Small-signal Modeling Method Research Articles

A Small-Signal Modeling Method for LLC Resonant Converter Based on Time-Domain Correction

A Small-Signal Modeling Method for <i>LLC</i> Resonant Converter Based on Time-Domain Correction

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.

Small Signal Modeling of LLC Converter with LED Load and Quasi-Resonant Controller Based Active Ripple Rejection

This paper has analyzed the defects of the traditional extended description function (EDF) based LLC small signal modeling method when driving light emitting diode (LED) load and proposed an accuracy improvement method. Detailed small signal model modeling methods have been deduced, and the accuracy of different modeling methods has been compared thoroughly. To suppress the second-order harmonic ripple in the direct current link-induced output current ripple, a quasi-resonant controller (QRC) is adopted to realize active ripple rejection (ARR). Considering the frequency of the second-order harmonic ripple changes with the grid voltage frequency, a single-phase software phase lock loop (SPLL) is adopted to extract the frequency of the second-order harmonic. By dynamically regulating the control parameter of the QRC according to the locked second-order frequency, output voltage ripple active rejection ability immune to grid voltage frequency deviation is obtained. Based on the deduced accurate small signal model, the digital controller is designed with stability, steady state and dynamics performance guaranteed. The accuracy of the proposed small signal model, the SPLL and the QRC-based ARR method has been verified at last.

MODELING AND CHARACTERISTIC ANALYSIS OF FRACTIONAL-ORDER BOOST CONVERTER BASED ON THE CAPUTO–FABRIZIO FRACTIONAL DERIVATIVES

This paper presents a novel approach for modeling Boost converters using the Caputo–Fabrizio (C-F) definition-based fractional-order model to address singular characteristics in fractional-order definitions and enhance model accuracy. A small signal modeling method is proposed to improve the accuracy of circuit parameter design and to derive state-averaged models, state-space equations, and transfer functions. The influence of capacitor and inductor orders on steady-state characteristics is analyzed and the influence of fractional-order on ripple characteristics is investigated through simulation. When the fractional-order approaches 1, the output voltage increases and the inductance current decreases, with waveform jitter mitigation. Moreover, boundary conditions for continuous conduction mode operation are established based on ripple characteristics. The numerical and circuit-oriented simulations verify the correctness of the proposed model. Finally, the orders and accurate parameters of capacitors and inductors based on the C-F definition are determined and the experiments are conducted. The comparison between the experimental and simulation results demonstrates that the proposed model can accurately describe the steady-state characteristics of the practical circuit systems, which further validates the accuracy of the proposed method.

Global Stability Analysis for Synchronous Reference Frame Phase-Locked Loops

This article analyzes the global stability of synchronous reference frame phase-locked loops (SRF-PLLs) from a large signal viewpoint. First, a large-signal model of SRF-PLL is accurately established, without applying any linearization method. Then, according to the phase portrait and Lyapunov argument, the global performance of SRF-PLL is discussed in the nonlinear frame. Compared with the small-signal analysis methods, the proposed analysis, not relying on the small-signal model and linearization method, provides a global discussion of the SRF-PLL performance. The contributions of this article are as follows. First, it is found that SRF-PLL has infinite equilibrium points, including stable points and saddle points. Second, it provides a way to divide the global region of SRF-PLL into many small regions. In each small region, the SRF-PLL only has one stable equilibrium point. And for any initial states <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\tilde{\theta }(t_0),\tilde{\omega }(t_0))$</tex-math></inline-formula> in a small region, all states <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\tilde{\theta }(t),\tilde{\omega }(t)),t&gt;t_0$</tex-math></inline-formula> will remain in this small region, and SRF-PLL will converge to the unique stable equilibrium point of this small region. Third, by dividing the global region of SRF-PLL into many small regions, it is found that when the frequency of grids varies largely, the SRF-PLL will converge to a new equilibrium point that is far away from the original equilibrium point. It is the reason why the frequency convergence of SRF-PLL has many oscillations and SRF-PLL has a rather slow dynamic, when the frequency changes largely. The experimental results are provided to verify the proposed global stability analysis of SRF-PLL.

A distributed and integrated control strategy for an islanded microgrid considering line loss and communication interruption

To improve the stability and economic operation performance of multi-distributed energy resources in networked islanded microgrid, a distributed and integrated control strategy is designed in this study. The strategy is based on the communication network in an islanded microgrid, which is able to achieve minimal generation cost, reliable communication, and stable voltage and frequency. These targets are achieved through the following methods. Firstly, a power regulation part is combined with droop controller to constitute an improved primary control, which can take the line loss factor into account and adjust the output power of each distributed energy resource to its optimal value. Secondly, an optimal path reconstruction method and a Kalman filter estimation method with sliding mode controller are developed to address the communication interruption problem in communication channels and output channels, respectively. In the end, the secondary controller is used to regulate voltage and frequency, and a small signal model method is applied to analyze the impact on the whole system when these designs are applied. The effect of the proposed strategies has been verified by the related case studies.

An electromagnetic simulation assisted small signal modeling method for InP double-heterojunction bipolar transistors

We present a convenient and practical electromagnetic (EM) assisted small-signal model extraction method for InP double-heterojunction bipolar transistors (DHBTs). Parasitic parameters of pad and electrode fingers are extracted by means of 3D EM simulation. The simulations with a new excitation scheme are closer to the actual on-wafer measurement conditions. Appropriate simulation settings are calibrated by comparing measurement and simulation of OPEN and SHORT structures. A simpler π-type topology is proposed for the intrinsic model, in which the base-collector resistance Rμ , output resistance R ce are deleted, and a capacitance C ce is introduced to characterize the capacitive parasitic caused by the collector finger and emitter ground bar. The intrinsic parameters are all extracted by exact equations that are derived from rigorous mathematics. The method is characterized by its ease of implementation and the explicit physical meaning of extraction procedure. Experimental validations are performed at four biases for three InGaAs/InP HBT devices with 0.8 × 7 μm, 0.8 × 10 μm and 0.8 × 15 μm emitter, and quite good fitting results are obtained in the range of 0.1–50 GHz.

Stacked Buck Converter: Current Ripple Elimination Effect and Transient Response

To balance the cost and volume when applying a low output current ripple, the power supply design should be able to eliminate the current ripple under any duty cycle in medium and high switching frequencies, and considerably reduce filter volume to improve power density. A stacked buck converter was eventually selected after reviewing the existing solutions and discussing their advantages and disadvantages. A stacked buck converter is used as a basis to propose the transient response and output current ripple elimination effect, boundary limit control method, and low output ripple dead time modulation method to make individual improvements. The principle, mathematical derivation, small-signal model, and compensator design method of the improvement method are presented in detail. Moreover, simulation results are used to mutually verify the correctness and effectiveness of the improvement method. A stacked buck converter with 330-V input, 50-V output, and 1-kW output power was implemented to verify the effect of the low output current ripple dead time modulation. Experimental results showed that the peak-to-peak value of the output current ripple was reduced from 2.09 A to 559 mA, and the RMS value was reduced from 551 mA to 91 mA, thereby effectively improving the output current ripple.

A fast small signal modeling method for GaN HEMTs

An accurate and efficient parasitic parameter extraction method is proposed for gallium nitride (GaN) high electron-mobility transistors (HEMTs). In this letter, a 19-element small signal equivalent circuit model is established to describe the characteristics of the device precisely. The simulation of the high frequency behavior is improved by introducing the series parasitic inductances into the cold pinch-off model. Through matrix transformation and equation derivation, the influence of Cpda and Cpga on parameter extraction is evaluated. It is proved that the error caused by Cpga and Cpda to the parameter extraction is less than 3%. Ignoring these influences can not only simplify parameter calculation, but also ensure its accuracy. The parasitic capacitances and parasitic inductances can be obtained simultaneously, improving the efficiency and the accuracy of parameter extraction. Meanwhile, accurate and ideal initial values are provided for the subsequent parameter optimization. Because of the accuracy of the initial values, parameter optimization eliminates the error caused by previous steps, and does not need multiple iterations, which improves the efficiency of the model parameter extraction. Compared with the traditional extraction method, the method in this letter can fast and accurately obtain the values of parameters. The simulated results show good agreement of scattering parameters up to 40 GHz.

Small-Signal Model and Dynamics of MMC-HVDC Grid Under Unbalanced Grid Conditions

Small-signal models (SSM) of modular multilevel converter (MMC) based HVDC grid under unbalanced grid conditions in recent literatures do not consider interactions between MMC and dc network. Therefore, it is necessary to correctly model the double-fundamental-frequency zero-sequence circulating currents (DFF-ZSCC) existing under unbalanced grid conditions, although they can be suppressed to avoid penetrating into dc side. In view of that, a general and modular small-signal modeling method of MMC-HVDC grid under unbalanced grid condition is developed. Firstly, a general d-q transformation process for multi-sequence and multi-frequency components is introduced to build the state-space model of MMC electric part in d-q frame. Secondly, the SSM of dc network, which is divided into dc- and double-fundamental-frequency parts, is developed based on the existing frequency-dependent-cascaded-pi (FDC-PI) cable model. Then, to interface MMC stations with dc network under unbalanced grid conditions, a general method to synchronize the variables of double fundamental frequency at dc side of each MMC station is introduced to compose the SSM of the entire HVDC grid from SSMs of each MMC and dc network. Finally, taking a three-terminal MMC-HVDC grid as an example, two SSMs of the MMC-HVDC grid with FDC-PI cable model and single-PI cable model are developed in Matlab, respectively. The small-signal dynamics and stability of both SSMs of the grid under unbalanced grid conditions are compared to validate the accuracy and stability of the proposed SSM of the whole HVDC grid. The simulation results validate the correctness and effectiveness of the proposed modular modeling method.

Z-domain modeling of peak current mode control for full-bridge DC-DC buck converters

Traditional local-averaged state-space modeling for peak current mode (PCM) controls fails to explain the subharmonic oscillation phenomenon when the spectrum is higher than half of the switching frequency. To address this problem, this paper presents a small-signal modeling method in the z-domain, and builds a discrete linear model for the current loop of a full-bridge DC-DC converter. This discrete model is converted into a second-order continuous model that is able to represent the system performance with a wider frequency range. A frequency-domain analysis shows that this model can be used to explain the subharmonic oscillations and unstable characteristics. This provides an engineering guideline for the practical design of slope compensation. The effectiveness of the proposed modeling method has been verified by simulation and experimental results with a prototype working in the Buck mode.

A Novel High-Gain DC-DC Converter Applied in Fuel Cell Vehicles

The DC-DC converter for fuel cell vehicles should be characterized by high-gain, low voltage stress, small size and high-efficiency. However, conventional two-level, three-level and cascaded boost converters cannot meet the requirements. A new non-isolated DC-DC converter with switched-capacitor and switched-inductor is proposed in this paper, which can obtain high-gain, wide input voltage range, low voltage stresses across components and common ground structure. In this paper, the operating principle, component parameters design, and comparisons with other high-gain converters are analyzed. Moreover, the state-space averaging method and small-signal modeling method are adopted to obtain the dynamic model of converter. Finally, simulation and experimental results verify the effectiveness of the proposed topology. The input voltage of the experimental prototype ranges from 25 V to 80 V. The rated output voltage is 200 V and rated power is 100W. The maximum efficiency is 93.1% under rated state. The proposed converter is suitable for fuel cell vehicles.

Stability Analysis of Constant Current-Controlled Primary-Side Regulation Flyback Converter

In low power applications, primary-side regulation (PSR) flyback converter with discontinuous conduction modulation (DCM) mode is widely used to realize constant output current for its simple structure and low cost. In peak current control method, the output current can be predicted from the primary peak current, demagnetization time, and switching period. Based on the current prediction, a pulsewidth modulation (PWM) mode and a pulse frequency modulation (PFM) mode are used. However, as the output current cannot be sampled directly in PSR flyback converter, traditional small-signal modeling method based on the control and output variables cannot be used. Moreover, there is no stability analysis for these constant current (CC)-controlled PSR flyback converters. In this article, a discrete matrix analysis method is proposed to analyze the stability of CC-controlled PSR flyback converter. An iterative matrix of the control and output variable perturbations is obtained, and the stability can be acquired from the eigenvalues. Oscillation occurs in the above PWM mode, and a stable control is realized in PFM mode. An improved PWM mode is thus proposed and analyzed for stable control. The analysis is verified in a PSR flyback converter with 1.92 A.

A Photovoltaic-Based DC Microgrid System: Analysis, Design and Experimental Results

Due to the exhaustion of fossil energy, the utilization of renewable energy resources is developing quickly. Due to the intermittent nature of the renewable energy resources, the energy storage devices are usually adopted in renewable power generation system to enhance the system reliability. In this paper, the photovoltaic-based DC microgrid (PVDCM) system is designed, which is composed of a solar power system and a battery connected to the common bus via a boost converter and a bidirectional buck/boost converter, respectively. As the photovoltaic (PV) panels might operate in a maximum power point tracking (MPPT) mode or constant voltage mode, meanwhile, the power can flow between the battery and the load bidirectionally. Therefore, for the sake of optimizing power utilization in the PVDCM system, a control strategy making the system able to switch from one operating mode to another smoothly and automatically is proposed in this paper. Moreover, the small-signal modeling method based on averaged state-space is no more applicable in this study, thus the nonlinear analysis method with discrete-time mapping model is adopted for stability analysis. Based on the stability analysis, the closed-loop parameters are designed to make sure the whole system can operate properly in all operating modes. The control strategy and stability analysis based on the nonlinear analysis method in the closed-loop design are verified by experiment results.

A Novel VSG-Based Accurate Voltage Control and Reactive Power Sharing Method for Islanded Microgrids

Islanded microgrids (IMGs) are more likely to be perturbed by renewable generation and load demand fluctuation, thus leading to system instability. The virtual synchronous generator (VSG) control has become a promising method in the microgrids stability control area for its inertia-support capability. However, the improper power sharing and inaccurate voltage control problems of the distributed generations (DGs) in microgrids still has not been solved with a unified method. This paper proposes a novel VSG equivalent control method named Imitation Excitation Control (IEC). In this method, a multi-objective control strategy for voltage and reactive power in a low voltage grid that considers a non-negligible resistance to reactance ratio (R/X) is proposed. With the IEC method, the voltage drop across feeders is compensated, thus the terminal voltage of each inverter will be regulated, which will effectively stabilize the PCC (point of common coupling) voltage and inhibit the circular current. Meanwhile, this method can realize accurate reactive power tracking the reference value, making it accessible for reactive power scheduling. What is more, the reasonability of the IEC model, namely the equivalent mechanical characteristic and transient process inertia support between VSGs and conventional synchronous generators (SG), is illustrated in this paper. Moreover, steady-state stability is proved by the small-signal modeling method, and the energy required by inertia support is given. Finally, the simulation result validates the effectiveness of the proposed method, and it is also demonstrated that the proposed method outperforms the conventional droop control method.

Research on Composite Control Strategy of Quasi-Z-Source DC–DC Converter for Fuel Cell Vehicles

The DC–DC converter for fuel cell vehicles requires high gain and wide voltage input range to boost the voltage of the fuel cell. However, with the traditional boost converter, it is difficult to meet the requirements of the fuel cell vehicle power system. Based on a quasi-Z-source network DC–DC converter, this paper proposes a composite controller, which includes a feedforward compensation network and feedback control to meet the control robustness requirement of the fuel cell vehicle power system. The dynamic model of the converter is obtained by using the state space averaging method and the small-signal dynamic modeling method. The input voltage and load disturbance experiments are performed on the DC–DC converter. Moreover, the converter is tested under the worldwide harmonised light vehicle test procedure (WLTP) to validate the effectiveness of the proposed composite controller. The simulation and experiment results show that the proposed composite controller effectively enhances the converter’s ability to resist input and load disturbance, and improves the dynamic response performance of the DC–DC converter for fuel cell vehicles.

H∞ Mixed Sensitivity Control for a Three-Port Converter

The three-port converter (TPC) obtains major attention due to its power density and ability to dispose different electric powers flexibly. Since the control models of the TPC are derived from particular steady state work point through small signal modeling method, the model parameters usually be deviated from their normal values with the change of operation and load conditions. Furthermore, there are couplings and interactions in power delivery between different ports, which have a significant influence in the dynamic control performance of the system. In this paper, the H∞ mixed sensitivity method is employed to design robust controllers for a TPC control system. Simulation results are given to demonstrate the effectiveness of the proposed scheme, and experimental studies are conducted on a prototype circuit to further validate the developed method. Compared to a traditional PI controller, it shows that a mixed sensitivity based robust controller manifest balanced performance in model parameters changes attenuation and dynamic control performance.

Small-Signal Modeling of the LLC Half-Bridge Resonant Converter

This paper proposes a small-signal modeling method for building an LLC half-bridge resonant converter. In recent years, the LLC half-bridge resonant converter has attracted the attention of many researchers because of its high-power conversion efficiency and high-power density. Generally, the LLC half-bridge resonant converter consists of many passive components, including stray and parasitic elements, resulting in a high-order system. Because the fundamental harmonic approximation (FHA) method for an LLC resonant converter only considers the fundamental harmonic and neglects higher harmonics, it is not accurate and introduces large errors in a higher-order system. In this paper, according to the operation principle of the LLC half-bridge resonant converter, a small-signal model is established. Based on the small-signal model, the input-to-output and control-to-output transfer function is derived. The experimental result verified that the proposed model yields a high accuracy, thereby highlighting the usefulness and versatility of the proposed model over other existing models.

(Invited) High-Speed GaN-Based Micro-Scale Light-Emitting Diodes for Visible-Light Communication

The increasing demand for wireless data communication and popularity of solid-state lighting has prompted research into visible-light communication (VLC) systems using GaN-based light-emitting diodes (LEDs). VLC is a promising candidate for next-generation (5G and beyond) light-fidelity (Li-Fi) network systems. To support multi-Gb/s data rates, VLC systems will require efficient LEDs with large modulation bandwidths. Conventional lighting-class LEDs cannot achieve high-speed operation due to their large chip size, large active region volume, and phosphor-converted output. Conversely, micro-scale LEDs (micro-LEDs) offer a viable path to high-speed operation due to their lower parasitic capacitance and ability for operation at high current densities where the carrier lifetime is significantly reduced. Furthermore, conventional c-plane LEDs suffer from polarization-related electric fields, which reduce the overlap between the electron and hole wave functions and lower the carrier recombination rate. Since modulation bandwidth is proportional to the carrier recombination rate (inversely proportional to the carrier lifetime), the overlap between the wave functions should be maximized for high-speed operation. Nonpolar and semipolar orientations have significantly reduced polarization effects and wave function overlaps approaching unity. These orientations can enable high-efficiency LEDs with simultaneously large modulation bandwidths, especially at relatively low current densities. In this work, we introduce VLC and discuss progress on the growth, fabrication, and characterization of high-speed micro-LEDs. Polar (0001), nonpolar (1010), and semipolar (2021) InGaN/GaN micro-LEDs on free-standing GaN substrates are investigated for their small-signal modulation characteristics as a function of current density, temperature, device area, and active region design. We demonstrate that the modulation bandwidths are well correlated with the wave function overlap in the active region by examining the orientation-dependence of the bandwidth. Record modulation bandwidths for GaN-based LEDs above 1 GHz are achieved for the nonpolar and semipolar orientations. We also show the modulation characteristics of an electrically injected nanowire-based LED, which achieves a modulation bandwidth of 1.2 GHz. Finally, we present a small-signal modeling method for determining the RC characteristics, differential carrier lifetime, carrier escape lifetime, and injection efficiency of the LEDs under electrical injection and discuss the results in the context of efficiency droop. Figure 1: Bandwidth vs. current density for the nonpolar LEDs (open black triangles), semipolar LED (open blue circles), and polar c-plane LED (open green squares) compared to other reported polar c-plane LEDs on sapphire or with a flip-chip design and compared to semipolar (1122) LEDs. The bandwidth characteristics for a nanowire-based LED are also included. Also shown are the crystal orientations used in the orientation-dependent bandwidth study. Figure 1

Stability Analysis Method of Parallel Inverter

In order to further provide theoretical support for the stability of an auxiliary inverter parallel system, a new model which covers most of control parameters needs to be established. However, the ability of the small-signal model established by the traditional method is extremely limited, so this paper proposes a new small-signal modeling method for the parallel system. The new small-signal model not only can analyze the influence of the droop parameters on the system performance, but also can analyze the influence of the output impedance of the inverter, the unbalanced and nonlinear loads, and the power calculation method and cut-off frequency of the low-pass filter on the system performance and stability. Based on this method, this paper carries out a comprehensive analysis on the performance of a parallel inverter system. And the correctness of the modeling method and analysis process of the system performance and stability are verified by the consistency of the simulation and experimental results.