Small-signal Model Research Articles

Transient Energy Dissipation Control of Energy Storage Devices in Wind Power Generation Systems

The transient stability of power systems with high penetration of wind power generation can be significantly improved through the utilization of variable virtual inertia if the energy source of rotational inertia can be expanded by energy storage devices (ESDs). This paper first establishes the relationship of energy conversion between ESD and mechanical kinetic energy inside a synchronous generator (SG). Then, the impact of the controllable inertia on system frequency characteristics and power angle oscillation is analyzed using the small-signal model corresponding to this system. Based on the analysis of the change of transient energy at different stages in the transient process, the control of transient energy dissipation is proposed employing ESDs for reliable inertia support. Finally, a typical simulation system with high penetration of wind power generation is carried out to demonstrate the viability of the proposed control scheme. The test results show that the fluctuation of SG’s power angle and system frequency can be reduced by regulating the variable inertia in transient events, significantly improving the reliability of the inertia support provided by the ESDs.

Modeling Excitable Cells with Memristors

This paper presents an in-depth analysis of an excitable membrane of a biological system by proposing a novel approach that the cells of the excitable membrane can be modeled as the networks of memristors. We provide compelling evidence from the Chay neuron model that the state-independent mixed ion channel is a nonlinear resistor, while the state-dependent voltage-sensitive potassium ion channel and calcium-sensitive potassium ion channel function as generic memristors from the perspective of electrical circuit theory. The mechanisms that give rise to periodic oscillation, aperiodic (chaotic) oscillation, spikes, and bursting in an excitable cell are also analyzed via a small-signal model, a pole-zero diagram of admittance functions, local activity, the edge of chaos, and the Hopf bifurcation theorem. It is also proved that the zeros of the admittance functions are equivalent to the eigen values of the Jacobian matrix, and the presence of the positive real parts of the eigen values between the two bifurcation points lead to the generation of complicated electrical signals in an excitable membrane. The innovative concepts outlined in this paper pave the way for a deeper understanding of the dynamic behavior of excitable cells, offering potent tools for simulating and exploring the fundamental characteristics of biological neurons.

Small‐signal rotor angle stability of multi‐virtual synchronous machine (n‐VISMA) microgrid

AbstractAutonomous microgrid is known to lack appropriate inertia and damping for grid stabilization. Due to this, virtual synchronous machine (VISMA) has been introduced to provide necessary ancillary services through control of power converters. In a multi‐VISMA (n‐VISMA) microgrid, relative rotor angle stability of the power system is dependent on the active power balance after small perturbation. Thus, the use of relevant analytical models are essential issues for microgrid stability analysis. This paper presents a comprehensive small‐signal stability analysis to study inherent electromechanical oscillations in the virtual rotors. The subsystems of the microgrid consisting of VISMA, network, load and the outer power control were all modelled in Synchronous Reference Frame. The small‐signal model (SSM) was tested on IEEE‐9 bus system with VISMA replacing electromechanical synchronous machines on the network. To validate the developed numerical analytics, dynamic responses of the SSM are compared with those of the non‐linear (NL) system dynamics and the results reveal that the developed linearized SSM is sufficient to accurately characterize behaviour of the VISMA microgrid when operated in autonomous mode. Eigenvalues analysis and parameter sensitivities of the critical modes were investigated. Oscillatory participations of the VISMAs and steady state stability limit of the microgrid have also been investigated.

A Spread-Spectrum Modulation Scheme for a 3 × 6 Indirect Matrix Converter Based on a Current Ripple Model

Focused on addressing harmonic suppression in multiphase indirect matrix converters (IMCs), this study explores spread-spectrum modulation technology through ripple analysis calculations. We introduce a current ripple spread-spectrum modulation (CR-SSM) method tailored for multiphase IMC systems. In this approach, a 3 × 6-phase IMC is modeled as a two-port network, and a small-signal model of the output side is established. The transfer function is utilized to analyze the two-port network in the complex frequency domain (s-plane). The time-domain expression of the output current ripple is derived in vector form. Subsequently, the distribution of the output ripple and locus are determined based on specified constraints. The carrier frequency is dynamically adjusted online according to the specified ripple locus. Compared to classical periodic PWM methods, this approach offers a broader range of frequency variations and achieves a more uniform output spectrum. Furthermore, CR-SSM optimizes system efficiency and enhances spread-spectrum modulation. Experimental results demonstrate that this method effectively enhances the quality of input and output waveforms in multiphase IMC systems.

Design and analysis of soft-switching and small-signal model grid-connected micro-inverter based on staggered parallel connection

Grid-connected micro-inverters, known for their straightforward wiring and operational stability, have garnered increasing interest from both industry and academia. However, the operational inefficiency of conventional inverters, the issue of distorted output waveforms, and the safety concerns with alternating current (AC) and direct current (DC) safety isolation limit the wide availability and utilization of micro-inverters. In order to overcome this problem, this research proposes a circuit topology consisting of two flyback circuits connected in parallel on the primary side of the transformer for safe isolation. Additionally, soft switches are incorporated into the flyback circuit at the front stage, with a voltage total harmonic distortion (THD) of less than 3.0 %. This study also develops a small-signal model to help with obtaining the current loop parameters. Parametric design and simulation studies with PLECS software confirmed the circuit architecture and control technique's accuracy. A 600 W prototype's design, analysis, and experimental validation are described. The proposed inverter has an efficiency of up to 97.2 %. The design and control methods employed in this paper offer a conceptual framework and engineering reference for relevant research and practical applications.

Generalized Pulse Width Modulation Switch Model for Converters Based on the Multistate Switching Cell in Discontinuous Conduction Mode.

This work introduces a generalized version of the pulse width modulation (PWM) switch model applied in the small-signal modeling of converters based on the multistate switching cell (MSSC) operating in discontinuous conduction mode (DCM). It consists of extending the concept formerly introduced by Vorperian for the representation of multiphase converters in DCM, yielding a circuit-based approach that does not rely on matrix manipulations unlike state-space averaging (SSA). The derived dc and ac models are valid for any number of switching states and any operating region defined in terms of the duty cycle, thus allowing for determining the voltage gain and distinct transfer functions. A thorough discussion of results is presented to demonstrate the applicability of the derived models to represent distinct configurations of the MSSC.

Stability and Reactive Power Sharing Enhancement in Islanded Microgrid via Small-Signal Modeling and Optimal Virtual Impedance Control

In the context of integrating Renewable Energy Sources, Microgrid (MG) development is pivotal, particularly as a foundational technology for Smart-Grid evolution. Despite advancements in control techniques, challenges persist in ensuring system stability and accurate power sharing across diverse operational conditions and load types. The objective of this research is to control numerous paralleled inverters-based distributed generators (DGs) that contribute to power sharing in an island MG. The proposed methodology involves developing an innovative small-signal model for islanding MGs that incorporate virtual impedances. Subsequently, optimization algorithms based on Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are proposed and compared for designing the virtual impedances. These algorithms analyze all potential operating points, aiming to minimize reactive power mismatches while maximizing MG stability. The suggested objective function facilitates the simultaneous achievement of these objectives. The proposed approaches were tested using MATLAB-Simulink software, and the comparison of the results between conventional approach and the proposed optimal approaches shows significant improvement in terms of the dynamic response during load changes, such as a decrease in response time by up to 20%, a reduction in overshoot percentage by approximately 15%, and a settling time improvement of nearly 25%. These quantified improvements highlight the effectiveness of the GA and PSO methods in minimizing the reactive power-sharing error while optimizing MG performance and stability.

A novel small-signal equivalent circuit model for GaN HEMTs incorporating a dual-field-plate

An accurate and novel small-signal equivalent circuit model for GaN high-electron-mobility transistors (HEMTs) is proposed, which considers a dual-field-plate (FP) made up of a gate-FP and a source-FP. The equivalent circuit of the overall model is composed of parasitic elements, intrinsic transistors, gate-FP, and source-FP networks. The equivalent circuit of the gate-FP is identical to that of the intrinsic transistor. In order to simplify the complexity of the model, a series combination of a resistor and a capacitor is employed to represent the source-FP. The analytical extraction procedure of the model parameters is presented based on the proposed equivalent circuit. The verification is carried out on a 4 × 250 μm GaN HEMT device with a gate-FP and a source-FP in a 0.45 μm technology. Compared with the classic model, the proposed novel small-signal model shows closer agreement with measured S-parameters in the range of 1.0 to 18.0 GHz.

A Series Impedance Reshaping Control Method Considering PLL Dynamics for Grid-Connected Inverters Under Weak Grid Conditions

Grid-connected inverters are the key part in renewable energy power generation systems. Usually, phase-locked loop (PLL) is adopted in grid-connected inverters to achieve synchronization. However, prior-art works have revealed that the negative resistance behavior in the low-frequency band caused by PLLs may lead to system instability under weak grids. In this paper, first, a comprehensive small-signal output impedance modeling of the LCL-filtered single-phase grid-connected inverter is derived for stability analysis, where the digital control delays and PLL dynamics have been taken into account. Then, a simple but effective virtual series based impedance reshaping method is proposed. With that, the inverter system can operate stably even under a very weak grid (e.g., short-circuit ratio (SCR) is as low as 1.2). Compared with the traditional grid impedance compensation by virtually increasing grid resistance or reducing the grid inductance, the proposed method does not require grid impedance estimation and is robust against system parameter variations. Thus, its feasibility is improved. Finally, experimental tests are carried out on a single-phase 5-kW prototype, validating the effectiveness of the proposed scheme.

Small-signal modeling comparison of dual active bridge converter

The dual active bridge (DAB) converter is a versatile DC-DC converter, which has AC components in the high-frequency transformer within the converter topology as well as DC components at the input and output sides. These AC components are constructed from infinite sinusoids of multiples of the converter's switching frequency. Different approaches have been proposed to model the DAB converter. The generalized averaging modeling (GAM) includes only the first order harmonic of the inductor current with the DC components of the input and output voltages and currents. For better model accuracy, harmonic-domain models have been employed, where the model includes all the harmonics of all the model state variables up to an arbitrary harmonic index. While the harmonic model provides a systematic approach to include the harmonics, this increases the model complexity. To avoid this complexity, the flexible harmonic model is used where harmonics can be selected per each state variable without needing to be in successive order. The aforementioned modeling approaches have been implemented on the DAB converter. This paper aims to compare between the dynamic performance of GAM and the harmonic modeling approaches under different disturbances, where the GAM approach provided a simple model with acceptable results that can be used for controller design, while the LTP model provided a more complex model with better accuracy that is suitable for harmonic studies. The models have been validated and compared using simulations executed on MATLAB /Simulink environment.

Direct observation of radio-frequency negative differential resistance in GaN-based single drift region IMPATT diodes

We report the direct observation of radio-frequency negative differential resistance, via on-wafer S-parameter measurements, in GaN-based impact ionization avalanche transit time (IMPATT) diodes. Clear signatures of reflection gain are observed from 18.7 to 30.6 GHz. These observations have been made possible by suppressing the reverse leakage current (and thereby parasitic shunt conductance) by optimization of the fabrication process, in conjunction with the use of pulsed measurements to suppress device self-heating. Consistent with avalanche-dominated behavior, the measured DC reverse bias current–voltage measurements show a positive temperature coefficient of breakdown. For the high-frequency on-wafer characterization, pulsed-bias S-parameter measurements with low (0.0067%) duty cycle were used to mitigate thermal effects. The measured avalanche frequency aligns closely with theoretical predictions based on Gilden and Hines' small signal model [Gilden and Hines, IEEE Trans. Electron Devices ED-13(1), 169–175 (1966)], measured impact ionization coefficients [Cao et al., Appl. Phys. Lett. 112(26), 262103 (2018)], and experimental saturation velocity measurements [Bajaj et al., Appl. Phys. Lett. 107(15), 153504 (2015)]; this excellent agreement confirms IMPATT operation and provides insights needed to further optimize device performance.

Stability analysis and control parameter optimization for AC-DC hybrid spot networks

AC-DC hybrid spot networks contain strong redundancy. It further enhances the power supply reliability of spot network systems and is helpful for the integration of distributed energy resources (DERs). However, there are few stability analysis studies of AC-DC hybrid spot networks. Focusing on the AC-DC hybrid spot network, which adopts a unified control strategy, its stability problem is studied in this article. A mathematical model of each unit is constructed for this system. Via linearization of spatial state equations, a small-signal model of the AC-DC hybrid spot network is established under different operation modes. Moreover, corresponding eigenvalue criteria are obtained, and the stability problem is analyzed by using the eigenvalue analysis method when the AC-DC hybrid spot network is subjected to a slight interference under the unified control strategy. The dominant factors of each eigenvalue are studied. Based on this approach, the influence of different control parameters on the system stability is demonstrated. Then, the control parameters are selected for control optimization. A simulation model is constructed in MATLAB/Simulink software. The eigenvalue criteria and simulation results validate the applicability of the small-signal model constructed in this article and the effectiveness of the optimization conclusions.

A compact Non-Quasi-Static small-signal model for GaN HEMT

In this work, we introduce a compact Non-Quasi-Static (NQS) model for the long-channel Gallium nitride high-mobility field effect transistor based on charge-based EPFL (École Polytechnique fédérale de Lausanne) HEMT model implemented in Verilog-AMS modeling language. The proposed model has been validated for the low-frequency (quasi-static) operating region as well as high frequencies up to sub-terahertz. This model has been derived from the analytical solution of the drift–diffusion and continuity equations based on physically valid assumptions. Polynomial approximation was used to make the model design-oriented and compatible with conventional circuit simulators for designing microwave circuits. Intrinsic trans-admittance parameters, obtained from the model for two devices with channel lengths of 1μm and 10μm has been validated with TCAD simulation results. Besides, the scattering parameters for the GaN HEMT equivalent circuit, have been validated with TCAD simulations and with our previous work, which already validated with experimental data. These results confirm the effectiveness of the proposed compact model for circuit simulations.

Simple Modeling and Analysis of Total Ionizing Dose Effects on Radio-Frequency Low-Noise Amplifiers

In this study, the degradation characteristics of radio frequency (RF)-low-noise amplifiers (LNA) due to a total ionizing dose (TID) is investigated. As a device-under-test (DUT), sample LNAs were prepared using silicon–germanium (SiGe) heterojunction bipolar transistors (HBTs) as core elements. The LNA was based on a cascode stage with emitter degeneration for narrowband applications. By using a simplified small-signal model of a SiGe HBT, design equations such as gain, impedance matching, and noise figure (NF) were derived for analyzing TID-induced degradations in the circuit-level performance. To study radiation effects in circuits, the SiGe-RF-LNAs fabricated in a commercial 350 nm SiGe technology were exposed to 10-keV X-rays to a total ionizing dose of up to 3 Mrad(SiO2). The TID-induced performance changes of the LNA were modeled by applying degradation to device parameters. In the modeling process, new parameter values after irradiation were estimated based on information in the literature, without direct measurements of SiGe HBTs used in the LNA chip. As a result, the relative contributions of parameters on the circuit metrics were compared, identifying dominant parameters for degradation modeling. For the TID effects on input matching (S11) and NF, the base resistance (RB) and the base-to-emitter capacitance (Cπ) of the input transistor were mostly responsible, whereas the transconductances (gm) played a key role in the output matching (S22) and gain (S21). To validate the proposed approach, it has been applied to a different LNA in the literature and the modeling results predicted the TID-induced degradations within reasonable ranges.

An Optimized Grid‐Forming Control Strategy for the Flexible Interconnection System in Distribution Transformer Areas

The flexible interconnection system (FIS) in distribution transformer areas can improve the local consumption capacity of high penetration rate distributed photovoltaics and solve the problem of the high loading rate of distribution transformers. This paper presents an optimized grid‐forming control strategy for the FIS in distribution transformer areas. First, the DC side impedance small signal model of the FIS is built, and the reason for the stability difference of the FIS is analyzed when the active power flows in different directions. An optimized control structure is then presented based on the conventional grid‐forming control strategy. The theoretical analysis shows that the optimized grid‐forming control strategy can improve the stability of the FIS. Finally, the controller hardware‐in‐the‐loop experiments based on RT‐LAB confirm the effectiveness of the presented optimized control strategy. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Smooth Transition Control Strategy for Operation Modes of Optical Storage Microgrid based on VSG

Addressing the challenge of suppressing voltage and frequency oscillations during mode transitions and achieving smooth transitions between grid-connected and islanded operation modes in peer-to-peer structured optical storage microgrids, is an urgent technical issue. This paper proposes a control strategy for smooth mode transitions based on numerical soft starters, focusing on the dynamic characteristics of voltage and frequency in optical storage microgrids during grid-connected and islanded operation modes. The numerical soft starter smoothens the input reference value of the current inner loop, reducing the impact of transient surge current on the current inner loop during transitions, thus ensuring the oscillations of bus voltage and frequency during microgrid mode transitions. In islanded operation mode, a VSG control strategy is introduced by constructing a small signal model to analyze the frequency response characteristics of the system under different inertia and damping characteristics, setting appropriate control parameters to provide strong frequency support for the system during islanded operation. Finally, an optical storage microgrid system is established using Matlab/Simulink to conduct simulation experiments under conditions such as grid-connected/islanded mode transitions, load fluctuations, and sudden changes in photovoltaic output power, validating the effectiveness of the proposed smoothing strategy.

Research on additional damping control strategy of flexible distribution transformer

Disturbances to the power system may lead to relative swing between synchronous generator rotors, causing low-frequency oscillation problems in the absence of damping. In this article, based on the single-machine infinity system containing flexible distribution transformer and synchronous generator, the linearized state equations of the system is deduced by the small-signal modeling. The mechanism of flexible distribution transformer on the rotor speed of synchronous generator is analyzed. The influence factors of flexible distribution transformer on the rotor speed of synchronous generator are analyzed. The equation of the additional damping provided by the flexible distribution transformer to this system is constructed. It was concluded that by controlling the output voltage of the regulating converter in the flexible distribution transformer, the rotor speed of the synchronous generator can be varied to increase the system damping. An additional damping control strategy for flexible distribution transformer is proposed. The simulation verifies that the proposed control strategy can effectively suppress the oscillation amplitude of each electrical quantity and shorten the oscillation duration when the system is subjected to large and small perturbations. The proposed additional damping control strategy of flexible distribution transformer can effectively improve the damping of the system and alleviate the problem of low frequency oscillation.

Analysis of Grid-Connected Stability of VSG-Controlled PV Plant Integrated with Energy Storage System and Optimization of Control Parameters

In the static stability analysis of the grid-connected photovoltaic (PV) generation and energy storage (ES) system, the grid-side is often simplified using an infinite busbar equivalent, which streamlines the analysis but neglects the dynamic characteristics of the grid, leading to certain inaccuracies in the results. Furthermore, the control parameter design does not consider the coupling relationships among parameters, resulting in arbitrary values and the inability to achieve overall optimality. To address these issues, this paper presents a comprehensive parameter optimization method for the oscillation characteristics of grid-connected PV generation and ES systems in various frequency ranges. Firstly, a detailed modeling of the grid-connected PV generation and ES system is conducted, resulting in the derivation of the system’s small-signal model. This study investigates the impact of parameters related to PV arrays, ES units, and the virtual synchronous generator (VSG) on the system’s characteristic roots using participation factors, sensitivity analysis, and eigenvalue root trajectories. Subsequently, based on the analysis of system root trajectories and the Particle Swarm Optimization (PSO) algorithm, a holistic parameter optimization design method for the system’s oscillation modes is proposed, and the parameter optimization results are obtained. Finally, the accuracy of the theoretical analysis is validated through perturbation testing using both Matlab/Simulink models and the small-signal model.

PI Current Controller Design for DC Drive System using 4- Quadrant DC-DC Converter and 3- Phase Rectifier

DC Motors is considered one of the important machines in control systems such as industrial robots, vehicles, and process control. Current control of a DC drive is very desirable because by controlling the current, the torque is controlled. Moreover, current control can be used to prevent large damaging armature currents during start-up. A good current loop is very important when setting up a DC drive. When the control of the current loop is good, the steady state motor current should respond exactly with the reference current, and the transient response to the step change in the reference current should be fast and well-damped. This paper presents two different types of current controller converters that are commonly used in DC motor drives. The first converter is a 4-quadratic switch-mode DC-DC converter, while the second controller is a 3-phase controller rectifier. Both current converters were simulated using Matlab Simulink, where a PI current controller for the inner loop current control DC motor controls these converters. The PI controller was designed based on the Bode plot frequency response method. In this research, the design procedure was based on the small signal model and then, verified using a large signal model. The simulation result showed that the performance using a 4-quadrant DC-DC converter gave better performance than a 3-phase rectifier.

Stability modeling of MMC-HVDC transmission system with differential flat control

AC asymmetry grid conditions put forward higher requirements for the stability control and performance of MMC-HVDC transmission systems. This thesis proposes a small-signal modeling method of an MMC-HVDC transmission system with differential flat control for AC asymmetry grid conditions, incorporating dynamic models of MMC internal characteristics, new control systems, circulation suppressors, and DC lines. To prove the accuracy of the pre-sended small-signal model, a two-terminal MMC-HVDC test system with differential flat control is constructed on the PSCAD/EMTDC platform.