID) is proposed, enabling stable operation with a 400-Hz phase-locked loop (PLL) bandwidth even under ultra-weak grids with a short-circuit ratio (SCR) of 1.28. Building on this, a grid-forming (GFM) control scheme is developed using a PLL-synchronized architecture. This approach retains the simplicity and implementation compatibility of conventional GFL methods while providing voltage and frequency support with robust performance under both strong and weak grid conditions.

Effective control design is closely tied to stability assessment methods, which provide essential theoretical support and stability specifications. Moreover, these assessment methods assist in risk localization, elimination, product specification determination, and adherence to grid codes.  Hence the second part addresses the need for decentralized stability assessment methods, which become increasingly important in converter-rich power systems. While passivity theory serves as a fundamental tool, its application in the low-frequency range is limited. To overcome these limitations, the thesis introduces a rotated passivity index by integrating passivity and multiplier theory. This extended formulation enables full-frequency-range stability assessment.

The third part of the thesis extends the proposed control and stability analysis framework to multi-converter systems. It begins by modeling the parallel operation of multiple converters. Building on this foundation, the previously developed control strategies and stability assessment methods are integrated into a unified framework that enables risk assessment, instability source identification, and mitigation across multi-converter environments.

In summary, this doctoral research ensures the stable operation of converter-dominated power systems by contributing across three levels: control design (GFL and GFM), theoretical tools for decentralized stability assessment, and system-level coordination in multi-converter networks. All proposed methods are validated through both simulation and experimental results. Together, these contributions form a coherent and practical methodology for next-generation grid integration.

Den snabba integreringen av förnybara energikällor omvandlar traditionella kraftsystem till omriktardominerade nät som kännetecknas av låg tröghet och komplexa dynamiska egenskaper. Denna förändring medför grundläggande utmaningar för en stabil drift, särskilt risken för lågfre­kventa svängningar där synkroniserings-, effekt- och spänningsregleringar är starkt kopplade. Avhandlingen angriper dessa lågfre­kventa stabilitetsproblem ur tre sammanhängande perspektiv: regleringsdesign på omriktarnivå, decentraliserad stabilitetsbedömning och systemsamordning i miljöer med flera omriktare.

Den första delen behandlar regleringsdesign för nätanslutna spänningskällsomriktare (VSC). Arbetet inleds med grid-following-omriktare (GFL), som traditionellt förutsätter en stark nätimpedans för stabil drift. Med hjälp av blockdiagrammodellering identifieras grundorsaker till instabilitet, varefter en aktiv dämpningsstrategi (Q-VID) föreslås. Den möjliggör stabil funktion med 400 Hz PLL-bandbredd även vid mycket svaga nät med en kortslutningskvot (SCR) på 1,28. Därefter utvecklas ett grid-forming-schema (GFM) baserat på en PLL-synkroniserad arkitektur. Lösningen behåller GFL-metodens enkelhet och kompatibilitet samtidigt som den ger spännings- och frekvensstöd med god prestanda i både starka och svaga nät.

Effektiv regleringsdesign kräver tillförlitliga stabilitets­bedömnings­metoder som ger teoretiskt underlag och specificerar stabilitetskrav. Sådana metoder stöder dessutom risklokalisering, åtgärder, produktspecifikationer och uppfyllnad av nätkoder. Därför utvecklas i den andra delen ett roterat passivitetsindex som kombinerar passivitets- och multiplikator­teori, vilket möjliggör decentraliserad stabilitetsanalys över hela det relevanta frekvensområdet.

I den tredje delen utvidgas den föreslagna reglerings- och stabilitetsramen till system med flera omriktare. En impedansbaserad modell av parallellkopplade omriktare ligger till grund för ett enhetligt ramverk som möjliggör riskbedömning, identifiering av instabilitetskällor och åtgärder utan global systeminformation eller deltagarfaktoranalyser.

Sammanfattningsvis säkerställer denna doktorsavhandling stabil drift i omriktardominerade kraftsystem genom bidrag på tre nivåer: regleringsdesign för GFL- och GFM-omriktare, teoretiska verktyg för decentraliserad stabilitetsbedömning samt systemsamordning i nät med flera omriktare. Samtliga föreslagna metoder har verifierats genom både simuleringar och laboratorieexperiment och utgör tillsammans en sammanhållen och praktiskt användbar metodik för nästa generations nätintegration.

The phase-locked loop (PLL) is a commonly used synchronization control method for grid-tied inverters. The PLL-synchronized inverters tend to have poor stability robustness with weak grid interconnections, especially when the PLL is designed with a high control bandwidth. To tackle this challenge, this article proposes an enhanced q-axis voltage-integral damping control, which not only stabilizes PLL-synchronized inverters in weak grids but also lifts the restriction on PLL bandwidth. This superior feature enables inverters to operate stably in ultraweak grids and with a superior transient response. The experimental tests confirm the performance of the method with 400-Hz PLL bandwidth under a short-circuit ratio of 1.28 of the grids.

The main purpose of this article is to elaborate on the limitations of using frequency-domain passivity theories in analyzing grid-inverter interactions within the low-frequency range. It primarily covers three levels of limitations: 1) the limitations and selection criteria of two kinds of passivity index, 2) potential conflicts between different passivity index tuning methods, and 3) the relationship between the frequency range of negative passivity index and system stability robustness. The findings suggest that caution should be exercised when applying passivity theory, particularly in the low-frequency range.

Power synchronization control (PSC) is designed for weak grid connections originally and its performance is weakened when connected to a strong grid. In this paper, an asymmetric AC voltage controller (AVC) is proposed to improve the performance of PSC in strong grids. The improvement is achieved by adding a coupling from d-axis to q-axis to the voltage control part. The effect of this d-to-q coupling is explained by small signal modeling. It is found that the asymmetric AVC gives an effective improvement in damping the low-frequency oscillation and stability robustness against the grid strengths. Theoretical analysis and experiments verify the effectiveness of the proposed asymmetric AVC.

The main purpose of this article is to elaborate on the pitfalls of using the frequency-domain passivity theories in grid-inverter interactions within the low-frequency range. It mainly covers the relationship between the passivity index and stability, considerations for control design guided by optimizing the passivity index, and issues with a negative infinite index. It is advised to exercise caution when applying passivity theory in the low-frequency range. These conclusions have been substantiated through numerical and experimental studies.

When grid-following voltage source converters (VSCs) operate in inverter mode, the phase-locked loop (PLL) dynamics introduce a negative-real-part impedance, which may lead to the instability of the closed-loop system, especially in a weak-grid connection. This undesirable property of the PLL may be offset by so-called active damping. Nevertheless, the interaction between the active damping and the adverse PLL impact is not fully understood. To this end, the properties of different active-damping methods are analyzed, with the focus on the q-to-q coupling of the input admittance. One important finding is that adding an integrator to the q-axis active damper can improve the system performance in a weak-grid connection. Simulations and experimental results verify the theoretical analysis.