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The stability of Modular multilevel converter (MMC) itself is the premise of analyzing the stability of MMC cascading with other cells, so this paper addressed the small-signal stability of MMC with dc voltage control mode which is the common operation mode of grid-side MMC in high-voltage direct current (HVDC) systems. First, the small signal model of MMC with open-loop control mode and dc voltage control mode while considering the dc voltage controller and current controller are established with the harmonic state-space (HSS) modeling method. Subsequently, eigenvalues and participation factors are analyzed to estimate the stability of MMC system and the influence of controller parameters, especially the proportional coefficients of dual-loop controllers, which can improve the design efficiency of control system. Finally, time-domain simulations in MATLAB/Simulink are provided to verify the accuracy of HSS small signal model and the effectiveness of the theoretical stability analysis.

In recent years, ultralow-frequency oscillation has repeatedly occurred in asynchronously connected regional power systems and brought serious threats to the operation of power grids. This phenomenon is mainly caused by hydropower units because of the water hammer effect of turbines and the inappropriate Proportional-Integral-Derivative (PID) parameters of governors. In practice, hydropower and solar power are often combined to form an integrated photovoltaic (PV)-hydro system to realize complementary renewable power generation. This paper studies ultralow-frequency oscillations in integrated PV-hydro systems and analyzes the impacts of PV generation on ultralow-frequency oscillation modes. Firstly, the negative damping problem of hydro turbines and governors in the ultralow-frequency band was analyzed through the damping torque analysis. Subsequently, in order to analyze the impact of PV generation, a small-signal dynamic model of the integrated PV-hydro system was established, considering a detailed dynamic model of PV generation. Based on the small-signal dynamic model, a two-zone and four-machine system and an actual integrated PV-hydro system were selected to analyze the influence of PV generation on ultralow-frequency oscillation modes under different scenarios of PV output powers and locations. The analysis results showed that PV dynamics do not participate in ultralow-frequency oscillation modes and the changes of PV generation to power flows do not cause obvious changes in ultralow-frequency oscillation mode. Ultra-low frequency oscillations are mainly affected by sources participating in the frequency adjustment of systems.

Active power modulation of line-commutated converter (LCC)-based high-voltage direct current (HVDC) system is increasingly utilised, especially for the case of damping low-frequency oscillation associated with synchronous machine (SM) in electromechanical timescale (around 1 Hz). Many papers have tried to analyse the mechanism of damping effects, but almost rely on numerical studies, which cannot reveal the dynamic interaction between SM and DC-power-modulated LCC. This study proposes a small-signal model of DC-power-modulated LCC based on motion equation concept. With this model, analytical investigation of low-frequency oscillation from the scope of damping and synchronising powers is presented. Comparisons of analytical results and eigenvalues draw some general conclusions which offer insight into the dynamic behaviour. By examining the case of an SM connected to a DC-power-modulated LCC, simulations in MATLAB/Simulink are conducted to verify the analytical results.

Inverter dead-time is known to make open-loop induction motor drives oscillatory, while operating at light-loads in particular. While dead-time compensation schemes exist, precise compensation of the same is often challenging as it involves factors such as device and driver delays and switching transition times, which are difficult to be quantified accurately. Hence, the effect of dead-time could be under or overcompensated. This paper presents a comprehensive analysis of the impact of such undercompensation and overcompensation on the stability of a 100-kW induction motor drive, along with experimental investigations of the same. The effects of undercompensation and overcompensation on the inverter output voltage are analyzed on a switching-cycle average basis. Further, small-signal models are proposed for an open-loop drive, when it is undercompensated and overcompensated. Stability analysis of the above motor drive is reported, which predicts oscillatory behavior with both under and overcompensation, over certain fundamental frequency ranges, respectively. Further, two different types of oscillatory behavior, characterized by different oscillating frequencies, are observed for the cases of under and overcompensation. The analyses are supported by simulations. Experimental investigations carried out also support the analyses and simulation results. [ABSTRACT FROM AUTHOR]

An improved version of the Small-Signal model of a single-electron transistor for high frequency is proposed in this paper. The modification is done by incorporating the parasitic elements for the high-frequency operation of single-electron transistor. The high-frequency operation introduces several spurious elements due to the physical structure and the testing instrument connection to the device under test. The impact of these elements on the matching network is significant but yet unpredictable. The formulation of the Small-Signal model considering the extrinsic and intrinsic elements is elaborated in this literature. The scattering parameters play an important role in the determination of the properties of a transistor working at high frequency. This study is carried out for determining the scattering parameters for single-electron transistor and their relationship with the other intrinsic as well as extrinsic parameters. [ABSTRACT FROM AUTHOR]

This paper proposed a generic modeling framework of the modular multilevel converter (MMC) based DC grid for small-signal stability studies. A modularized modeling method is employed to form the overall state-space model and small-signal model with considering the detailed dynamics of MMC internal electrical quantities, MMC control patterns and the DC network. The validity and accuracy of the state-space model and small-signal model for a five-terminal MMC system are verified versus the electromagnetic transient model in PSCAD/EMTDC. Based on the small-signal model, the impact of the DC reactors on the small-signal stability of the tested system is investigated through root locus analysis. Key DC reactors that have a dominant effect on the stability are identified. Critical values of the DC reactors that preserve stability are recognized. Damping control is designed and installed according to the participation factor analysis. The time-domain simulation results show excellent agreement on the oscillating frequency calculated by eigenvalue studies and verify the validity of the proposed damping control. [ABSTRACT FROM AUTHOR]

Nowadays Z-source networks are the most promising power converter networks that cover almost all electric power conversion (dc-dc, dc-ac, ac-dc and ac-ac) applications. However, the controller design is critical for Z-source converter (ZSC) due to the presence right-half-plane zero (RHPZ) in the control-to-capacitor-voltage transfer function. This RHPZ exhibits non-minimum phase undershoot in the capacitor voltage and also in the dc-link voltage waveforms. A perfect small-signal model is required to predict locations of the RHP zero and its dynamics. This paper contributes towards the small-signal analysis of ZSC under continuous conduction mode considering the parasitic resistance of the inductor, equivalent series resistance of the capacitor, internal resistances of active switch and forward voltage drop of the diode. The maximum allowable value of shoot-through duty ratio (STDR) and voltage gain for different values of the internal resistance and load resistance are discussed in this paper. The accuracy of the developed small-signal average model is compared with detailed circuit model in MATLAB/SIMULINK. Finally, the steady-state simulation results of ZSC are validated with hardware results. [ABSTRACT FROM AUTHOR]

The control design of inductive power transfer (IPT) systems has attracted a lot of attention in the field of wireless power transmission. Due to the high-order resonant networks and multiple loads in IPT systems, a simplified model of an IPT system is preferred for analysis and control design, and a controller with strong robustness is required. Hence, an active disturbance rejection control (ADRC) for IPT systems is proposed in this paper. To realize the employment of ADRC, firstly a small-signal model of an LC series-compensative IPT system is derived based on generalized state-space averaging (GSSA), then the ADRC is implemented in the designed IPT system. The ADRC not only provides superior robustness to unknown internal and external disturbances, but also requires few knowledge of the IPT system. Due to the convenient realization of ADRC, the designed IPT system retains its simple structure without any additional circuits. Finally, a frequency domain analysis and experimental results have validated the effectiveness of the employed ADRC, especially its robustness in the presence of frequency drifts and other common disturbances. [ABSTRACT FROM AUTHOR]

The small time constants of power electronics devices lead to dynamic couplings with the electromagnetic transients of power networks, and thus complicate the modeling and stability analysis of power-electronics-based power systems. This paper presents a computationally efficient approach to assess the small-signal stability of inverter-fed power systems. The power system is partitioned into individual components, including the power inverters, network impedances, and power loads. The state-space model of individual inverter is first built, where the frequency response and eigenvalue analysis collectively characterize the contributions of different controller parameters to the terminal behavior in a wide frequency range. These component models, together with the network equations, are then algebraically assembled based on the interconnection relations at their terminals. As a consequence, the state matrix of the whole system, which is essential to the system stability analysis, can be reformulated in a computationally efficient way. The experimental results are finally given to validate the effectiveness of the modeling method and system stability analysis. [ABSTRACT FROM AUTHOR]

As a supplement of the droop control, the concept of secondary controlled microgrid (MG) has been extensively studied for voltage and frequency restoration. However, the low band-width communication (LBC) channels are needed to exchange information between the primary and secondary controllers, and the performance of the secondary controller degrades due to the uncertain communication delay and data drop-out in the LBC lines. Recently, a washout filter-based power sharing method was presented without communication lines and additional control loops. In this paper, the equivalence between secondary control and washout filter-based power sharing strategy for islanded MG is demonstrated, and the generalized washout filter control scheme has been obtained. Additionally, the physical meaning of control parameters of secondary controllers is also presented. Besides, a complete small-signal model of the generalized washout filter-based control method for islanded MG system is built, which can be utilized to design the control parameters and analyze the stability of MG system. Finally, extensive simulation and experimental results are provided to confirm the validity and effectiveness of the derived equivalent control scheme for islanded MG. [ABSTRACT FROM AUTHOR]

Large‐scale integration of wind power is one of the main challenges in today's power systems. Therefore, there is an increased importance to generate more accurate yet simplified wind farm (WF) models. The current modelling techniques of WFs depend on aggregationto reduce the degree of model complexity and computational time. The two techniques of aggregation are adopted in the literature: fully aggregated model (FAM) and multi‐machine model where the WF is divided into a number of aggregated models for different sections of the WF. A small‐signal model based comparison between the two techniques of aggregation is introduced in this study. The aim is to investigate the impacts of the full aggregation of the wind turbines on the overall system critical modes under weak grid conditions as compared to the multi‐machine modelling approach. The comparison is done for different operating conditions (output active and reactive power) of the WF and also under different short‐circuit ratios to reveal to what extent the FAM can be relied on to provide an accurate response of large WFs. [ABSTRACT FROM AUTHOR]

A dc microgrid is a low inertia system dominated by power converters. As a result, the change rate of the dc voltage is very fast under power variation. In this study, a distributed virtual inertia control is proposed to enhance the inertia of the dc microgrid and decrease the change rate of the dc voltage. The inertia of the dc microgrid can be enhanced by the kinetic energy in the rotor of the permanent magnet synchronous generators (PMSG)‐based wind turbine, the energy stored in batteries and the energy from the utility grid. By introducing a virtual inertia control coefficient, a general expression of the inertial power provided by each controllable power sources is defined. The proposed inertia control is simply a first‐order inertia loop and is implemented in the grid‐connected converter, the battery interfaced converter and the PMSG interfaced converter, respectively. The small‐signal model of the dc microgrid with the proposed inertia control is established. The range of virtual inertia control coefficient is determined through stability analysis. Finally, a typical dc microgrid is built and simulated in Matlab/Simulink, and the effectiveness of the proposed control strategy and correctness of the stability analysis are verified. [ABSTRACT FROM AUTHOR]

This paper presents a detailed steady-state analysis and ac small-signal modeling of the power stage of pulse-width modulated A-source converter. The voltage and current waveforms along with their corresponding expressions describing the converter operation are presented in detail. The input-to-output and input-to-capacitor dc voltage transfer functions are determined. The minimum inductance required to ensure continuous conduction mode is derived. The expressions for the semiconductor devices stresses are also presented. The dc, averaged equivalent circuit is derived using the circuit averaging technique. A complete derivation of the small-signal model including the converter parasitic resistances are presented followed by the power stage transfer functions relevant to the capacitor voltage loop, such as: 1) duty cycle-to-capacitor voltage; and 2) input-to-capacitor voltage. In addition, the expressions for the network input impedance and output impedance are derived. Finally, experimental validations of the derived small-signal models are performed, both in frequency and time domain for a laboratory prototype of an A-source converter. The theoretical predictions were in good agreement with the experimental results over a wide range of frequencies. [ABSTRACT FROM AUTHOR]

The future extensive usage of open communication networks for secondary voltage control in autonomous microgrids (MGs) inherently introduce time delays, which would degrade the system performance or even cause instability in the worst case. However, existing literatures have largely ignored these communication delays between the microgrid central controller and primary local controllers. To fill the knowledge gap, this paper proposes an analytical method to determine the stability robustness of secondary voltage control in MGs by taking into account the communication latency effect. Based on static output feedback, a closed loop small-signal model of an MG installed with proportional-integral secondary voltage controllers is first derived. Delay-dependent criteria are then formulated to detect the stability posture of MG system by tracing critical eigenvalues and cluster treatment of characteristic roots, in the forms of delay margin for a single delay and stability tableau over the delay domain for multiple delays, respectively. By a series of trial declarations, the qualitative impact of secondary controller gains on system stability regions against uncertain delays is investigated, from which it can be observed that generally the increase of integral gains would yield to a less delay-dependent stability of control system and the results can be utilized to guide the controller design for a compromise between the dynamic performance and stability robustness. The effectiveness of the proposed methodology is verified by a simulation study. [ABSTRACT FROM AUTHOR]

By measuring scattering parameters over a wide range of bias points, we study the intrinsic gate capacitance as well as the charge partitioning of vertical nanowire tunnel field-effect transistors (TFETs). The gate-to-drain capacitance ${C} _{ {gs}}$ is found to largely dominate the ON-state of TFETs, whereas the gate-to-source capacitance ${C} _{ {gs}}$ is sufficiently small to be completely dominated by the parasitic components. This indicates that the tunnel junction on the source side almost completely decouples the channel charge from the small-signal variation in the source, while the absence of a tunnel junction on the drain side allows the channel charge to follow the drain small-signal variation much more directly. [ABSTRACT FROM AUTHOR]

Summary: Multiple‐output flyback converters are widely used in switching power supplies due to their low component count and cost‐effective structure. The main problem of this structure is how to balance output voltages in different load conditions. This paper proposes a new approach for single‐input multiple‐output flyback converters operating in DCM and CCM by a small‐signal averaged model. The averaged model is derived by presenting the piecewise‐linear waveform for the inductor currents inside the converter. In DCM, the magnetizing current and currents through the output windings reach zero when the switch is turned off. In CCM, the magnetizing current of the converter is continuous over a switching interval and this possibility exists that only some of the output diodes completely conduct when the switch is off. The proposed model of the converter can be used in a wide range of operations within identical and non‐identical loading conditions. Using a laboratory prototype, several case studies and input‐to‐output transfer functions are considered to verify the proposed model. The controller design is performed for the both CCM and DCM, and then dynamic characteristics of the overall system are evaluated. [ABSTRACT FROM AUTHOR]

In this paper, a framework for stability analyses of a typical inverter-based islanded microgrid with two types of nonlinear loads is presented, namely ideal constant power loads (CPLs), which are the loads supplied by tightly regulated power electronics converters, and dynamic CPLs, which are used to represent motor-drive systems with large time constants. The comprehensive dynamic model of the considered microgrid is first developed, based on which a bunch of small-signal models are deduced using Taylor expansion made at different stable operating points. Afterward, eigenvalue-theorem-based stability analysis and parametric sensitivity analysis are successively performed on the obtained small-signal models to verify the stability of the system, predict the system's unstable regions, and identify the effects of parameters on the stability boundaries. In the meantime, the impacts of different kinds of nonlinear loads on the system stability are studied. Hardware-in-the-loop (HIL) real-time simulation platform of a 30-kVA microgrid, which is mainly formed by a 10-kVA photovoltaic (PV) system, a 10-kVA wind energy conversion system, a 10-kVA lithium-ion battery energy storage system, and two CPLs, is established in Typhoon HIL 602 device. The validity of the theoretical results is verified by real-time simulation results. [ABSTRACT FROM AUTHOR]

A large scale of renewable energy employing grid connected electronic inverters fail to contribute inertia or damping to power systems, and, therefore, may bring negative effects to the stability of power system. As a solution, an advanced Virtual Synchronous Generator (VSG) control technology based on Hamilton approach is introduced in this paper firstly to support the frequency and enhance the suitability and robustness of the system. The charge and discharge process of power storage devices forms the virtual inertia and damping of VSG, and, therefore, limits on storage capacity may change the coefficients of VSG. To provide a method in keeping system output in an acceptable level with the capacity restriction in a transient period, an energy control algorithm is designed for VSG adaptive control. Finally, simulations are conducted in DIgSILENT to demonstrate the correctness of the algorithm. The demonstration shows: (1) the proposed control model aims at better system robustness and stability; and (2) the model performs in the environment closer to practical engineering by fitting the operation state of storage system. [ABSTRACT FROM AUTHOR]

When multiple stable systems are combined into one system, the newly formed hybrid system has a certain possibility to be unstable. Such a natural phenomenon has been verified in the fields of chemistry and biology over the last century. The implementation of electric springs (ESs) in large quantity over the power grids can also suffer from the same issue if specified design are not performed. As an initial feasibility study of multiple ES in smart grids, in this paper, based on the concept of relative stability, a method of tuning Kp and Ki of the proportional-integral controllers of the ES to ensure the overall system stability of a weak grid is investigated and is achieved through the aid of simulation on an extended low-voltage (LV) network of IEEE 13-node test feeder. Both simulation and experimental results validate that as the number of ES in the isolated LV network (weak grid) increases, more stringent values of Kp and Ki are required to achieve system stability. Besides, a hypothesis that if the optimal values of Kp and Ki are adopted, a maximum number of ES can be stably installed over the grid is proposed. It is also shown experimentally that by eliminating the instability of voltage fluctuation in the distribution line, the subsequent frequency fluctuation of the power generation can also be eliminated. [ABSTRACT FROM PUBLISHER]

The modeling, small-signal stability analysis, and control of quasi-Z-Source Matrix Converter (qZSMC), and also its application in Wind Energy Conversion System (WECS) are discussed. First, the small-signal model of the qZSMC, composed of an input filter, a Three-Phase Quasi-Z-Source Network (TPQZSN), and a Matrix Converter (MC), is derived. Then, a comprehensive stability study is carried out and it is shown that, unlike the conventional MC, the qZSMC does not have problem working stable for its entire range of operation. The small-signal model is used to obtain system transfer functions and perform a frequency domain analysis. A guide to choose proper passive components of qZSMC is also presented. The qZSMC is further employed as grid interface by a Permanent Magnet Synchronous Generator (PMSG) based WECS (PMSG-WECS). A modified predictive control (MPC) is developed, allowing shoot-through states to be inserted within the deliberately made sequences of zero switching states in MC switching pulses. The proposed MPC is then compared to its conventional version, showing that by the MPC, the grid-current ripples are reduced considerably. Simulation study is used to assess the effectiveness of proposed WECS and MPC, and to highlight the promising features of the proposed WECS in comparison to Conventional MC-based PMSG-WECS (CMC-WECS). [ABSTRACT FROM AUTHOR]

This work develops the first frequency-dependent small-signal model for graphene electrolyte-gated field-effect transistors (EGFETs). Graphene EGFETs are microfabricated to measure intrinsic voltage gain, frequency response, and to develop a frequency-dependent small-signal model. The transfer function of the graphene EGFET small-signal model is found to contain a unique pole due to a resistive element, which stems from electrolyte gating. Intrinsic voltage gain, cutoff frequency, and transition frequency for the microfabricated graphene EGFETs are approximately 3.1 V/V, 1.9 kHz, and 6.9 kHz, respectively. This work marks a critical step in the development of high-speed chemical and biological sensors using graphene EGFETs. [ABSTRACT FROM AUTHOR]

This paper investigates the back-gating effects due to traps, and presents a new nonlinear trap modeling approach suitable for gallium nitride (GaN) high electron mobility transistors (HEMTs). It is shown that the traps have nonidentical influence on the channel compared with the gate. The potential due to trapped electrons in the buffer and the gate–source voltage need to be differentiated to model their respective influence on conductivity of the 2-D electron gas. Hence, the back-gating potential due to traps cannot be included in the transistor model by directly offsetting the gate–source voltage. A new modulation factor is therefore introduced to create an effective back-gating potential, and thereby improve the modeling of trapping effects. The proposed nonlinear trap model is shown to accurately predict the trapping behavior for a large voltage operating region. A detailed procedure is presented to derive the model parameters from basic device measurements. The model is experimentally validated and shown to accurately predict dc-, pulsed-IV, and large-signal waveform performance for a commercial GaN HEMT. [ABSTRACT FROM PUBLISHER]

With increasing the share of wind farms in generation profile, their contribution to frequency regulation has become crucial. This study presents an optimal robust first‐order frequency controller in the wind farms, which collectively emulates the inertial response as well as governor droop of synchronous generators. To account for various uncertainties associated with system inertia, damping, and doubly‐fed induction generator (DFIG)‐based wind turbine's parameters, the robustness of controller is verified through the 16‐plant theorem. An analytic method based on the small‐signal model of the system is utilised to determine the stability region of the first‐order controller. To evaluate the performance of the proposed controller, a DFIG‐based wind farm equipped with this controller is added to IEEE 39‐bus test system which is updated with wind farms in MATLAB/Simulink environment, and the response of proposed controller is investigated under different conditions. Simulation results verify the robustness as well as the effectiveness of the proposed controller in system frequency regulation. [ABSTRACT FROM AUTHOR]

This paper presents a simple method to analyze the behavior of feedback loops that contain a naturally-sampled single-edge pulse-width modulator. A small-signal model is derived by means of simple geometric arguments. It is shown how this small-signal model can be used to analyze the stability of the continuous-time pulse-width modulated feedback loop by using standard $z$-domain techniques. The strategy relies on familiar concepts like transfer functions and small-signal gains and does not require any in-depth knowledge of nonlinear systems. A simple design process, where the continuous-time compensator is designed directly in the $z$-domain, is developed and detailed design equations are derived for a PI current regulator. It is shown how the proposed strategy can accurately predict instability that cannot be explained by means of the well-known average model of the pulse-width modulator. The theoretical analysis is confirmed by means of detailed time-domain simulations. The mechanisms that lead to instability are discussed and an equation for the critical loop gain is derived. [ABSTRACT FROM PUBLISHER]

The model of a grid-connected inverter used for the corresponding controller design depends on the equivalent resistance and inductance between the inverter and the grid. These parameters are not fixed and change with operating conditions, temperature, and age. This paper analyses the effectiveness of the application of the model reference adaptive control (MRAC) approach in obtaining an accurate model of a grid-connected inverter system. Active and reactive power based MRAC approaches are used to estimate the equivalent resistance and reactance between the inverter and the grid. Detailed stability analysis of the MRAC approach is presented. The system models for the MRAC controller design are derived and guidelines on the controller parameters selection are proposed. Experimental results validate the feasibility of the proposed scheme. [ABSTRACT FROM AUTHOR]