Nyquist Stability Criterion Research Articles

Robust Controller Design for a Grid-Connected VSI via an LCL Filter in the Presence of Unknown Grid Impedance

Inverters connected to the grid can become unstable under specific grid impedance conditions. In order to find a solution to this problem, it is possible to ensure system stability and their robustness to R-L type grid impedances by satisfying two conditions. The first condition is to ensure that the closed-loop poles of the system are in stable positions to variations in the grid impedance. The second condition is reliant on the admittance model of the equivalent circuit. Specifically, the product of this admittance and the grid impedance must adhere to the Nyquist stability criterion. In this work, the stability of the converter connected to the grid through an LCL filter is analysed. For this purpose, the output admittance is modelled in the Laplace domain taking into account the behaviour of the discrete controller. In addition, to ensure that the closed-loop poles are in stable positions, the system open-loop response is analysed. These two conditions are examined across scenarios where system states are partially or completely fed back, for different system parameter values. Consequently, a robust controller is designed for variations of the R-L type grid impedance.

Physics-supported Bayesian machine learning for chatter prediction with process damping in milling

Chatter stability of milling operations is a complicated phenomenon causing serious productivity issues in the manufacturing industry, yet a shop-floor implementable solution is lacking. This paper follows a physics-supported Bayesian machine learning approach and incorporates the potential effect of process damping on the stability of the process. Using a likelihood function based on the Nyquist stability criterion, the learning system monitors the actual stability state of the process during arbitrary cuts and refines the underlying model parameter uncertainties in the structural dynamics, cutting force coefficients, as well as the process damping. The framework can operate with limited training data and display the remaining uncertainties in stability predictions to the machine operator. Experimental case studies show the effectiveness of the proposed method and highlight the importance of considering process damping for certain endmills.

Frequency method for determination self oscillations in control systems with a piezo actuator for astrophysical research

For the control system with a piezo actuator in astrophysical research the condition for the existence of self-oscillations is determined. Frequency method for determination self-oscillations in control systems is applied. By using the harmonious linearization of hysteresis and Nyquist stability criterion the condition of the existence of self-oscillations is obtained.

Impedance analysis of voltage prediction compensation scheme for DC-link oscillation suppression in cascade drive system

The dc-link voltage oscillation caused by the negative impedance characteristic of the constant power load is a significant issue in the series LC branch-permanent magnet synchronous motor (PMSM) cascade system. To this end, this paper proposes a voltage prediction compensation (VPC) strategy to suppress the dc-link voltage oscillation by adding a voltage stability constraint term to the finite control set model predictive current control (FCS-MPCC). First, the linearized q-axis reference voltage is obtained by taking the derivation of the cost function of the VPC, thereby deriving the input impedance of the inverter-permanent magnet motor system. Then, the impedance matching criterion and Nyquist stability criterion are used to theoretically prove that the proposed strategy can effectively improve system stability, and the robustness of the proposed method to changes in motor parameters is analyzed. Finally, experimental verification was conducted on a 1 kW motor platform. The results show that when the motor is running under rated working conditions, after adding the stability constraint, the dc-link voltage fluctuation drops from 40 V to 7 V; the q-axis current pulsation rate also drops to 3.8 %. Theoretical analysis and experimental results show that the VPC strategy can effectively suppress the dc-link voltage oscillation of the cascade drive system.

A novel coordinate transformation stability criterion and parameter selection for grid-connected inverter

The negative resistance of grid-connected inverter (GCI) and the increasing number of GCI in power grid pose great challenges to the stability of GCI. This paper proposes a coordinate transformation stability criterion (CTSC) based on the single-input single-output (SISO) impedance model for GCI system. A low complexity fractional polynomial model of GCI is derived by the Pade approximation and the SISO impedance model in the αβ domain. CTSC is proposed by applying the Nyquist stability criterion, which simplifies the graph trajectory criterion to a numerical criterion. Since the effect of parameter on stability is usually limited to the neighborhood, average parameter assessment metric (APAM) is proposed based on CTSC to evaluate the impact of each parameter over a wide range. Additionally, joint parameter assessment metric (JPAM) is proposed to simultaneously adjust multiple parameters on stability. Finally, compared with the three criteria for conservatism analysis, CTSC possesses the lowest conservatism. The theory proposed in this paper is verified by experiment.

Non-parametric fractional-order controller design for stable process based on modified relay

The relay feedback approach is an effective approach for real-time process control. However, it requires accurate limit cycle data. This paper proposes a novel relay feedback approach for fractional-order (FO) controller design to regulate the stable process performance. The proposed methodology does not require prior knowledge of the process and assures accurate limit cycle. Accurate limit cycle parameters are first estimated using the proposed relay. Then, the FO controller is designed based on the output of the limit cycle obtained through the proposed relay, phase, and Nyquist stability criteria. Further, the accuracy of the proposed relay is verified analytically through harmonic analysis. Various performance parameters and indices are estimated and compared with recently published techniques to assess the effectiveness. Additionally, disturbance and parametric uncertainty analyses are conducted to examine the disturbance rejection capacity and robustness. The efficacy of the proposed methodology is further validated on a real-time liquid-level control four-tank process.

Dynamic Stabilization of a Centralized Weak Grid-Tied VSC System Considering PV Generator Dynamics

This paper addresses the instabilities and dynamic interactions in a centralized vector-controlled voltage-source converter interfacing a single-stage utility-scale photovoltaic (PV) generator to a high-impedance grid system. The dynamic resistance of the PV generator is considered, and effective active stabilization methods to guarantee the entire system's stability are proposed. Further, a complete state-space linearized model is developed, and different operating conditions alongside the maximum-power operation (MPO) are considered, such as fixed-voltage operation (FVO) and fixed-current operation (FCO). It is found that with the change of the PV generator operation from the FVO or MPO to the FCO region under the weak grid and nominal dc-link capacitance conditions, the dominant eigenmodes are relocated to the open-right-half-plane of the S-plane. This eventually induces inevitable high- and low-frequency oscillation instabilities. Further, it is found that medium-frequency oscillation instability is induced in the FVO region under a weak grid and reduced dc-link capacitance conditions. Active compensators are proposed to reduce the interaction dynamics and stabilize the entire system by reshaping the converter transfer functions; hence, the Nyquist stability criterion is maintained. Finally, detailed nonlinear time-domain simulation results are provided, showing the effectiveness of the proposed method in preserving the system's stability under a wide range of operation conditions.

Impedance-Based Stability Analysis of Grid-Connected Inverters under the Unbalanced Grid Condition

As a common interface circuit for renewable energy integrated into the power grid, the inverter is prone to work under a three-phase unbalanced weak grid. In this paper, the instability of grid-connected inverters under the unbalanced grid condition is investigated. First, a dual second-order generalized integrator phase-locked loop (DSOGI-PLL)-based inverter under balanced and unbalanced conditions is modeled. A fourth-order impedance model is established to describe its impedance characteristics under the unbalanced grid condition. To analyze this multi-input multi-output system, a simplified stability analysis method based on the generalized Nyquist stability criterion and matrix theory is proposed. Then, the influences of circuit and control parameters on the stability of the grid-connected inverter system under the unbalanced grid condition are investigated. Finally, the accuracy of the derived frequency-coupled impedance model is verified via simulations, and the effectiveness of the proposed simplified stability analysis method on the system stability analysis is verified via both simulations and hardware experiments.

Feedback Stability of Generalized Positive Real and Negative Imaginary Systems

This paper derives necessary and sufficient conditions for robust stability of a feedback interconnection of linear time-invariant (LTI) systems that exhibit positive realness on finite nonzero frequencies (excluding pole locations) through a weighting function, i.e. a multiplier. This class of LTI systems importantly includes the well-studied negative imaginary systems without poles at the origin as a subset. Under the assumption that the instantaneous gain of the loop transfer function is zero, it is shown that the aforementioned feedback interconnection is stable if and only if the static (a.k.a. DC) loop gain is less than unity. This condition is identical to the one that guarantees feedback stability of negative imaginary systems, but is applicable to a much wider class of systems beyond negative imaginariness. Our proof is based entirely on the multivariable Nyquist stability criterion — it does not make use of realisations of the transfer functions. Comparisons with integral quadratic constraint based robust stability results are also made.

Improved Power Sharing and Energy Management Platform in Microgrid Considering Stochastic Dynamic Behavior of the Electric Vehicles

In this study, an improved model of optimal power sharing and energy management as well as total harmonic distortion (THD) control in AC microgrids in order to control the voltage and frequency parameters by considering the random behavior of electric vehicles (EVs) is presented. The proposed model is developed based on the primary and secondary controller. The primary controller is planned with the purpose of optimal power-sharing, reduction of feeder's impedance mismatch and also THD reduction. The primary controller is modeled with the hybrid Event-Triggered approach and virtual impedance method. The secondary controller has been modeled using the particle swarm optimization (PSO) algorithm with the aim of reducing the power distribution error and optimizing the virtual impedance parameters, as well as considering the participation of EVs in the stochastic power flow equations. In addition to comparing the performance of the proposed model with conventional methods, it has also been compared with other meta-heuristic methods. The results of this have been verified in two software environments (MATLAB/Simulink) and experimental setup (dSPACE model 1202) in different scenarios and also the stability of the proposed model based on the Nyquist stability criterion, the Root Locus method and small signal analysis has been presented.

A Sub-Synchronous Oscillation Suppression Strategy Based on Active Disturbance Rejection Control for Renewable Energy Integration System via MMC-HVDC

To realize the consumption of renewable energy such as wind power and photovoltaics in the power system, renewable energy integration system via modular multilevel converter (MMC)-based high voltage direct current (MMC-HVDC) has been widely applied. However, with the large-scale grid connection of renewable energy units, sub-synchronous oscillation (SSO) is prone to occur. Aiming at the problem, this paper proposes an SSO suppression strategy for renewable energy integration system via MMC-HVDC based on active disturbance rejection control (ADRC) theory. Using the direct drive permanent magnet synchronous generators (PMSG)-based wind farm integration system via MMC-HVDC as an example, firstly the topology and control system principles of the system are described, and a simulation model is built in PSCAD/EMTDC. Moreover, the SSO mechanism of the system is revealed by Nyquist stability criterion, and the major factors affecting the SSO of the system are simulated and analyzed. Subsequently, an additional sub-synchronous damping controller (ASSDC) is proposed based on ADRC theory. Compared to traditional additional damping controllers, the proposed controller considers disturbances of the system during the designing process and has stronger robustness. In addition, when faults happen, the speed of the system with ASSDC reaching a steady-state operating point rises by 33.7% as compared to the system without ASSDC. Finally, the effectiveness of the proposed suppression strategy is verified through simulation analysis.

Observer-Based Single-Sensor Control Schemes for LCL-Filtered Grid-Following Inverters

In the single-sensor grid-following control of <i>LCL</i>-type grid-connected inverters, extended-observers, which behave as &#x201C;virtual sensors,&#x201D; are typically employed for active damping, disturbance rejection, current tracking, and grid synchronization. However, most of the existing observer-based single-sensor control schemes choose grid current as the system measurement and output, and the performance of other combinations is still unclear. Hence, in this article, with the help of impedance modeling and Nyquist stability criterion, a systematic comparative assessment for selecting different measurements and controlled outputs is introduced. In this comparison, the sub- and super-synchronous oscillation issues induced by grid faults, lower current reference, high phase-locked loop (PLL) bandwidth and large grid inductance, are investigated. In addition, two easily overlooked interval stability corollaries are proved, facilitating the system stability analysis. Finally, the correctness of the theoretical analysis is verified by a series of steady-state and transient experimental tests.

Impedance Modeling and Mechanism Analysis of Low-Frequency Oscillations in Single-Phase MMC-RPC Integrated Vehicle-Grid Coupling System

The single-phase modular multilevel converter-based railway static power conditioner (MMC-RPC) has significant advantages in governing the power quality problems in the traction power supply system. The mechanism analysis of low-frequency oscillations (LFOs) in the MMC-RPC integrated vehicle-grid coupling system when electric multiple units are put into operation is a critical issue, which has been investigated in this article. The third-order ac admittance models of single-phase MMC-RPC and vehicle rectifiers are developed for the first time. To comprehensively study the small-signal stability of the MMC-RPC integrated vehicle-grid coupling system, this article proposes a modal analysis method based on modal phase margin and parameter sensitivity and combined with the generalized Nyquist stability criterion. It is found that LFOs around 10 Hz or 48 Hz are prone to occur due to the interactions of MMC-RPC or vehicle rectifiers with the traction power grid. To reveal the LFO mechanism, dominant modes and key parameters leading to LFOs in different working scenarios are clarified, and a series of guidelines are proposed for LFO elimination. Furthermore, the effects of control loops and power flow of MMC-RPC on system stability are revealed in detail. Finally, real-time hardware-in-the-loop experimental results validate the theoretical analysis.

Small-Signal System Frequency Stability Analysis of the Power Grid Integrated With Type-II Doubly-Fed Variable Speed Pumped Storage

This article proposes a structurally distinctive doubly-fed variable speed pumped storage (VSPS), denoted as the Type-II VSPS. Where, the speed is controlled by a back-to-back (BTB) converter while the power is controlled by a speed governor, which is the exact opposite of the control method for conventional VSPS. The small-signal frequency stability analysis of a power grid integrated with the Type-II VSPS is carried out to investigate the influence of this type of VSPS on power grid stability. Firstly, the transfer function models of hydraulic and electric subsystems of the Type-II VSPS are established, and the system small-signal stability analysis is carried out based on the obtained models and Nyquist stability criterion. Secondly, an improved system frequency response (SFR) model for the power grid integrated with Type-II VSPS is presented. Such a model is applied to investigate the frequency response of the modern power grid integrated with a large-scale VSPS (the current single unit capacity has reached 450 MW). Furthermore, the small-signal stability of the modern power grid is analyzed based on the Nyquist stability criterion. Finally, time-domain simulations and experiments are conducted to validate the effectiveness of the small-signal stability analysis.

Research on Coordinated Control Strategy of Energy Storage Type Railway Power Conditioner

In order to improve the power quality of high-speed railway traction power supply system and enhance the robust stability of railway power conditioner (RPC), a coordinated control strategy based on the energy storage system (ESS) integrated RPC (ESS-RPC) is proposed in this article. It is found that the dc impedance characteristics of the back-to-back system are different when the parameters of the ESS-RPC system are perturbed under conventional control, which will affect the dc voltage of the back-to-back system and then affect the power quality of the traction system. In this article, it is analyzed that the stability difference of the bidirectional power flow of ESS-RPC under parameter perturbation is due to the negative impedance of the dc terminal and the right shift of the dominant pole. After the analysis, a coordinated control strategy of ESS-RPC is proposed to solve this problem. The small-signal analysis of the ESS-RPC system under conventional control and coordinated control is carried out, respectively, and the robust stability of the two control strategies is judged by the Nyquist stability criterion. Simulation and experimental verification are carried out in the MATLAB/Simulink environment and semisimulation platform (Modeling Tech) to analyze the impact of the proposed coordinated control strategy on the power quality of the traction power supply system and verify the effectiveness and accuracy of this coordinated control strategy.

Admittance-Based Stability Analysis of Current-Controlled VSG Considering the Frequency Coupling Characteristics

Due to the dynamic interaction between the inverter and the grid, the inverter may have power oscillation problems under a weak grid. In this article, considering frequency coupling, the more precise broadband sequence admittance model of the current-controlled virtual synchronous generator (CVSG) is established, and the admittance characteristics of CVSG and traditional grid-connected inverter (TGCI) are compared and analyzed. The amplitude of the sequence admittance of CVSG is generally larger than that of TGCI in the low-frequency region, and in the entire frequency sweep range, the coupling admittance amplitude of CVSG is larger than that of TGCI. In the low-frequency region, the coupling admittance has a great impact on the stability of CVSG and TGCI, so the coupling admittance cannot be neglected when analyzing the stability of the system. The generalized Nyquist stability criterion is used to compare and analyze the influence of power grid strength, phase-locked loop (PLL) bandwidth, and output power on the stability of CVSG and TGCI according to the established admittance model. It can be seen from the stability analysis results that, compared with TGCI, when the PLL bandwidth is relatively large, CVSG has stronger adaptability to the weak grid and power changes. Finally, experiments verify the correctness of the theoretical analysis.

A Water Tank Level Control System with Time Lag Using CGSA and Nonlinear Switch Decoration

Tank level control has some unavoidable factors such as disturbance, non-linearity, and time lag. This paper proposes a simple and robust control scheme with nice energy-saving effects and smooth output to improve the quality of the controller and meet real-world application requirements. A linear controller is first designed using a third-order closed-loop gain-shaping algorithm. We then use an arcsine function to modify the system with non-linear switching to reduce the effect of the non-linear modification on the dynamic performance of the control system. Furthermore, we use the Nyquist stability criterion to demonstrate the stability of the closed-loop system in the presence of time lag. The results of the final simulation experiment show that the controller not only has high control quality but also has the characteristics of energy saving and smooth output under the condition of lag and pump performance constraints. These features are necessary for extending the life of the pump and enhancing the applicability of the tank level controller.

Stability analysis of some neutral delay-differential equations with a frequency-domain approach

&lt;p style='text-indent:20px;'&gt;Two general schemes of neutral delay differential equations are considered. They represent non delayed systems with delayed, nonlinear feedback control. The stability conditions in terms of system parameters are derived using an approach based on feedback systems, namely, the Nyquist stability criterion. It is also shown that those results coincide with some already found in the literature, and others derived here, which are based on classical tools, that investigate directly the roots of characteristic equation. Finally, some examples are given to illustrate the usefulness of this approach.&lt;/p&gt;

Green energy-saving robust control for ship course-keeping system based on nonlinear switching feedback

To further save energy and reduce carbon emissions, a simple and robust green energy-saving control algorithm was proposed under the premise that the ship achieved an excellent course-keeping effect. To this end, the controller is designed by employing the third-order closed-loop gain shaping algorithm, and the final control law is obtained via the nonlinear switching feedback technique. The robustness of the system is proved by the Nyquist stability criterion. An evaluation model is carefully established for energy-saving and carbon-reduction of the course-keeping controller. The nonlinear Nomoto and Norrbin models for MV “Yukun” are implemented for simulating and further assessing under normal and heavy sea conditions. Compared with the nonlinear decoration controller, the proposed controller enhances the ship's course-keeping accuracy, shortens the delay time and settling time of the controller, lessens the steering angle and steering frequency of the rudder, increases the robustness of the system, and reduces the comprehensive energy-saving index by 26.1% under normal sea conditions. Meanwhile, good controller performance and green energy-saving effects are more in line with the requirements of navigation practice, which is essential for ships to achieve safe, economical, green, and low-carbon navigation.

Output Impedance Derivation and Small-Signal Stability Analysis of a Power-Synchronized Grid Following Inverter

In recent years, grid-following inverters (GFLIs) and grid-forming inverters (GFMIs) have established their position as the mainstream synchronization techniques for the grid integration of inverter-based resources into power systems. However, both of these integration techniques have their shortcomings in weak, strong, and/or series-compensated grids. Recently, in the literature, a power synchronized GFLI has been proposed that does not suffer from the issues exhibited in GFLIs and GFMIs. This article provides an analytical output impedance of this power-synchronized GFLI that uses a linear parameter-varying controller (LPV-PSGFLI). This impedance is then used for impedance-based stability analysis via the Nyquist stability criterion. In addition, the derived impedance is validated via system identification, and a comparison between a conventional GFLI and an LPV-PSGFLI is made under various system strengths. It is seen that the LPV-PSGFLI can inject power into the grid, whereas the conventional GFLI fails when both are integrated into a very weak grid. Finally, the accuracy of the impedance-based stability analysis using the derived output impedance is validated in Matlab/PLECS and in experiments in various scenarios.