Accurate Small-signal Model Research Articles

Small-signal behavioral-level modeling of InP HBT based on SO-BP neural network

In this paper, Snake Optimizer-Back Propagation (SO-BP) neural network algorithm has been proposed to model the small-signal characteristic of InP heterojunction bipolar transistors (HBTs). The SO algorithm can effectively improve the problem of local optima encountered by the BP neural network algorithm. The InP HBT small-signal models have been constructed by using Back Propagation (BP) algorithm, the Genetic Algorithm-Back Propagation (GA-BP) algorithm and the Snake Optimizer-Back Propagation (SO-BP) algorithm. The experimental results verify that the proposed SO-BP neural network algorithm model has the lowest error rate between simulated and measured data. Hence, the SO-BP algorithm is a more effective approach for modeling the small-signal characteristic of InP HBT. The accurate small-signal behavioral-level model of HBT has significant reference value for the application of microwave and millimeter-wave integrated circuits (MMICs).

Envelope-Detection-Based Accurate Small-Signal Modeling of Series Resonant Converters

Resonant converters have many desirable characteristics such as high efficiency, low component count and low electromagnetic interference production. The resonance phenomenon that enables this also makes their design and control a challenging process. Attempts have been made to determine the small signal control to output dynamics for resonant converters, however they either involve complex mathematics or numerical solutions which do not provide much insights and make it difficult to design controllers. This paper uses Fundamental Harmonic Approximation to model the different stages of Series Resonant Converter. Herein the small signal perturbations in control variable i.e. the switching frequency, result in perturbations in inductor current envelop that is analysed in the Laplace Domain. This current envelop is then used to analytically derive the control to output transfer function for the Series Resonant Converter. The modeling process is verified and validated by comparing the analytical frequency response with that obtained from Simulink simulation and experimental results. For wide output voltage application designs, the system performance and stability vary with the changing operating point. An example demonstrating the utility of the developed model in analysing such systems is also presented.

A SOGI-based adaptive controller design for second-harmonic currents suppression of variable frequency loads in DC buildings

DC buildings with integrated DC transformers (DCTs), as a typical representative of photovoltaics, energy storage, direct current, and flexibility (PEDF) building systems, are a crucial approach to reducing carbon emissions. Heating, ventilation, and air conditioning (HVAC) systems are typical loads in DC buildings that primarily aim to enhance the air quality and thermal comfort. However, the variable frequency drives (VFDs) used in HVAC systems can generate second-harmonic currents (SHC), which decrease equipment reliability and system power efficiency. To prevent SHC on the low-voltage side from flowing to the high-voltage bus, even in the grid, a second order generalized integrator (SOGI)-based adaptive controller for suppressing the SHC of variable frequency loads in DC buildings is proposed. The controller employs a phase-locked loop (PLL) to provide feedback on the VFD output frequency to the DCT control loop's notch filter, enabling adaptive suppression of the variable frequency SHC. Firstly, an accurate small-signal model of DCT based on Fourier series is established, which considers the inductor current. Then, the formula for DCT equivalent impedance is derived based on the model, and the feasibility of suppressing the SHC by increasing the equivalent impedance at variable frequency is analyzed. To enhance the stability of DC buildings, the parameters of the controller are designed to improve dynamic performance. Finally, the simulation results and experimental results verify the effectiveness and feasibility of the proposed adaptive controller compared to other suppression strategies.© 2017 Elsevier Inc. All rights reserved.

Accurate Small-Signal Terminal Characteristic Model and SISO Stability Analysis Approach for Parallel Grid-Forming Inverters in Islanded Microgrids

This paper derives a small-signal terminal characteristic model for the grid-forming inverter with droop-control in the synchronous reference ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -) frame, accurately covering the dynamics of the power controller, the voltage and current control loops and all circuit components, where a new set of terminal characteristics is proposed to characterize the small-signal dynamics of fundamental frequency introduced by the fundamental frequency-active power droop scheme. Based on the terminal characteristics of individual inverters, the stability of parallel grid-forming inverters can be predicted by the generalized Nyquist criterion (GNC). Furthermore, to simplify the stability analysis process and reduce calculation complexity, a single-input single-output (SISO) stability analysis approach is proposed by exploring the interaction among the droop-control of parallel inverters through analyzing mathematical feature of proposed terminal characteristic model of individual inverters as well as the return ratio of the parallel inverters, which uses <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d-d</i> channel element of system return ratio matrix and Nyquist criterion to predict the stability. Finally, simulation and experimental results validate the effectiveness of proposed small-signal model and SISO stability analysis approach.

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.

A Closed-Loop High-Frequency Current Shaping Method to Achieve Trapezoidal Transformer Current in a Current-Fed Dual Active Half-Bridge Converter for Minimum RMS Current and Wide-Range ZVS

This article proposes the use of primary and secondary side duty ratio control along with the phase shift control in a current-fed dual active half-bridge (DAHB) converter to achieve trapezoidal transformer current, which results in zero voltage switching (ZVS) of all the switches and minimum rms current even at light loads, for a wide range of input voltage. The high-frequency transformer current is directly sensed at specific transition instants by a delay-adjusted sampling strategy to be used as control variables in a current control structure. This is better because the voltage control of capacitor voltages would have required more expensive sensors. A simple and accurate small-signal model of the converter is developed, and the relevant transfer functions are derived. The controller design details are provided. Finally, experimental results on a 1-kW laboratory prototype demonstrate the effectiveness of the closed-loop duty ratio control in achieving trapezoidal transformer current resulting in improved efficiency and ZVS of the switches, compared to a simple phase shift control.

Accurate High-Frequency Modeling of the Input Admittance of PWM Grid-Connected VSCs

This article addresses high-frequency admittance modeling of current-controlled voltage source converters (VSCs). Recent studies have shown that harmonic instability may also occur at frequencies above the Nyquist frequency. To form an accurate multiple-frequency model in this frequency range, sidebands that originate from modulation and sampling must be examined. In this article, an accurate small-signal model is developed taking into account an adequate digital pulsewidth modulator (DPWM) representation, which allows to predict dependence of the frequency response on the steady-state dc (SS-dc) operating point. It is shown that when center-pulse sampling is implemented, pulsewidth modulation sidebands do not create additional loops leaving only sampling sidebands to be considered. Using the same approach as for SS-dc operation, a model that accurately represents admittance measurements during sinusoidal ac (S-ac) operation is developed. Its basis is a novel DPWM model suitable for S-ac regime, which allows to predict dependence of the VSC’s input admittance on the grid voltage magnitude. Experimental and simulated admittance measurements, performed on a single-phase two-level VSC during various SS-dc and S-ac regimes, match with the proposed models up to twice the sampling frequency.

Accurate Small-Signal Modeling and Stability Analysis of Wide-Input Buck Converter Considering Modulation Waveform Ripples

Buck converters are widely used in consumer electronics, electric vehicles, and dc microgrids. Small-signal models are necessary tools to design high-quality controllers. However, most of them neglect modulation waveform ripples, which introduces significant errors under high-bandwidth controls. Recently, two models explain the influences of nondifferentiable modulation waveform ripples by their left-side derivatives at crossing points. However, this conclusion is built on the premise that infinite sideband components caused by switching have been considered, which largely complicates these models. The accurate small-signal model with finite sideband components is proposed for nondifferentiable modulation waveform ripples in this article. Based on it, the stable working region and control design of wide-input high-bandwidth Buck converters are talked about. Simulations and experiments validate the accuracy and effectiveness of the proposed model.

Small-Signal Model of an Inductive Power Transfer System Using LCC–LCC Compensation

The LCC–LCC compensation is widely used in the inductive power transfer systems. However, there is no simple and accurate small-signal equivalent circuit model for this resonant converter. Based on the extended describing function method, this article proposed a full-order (17th-order) equivalent circuit model to accurately predict the small-signal behaviors. For simplification, the full-order model is gradually simplified to a ninth-order model and finally to a fifth-order model. The input to output transfer function are analytically derived for the first time. Both simulation and experimental results are presented to justify the effectiveness of the model, and the model is accurate up to one-fifth of the switching frequency.

A phase-locked loop with an improved dynamic response under abnormal grid conditions

The cascaded delayed signal cancelation (CDSC) method has attracted much attention recently as an efficient filtering technique to improve synchronous reference frame phase-locked loop (PLL) performance in grid synchronization under adverse grid conditions. The CDSC-based PLL suffers from slow transient response. Therefore, this study proposes a solution for grid synchronization under abnormal conditions utilizing an arbitrary time-delay operator to mitigate the DC offset and frequency adaptive CDSC operators for harmonic filtering. An accurate small-signal model was derived, opening the door to design the loop filter. The coefficient diagram method was adopted to systematically design the gains of the proportional–integral controller and a lead–lag compensator, yielding a faster dynamic response than the symmetrical optimum method-based design. The proposed PLL effectiveness was verified numerically under abnormal conditions, showing better dynamic and steady-state performance than other related PLLs. The proposed PLL requires less than two grid cycles to synchronize without ripples, meeting the grid code's requirement.

An Accurate Small Signal Dynamic Model for LCC-HVDC

This paper develops an accurate small signal model for line commutated converter based HVDC (LCC-HVDC). The overall process of the model establishment is demonstrated from five parts: AC system, DC system, control system, phase-locked loop (PLL) and the converter. Considering the limitations of the traditional converter equations, the proposed small signal model takes the commutation process into account so that the overlap angle and AC current are calculated with the actual value rather than the estimated value. The accuracy of the proposed model is verified both in the time-domain simulation in PSCAD/EMTDC and by eigenvalue analysis. The results show better performance than the traditional modeling methods, which provides valuable guidance for future LCC-HVDC project design.

A Simple, Accurate Small-Signal Model of a Coupled-Inductor-Based DC-DC Converter Including the Leakage Inductance Effect

This brief proposes a method to dynamically modeling the coupled-inductor double-boost converter operating in continuous-conduction mode. Such method has the advantage of including the leakage inductance effect on the dynamic behavior of the converter in a simple, straightforward approach. The presence of the leakage inductance is initially neglected and a traditional circuit-averaging technique is used. The averaged models are then refined by accounting the impacts of the reported inductance. Since its major impact is on the damping factor of the system, this dynamic change is modeled by equivalent resistors. Equations for describing the equivalent resistors are derived based on the analysis of the duty cycle loss caused by leakage inductance in the static gain of the converter. The effect on the averaged small-signal model is shown by a closed-form control-to-output transfer function and experimental results demonstrate its accurate performance.

Small-Signal Stability Analysis for Multi-Terminal LVDC Distribution Network Based on Distributed Secondary Control Strategy

This paper presents a detailed and accurate small-signal analysis model for a four-terminal low-voltage direct current (LVDC) distribution network with distributed secondary control strategy. To tackle the contradiction between power sharing accuracy and average voltage recovery ability of voltage source converters (VSCs), a distributed secondary control strategy is adopted, which is based on average consensus algorithm and local voting protocol. Furthermore, to analyze the stability of LVDC distribution network based on the proposed distributed secondary control strategy, a detailed and accurate small-signal analysis model is formulated which is derived from various non-linear state-space sub-models. The time-domain simulation and electromagnetic simulation are carried out to verify the validity and accuracy of the proposed model. Based on this model, the influence rules of main eigenvalues are summarized with the variation of PI control and DC line parameters. Time-domain simulations conducted in PSCAD are used to validate the operational limits of the secondary controllers and DC line obtained from the small-signal stability analysis.

A new control strategy applied in X-ray source to improve imagining quality

ABSTRACT Image quality of X-Ray tubes will deteriorate with age. Experiment shows that the rise time of long-term service X-Ray source is long, leading to decrease in image black and white contrast. In order to acquire good consistency of image quality, the control parameters must be modified with service time. However, small signal model of X-ray sources is uncertain. Thus, it’s necessary to acquire accurate small signal model of system online. Then two types of software phase lock loop (SPLL) are proposed for online small signal model estimation of system with X-Ray tube: SPLL with notch filter and SPLL based on synchronous reference frame. More accurate online small signal model can be obtained by employing the latter method. Next piece-wise proportional integral (PI) control strategy based on online small signal model estimation of system with X-Ray tube is proposed to ensure that X-Ray sources, in use for different time periods have almost the same transient time. Finally simulation and experimental results show that black and white contrast of image obtained by X-ray system with long service time tube is improved dramatically to meet detection requirement.

Research on the Modeling Method of Microwave Power Module Cascade Converter

It is difficult to obtain the accurate small signal modeling by traditional modeling method especially for the complex converter. System identification is a new method to construct the high voltage cascade converter small signal modeling. The first-stage and the second-stage can be analyzed on the whole. The improved least-square parameter estimation is used to analyze the sampling data of input and output. Furthermore, the system parameter and accurate system modeling can be acquired. Comparing the step response of system model with the Pspice stimulating result, the validity of the method is verified.

Sampled-Data Modeling for PCM and ZVS Controlled Critical Conduction Mode (CrCM) Active Clamp Flyback (ACF) Converter at Variable Switching Frequency

Critical conduction mode (CrCM) active clamp flyback (ACF) converter is regarded as a good candidate for low power adaptor applications. However, the most adopted control strategy of variable-frequency peak current mode (VF-PCM) and discrete zero voltage switch (ZVS) control makes it difficult to get the accurate small signal model. Therefore, by using sampled-data modeling method, this paper proposes an exact small signal model of CrCM ACF converter for the first time. In the modeling process, the influence of discrete-ZVS control is firstly considered. The conduction time of power switch is regarded as the control signal, which is different from constant-frequency converter. The total current close-loop transfer function is simplified by the linear combination of single VF-PCM and discrete-ZVS control model. After considering the sampling effect and the modulator gain from the derived sampled-data model respectively, the control-to-output transfer function of CrCM ACF converter is developed. The analytical results are analyzed by comparing with single VF-PCM and the widely used average model. Finally, to validate the accuracy of the proposed model, a 65W 20V output CrCM ACF converter is simulated and measured. The verification shown that the proposed sampled-data model is basically agreement with the simulation and experimental results.

Equivalent Circuit Modeling of LLC Resonant Converter

LLC resonant converter is widely used in industry. However, up to now, no simple and accurate small-signal equivalent circuit model is available. This article proposes an equivalent circuit model of LLC resonant converter. The simple equivalent circuit model is derived based on modification and simplification of extended describing function method, which has already been successful deriving equivalent circuit model in series resonant converter [15] . The model can well predict the small-signal behaviors observed in pulse-frequency-modulated LLC resonant converter, whenever switching frequency is below, close to, or above the resonant frequency. For the first time, analytical expressions for control to output voltage, input to output voltage, input impedance, and output impedance are provided to aid closed-loop feedback design. SIMPLIS simulation and experimental results are presented to prove the accuracy of the model.

Small-Signal Modeling and Cross-Regulation Suppressing for Current-Mode Controlled Single-Inductor Dual-Output DC–DC Converters

A current-mode control, which can be applied to three basic single-inductor dual-output (SIDO) dc-dc converters to suppress cross-regulation, is proposed in this article. The control circuits and operation principles under different inductor current trends and switch sequences are introduced. The SIDO boost converter operating in continuous conduction mode (CCM) is taken as an example to establish the complete and accurate small-signal model in detail. Based on which, the optimal compensators design are presented in this article. And then, the cross-regulation and transient performance are analyzed via Bode plots, and the SIMPLIS simulation results are presented to validate the small signal model. In addition, the stability condition for current mode controlled CCM SIDO boost converter is studied by using Routh-Hurwitz criterion. Finally, experimental results verify the correctness of the theoretical analysis. The research results indicate that the proposed current-mode control significantly reduces the cross-regulation of SIDO dc-dc converter compared with the existing control schemes.

Small-signal modeling and parameter extraction method for a multigate GaAs pHEMT switch

This paper presents an accurate small-signal model for multi-gate GaAs pHEMTs in switching-mode. The extraction method for the proposed model is developed. A 2-gate switch structure is fabricated on a commercial 0.5 μm AlGaAs/GaAs pHEMT technology to verify the proposed model. Excellent agreement has been obtained between the measured and simulated results over a wide frequency range.

Accurate Small-Signal Equivalent Circuit Modeling of Resonant Tunneling Diodes to 110 GHz

This article presents a novel, on-wafer deembedding technique for the accurate small-signal equivalent circuit modeling of resonant tunneling diodes (RTDs). The approach is applicable to stabilized RTDs, and so enables the modeling of the negative differential resistance (NDR) region of the device’s current–voltage ( $I$ – $V$ ) characteristics. Furthermore, a novel quasi-analytical procedure to determine all the equivalent circuit elements from the deembedded S-parameter data is developed. Extraction results of a $10\,\,\mu \text{m}\,\,\times 10\,\,\mu \text{m}$ stabilized, low-current density RTD at different bias points show excellent fits between modeled and measured S-parameters up to 110 GHz.