Passivity-based Stability Criterion Research Articles

Stability Analysis of Buck Converter Based on Passivity-Based Stability Criterion

Recently, the stability of DC microgrids has attracted increasing attention. The traditional stability analysis method cannot not meet the requirements for the complexity and bidirectional energy flow of the system. In this paper, a passivity-based stability criterion (PBSC) is proposed to analyze the stability of the cascade system. In order to realize the passivity of the system, an improved feedback control method based on the traditional double-loop control strategy is proposed, which will improve the stability region and guarantee the passivity of the system. Moreover, a Buck-CPL simulation model is established based on MATLAB/Simulink R2008, and the correctness of the theoretical analysis is verified by experiments.

Passivity-Based Stability Analysis and Generic Controller Design for Grid-Forming Inverter

With the remarkable growth of renewable energy resources, the grid-forming (GFM) inverter with the function of grid voltage/frequency support attracts much attention. Due to the inverter-grid interaction, the stability of the GFM inverter is a critical issue. The passivity-based analysis approach, which was widely applied to the conventional grid-following inverter, has been proved to be promising. Yet, its application to the GFM inverter is still insufficient. To this end, this paper conducts a comprehensive passivity-based analysis for the GFM inverter with single-loop voltage control. It finds that the two indices of the passivity-based stability criterion, i.e., the individual stability and the output impedance passivity, bring identical constraints on the voltage controller, and the passivity cannot be ensured with typical voltage controllers. To shrink the unexpected non-passive frequency ranges, a generic grid-current feedforward scheme is explored, and the proper feedforward functions compatible with different voltage controllers are derived. With the proposed scheme, the passivity can be guaranteed up to the Nyquist frequency. Finally, experimental results from a 6-kVA prototype are provided to verify the theoretical analysis.

A Generalized Passivity-Based Stability Criterion for Assessing Large Signal Stability of Interconnected DC Power Systems

With the growing need to support large dynamic electric loads in microgrid environments, there has been a necessary push toward highly regulated dc distribution through power electronics. Unfortunately, these systems are nonlinear by nature and provide potentially destabilizing behavior at their source interfaces. To complicate matters further, many systems are built from independently designed subcomponents with little information shared between designs. It is, therefore, necessary to have stability-driven design requirements for each subsystem to enforce stable dynamics upon system integration. Traditional techniques are currently limited to either overly conservative large signal small-gain methods or small signal transfer function approaches that are unreliable for assuring large signal stability. This article proposes a generalized passivity-based stability criterion that conservatively estimates the domain of stability for an integrated nonlinear system. Through passivity partitioning and uniquely driven domain of passivity estimation techniques, this methodology provides interface conditions that certify stability while only requiring a reduced subset of knowledge of each connected subsystem <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</b>

Passivity-based stability analysis of parallel single-phase inverters with hybrid reference frame control considering PLL effect

The passivity-based stability criterion (PBSC) is an effective tool to analyze the interactive stability issues between the multi-parallel inverters and the grid. However, when using the passivity theory to evaluate the interactive stability, the influences of grid synchronization and multisampling on the passivity of inverter output admittance are overlooked in previous studies. To fill this gap, the impact factors in the grid-connected control, such as multisampling, capacitor current feedback active damping (CCF-AD) and various phase-locked loops (PLLs), on the passivity of inverter output admittance is investigated in this paper. Moreover, the stability of the interconnected system in the inductive and capacitive grid scenarios are also assessed. Since the effective control delay are determined by the multisampling coefficient, the passivity of inverter output admittance in the high-frequency range is mainly affected by multisampling and CCF-AD, whereas the passivity in the low-frequency range is related to the bandwidth of PLLs. In case of an identical PLL bandwidth, the non-passive region of admittance when using SOGI-PLL appears in a lower frequency band, and thus the non-passive region is the smallest in comparison, which provides stronger robustness. Finally, simulation studies and experimental results are presented to verify the effectiveness of the theoretical analysis.

Real-Time Stability Analysis and Control of Multiconverter Systems by Using MIMO-Identification Techniques

DC distribution systems typically consist of several feedback-controlled switched-mode converters forming a complex power distribution system. Consequently, a number of issues related to stability arise due to interactions among multiple converter subsystems. Recent studies have presented methods such as passivity-based stability criterion, where the stability and other dynamic characteristics of an interconnected system can be effectively analyzed using bus-impedance measurement. Studies have presented online measurement techniques, where the bus impedance is obtained by combining together the measurements of input and output impedances of single converters in the system. Since the converters are coupled, the presented measurement techniques require several measurement cycles in order to sequentially measure the individual impedances to be combined to obtain the overall bus impedance. This paper presents a measurement technique based on injection of orthogonal binary sequences. Applying this method, all the impedances in the system can be simultaneously measured during one measurement cycle. Therefore, the overall measurement time of the bus impedance is reduced compared to conventional measurement techniques. Furthermore, the method guarantees that the system dynamics do not change between measurements, and therefore, the computed bus impedance is not distorted. Experimental results are presented and used to demonstrate the effectiveness of the proposed method in the design of a stabilizing controller for a notional dc system using positive feed-forward control.

Stability Analysis of PV Plant-Tied MVdc Railway Electrification System

As ac electric railways have various problems (e.g., power quality issues, complex catenary networks, limited supply region, and passing neutral section), the medium-voltage direct current (MVdc) railway electrification system (RES) may be a potential alternative electric railway mode and can be freely accessed to the renewable energy systems. However, some instability issues may be aroused due to the interaction between flexible MVdc RES and electronic-based dc–dc equipment. In this paper, a comprehensive small-signal impedance model, combining a photovoltaic (PV) plant and an MVdc RES, is performed, while available electric variables and control parameters are taken into consideration. Then, a novel passivity-based stability criterion (PBSC) is introduced to determine the instability issue about associate influential factors, including proportional and integral parameters of traction substation and PV converters, the power of train converters, and the dc catenary length. A virtual impedance control scheme is designed to stabilize the system. The experimental results demonstrate that the PBSC can identify the instability in the MVdc RES. The results also match well and support the conclusions obtained.

Analysis and Design of DC-Bus Voltage Controller of Energy Storage Systems in DC Microgrids

In this paper, a novel voltage controller of energy storage system (ESS) in DC microgrids (DC-MG) is proposed to enhance the DC-bus voltage stability. At first, a mathematical model of the DC-MG is developed in a state-space form. Then, the voltage controller of the ESS is designed by using the methodology of the IDA-PBC (interconnection and damping assignment-passivity-based control) with an integral action. System stability has been analyzed with passivity-based stability criterion (PBSC). The proposed controller gives the robust performance to the parameters variation. The validity of the proposed control scheme has been verified by the hardware-in-the-loop simulation (HILS) results.

Passivity-based active stabilization for DC microgrid applications

In this paper, an improved active stabilization strategy of the interface converters in microgrid applications is proposed on the basis of the passivity-based stability criterion (PBSC). As a critical part of AC and DC hybrid microgrids, the DC microgrid is taken as an example. In particular, a stabilization method with a proportional-integral (PI) controller and firstorder high-pass filter (HPF) is proposed to meet the passivity requirements of the overall control diagram with respect to the output voltage. Meanwhile, an output current feedback control loop is introduced to ensure the output impedance passivity. Moreover, a small-signal model of the parallel interface converter system is established to comprehensively study the influence of control parameters on the passivity of the converters. Based on the active stabilization method proposed in this study, by manipulating the control diagram of each interface converter, the passivity and stability of the DC microgrids with variable configuration can be guaranteed. Therefore, a generic and simplified design approach is realized. A simulation model with three interface converters is implemented in MATLAB/Simulink, and the effectiveness of the proposed passivity-based active stabilization algorithm is verified by using this simulation model.

Stabilizing Controller Design for Multibus MVdc Distribution Systems Using a Passivity-Based Stability Criterion and Positive Feedforward Control

A power-electronics-based dc distribution system is a complex and extensively interconnected system consisting of multiple power converters. As a result, a number of system-level challenges related to stability arise due to interactions among multiple converter subsystems. The design of this type of system is difficult due to limited understanding of the problem and general lack of proper analysis tools for multibus systems. Conventional stability criteria, such as the Middlebrook criterion and its extensions, apply only to single-bus systems. This paper proposes a stability analysis and stabilizing controller design technique for multibus MVdc converter systems. First of all, an unterminated two-port modeling technique is used to construct the impedances of all system buses. Then, overall system stability is evaluated utilizing the recently proposed passivity-based stability criterion. In order to ensure good stability margin and dynamic performance, the new concept of an allowable impedance region is introduced based on the Nyquist contour of the bus impedance. Finally, a stabilizing controller is designed using a positive feedforward control technique to ensure passivity of the system buses, providing stability and good performance. Validation of the proposed techniques is provided through the simulation and experimental results.

Stability of Distributed Power Delivery Systems With Multiple Parallel On-Chip LDO Regulators

High quality power delivery for high performance integrated circuits is a significant design challenge. To provide high quality power, the on-chip power needs to be regulated with ultra-small locally distributed power efficient converters. While the quality of the power supply can be efficiently addressed with distributed on-chip power supplies, the stability of these parallel connected voltage regulators is a primary concern. A passivity-based stability criterion is proposed for maintaining a stable power delivery system composed of multiple regulators. To evaluate the proposed approach, a fully integrated power delivery system with distributed on-chip low-dropout (LDO) regulators has been fabricated in a 28 nm CMOS process. The experimental results of a distributed power delivery system composed of six on-chip LDO regulators satisfy this stability criterion, yielding a stable system response within $-$ 25 $^\circ {\text{C}}$ to 125 $^\circ {\text{C}}$ , 10% voltage variations, and 50% to 200% load sharing variations. The system is believed to be one of the first successful silicon demonstrations of stable parallel analog LDO regulators.

Comprehensive Review of Stability Criteria for DC Power Distribution Systems

Power-electronics-based dc power distribution systems, consisting of several interconnected feedback-controlled switching converters, suffer from potential degradation of stability and dynamic performance caused by negative incremental impedances due to the presence of constant power loads. For this reason, the stability analysis of these systems is a significant design consideration. This paper reviews all the major stability criteria for dc distribution systems that have been developed so far: the Middlebrook Criterion, the Gain Margin and Phase Margin Criterion, the Opposing Argument Criterion, the Energy Source Analysis Consortium (ESAC) Criterion, and the Three-Step Impedance Criterion. In particular, the paper discusses, for each criterion, the artificial conservativeness characteristics in the design of dc distribution systems, and the formulation of design specifications that ensure system stability. Moreover, the Passivity-Based Stability Criterion is discussed, which has been recently proposed as an alternative stability criterion. While all prior stability criteria are based on forbidden regions for the polar plot of the so-called minor loop gain, which is an impedance ratio, the proposed criterion is based on imposing passivity of the overall bus impedance. A meaningful simulation example is presented to illustrate the main characteristics of the reviewed stability criteria.

A passivity-based stability criterion for reaction diffusion systems with interconnected structure

In this paper, stability of a class of reaction diffusion systems is studied. Conditions on global asymptotic stability of the homogeneous equilibrium are derived based on the diagonal stability of a dissipativity matrix. This work extends previous result on global asymptotic stability from cyclic systems to general systems with interconnected structure. In addition, it reformulates the approach using an input-output formalism that makes the results easier to understand and apply. A biological example from the Mitogen-Activated Protein Kinase (MAPK) system is provided at the end to illustrate the new approach and the main result.

A passivity-based stability criterion for a class of biochemical reaction networks

This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. The main result determines global asymptotic stability of the network from the diagonal stability of a dissipativity matrix which incorporates information about the passivity properties of the subsystems, the interconnection structure of the network, and the signs of the interconnection terms. This stability test encompasses the secant criterion for cyclic networks presented in [1], and extends it to a general interconnection structure represented by a graph. The new stability test is illustrated on a mitogen-activated protein kinase (MAPK) cascade model, and on a branched interconnection structure motivated by metabolic networks. The next problem addressed is the robustness of stability in the presence of diffusion terms. A compartmental model is used to represent the localization of the reactions, and conditions are presented under which stability is preserved despite the diffusion terms between the compartments.