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Constant on-time current mode (COTCM) Buck converters are widely used in power management integrated circuit (ICs) for microprocessors. Small-signal models are necessary tools to design high-quality controllers. Existing models neglect output voltage ripples (OVRs) and spectrum extension caused by switching, which makes significant errors under high control bandwidth. This article adopts Fourier series to describe OVRs precisely. Then, influences of OVRs on COTCM are analyzed. Finally, spectrum coupling from current loop and voltage loop is incorporated to obtain a high-frequency model, and four universal analytical expressions in frequency domain are obtained with the aid of matrix calculation. Based on the proposed model and genetic algorithm, an optimal controller design method is developed. Simulation and experiment validate the accuracy of proposed model and the effectiveness of proposed design method. [ABSTRACT FROM AUTHOR]

For grid-connected or interconnected microgrids, the transition to an autonomous and decentralized architecture was hampered by two perplexing issues: how to guarantee voltage-supporting capacity, while fully and controllably utilizing local power generation, and how to switch between islanded and grid-connected modes flexibly and seamlessly. Through a combination of benefits of interlinking converters and switches, the flexible transfer converters (FTCs), positioned at the interfaces between the utility grid and microgrids, are offered as a solution in this article. The basic concepts and classifications of the FTC are first presented, and a general-purpose FTC and a universal control strategy for distributed generations are then proposed as an example, which contribute to appropriate power dispatch and flexible mode transfer in a communication-free design, leading to a fully autonomous microgrid. Simple and economic operation rules, as well as high interoperability with existing assets, makes this solution promising for distributed microgrid applications. Further, generalized small-signal models of the target system are derived for stability analysis and parameter design. Finally, comprehensive case studies in simulations and experiments are provided to validate its effectiveness. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In an autonomous ac microgrid system, a peer-to-peer decentralized solution would be a preferred choice for the coordinative control of distributed generation units. However, due to the dispersed sources and loads, and mismatched line impedances, it is hard to achieve satisfactory power sharing performance and power quality without communication links. Therefore, a comprehensive decentralized solution based on dual-frequency-droop is proposed in this article. With only local information, appropriate virtual impedances could be obtained to compensate the mismatched complex line impedances in the required frequency range, and hence active, reactive, unbalanced, and harmonic powers could be shared accurately among parallel inverters under various load conditions. Then, the frequency deviation caused by the droop control is effectively attenuated without affecting power sharing through a dynamic droop-slope regulator. Moreover, the causes of steady-state ripples on virtual impedance waveforms are carefully analyzed, and the design criterions to eliminate these ripples are provided. Finally, case studies are provided in simulations and experiments to validate the effectiveness of this method. [ABSTRACT FROM AUTHOR]

The proportional-integrator (PI) controller in the synchronous reference frame (dq-frame) and the proportional-resonant (PR) controller in the stationary reference frame (αβ-frame) are two typical linear current control schemes for three-phase voltage source converters. It is generally believed that the plant model is mathematically uncoupled in αβ-frame. Hence, the decoupling control required to attenuate the axis cross-coupling effect in dq-frame is regarded as not necessary in αβ-frame. However, detailed analysis with complex coefficient transfer functions reveals differences in the control performance between the fully decoupled PI control scheme in dq-frame and the PR control scheme in αβ-frame. When regulating sinusoidal currents in αβ-frame, the α-axis and β-axis current references are strongly correlated with each other, which implies a cross-coupling effect equivalent to that of dq-frame. In analogy to the dq-frame decoupling control, cross-coupling terms can be employed together with the conventional PR control scheme. It can bring the benefit of improving the transient response of current tracking and reducing the sensitivity of the resonant controller to frequency variation, especially for low-switching-frequency applications with limited current control bandwidth. Furthermore, the cross-coupling terms based on reference current feed-forward are proposed to improve the performance of both positive- and negative-sequence current control. Experimental results are shown to validate the analysis and the performance of the proposed control scheme. [ABSTRACT FROM AUTHOR]

As a key parameter in microgrids, feeder impedance is closely related to power distribution, power quality, and system stability. This letter proposes a novel noninvasive feeder impedance estimation method, which uses the microgrid central controller (MGCC) and inherent harmonic signals introduced by a nonlinear or unbalanced load. First, the sequence impedance model for a droop-controlled inverter is built to demonstrate that the inverter output impedance is negligible at low-order harmonic frequencies. Then, the bus voltage and output current at a specific dominant harmonic frequency are extracted in MGCC, based on which feeder impedance can be obtained. Finally, the estimated feeder impedance is used to generate proper virtual impedance to enhance power sharing and voltage quality as an example, based on a hierarchical control structure. Experimental results are provided to validate the proposed method. [ABSTRACT FROM AUTHOR]

Digital control delay is studied as one of the leading factors causing instability in grid-tied voltage source inverter (VSI) systems. However, how this delay affects the small-signal output impedance of the VSI and how the change in impedance shape further influences the system stability are still not clear. This article, for the first time, thoroughly analyzes the impact of delay on the dq-frame output impedance of the VSI operating in both the single current loop control mode and the dual-loop control mode. It is found that when delay is considered, a distinct magnitude drop and a phase rise always exist at the high-frequency area of the impedance, which is named the “impedance trough.” By studying the dq-frame output impedance of the VSI, the origin of the impedance trough, and its analytical relationships with the current loop dynamics, voltage loop dynamics, and delay values are unveiled. Meanwhile, the influence of the impedance trough on the stability of the grid-tied VSI system under these two control modes is evaluated through d–d channel impedance matching and generalized Nyquist criterion (GNC). It is demonstrated that the joint effects of delay and control parameters result in the impedance mismatch between the grid and the VSI, which is the root cause of high-frequency oscillations in the grid-tied system. Finally, experimental results verify the analysis. [ABSTRACT FROM AUTHOR]

In an islanded microgrid composed of droop-controlled parallel inverters, the system frequency endures deviations as the load changes. To compensate for frequency deviation without involving communication infrastructures among distributed generators (DGs), the proportional-integral regulator based secondary frequency control (PI-SFC) method has been proposed in the literature. However, PI-SFC may incur real power-sharing errors because the integrator accumulates disturbances and noise in each DG, leading to different compensation values of nominal real power. To achieve frequency restoration while maintaining equal real power sharing among DGs, this article proposes a small-ac-signal injection-based secondary frequency control (SACS-SFC) method, which is implemented by injecting an additional ac signal into the output voltage of each DG. Furthermore, a droop relation between the frequency of the injected SACS and the compensation value of nominal real power is innovatively established to trim the output real power of each DG to be equal. Frequency deviations caused by primary droop control are thus eliminated, and even real power sharing can be maintained among DGs. Moreover, the control parameters of the proposed SACS-SFC are comprehensively designed via steady state and dynamic model of the system. Simulation and experimental results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article studies the modeling of high-bandwidth buck converters under constant-frequency voltage-mode control, where the traditional small-signal averaged model fails due to two major factors in the pulsewidth modulation (PWM), i.e., the large harmonics of modulation waveform and the considerable sideband components. Several modified small-signal models have been proposed to improve the predictions of the frequency domain characteristics. However, these models are less generalized or with high complexity, and may hardly be used in the closed-loop design of real applications. To handle this issue, this article proposes a generalized multifrequency small-signal model (G-MFSSM) for high-bandwidth buck converters, which makes further progress in accuracy while maintaining simplicity in deriving the analytical transfer functions for a closed-loop design. The generalized average model is adopted to precisely describe the first-order harmonic of the modulation waveform, from which a correction factor is extracted to evaluate the influence of the ripple. Furthermore, two dominant sideband components are selected optimally for extremely accurate loop gain predictions. Finally, a closed-loop design procedure is presented for wide-input, high-bandwidth buck converters based on the proposed G-MFSSM. The validity of the proposed G-MFSSM is verified by simulations and experiments. [ABSTRACT FROM AUTHOR]

A dc terminal impedance model of voltage-source converter (VSC) is required to analyze the stability of multiterminal high-voltage direct current system. This article proposes a comprehensive dc terminal impedance model for conventional three-phase two-level VSC under different control modes. The control strategy includes inner decoupled current control and outer control, the latter contains dc voltage control, active/reactive power control, and droop control for grid-connected VSC and ac voltage control for VSC connected to a load. When a VSC is connected to the ac grid, the phase-locked loop (PLL) is also taken into account. The influences of PLL dynamics, control time delay and dead time on the dc-side impedance are explained. Also, how the parameters of the inner current control and outer control affect the characteristics of dc terminal impedance is analyzed in detail. Finally, experimental measurements verify the proposed impedance models and analysis. [ABSTRACT FROM AUTHOR]

Parallel droop-controlled inverters with renewable energy sources are widely employed in islanded ac microgrids, where dynamic interactions among them may cause small-signal stability issues. Since the active power-frequency droop scheme is applied, the dynamic interactions among inverters exist not only in bus voltage and transmitted current, but also in variable system fundamental frequency. This paper introduces a novel small-signal terminal characteristic model for droop-controlled inverter. Besides conventional impedance and admittance, a new set of terminal characteristics is proposed to characterize the dynamics of fundamental frequency. Furthermore, the small-signal model of parallel inverters is constructed based on the terminal characteristics of individual inverters. Covering the fundamental frequency interactions, a stability prediction approach based on generalized Nyquist criterion is proposed for parallel droop-controlled inverters. Besides the product of impedance and admittance, an additional term is added in the system return ratio, which consists of the proposed terminal characteristics associated with the fundamental frequency. Finally, experimental results validate the effectiveness of this proposed stability prediction approach. [ABSTRACT FROM AUTHOR]

To address the unbalanced and harmonic power sharing issue among parallel inverters caused by feeder impedance mismatch in islanded microgrids, an adaptive virtual impedance control method is proposed based on the injection of an extra small ac signal (SACS) in the output voltage of each inverter. Similar to the principle of active power–frequency droop, the frequency of the injected signal droops with the output unbalanced and harmonic power, while the active power produced by the injected SACS is detected to adjust the virtual impedance at the fundamental negative sequence and selected harmonic frequencies, which will tune the distribution of unbalanced and harmonic power in the system. When the injected SACSs of each inverter synchronize with each other and reach a common frequency in steady state, the virtual impedance of each inverter will be matched to each other for evenly sharing the unbalanced and harmonic power. This proposed method requires neither communication links among parallel inverters nor feeder impedance information. Furthermore, the control parameter design method based on modeling and stability analysis of the proposed control structure is discussed in detail. Finally, simulation and experimental results are provided to validate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Small-signal stability of ac power systems is able to be assessed by measuring their terminal impedance, and a transformerless series injector is very attractive for wideband measurement of load impedances. A typical implementation of the transformerless series injector is paralleled H-bridge (PHB) converters, where dc voltage imbalance will occur when system current magnitude is larger than a critical point, and thus the operation region of the series injector is seriously restricted. To address this issue, this paper presents a deep analysis on the mechanism behind dc voltage imbalance for PHB-based series injector, and it is revealed that a positive feedback exists in the dc voltage balancing loop under high system current magnitude. Then an enhanced control scheme is proposed to balance dc voltages in full system current range, where a reactive component is injected in the output voltage while reactive circuiting current is introduced among H-bridge converters for redistributing active power. Furthermore, the system behavior with the proposed scheme is comprehensively analyzed and the reference design for the injected reactive component magnitude in the output voltage is offered. Finally, the imbalance mechanism and the proposed scheme are validated by simulation and experimental results. [ABSTRACT FROM AUTHOR]

In this paper, a generalized droop control (GDC) is proposed for a grid-supporting inverter based on a comparison between traditional droop control and virtual synchronous generator (VSG) control. Both the traditional droop control and VSG control have their own advantages, but neither traditional droop control nor VSG control can meet the demand for different dynamic characteristics in grid-connected (GC) and stand-alone (SA) modes at the same time. Rather than using a proportional controller with a low-pass filter, as in a traditional droop control, or fully mimicking the conventional synchronous generator parameters in a VSG control, the active power control loop of the GDC can be designed flexibly to adapt to different requirements. With a well-designed controller, the GDC can achieve satisfactory control performance; unlike a traditional droop control, it can provide virtual inertia and damping properties in SA mode; unlike a VSG control, the output active power of an inverter with GDC can follow changing references quickly and accurately, without large overshoot or oscillation in the GC mode. Moreover, given specific controller parameters, the GDC can function as both a traditional droop control and a VSG control. The GDC's controller parameter design is more intuitive and flexible, and this paper provides a distinct design process. Finally, the effectiveness of the proposed control method is validated by the simulation and experimental results. [ABSTRACT FROM AUTHOR]

The coupling between the active and the reactive power of the droop-controlled inverter is critical in the low-voltage microgrid. The conventional virtual power-based control strategy can decouple the active and the reactive power of the inverter, whereas the active power of the load is probably not equally shared among the parallel inverters in the microgrid. To tackle this issue, this paper proposes an improved virtual power-based control method for the droop-controlled parallel inverters with a unified rotation angle in the power transformation. Meanwhile, the optimal value of the unified rotation angle is rigorously derived through investigating the relative stability of the system by innovatively adopting Routh Stability Criterion. Moreover, the proposed method is enhanced by introducing low-pass filters in the coupling path for further mitigating the coupling between the active and the reactive power of the inverter. Additionally, the stability analysis and parameter design for the proposed method are comprehensively presented. Finally, the effectiveness of the proposed method is validated by the simulation and experimental results. [ABSTRACT FROM AUTHOR]

Paralleled inverters are widely employed as the power source in the AC distributed power system, whose output impedance and stability status are required in the impedance-based stability analysis of the whole system. This paper presents an output impedance model as well as a stability prediction method for three-phase paralleled inverters with master–slave sharing scheme. While the output impedance of three-phase paralleled inverters is generally modeled under synchronous reference frame (SRF), the terminal characteristics of individual inverters operating standalone are innovatively adopted in the proposed output impedance model, with no need for knowledge about inner parameters of the inverters. Furthermore, the stability criterion is derived with this model according to the generalized Nyquist criterion, where the stability of paralleled inverters can be predicted by investigating characteristic loci of two return ratios. Meanwhile, the terminal characteristics of individual inverters controlled under SRF is comprehensively modeled. Finally, the proposed output impedance model and stability criterion were experimentally verified. [ABSTRACT FROM AUTHOR]