Inverted Model Research Articles

Comprehensive Modeling, Analysis, and Comparison of State-Space and Admittance Models of PLL-Based Grid-Following Inverters Considering Different Outer Control Modes

The phase-locked loop (PLL)-based grid-following inverters have been widely used as the interface between renewable energy resources (e.g., wind and solar power) and the utility grid. In addition to the basic PLL and inner current control loop that are responsible for tracking the phase angle of the point of common coupling (PCC) voltage and regulating the current injection according to the estimated phase angle, respectively, these grid-following inverters are commonly also equipped with outer power and voltage control loops. Some examples are outer active power/dc-link voltage control loops and outer reactive power/PCC voltage control loops, which provide the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula> -axis current references for the inner current control loop. However, the existing literature generally focuses on specific outer control modes within a specific small-signal modeling framework, e.g., state-space or admittance modeling framework. In addition, different research groups usually repeatedly derive these small-signal models without a systematic modeling and analysis procedure. Furthermore, the systematic and comprehensive comparative modal and admittance analysis of these outer control modes is still missing in the literature. To avoid reinventing the wheel, provide the small-signal stability analysis community with handy both state-space and admittance models, and investigate the effects of various outer control loops on the small-signal models, this article presents a comprehensive and systematic small-signal modeling, analysis, and comparison framework of the PLL-based grid-following inverters, where the state-space and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula> -domain admittance models of eleven control modes are derived step by step in a completely followable style. All of these derived small-signal models are verified by the time-domain step responses and frequency-domain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula> -domain admittance measurement. The insights into the effects of these outer control modes on the poles and residues of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula> -domain admittance model are also explored, which help to understand how these outer control modes contribute to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula> -domain admittance shaping.

Проектирование системы фазовой автоподстройки частоты

The article is devoted to the development of a phase locked loop (PLL) system using the CD4046 integrated circuit. To achieve this goal, the principles of operation of two types of phase detectors were investigated. In the second half of the article, the main transfer functions of the PLL system are derived, an example of calculating the feedback controller is considered. The reliability of the calculation results is confirmed by modeling a computer model of a resonant voltage inverter.

DC Bus Voltage Control of Wind Power Inverter Based on First-Order LADRC

The wind power grid-connected inverter system has the characteristics of non-linearity, strong coupling, and susceptibility to grid voltage fluctuations and non-linear loads. To obtain the ideal control effect, the improved linear active disturbance rejection controller (LADRC) controls the voltage outer loop. Firstly, the mathematical model of the wind power grid-connected inverter is analyzed, on this basis, a linear active disturbance rejection control based on the reduced-order linear extended state observer is designed, reduce the phase lag of the observer, improve the system&#x2019;s disturbance observation accuracy; reference lead correction lag correction method, the observer gain is improved and connected in series to the total disturbance channel to reduce the noise amplification effect of the observer; through frequency domain response characteristic analysis, the results show that the improved LADRC has better disturbance rejection performance. The simulation results of various working conditions show that the improved method has better rapidity and immunity compared with traditional LADRC.

An Improved Three-Level Cascaded Control for LCL-Filtered Grid-Connected Inverter in Complex Grid Impedance Condition

The passivity-based control (PBC) with Euler&#x2013;Lagrange (EL) model has been used for LCL-filtered grid-connected converter. However, the impacts of the control delay and the interaction resonances under capacitive grid impedance are rarely considered for PBC method. Nonlinear Lyapunov&#x2019;s stability theory is hard to estimate the stability of the system and accurately design the controller parameters considering the control delay. This paper derived the impedance model of LCL-filtered grid-connected inverter with grid current control based on PBC method. The passive theory and the zero-pole maps are applied to reveal the influence of the digital delay and differential item of inverter current loop. A new three-level cascaded control method is then proposed based on traditional PBC method to achieve stability and high robustness in complex grid. Furthermore, controller parameters are designed accurately to maintain passivity within switching frequency ranges and parameter variations of the LCL filter are investigated. Final validation of the effectiveness and performance of the proposed control structure is performed by simulation and experimentation.

Patient Satisfaction and Maintenance Requirements of Classical Implant Locators versus Customized Attachments in Mandibular Implant-Retained Overdentures

Objectives: This study was performed to compare implant locators versus customized mandibular implant-retained overdentures considering patient satisfaction and prosthesis maintenance. Materials and methods: 12 completely edentulous patients from the prosthodontic department-Cairo university outpatient clinic were selected according to specific inclusion criteria. The patients were then allocated randomly into two groups using closed envelopes. For both groups, each patient received dental implants in the planned position. The patients were left for 3 months for implant healing. For group (A) the patients received two locator attachments. The attachment collar height was selected based on the soft tissue thickness keeping the retentive part 1 mm above the soft tissue level. The denture was relieved opposite the locator housing and the attachment was picked up using cold-cured resin. For group B, the implants were exposed, and healing collars were placed. After 2 weeks, the implants were scanned using an intraoral scanner. The denture was readapted using a light body closed mouth impression. The relined denture was scanned from both the fitting and the occlusal side. The scanned fitting surface was used to create an inverted virtual model and preceded till creating custom locator attachments. The generated custom attachment abutment was milled from grade V titanium blanks using a 5-axis milling machine. The abutments were anodized into gold color using an electric anodizer. The attachments were then sterilized and placed in the patient mouth as set before in the design. The pick-up of the housing was done in the same manner as group A. For both groups, the patients were given instructions for using and maintaining the overdenture. Initial denture corrections were made in the first 2 weeks if any complaint existed. The patients were recalled periodically at 3 months, 6 months, 9 months &amp; 12 months respectively. Results: Likert scale out of 5 was followed for patient denture satisfaction along 3, 6, 9, and 12 months for groups A &amp; B. Applying an Independent t-test for significance evaluation between group A and group B, precluded the higher significance of group B than group A for all follow up as P-value &lt;0.05.For prosthetic maintenance along twelve months follow-up, group B revealed a lower insignificant different incidence of prosthetic complications than group A using the Chi-square test for significance testing between proportions as P-value &gt;0.05. Conclusions: Customized locator attachments are highly recommended to retain mandibular overdentures, as they exhibited better maintenance values and more wear resistance with minimal loss of retention. Moreover, can be utilized by any presented implant system in the market, in addition, Patients were completely satisfied with their customized locators retaining their implant-supported overdentures.

A Sensitive and Accurate Walking Speed Prediction Method Using Ankle Torque Estimation for a User-Driven Treadmill Interface

To achieve safe and immersive interface with a user-driven treadmill (UDT), robustness of the user position must be ensured by sensitively estimating and accurately converging to the intentional walking speed (IWS). The existing IWS estimation using a linear observer with the cart model (1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order dynamics) can exponentially converge to the true IWS. However, when the estimation sensitivity is increased by increasing the gain, this method causes severe postural instability due to the generation of excessive anomalous forces. Thus, the existing method has an implicit limitation with regards to increasing the position robustness because of the postural instability issues. In this paper, to simultaneously achieve sensitive and accurate IWS estimation while reducing postural instability on a UDT, in addition to the cart model, we have also utilized the inverted pendulum-based gait model (IPGM) as a 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order dynamic to estimate the intentional walking acceleration (IWA) generated by the ankle torque. Thus, the proposed IWS prediction method uses the cart model for accurate convergence to IWS and the IPGM to follow sensitively the change in the IWS. In the proposed method, the internal states of the existing observers applied to the 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> and 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order dynamics are shared recursively to estimate the ankle torque acting as a disturbance for the IPGM and to sensitively predict the change in the IWS. Experiments show that the proposed method can significantly facilitate the users in following a profile of desired walking speeds more accurately than the existing IWS estimation method under the same position robustness setup.

Investigation of Inverter Temperature Prediction Model in Wind Farm Based on SCADA Data

The inverter is one of the key components of wind turbine, and it is a complex circuit composed of a series of components such as a variety of electronic components and power devices. Therefore, it is difficult to accurately identify the operation states of inverter and some problems regarding its own circuit, especially in the early stages of failure. However, if the inverter temperature prediction model can be established, the early states can be identified through the judgment of the output temperature. Accordingly, considering whether the inverter heats up normally from the perspective of heat dissipation, a method for the early operation state identification of the inverter is provided in this paper. A variable selection method based on fusion analysis of correlation and physical relationship is adopted to extract variables as input variables, which have high correlation with inverter temperature. Then multi-input and multi-output temperature prediction model of inverter is established based on a non-linear autoregressive exogenous model (NARX) network, and the prediction temperature residual is used as the real-time standard to evaluate the inverter states. For validating this, the validity and reliability of the established temperature prediction model are verified through case analysis, and the performance comparison with various models demonstrates that the proposed method has higher accuracy. The construction method of the prediction model can be used for reference to other aspects of wind turbine. All these bring huge benefits to wind energy industry.

Improving Power Density of a Three-Level ANPC Structure Using the Electro-Thermal Model of Inverter and a Modified SPWM Technique

Multilevel inverter structures have become an interesting substitute for the well-known two-level inverters in a variety of applications due to their exceptional characteristics when compared to conventional inverters. One major issue regarding multilevel structures is the unequal junction temperature of the switches which deteriorates the power density and increase the cost of the inverter by reducing the maximum achievable output power with a given thermal model and cooling system. Hence, on account of the aggressive goals of power density and cost in a majority of power electronic applications, this article proposes a new technique for reducing the maximum junction temperature of switches in a three-level active neutral-point clamped (ANPC) inverter based on a junction temperature estimation method and a modified SPWM control scheme. This technique can ensure up to a 12% rise in the power density value when compared to basic SPWM techniques with no loss distribution algorithm. Moreover, the suggested approach can be used as a protection stage in the inverter which protects the inverter in transient loads, while allowing for reaching the maximum power capability of the inverter. Finally, the simulations of the proposed technique are validated with experimental results of a 400 V, 20 kW three-level ANPC inverter, controlled by the conventional and proposed techniques.

Control of LPV Modeled AC-Microgrid Based on Mixed H2/H∞ Time-Varying Linear State Feedback and Robust Predictive Algorithm

This paper presents a robust model predictive control (RMPC) method with a new mixed H2/<inline-formula> <tex-math notation="LaTeX">$\text{H}\infty $ </tex-math></inline-formula> linear time-varying state feedback design. In addition, we propose a linear parameter-varying model for inverters in a microgrid (MG), in which disturbances and uncertainty are considered, where the inverters connect in parallel to renewable energy sources (RES). The proposed RMPC can use the gain-scheduled control law and satisfy both the H2 and <inline-formula> <tex-math notation="LaTeX">$\text{H}\infty $ </tex-math></inline-formula> proficiency requirements under various conditions, such as disturbance and load variation. A multistep control method is proposed to reduce the conservativeness caused by the unique feedback control law, enhance the control proficiency, and strengthen the RMPC feasible area. Furthermore, a practical and efficient RMPC is designed to reduce the online computational burden. The presented controller can implement load sharing among distributed generators (DGs) to stabilize the frequency and voltage of an entire smart island. The proposed strategy is implemented and studied in a MG with two DG types and various load types. Specifically, through converters, one type of DGs is used to control frequency and voltage, and the other type is used to control current. These two types of DGs operate in a parallel mode. Simulation results show that the proposed RMPCs are input-to-state practically stable (ISpS). Compared with other controllers in the literature, the proposed strategy can lead to minor total harmonic distortion (THD), lower steady-state error, and faster response to system disturbance and load variation.

Retracted] Infrared Spectroscopic Measurement of Dissolved Organic Matter and Nanomaterials in Water Based on Parallel Factor Algorithm

Infrared spectroscopy can separate carbon sugars and amino sugars that have collapsed in soil water very quickly. In this study, the midinfrared (MIR) and near‐infrared (NIR) spectra collected from soil water isolates or soil masses are sentenceless, assessing different agricultural groupings of flooded carbon and aminosaccharides. Soil was collected from five fields in two regions in western Canada and two regions in eastern Canada, where least squares backslide (PLSr) was inadequate. The inverted model of DOC recovery at the Eastern Peace River estuary can provide the optical functionality of traditional systems. The introduction of overflow DOCs from various sources rather than distance meters has been found to be a major contributor to the complexity of optical neighborhoods, resulting in a bias in DOC evaluation. The impact of voluntary DOC liability on the relationship between DOC and CDOM can be forgotten at a critical turn in the CDW. A slightly mitigating approach can overlook the impact of voluntary DOC responsibility on the relationship between DOC and CDOM. CDW is responsible for the continued responsibility of the Subei coastal currents for the normal material of the former Yellow Sea Delta, for the warm West Coast currents of the Yellow Sea for the materials of the Yellow Sea, and for the materials of the Changjiang Basin. The results of this study more thoroughly assess the state differences of DOM inputs from different sources within the CDW to determine the magnitude of the impact on DOC evaluation across the East China Sea CDOM. It suggests that it is necessary.

Approximation capabilities of measure-preserving neural networks

Measure-preserving neural networks are well-developed invertible models, however, their approximation capabilities remain unexplored. This paper rigorously analyzes the approximation capabilities of existing measure-preserving neural networks including NICE and RevNets. It is shown that for compact U⊂RD with D≥2, the measure-preserving neural networks are able to approximate arbitrary measure-preserving map ψ:U→RD which is bounded and injective in the Lp-norm. In particular, any continuously differentiable injective map with ±1 determinant of Jacobian is measure-preserving, thus can be approximated.

High-Performance Power Converter for Charging Electric Vehicles

This paper presents the analysis, modeling, simulation and practical studies of resonant inverters with a voltage limitation on the resonant capacitor. The power circuits obtained in this way are characterized by the fact that the power consumption does not depend on the load changes, but is a function of the operating frequency, the value of the resonant capacitor and the supply voltage—these are the so-called inverters with energy dosing. Analytical dependences, simulations and experimental results were determined, which described the behavior of the studied power electronic devices. The obtained expressions for the inverter current in the different stages of the converter operation were the basis for the creation of the engineering methodology for their design and prototyping. Based on the derived basic ratios and characteristics, the capabilities of these devices for self-adaptation to the needs and changes of the load were demonstrated. A comparison of the characteristics of classical resonant inverters and those with energy dosing was made, thus demonstrating their qualities and advantages. The presented results display the properties of this class of circuits and the challenges to their effective application to find the optimal solution for the implementation of charging stations for different specific needs. On the other hand, the limitations in the use of these circuits were that no power was consumed from the power supply during the whole period, the lack of limitation of the maximum current through the transistors and the need for sufficient time to dissipate energy in the resonant inductor when working with high-resistance and low-power loads.

Equivalent Input Disturbance-Based Control Design for Three Phase Dual-Stage Grid-Tied Photovoltaic System Considering Dead Time Effect

Grid-tied inverter is the prominent component of the three-phase dual-stage photovoltaic (PV) grid-tied power generation system. However, the disturbances caused by dead time effect will pose the reduction of grid-tied current quality and even cause the imbalance of inverter itself or other circuit devices. In this paper, a current control strategy is proposed to damp dead time effect for the three-phase dual-stage PV grid-tied inverter system, and its design, stability analysis, and implementation are carried out. First, the inverter model is modified by regarding the dq reference frame coupling terms, uncertainties, and external and internal disturbances as an unknown lumped disturbance. Then, a current control scheme based on compensation of equivalent input disturbance is introduced, and it estimates and compensates the unknown lumped disturbance, which effectively realizes the inverter model decoupling and comprehensive disturbance rejection. Last, simulation results demonstrate the effectiveness and superiority of the proposed current controller.

Robust Control of GTIs under wide grid impedance ranges: An approach combining metaheuristics and LMIs

This paper provides a new design procedure for robust state feedback current controllers suitable for grid-tied inverters under wide grid impedance ranges. The proposed procedure is based on the combination of particle swarm optimization and linear matrix inequalities. The control gains, designed offline, are obtained through the minimization of a novel objective function that takes into account the grid current tracking error in the stationary reference frame, limits for the control signal, and robust stability. Linear matrix inequalities are used in the design stage to theoretically certify the closed-loop robust stability systematically and efficiently, based on a polytopic model of the grid-tied inverter, which avoids the need for exhaustive and time-consuming a posteriori tests. Real-time simulations and experimental results are presented, attesting that the closed-loop system with control gains provided by the proposed procedure is robustly stable for wide ranges in the grid inductances. Moreover, the grid currents exhibit an optimized transient performance and steady-state responses in compliance with harmonic distortion limits from IEEE 1547 Std., even encompassing operation from stiff to weak grid conditions and in the presence of distorted grid voltages. To provide a comparison, results based on other well-established state feedback design techniques are also presented, highlighting the superior performance obtained with the proposed procedure.

Analysis of Rotor Position Detection Performance According to the Frequency of Square Waveform Voltage in the Harmonic Injection Sensorless Method through HILS

In this paper, the rotor position estimation performance of the sensorless scheme for permanent magnet synchronous motors (PMSMs) implemented through the injection of high-frequency square-wave voltage according to the frequency of the square-wave voltage is presented through HILS (Hardware In the Loop Simulation) experiments. An inverter using an IGBT device usually has a switching frequency of around 15 kHz. On the other hand, GaN devices that can be switched on and off at frequencies higher than 100 kHz have been recently developed, and research is being actively conducted to apply GaNs to a variable speed system. The purpose of this study is to conduct HILS experiments to analysis the rotor position estimation ability of the sensorless technique in cases where a high switching frequency was applied, such as GaN devices, with that of a system having a usual switching frequency, such as IGBT. In the HILS system used in this study, an inverter and motor model implemented with Simulink are located in a real-time simulator. A sensorless motor control method was implemented with an FPGA control board, which includes a PWM interrupt service routine of 100 kHz frequency and a harmonic injection and position detection algorithm. The HILS experiments show rotor position detection errors according to the various frequency of the harmonic voltage injected for estimating the rotor position with a PWM frequency of 100 kHz cases. According to the experimental results, good position estimation was possible not only when the harmonic of 10 kHz corresponding to 1/10 of the PWM frequency was injected, but also when the harmonic of 1 kHz corresponding to 1/100 of the PWM frequency was injected. The experiments suggest that position estimation errors decrease as the frequency of the harmonic voltage increases, and, based on the foregoing, it is thought that the application of a GaN device capable of realizing a high switching frequency in a variable speed drive system can be another advantage.

Model-Based Voltage Quality Analysis and Optimization in Post-Fault Reconfigured N-Level NPC Inverter

This article proposes a model-based voltage quality analysis and optimization method for post-fault reconfigured N-level Neutral Point Clamped (NPC) inverter. It is found that the voltage quality of post-fault reconfigured multilevel inverters (MLIs) has significant degradation which could cause issues in critical applications. To analyze and solve the voltage quality problem, existing voltage quality and mathematical analyses of MLIs were reviewed. Significant limitations of existing voltage quality analysis methods and shortages of existing mathematical analysis were found. Thus, a suitable mathematical model of N-level NPC inverter is proposed in this article to accurately describe voltage quality of a reconfigured N-level NPC inverter. The mathematical model is validated by simulation and experimental results and used for voltage quality analysis. In addition, based on the accurate mathematical model and results of voltage quality analysis, an optimization method is proposed to alleviate the voltage quality degradation of post-fault reconfigured N-level NPC inverter. A five-level NPC inverter and a reconfiguration method were used as an example to illustrate the proposed optimization method. Experimental and simulation results validate the effectiveness of the proposed optimization method.

Grid-Connected Resonance Suppression Of Group-Series Photovoltaic Cluster Inverters Based On Hybrid Damping

Grid-connected group-series photovoltaic cluster inverter system will cause resonance, which will adversely affect the system. To suppress grid-connected resonance, the mathematical model, resonance mechanism and resonance characteristics of the cluster inverters are analyzed, and a global resonance suppression strategy based on hybrid damping is proposed. In the current loop of the inverter, capacitive current feedback and parallel voltage proportional feed-forward are introduced as active dampers to reduce the harmonics of the parallel current. On this basis, RLC type second-order resonance suppression circuit is added as passive damping to suppress system resonance, so that the output current of the inverters can meet the grid-connected conditions when the cluster is connected to the grid. The simulation and experimental results show that the total harmonic distortion of the grid-connected current decreases from 10.54% to 1.97% after three series photovoltaic cluster inverters adopt this strategy, which effectively suppresses the grid-connected resonance.

Harmonic Suppression Strategy of Photovoltaic Grid Connected Inverter Based on Repetitive and PI Control

To address the serious harmonic problem of grid connected current in photovoltaic grid-connected inverter, a harmonic suppression strategy based on Repetitive and PI control is proposed in this thesis. According to this strategy, the mathematical model of LCL photovoltaic grid-connected inverter is established with the harmonic mechanism analyzed, the repetitive and PI control is added into the current controller, and the capacitive-current feedback is added to enhance the system damping. Furthermore, it puts PI control on the inner loop and the repetitive control on the outer loop to improve the dynamic performance and achieve the harmonic suppression of the system. Moreover, the simulation results show that this method improves the dynamic response ability of the system, and effectively suppress the grid-connected current harmonics as THD of grid-connected current is 19.65% lower than that of PI controller.

Composite Control Strategy of Output Current of LCL Photovoltaic Grid-Connected Inverter

In order to further optimize the output current harmonic suppression effect of photovoltaic grid-connected inverters, a composite control strategy of LCL type photovoltaic grid-connected inverter output current is proposed. This strategy combines proportional complex integral (PCI) control and repetitive control (RC) in parallel, draws a composite control block diagram, introduces a transfer function, and designs PCI and RC control parameters. Prove that the compound control can reduce current harmonics, achieved the purpose of reducing the steady-state error of the fundamental frequency. And adopts a new PCI composite control strategy, which helps to save the cost of the control system. By building the MATLAB/Simulink simulation platform and establishing the PCI+RC composite control model of LCL photovoltaic grid-connected inverter, the comparison of the simulation results shows that compared with the PI+RC control strategy, the total harmonic distortion rate of the grid-connected current is reduced by 25.77. %, significantly improving the quality of grid-connected current.

Small-signal modeling and analysis of a three-phase virtual synchronous generator under off-grid condition

The current small-signal models of inverters that mimic synchronous generators usually use the steady-state equation of feeder line and load, and ignore the dynamic characteristics of voltage and current controller of inner loop. Thus, some important dynamics of the system will be omitted. To capture the dynamics more accurately, firstly, a small-signal model of a three-phase isolated inverter that mimics a synchronous generator was developed in this paper, and a comparison between the corresponding simulink model and the small-signal model was presented to validate the model correctness. Then, participation factor was calculated, which showed the relation between the state variables and eigenvalues. Based on the model, several root locus plots as a function of the system parameters was obtained. An individual eigenvalue sensitivity analysis of a certain eigenvalue close to the real axis disclosed different parameters’ contribution to the oscillation mode. Finally, a disturbance test with simulink model and the small-signal model under multiple sets of parameters was carried out and the results can accurately reflect the oscillation mode, which verified the correctness of the parameters effect on the conjugate eigenvalues.