Grid-connected inverters are known to become unstable when the grid impedance is high. Existing approaches to analyzing such instability are based on inverter control models that account for the grid impedance and the coupling with other grid-connected inverters. A new method to determine inverter-grid system stability using only the inverter output impedance and the grid impedance is developed in this paper. It will be shown that a grid-connected inverter will remain stable if the ratio between the grid impedance and the inverter output impedance satisfies the Nyquist stability criterion. This new impedance-based stability criterion is a generalization to the existing stability criterion for voltage-source systems, and can be applied to all current-source systems. A single-phase solar inverter is studied to demonstrate the application of the proposed method.

Impedance-Based Stability Criterion for Grid-Connected Inverters

This paper presents a review of control strategies, stability analysis, and stabilization techniques for dc microgrids (MGs). Overall control is systematically classified into local and coordinated control levels according to respective functionalities in each level. As opposed to local control, which relies only on local measurements, some line of communication between units needs to be made available in order to achieve the coordinated control. Depending on the communication method, three basic coordinated control strategies can be distinguished, i.e., decentralized, centralized, and distributed control. Decentralized control can be regarded as an extension of the local control since it is also based exclusively on local measurements. In contrast, centralized and distributed control strategies rely on digital communication technologies. A number of approaches using these three coordinated control strategies to achieve various control objectives are reviewed in this paper. Moreover, properties of dc MG dynamics and stability are discussed. This paper illustrates that tightly regulated point-of-load converters tend to reduce the stability margins of the system since they introduce negative impedances, which can potentially oscillate with lightly damped power supply input filters. It is also demonstrated that how the stability of the whole system is defined by the relationship of the source and load impedances, referred to as the minor loop gain. Several prominent specifications for the minor loop gain are reviewed. Finally, a number of active stabilization techniques are presented.

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DC Microgrids—Part I: A Review of Control Strategies and Stabilization Techniques

DC microgrids (MGs) have been gaining a continually increasing interest over the past couple of years both in academia and industry. The advantages of dc distribution when compared to its ac counterpart are well known. The most important ones include higher reliability and efficiency, simpler control and natural interface with renewable energy sources, and electronic loads and energy storage systems. With rapid emergence of these components in modern power systems, the importance of dc in today's society is gradually being brought to a whole new level. A broad class of traditional dc distribution applications, such as traction, telecom, vehicular, and distributed power systems can be classified under dc MG framework and ongoing development, and expansion of the field is largely influenced by concepts used over there. This paper aims first to shed light on the practical design aspects of dc MG technology concerning typical power hardware topologies and their suitability for different emerging smart grid applications. Then, an overview of the state of the art in dc MG protection and grounding is provided. Owing to the fact that there is no zero-current crossing, an arc that appears upon breaking dc current cannot be extinguished naturally, making the protection of dc MGs a challenging problem. In relation with this, a comprehensive overview of protection schemes, which discusses both design of practical protective devices and their integration into overall protection systems, is provided. Closely coupled with protection, conflicting grounding objectives, e.g., minimization of stray current and common-mode voltage, are explained and several practical solutions are presented. Also, standardization efforts for dc systems are addressed. Finally, concluding remarks and important future research directions are pointed out.

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DC Microgrids—Part II: A Review of Power Architectures, Applications, and Standardization Issues

This paper analyzes the small-signal impedance of three-phase grid-tied inverters with feedback control and phase-locked loop (PLL) in the synchronous reference ( d-q ) frame. The result unveils an interesting and important feature of three-phase grid-tied inverters – namely, that its q–q channel impedance behaves as a negative incremental resistor. Moreover, this paper shows that this behavior is a consequence of grid synchronization, where the bandwidth of the PLL determines the frequency range of the resistor behavior, and the power rating of the inverter determines the magnitude of the resistor. Advanced PLL, current, and power control strategies do not change this feature. An example shows that under weak grid conditions, a change of the PLL bandwidth could lead the inverter system to unstable conditions as a result of this behavior. Harmonic resonance and instability issues can be analyzed using the proposed impedance model. Simulation and experimental measurements verify the analysis.

Analysis of D-Q Small-Signal Impedance of Grid-Tied Inverters

In the first part of this paper, three-phase power factor correction (PFC) rectifier topologies with sinusoidal input currents and controlled output voltage are derived from known single-phase PFC rectifier systems and/or passive three-phase diode rectifiers. The systems are classified into hybrid and fully active pulsewidth modulation boost-type or buck-type rectifiers, and their functionality and basic control concepts are briefly described. This facilitates the understanding of the operating principle of three-phase PFC rectifiers starting from single-phase systems, and organizes and completes the knowledge base with a new hybrid three-phase buck-type PFC rectifier topology denominated as Swiss Rectifier. Finally, core topics of future research on three-phase PFC rectifier systems are discussed, such as the analysis of novel hybrid buck-type PFC rectifier topologies, the direct input current control of buck-type systems, and the multi-objective optimization of PFC rectifier systems. The second part of this paper is dedicated to a comparative evaluation of four rectifier systems offering a high potential for industrial applications based on simple and demonstrative performance metrics concerning the semiconductor stresses, the loading and volume of the main passive components, the differential mode and common mode electromagnetic interference noise level, and ultimately the achievable converter efficiency and power density. The results are substantiated with selected examples of hardware prototypes that are optimized for efficiency and/or power density.

The Essence of Three-Phase PFC Rectifier Systems—Part II

This paper addresses stability problems in power systems with loads that exhibit constant-power behavior. Instability may occur in such systems due to the negative incremental impedance of constant-power loads (CPLs). Existing approaches to stabilizing such systems require modification of the source and/or the load control characteristics, or isolating the CPL from the rest of the system by additional active devices, which are difficult to implement and often conflict with other system requirements such as control bandwidth, size, weight, and cost. In this paper, we investigate passive damping as a general method to stabilize power systems with CPL. Using a representative system model consisting of a voltage source, an LC filter, and an ideal CPL, we demonstrate that a CPL system can be stabilized by a simple passive damping circuit added to one of the filter elements. Three different damping methods are considered and analytical models are developed for each method to define damping parameters required for stabilizing the system. Time- and frequency-domain measurements from an experimental system are presented to validate the methods.

Constant-Power Load System Stabilization by Passive Damping

A new method to reduce common-mode (CM) electromagnetic interference (EMI) emission at the dc input of variable-speed motor drives is presented. Unlike conventional passive or active filtering techniques that rely on impedance mismatch or active noise cancellation, the proposed method uses a passive circuit with matched impedance to cancel the inverter CM current. In the proposed approach, a star-connected three-phase RC circuit is placed at the output of the inverter to extract the CM voltage. An inductor is connected between the star point of the RC circuit and the middle of the dc bus capacitor to inject a CM current into the dc input. A Wheatstone bridge is then identified in the CM equivalent circuit of the system with these additional components. By properly selecting the inductor, the Wheatstone bridge can be balanced, resulting in near-ideal cancellation of the input CM current. Development of the method is presented and an experimental setup is used to demonstrate its effects. A comparison with conventional EMI filtering methods in terms of overall filter volume is also presented.

Conducted Common-Mode EMI Reduction by Impedance Balancing

Damping of EMI filter input impedance to avoid resonance with the source output impedance is presented. Optimization of the damping resistor to maximize the damping effects for a given damping capacitor or inductor while minimizing the power loss is proposed. Three different damping circuits are studied, and for each, an analytical model defining the optimal damping resistance is presented. Performances of these damping circuits are compared in terms of achievable damping effects and power dissipation, as well as size and volume of damping capacitors and inductors. A case study is also presented to illustrate the application of the proposed design.

Optimal Damping of EMI Filter Input Impedance

A systematic and practical method to parameterize three-phase electric machine models for electromagnetic interference (EMI) simulation is presented. The proposed behavioral model consists of multiple sections of linear RLC circuits and is intended for time-domain simulation with inverters and other power electronic circuits found in typical motor drive systems. The proposed parameterization method uses a differential-mode (DM) and a common-mode (CM) impedance measurement of the machine and takes advantage of the separation among different parallel and series resonant frequencies of each impedance to determine the parameters of each stage in a noniterative manner. The proposed method can also be applied to model three-phase cables and transformers.

Parameterization of Three-Phase Electric Machine Models for EMI Simulation

This paper addresses stability problems of power systems with actively controlled loads that exhibit constant-power behavior. Instability occurs in such systems due to the negative incremental resistance of the constant-power loads (CPL). Existing approaches to stabilizing such systems require modification of the source and/or the load control characteristics, or isolating the CPL from the rest of the system by additional active devices, which are difficult to implement and often conflict with other system requirements such as control bandwidth, size, weight, and cost. In this work, we propose passive damping as a general method to stabilize power systems with CPL. Using a representative system model consisting of a voltage source, an LC filter, and an ideal CPL, we demonstrate that a CPL system can always be stabilized by a simple passive damping circuit added to one of the filter elements, no matter how the original system behaves. Three different damping methods are considered and for each analytical models are developed to define their parameters required for stabilizing the system. The different damping methods are also compared in terms of their stabilization capabilities and impact on other system performances such as filter attenuation. Time- and frequency-domain measurements from an experimental system are presented to validate the proposed methods.

Lei Xing

Papers

Constant-Power Load System Stabilization by Passive Damping

Conducted Common-Mode EMI Reduction by Impedance Balancing

Optimal Damping of EMI Filter Input Impedance

Parameterization of Three-Phase Electric Machine Models for EMI Simulation

Stabilization of constant-power loads by passive impedance damping