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An electrical transient model (ETM) of insulated-gate bipolar transistor (IGBT)-diode switching cell is developed by coupling a temperature-dependent IGBT model with power loss model. The nonlinear behavior of IGBT and the reverse recovery characteristic of the diode are considered in this model to simulate the transient switching waveforms. Based on the transient waveforms of ETM under various operating conditions, the power loss estimation method (PLEM) for IGBT is developed. In addition to traditional modeling techniques that only uses ideal switch, this paper uses the model to replicate the power loss behaviors of semiconductor devices in circuit simulation by looking up tables. The proposed ETM is simulated in PSCAD/EMTDC with nanosecond time step, whereas the overall system application can be simulated with conventional time step in range of microsecond. By this way, the model can promise reasonable accuracy as well as an acceptable fast solving speed. The proposed ETM and PLEM have been implemented in PSCAD/EMTDC simulator and validated by experimental results using a double pulse test bench and boost converter test platform. [ABSTRACT FROM AUTHOR]

This paper presents two novel measurement methods to characterize silicon carbide (SiC) MOSFET devices. The resulting data are utilized to significantly improve the extraction of a custom device model that can now accurately reproduce device switching behavior. First, we consider the $I_{\text{d}}- V_{\text{ds}}$ output characteristics of power devices such as SiC transistors. These are typically measured using traditional curve tracers, but the characterization of the high-voltage and high-current (HVHC) region is very challenging because of device power compliance and self-heating. In this paper, we introduce a measurement technique that overcomes self-heating and derives the HVHC region from switching waveforms. The switching transient characteristics of devices are used to determine drain current $(I_{\text{d}})$ as a function of drain–source voltage $(V_{\text{ds}})$ in the HVHC range. Second, we consider another challenging characterization area: measurement of nonlinear capacitances when device is turned on. These capacitance characteristics of on-state devices are important for correcting disagreements between simulations and measurements in turn-off switching transient waveforms and cannot be measured using a conventional capacitance-voltage meter. We introduce S-parameter measurements as an effective method to obtain the capacitance characteristics of both off-state devices and on-state devices. These novel measurement techniques have been applied to the modeling of a SiC device. The extracted device model, a modified version of the popular Angelov−GaN high-electron-mobility transistor model, shows significant improvement in terms of the accuracy of switching waveforms of devices over a wide range of operating conditions. [ABSTRACT FROM AUTHOR]

This paper presents an improved compact model for a discrete silicon-carbide (SiC) MOSFET. This compact model based on the previous model features a new behavioral model of output characteristics and new nonlinear models of internal capacitors. Simulation with the improved compact model is in better agreement with measurement than that with the previous compact model, as well as transient behavior of the drain–source voltage, the drain current, and the leakage current out of a heatsink. Furthermore, the improved model is useful for constructing the accurate compact model that can reproduce the high-frequency characteristics of the transient waveforms of SiC-MOSFET s. This successful validation indicates that the improved compact model would be a promising tool for a full-simulation-based design system of the power converters using SiC-MOSFETs. [ABSTRACT FROM AUTHOR]

This paper introduces a novel modeling approach that allows to obtain fast simulations of pulsewidth-modulated dc–dc switched-mode power supplies (SMPS). The proposed methodology combines the use of precise switched models during transient evolutions and averaged models during steady-state or slowly varying conditions. In that way, the resulting mixed modeling approach enables to obtain the detailed switching behavior of SMPS in the context of long-term simulations. The commutation between models is automatically performed in runtime by an algorithm that detects the transient or slowly varying condition according to the evolution of some model variables. When the precise switched model is used, the mentioned algorithm also adjusts the averaged model parameters so that its results are accurate irrespective of the operating point. This paper also describes the implementation of the methodology in the Modelica language and reports simulation experiments showing that the results are as accurate as those obtained using precise switched models, but several times faster. [ABSTRACT FROM AUTHOR]

Models that accurately predict the output voltage ripple magnitude are essential for applications with stringent performance target for it. Impact of the dc input ripple on the output ripple for a frequency-controlled series resonant converter (SRC) using a discrete-domain exact discretization modeling method is analyzed in this paper. A novel discrete state-space model along with a small-signal model for the SRC considering three state variables is presented. The audiosusceptibility (AS) transfer function that relates the input-to-output ripple is derived from the small-signal model. Analysis of the AS transfer function indicates a resonance peak and an expression is derived connecting the AS resonance frequency for the input ripple based on the SRC component values. Further analysis is done to show that a set of values for the SRC parameter exists, which forms a design space, for which the normalized gain offered by the SRC for the input ripple is less than unity at any input ripple frequency. A test setup to introduce the variable frequency ripple at the input of the SRC for the experimental evaluation of the AS transfer function is developed. Influence of stray parameters on the AS gain, AS resonance frequency, and on the SRC tank resonance frequency is evaluated. An SRC is designed at a power level of 10 kW. The analysis using the derived analytical model, simulations, and experimental results are found to be closely matching. [ABSTRACT FROM AUTHOR]

Switched-capacitor (SC) converters have drawn more and more attention in recent years due to their unique advantages. The accurate analysis methods will fully determine an SC converter's steady-state and dynamical performance. Proper design of SC converters requires full understanding of all impacts on circuit operation including steady-state and dynamical performance. Some previous modeling methods for SC converters have established a popular static model for SC converters which is composed of an ideal transformer and equivalent output resistance. This paper presents a dynamic capacitor ampere-second balance transient calculation modeling method. The instantaneous state of input voltage, instantaneous state of output voltage, instantaneous state of voltage of flying capacitor, “on time” and “off time,” as well as switching period are all included in the proposed model. The proposed modeling method was applied in both the dual-phase SC converters and the two-switch boosting SC converters. This modeling method was validated by the simulation and experimental results. The proposed model can be used to accurately predict and optimize the performance in the design phase for the low and high power SC converters. Based on the proposed modeling method, the SC converters could be controlled by a variable frequency control method. [ABSTRACT FROM AUTHOR]

For dc–dc converters with pulsating output current, such as boost and buck–boost converters, the use of leading-edge or trailing-edge pulse width modulation (PWM) can result in distinctly different behavior. This phenomenon is not readily captured by the usual averaged model but can be predicted with a discrete-time model. However, the discrete-time model, which tracks the dynamics of state variables over a switching period, is usually more complex and less convenient to apply for the design of the feedback control. Based on the low-pass characteristics of dc–dc converters, an approximate discrete-time model is proposed in this paper, and upon transforming to the s-domain, the model results in transfer functions that can be conveniently used for deriving practical closed-loop parameters. With the proposed model, the loop gain, the input and output impedances are derived and analyzed. The effects of applying different types of PWM on the stability of a single dc–dc converter and a system of cascaded dc–dc converters are discussed. Finally, prototypes of a buck converter, a boost converter, and a cascaded system of buck and boost converters are constructed to verify the effectiveness of the approximate discrete-time model. [ABSTRACT FROM AUTHOR]

An increasing number of power-electronic-based distributed generation systems and loads generate not only characteristic harmonics but also unexpected harmonics. Several methods, such as impedance-based analysis, which are derived from the conventional average model, are introduced to perform research about the harmonic interaction. However, it is found that the linear-time-invariant-based model analysis makes it difficult to analyze these phenomena because of the time-varying properties of the power-electronic-based systems. This paper investigates a grid-connected converter by using the harmonic state-space (HSS) small-signal model, which is based on a linear time-varying periodically theory. The proposed model can include the switching behavior of the model, where it makes the model possible to analyze how harmonics are transferred into both the ac-side and dc-side circuits. Furthermore, a harmonic matrix of the grid-connected converter is developed to analyze the harmonic interaction at the steady-state behavior. Besides, the frequency-domain results are compared with time-domain simulation results by using the HSS modeling to verify the theoretical analysis. Experimental results are finally discussed to verify the proposed model and study. [ABSTRACT FROM PUBLISHER]

By the logical statements and linear inequalities, a new modeling method named bi-switching status modeling (BSM) method is presented to model the dc–dc converters in this paper. Compared with other modeling methods, such as the state-space averaging method and the mixed logical dynamical (MLD) method, first, the BSM method can describe continuous conduction mode and discontinuous conduction mode operations of the dc–dc converters as a unified bi-switching status model. Second, the BSM method is more precise than the state-space averaging method because there is no approximate assumption. Third, the constrains of the operating modes in the BSM method can be simplified as a consolidated inequality, which means that the model obtained by the BSM method is more concise than that obtained by the MLD method. Simulation and available experiments of a buck converter verify the effectiveness of the proposed BSM method. [ABSTRACT FROM PUBLISHER]

In this paper, average modeling and analysis of a dual-supercapacitor bank, actively balanced by a bidirectional buck–boost converter, is presented. In such a system, natural balancing is achieved when the converter is operated in open loop with 50% duty cycle, eliminating the need for measuring the voltage of each storage device. Nevertheless, excessive currents arise even for slight voltage misbalance because of the highly underdamped nature of the system. In order to remedy this drawback, bidirectional pulse-by-pulse inductor current limitation is introduced, which is equivalent to adding a peak-current-mode-like control loop to the system. Since the duty cycle never exceeds 50%, compensation ramp is not required to maintain stability. On the other hand, while the uncontrolled system dynamics is linear, introducing the current limit mechanism turns the closed-loop dynamics into a nonlinear one, burdening the analysis task and thus calling for suitable average model to perform fast simulations for system analysis. Therefore, dynamical equations of the system are developed in order to derive the switching-cycle-averaged model and reveal the tradeoff between current limit level, balancing time and efficiency for the worst case of imbalance. Simulations and experiments support the presented findings. [ABSTRACT FROM PUBLISHER]

A recently reported modeling methods for a switched capacitor converter either assume output as “firm” voltage or a resistor to facilitate calculation. When the size of output filter capacitor is moderate, accompanied by noticeable output ripple, previous modeling results may not provide accurate prediction and design guidelines. In this paper, a new modeling technique taking into account the output capacitor effect is proposed for simple dual-phase switched capacitor converters without complex coupling loops. The proposed model employs transient calculation, takes charge redistribution phase into account, and includes the duty cycle, switching frequency as well as output capacitor simultaneously in the final output impedance formula, which enhances accuracy of the model. It is suitable for interleaved and noninterleaved switched capacitor converters. The simulation and experimental results for the unity gain SC converter are provided to verify the proposed theory. [ABSTRACT FROM PUBLISHER]

Switched-capacitor (SC) converters were initially introduced for low-power applications and monolithic integration. In recent years, SC converter has found high-power applications. However, voltage regulation remains an issue. This paper addresses regulation challenges for high-power SC converters, based on charge-balance transient-calculation (CT) modeling method and peak current stress estimation. With the help of CT model, due to its accuracy and comprehensive relationship, circuit and control parameters’ impacts on regulation become straightforward and concerns on components stresses can be addressed quantitatively. The suitability of CT method for regulation analysis is confirmed by comparison with traditional modeling methods. The CT method is used in a 1-kW 3X two-switch boosting switched-capacitor converter (TBSC) circuit for steady-state analysis and current stress estimation. The soft rising input current and nature interleaving properties of 3X TBSC make it well suited for high-power application. Finally, the small-signal model of the 3X TBSC is developed and a closed-loop operation is achieved under 1 kW power rating. [ABSTRACT FROM AUTHOR]

Nonlinearities have been the major obstructions that limit the computational efficiency in power electronic circuit simulation for a long time. Yet there is no standard way for dealing with them. This paper presents a new method that makes the handling of nonlinearities fast and stable. In the proposed method, nonlinearities are transformed into a uniform representation—a constant resistor in parallel with a companion current source, thus making the system admittance matrix constant for fixed time-step simulation. To solve for the corresponding companion current source, nonlinearities are treated as either current or voltage sources and a diagonal time-varying matrix equation is developed. Three methods are proposed for solving the matrix equation—precomputed inversion or factorization, modified Gaussian elimination, and updating inverse using the Sherman–Morrison formula—that can fit different system sizes and applications. The proposed method is validated by two common power electronic converter topologies, both in offline and real-time simulation. Offline tests show that the proposed method achieved the same accuracy with the mature simulation software while being more than ten times faster. The same test cases are also implemented into field programmable gate arrays based real-time simulation experiments for verification. [ABSTRACT FROM AUTHOR]

The continuously innovated topologies of the nonisolated multiphase dc–dc converter (NMDC) demand generalized and flexible models for the controller design. However, the increased phase number, coupling of inductors, stray circuit parameters, and asymmetric problems make the modeling work difficult. In this paper, a novel switching period averaging method aiming to simplify the modeling process is proposed. The method takes full advantage of the linear characteristic of the circuit differential equations to find out the relationship between averaged state variables and switch duty cycles. Then, the generalized model applicable to several different topologies of the NMDC is derived. The analytical solutions of steady-state model, dynamic model in both time and frequency domain are all approached. In order to verify the results, a MATLAB/Simulink model and the corresponding experimental prototype of a four-phase boost converter with two groups of two-phase coupled inductors are built. Both results coincide with the theoretical derivation, which indicates the effectiveness of the proposed method. Finally, a design process of the H\infty controller for the NMDC is presented to show the application of this model. [ABSTRACT FROM AUTHOR]

Switched-capacitor (SC) converter is a type of variable structure systems. SC converters are typically equipped with open-loop control or some linear feedback control methods. However, these approaches provide slow dynamic response speed, small operation region, and large voltage ripple. Some new nonlinear control methods have been proposed in the literature to overcome these barriers. However, such control methods are usually proposed for applications involving low-power SC converters due to the limitations of them. This paper presents a nonlinear constant on-time variable frequency one-cycle control (CVFOCC) strategy based on dynamic capacitor ampere-second balance transient calculation (CASBTC) modeling method and one-cycle control (OCC) technique for high-power SC converters. This method successfully addresses the regulation issue of high-power SC converters. A high-power 3X Two-switch Boosting Switched-Capacitor converter (TBSC) is employed as an example topology. Simulation and experimental results both demonstrate that CVFOCC method could significantly improve the dynamic response speed and achieve excellent line and load regulation for the high-power SC converter in wide operation range. [ABSTRACT FROM AUTHOR]

Switched capacitor converters with ideal switches exhibit discontinuities in the electrical variables, i.e., state jumps at the switching time instants. This feature introduces some difficulties for the determination of compact dynamic models for these power converters. In this paper, we tackle the issue by considering a switched model where the dynamics of the modes are represented through differential algebraic equations. For this class of systems the classical averaged model fails. By including a suitable jump mode that approximates the state discontinuities, a generalized frequency-dependent averaged model is proposed. The effectiveness of the switched and averaged models is numerically and experimentally verified by analyzing the ladder, series–parallel, Fibonacci, and Dickson topologies, and by considering different switching frequencies, voltage sources, and circuits parameters. [ABSTRACT FROM PUBLISHER]

The objective of this paper is to propose an efficiency model to evaluate the impact of the pulse width modulation (PWM) duty cycle jitter on the efficiency of switching-mode power converter. By taking the product of two perturbation terms into consideration, which is ignored in the conventional average small-signal model, the average efficiency model is proposed first. Due to the nonlinear characteristic of the PWM generator, the multifrequency efficiency model is also developed by considering the sideband frequency. Three different perturbation waves are induced to the control loop of the converter to generate the jitter to observe its impact on the efficiency. The mathematical expression of the efficiency drop based on the proposed multifrequency model is derived. The reason of control-to-output gain's magnitude spike on the Bode plot can be explained by the derived equations. Eventually, the methods to reduce the efficiency drop caused by the jitter are suggested. In spite of various perturbation frequencies, amplitudes, and waveforms, the mathematical calculation, the computer simulation, and the hardware measurement of the efficiency drop are consistent which validate the accuracy of the proposed multifrequency efficiency model. [ABSTRACT FROM AUTHOR]

Many analytical methods of establishing accurate models of the switched-capacitor (SC) converters have been developed. These methods are applicable to simple low-order SC converters and can permit only a general efficiency calculation of SC converters. They do not provide analytical solutions that describe how individual electrical component in the circuit practically affects the SC converter at different frequencies. Such an analysis is important for the optimal design and realization of a complex (high-order) SC converter. This is particularly true for those SC converters which have more than two operating states. For complex SC converters, a constituent capacitor may have a profound effect on the converter's efficiency and is dependent on the configuration of the switches and the arrangement of the energy flow paths. In this paper, the relationship of the value of capacitors and the efficiency of complex SC converters is derived and investigated using an energy-flow-path analysis. Optimal design of SC converters can be achieved through a systematic component value selection by: 1) increasing the proportion of energy flow through the most efficient paths; and 2) increasing the efficiency of the paths that have a higher energy flow. The design of complex SC converters in terms of optimizing their power efficiency is discussed using an exponential SC converter as an illustration. The results of both calculation and experimental measurement show that the approach is effective. [ABSTRACT FROM AUTHOR]

The operation and efficiency of on-chip switched-capacitor (SC) converters are highly affected by the parasitic bottom plate capacitor present in on-chip capacitor technologies. Existing modeling frameworks do not in a comprehensive manner take the effect of the bottom plate capacitor on converter operation and efficiency into account. This paper extends an existing SC state space modeling framework to include the bottom plate capacitor. The developed model is used in a Pareto optimization procedure to optimally select the component values of a 2:1 on-chip SC converter. Implemented in a 32 nm SOI CMOS technology that features the high-density deep trench capacitor, the on-chip converter achieves $86\%$ maximum efficiency at 4.6\,\text{W}/\text{m}\text{m}^2 power density while converting from a 1.8 V input voltage to 830 mV output voltage. [ABSTRACT FROM AUTHOR]

The paper aims at clarifying the carrier-trapping influence on the electrical characteristics of silicon carbide (SiC) power MOSFETs and its inclusion in the simulation of SiC power mosfet-based circuits. Special focus is given on the degradation of the switching characteristics due to carrier trapping at SiC/SiO2 interface defects. A compact SiC power mosfet model, considering the trap density in the framework of a complete surface-potential description, has been developed by for accurate circuit simulation including power-loss prediction. The carrier trapping is verified to cause a switching delay, which results in switching loss increase. To achieve low power loss, trap-density reduction is shown to be vital. The maximum allowable trap density, which does not affect switching power loss, is discussed. [ABSTRACT FROM AUTHOR]

Nonlinear, voltage-dependent capacitances of power semiconductor devices are capable of having significant impact on the operation of switched-mode power converters. Particularly at high switching frequency, these nonlinearities play a significant role in determining switching times, losses, and converter dynamics during switching transitions. In order to accommodate the well-established design and analysis techniques commonly used for linear circuits, this paper examines the nonlinear voltage-dependence of switching device capacitances and proposes a circuit-oriented analysis technique that allows the parasitic capacitances to be replaced with linear equivalents. The multitude of developed equivalents are verified through full nonlinear simulation in both MATLAB/Simulink and SPICE, as well as through experimental results. [ABSTRACT FROM AUTHOR]

At a certain level of abstraction, power converters can be represented as linear circuits connected to diodes and controlled electronic switches. The evolutions of the electrical variables are determined by the state-dependent switchings, which complicate the mathematical modeling of controlled power converters. Differently from the complementarity models previously presented in the literature, the model proposed in this paper allows to represent as a linear complementarity system also closed-loop power converters, without requiring the a priori knowledge of the converter modes. A model construction procedure, not dependent on the specific converter topology, is presented. The discretization of the continuous-time model allows to formulate mixed linear complementarity problems for the computation of the control-to-output frequency response and the evolutions of both transient and steady-state currents and voltages. As illustrative examples, Z-source, boost, and buck dc-dc power converters under voltage-mode control and current-mode control operating both in continuous and discontinuous conduction modes are considered. [ABSTRACT FROM AUTHOR]

This article presents a dynamic averaged model of active neutral point clamped inverter (ANPCI). The proposed model helps in significant reduction of computational resources required for system-level studies in various applications which employ ANPCI as main power conversion stage. The average model derived in this article can consider the effect of various nonidealities in ANPCI, and also its capacitor voltage-balancing issues. The model is also modular in nature, i.e., it can be extended for an N-level ANPCI. PSCAD/EMTDC simulations and experiments are performed for steady-state and transient conditions to show that the averaged model developed in this article accurately predicts the steady-state and dynamic waveforms of ANPCI in both open-loop and closed-loop operations, even for large simulation time-steps. For the closed-loop operation, synchronous reference frame $dq$ -based controller is developed and implemented in a digital signal processor. In addition, the strength of the model is demonstrated by comparing the simulation waveforms and computational times required for simulating an ANPCI-based solar PV system using switching circuit model and the proposed averaged model. [ABSTRACT FROM AUTHOR]

Steady-state operation of dual active bridge (DAB) ac–dc converters can show a high dependence on the circuit nonidealities and on the transient nature of the consistently changing phase-shifts necessary to achieve ac–dc operation. These aspects are not fully captured using traditional modeling approaches derived from dc–dc DAB converter analyses. To address these issues, this article presents a unified modeling approach comprising of hybrid frequency and time-domain analyses that encompass the transient nature of the ac–dc converter while providing the advantages of steady-state frequency-domain analysis. The limitations of conventional modeling approaches are quantified and addressed. Additionally, a comprehensive analysis of modeling error trends with converter parameters is presented, which demonstrates the effectiveness of the proposed method over conventional methods. Finally, using the proposed modeling approach, a numerical optimization routine is proposed to find the optimal-conduction-loss modulation trajectory. The effectiveness of the method is verified by experimental testing on a 1 kW, 230–28 V fully GaN-based single-phase DAB ac–dc converter. [ABSTRACT FROM AUTHOR]

Traditional SiC MOSFET switching models cannot predict the turn-off losses precisely in the condition of small driver resistance and small load current, because they have not considered a special case in which the SiC MOSFET closes its channel before the SiC diode turns into the freewheeling-state during turn-off transient. To solve this problem, this article presents an improved SiC MOSFET turn-off model that considers the special case. The parasitic elements of circuit and the nonlinear characteristics of SiC MOSFET are also included in the proposed model to improve its accuracy. Experimental results show that the improved model can predict the turn-off transient of SiC MOSFET precisely. Moreover, the investigation of turn-off behavior shows that SiC MOSFET can achieve ultralow turn-off loss in the special case, because the channel current of SiC MOSFET can fall to 0 before the drain-source voltage rises to a high value. Driver resistance and load current are the decisive factors of achieving the special case, and this article gives the criterion of them. Besides, further studies show that lower common-source inductance, larger drain-source capacitance of MOSFET, and larger capacitance of diode can help to achieve ultralow turn-off loss. Experiments are carried out and the experimental results verify the analysis results. [ABSTRACT FROM AUTHOR]

To accurately capture the dynamics of a large-scale ac/dc system as a whole and the interactions between its individual components, a simulation method with high precision and efficiency is in great demand. For this purpose, we develop a multi-domain co-simulation method, in which the target system is partitioned into multiple dc and ac subsystems, represented by our proposed shifted-frequency phasor (SFP) models and the traditional EMT models, respectively. SFP models can be simulated with a much larger time step, leading to a significant improvement in simulation efficiency under a given requirement of precision. Further, a new interface model, namely, hybrid multi-domain transmission-line model (HMD-TLM), is developed to reflect the interactions between SFP models and EMT models, with the additional benefit of producing instantaneous and phasor waveforms simultaneously. Thus, the multi-domain co-simulation is implemented based on the efficient SFP models, the HMD-TLM, and a designed time sequences of simulation. The performance (efficiency and accuracy) of the proposed method has been validated on the well-known CIGRE ac/dc system as well as a practical system integrating large ac grids and modular-multilevel-converter-based multi-terminal dc grids. [ABSTRACT FROM AUTHOR]

Improvements are proposed for generalized average models of dual active bridge (DAB) converters. Generalized average modeling involves a tradeoff between accuracy and tractability. To maintain an acceptable level of complexity, existing DAB models are derived using a first harmonic approximation. These models provide accurate small-signal representations, but are limited as large-signal analysis tools due to persistent steady-state error. This study proposes a modeling framework that provides accurate large and small-signal models without significant increases in the overall complexity. The framework describes DAB operation with a triple phase shift modulation, and is easily simplified for single, dual, or extended phase shift modulation schemes. The special case of a single phase shift modulation, which experiences the most significant large-signal error, is given additional consideration. The framework is applied to open and closed-loop operation, and both large- and small-signal models are discussed. Models are validated in simulation and hardware experiments using a small scale DAB prototype. [ABSTRACT FROM AUTHOR]

This letter addresses the simulation of the steady-state response of switching power converters. The proposed approach is based on the interpretation of the voltage and current variables of a periodically switched linear circuit in terms of a series expansion and on the generation of augmented time-invariant constitutive relations of the circuit elements. The circuit solution is obtained from an augmented time-invariant nodal equation generated from topological information and circuit inspection only. The feasibility and strength of the approach are demonstrated on a dc-dc boost converter. [ABSTRACT FROM AUTHOR]

Due to a large number of converters in dc grids, the simulation speed using traditional electromagnetic simulation tools becomes very slow. An associated discrete circuit (ADC) switch model can improve the simulation efficiency greatly by avoiding the modification of system matrix during switching. However, existing ADC switches induce virtual power losses due to simulation errors during switching transients. The mechanism of the virtual power loss is analyzed, and a power loss model is established. An improved ADC switch model is designed by adding compensation sources to mitigate the simulation errors. Theoretical analyses are carried out to prove this improvement. A fast algorithm to obtain the initial values of the compensation sources is proposed by utilizing the complementary operation of IGBTs. The improved ADC switch provides fast simulation speed and high accuracy. The modeling is particularly suitable for investigating long term system dynamics of dc grids with multiple converters and fast converter transients at the same time. [ABSTRACT FROM AUTHOR]