Output Impedance Model Research Articles

DC‐link voltage stability analysis for three‐level boost + full‐bridge LLC cascaded converter using impedance modeling

AbstractThe cascade converter system has been widely concerned along with the medium power operating conditions, and it is crucial to address the intricate interplay among individual modules to ensure stability of both the source and load subsystems. This paper analyzes the DC‐link voltage stability based on impedance matching and proposes a normalized sensitivity calculation method based on the control strategy, which prevents the complex products and matrix calculations of traditional methods. The three‐level boost (TLB) output impedance model is derived based on state‐space averaging for open‐loop and considering the double‐loop, and the full‐bridge LLC (FBLLC) input impedance model is derived based on the fundamental equivalent circuit. Then the effect of the double‐loop PI parameters on the output impedance of the TLB is analyzed in detail based on the normalized sensitivity and verified by the Bode plots. The experimental results of the 30 kW prototype indicate that the control parameters were varied by a factor of 10 compared to the theoretical control group. The most significant alteration was the modification of the kp_i, resulting in an 8.9% increase in the DC‐link voltage ripple, while the ki_v was modified, resulting in a 0.53% increase, indicating that the effects of the PI parameter are consistent with the normalized sensitivity results.

A Hybrid Beat Frequency Oscillation Suppression Strategy for DC Microgrids

In DC microgrids, parallel-connected power converters are commonly used to integrate distributed energy sources. However, interactions of power switching noises among these power converters could lead to large low-frequency beat frequency oscillations under certain conditions, which degrades system performance and reliability, especially for DC microgrids with parallel connected Boost converters. In this research, the output impedance model for multiple parallel-connected Boost converters is developed for beat frequency oscillation analysis, and then a hybrid method is proposed to address this issue. The proposed method includes separated switching frequency channels and additional line inductors. Experimental results validate the effectiveness of the proposed method.

A Series Impedance Reshaping Control Method Considering PLL Dynamics for Grid-Connected Inverters Under Weak Grid Conditions

Grid-connected inverters are the key part in renewable energy power generation systems. Usually, phase-locked loop (PLL) is adopted in grid-connected inverters to achieve synchronization. However, prior-art works have revealed that the negative resistance behavior in the low-frequency band caused by PLLs may lead to system instability under weak grids. In this paper, first, a comprehensive small-signal output impedance modeling of the LCL-filtered single-phase grid-connected inverter is derived for stability analysis, where the digital control delays and PLL dynamics have been taken into account. Then, a simple but effective virtual series based impedance reshaping method is proposed. With that, the inverter system can operate stably even under a very weak grid (e.g., short-circuit ratio (SCR) is as low as 1.2). Compared with the traditional grid impedance compensation by virtually increasing grid resistance or reducing the grid inductance, the proposed method does not require grid impedance estimation and is robust against system parameter variations. Thus, its feasibility is improved. Finally, experimental tests are carried out on a single-phase 5-kW prototype, validating the effectiveness of the proposed scheme.

On the Impedance and Stability Analysis of Dual-Active-Bridge-Based Input-Series Output-Parallel Converters in DC Systems

Dual-active-bridge-based (DAB-based) input-series output-parallel (ISOP) converters have become increasingly popular due to their promising features made up of the advantages of the modular power electronics and the DAB converter. The modeling of the DAB converter and the DAB-based ISOP converter has been widely explored for control design in order to analyze the stability and improve the performance of the converter itself such as the voltage balancing and power sharing of DAB submodules. However, the modeling on the impedance of the DAB-based ISOP converter, which can be quite useful for system-level stability analysis and optimization, has not been addressed sufficiently so far. To solve this issue, this paper presents comprehensive impedance modeling of the DAB-based ISOP converter, where the output voltage control and the input voltage balancing control are applied to the converter to achieve the equal power sharing of the submodules. The proposed input impedance model and output impedance model of the DABbased ISOP converter are validated through the frequencydomain sweep in simulation and experiment. With the validated impedance models, the instability phenomenon and the frequency of the main harmonic component in oscillating waveforms can be accurately predicted at the source side and at the load side of the converter respectively.

Harmonic Suppression Strategy of LCL Grid-Connected PV Inverter Based on Adaptive QPR_PC Control

To reduce the influence of voltage harmonics on the grid current, a control strategy based on adaptive quasi-proportional phase compensated resonance (QPR_PC) is proposed. Firstly, the LCL grid-connected photovoltaic inverter system model is established, and the stability performance of the three-level inverter system under double closed-loop control is analyzed using the output impedance model of the inverter. Then, a QPR regulator for the zero steady-state error tracking of AC signals is studied. To solve the problem that the system has poor robustness against frequency changes when the traditional QPR regulator is used in the static coordinate system, this paper improves the traditional QPR regulator to optimize the response characteristics of the closed-loop system. Based on the QPR regulator, a phase margin compensation structure is introduced to form QPR_PC control. Then adaptive frequency design is added to ensure good control even when the power grid frequency drifts, which is the control strategy proposed in this paper. Verification shows that the proposed method improves the phase margin of output impedance at a specific frequency, restrains the interference of the 3rd, 5th, and 7th harmonics of grid voltage, and improves the dynamic performance of the system and the quality of grid-connected current. Finally, the simulation results show that the total harmonic distortion rate of grid-connected current is reduced by 1.03% after adopting this strategy, which verifies the effectiveness and correctness of the proposed method.

Detecting Speed Improvement and System Stability Enhancement for DC Microgrids Islanding Detection Based on Impedance Characteristic Analysis

Islanding detection is the essential basis for the safety and protection of dc microgrids. Due to the advantages of rapid detection speed and small nondetection zone, the positive feedback islanding detection technique has attracted much interest in recent years. The implementation of a positive feedback loop facilitates the islanding detection for dc microgrids, but it may reduce the system stability margin at the grid-connected state. In this article, the dc output impedance model of voltage source converter and distributed generators are developed to reveal the dynamic interactions and instability mechanism accurately between the two subsystems considering the impact of islanding detection with voltage positive feedback of selected frequency (VPFOSF). Then, the stability region of the interconnected system based on the output admittance model is derived to guide the design method of the damping compensator. Moreover, a grid-current-based active-damping control scheme is further proposed to mitigate instability caused by the VPFOSF loop. Thus, the conflict among islanding detection rapidity, power quality, and grid-connected system stability is effectively addressed. In the end, both the simulations and experimental results are provided to validate the effectiveness of the proposed control method.

Single Grid-Current Sensor-Controlled Weak-Grid-Following Inverters: A State-and-Disturbance-Observer-Based Robust Control Scheme Achieving Grid-Synchronization and Disturbance Rejection

With the aim of reducing the number of sensors, this article investigates the single-sensor grid-following control for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -filtered inverter system, and proposes an intuitive robust stability analysis method in the linear framework to handle power control and grid voltage variations in engineering practice. Specifically, through the use of a state-and-disturbance observer, the lumped-disturbance compensated suppression and nominal system full-state feedback technologies are equivalently realized. And the lumped-disturbance estimation carrying voltage phase information at the point of common coupling is further used as synchronization target of the phase-locked loop (PLL) to achieve grid-following control, and the resulting phase-shift is further corrected by accurate phase compensation. In addition, due to the nonlinear nature of the PLL and the power control and grid voltage variations, the system analysis is faced with the dilemma of complex nonlinear analysis or small-signal analysis without a fixed equilibrium point. In this case, a PLL small-signal model with bounded parameter perturbation characterizing power control and grid voltage variations is developed, and further incorporated into the output impedance modeling of the single-sensor grid-following controlled inverter. According to the edge theorem, the system stability in the studied uncertain region is analyzed via four edge output impedances, and appropriate control parameters are selected accordingly. Finally, the experimental results from a downscaled prototype are provided to verify the effectiveness of the proposed single-sensor grid-following control scheme.

Stability analysis of doubly-fed wind generation systems under weak power grid based on virtual synchronous control combined with adaptive robust control

Doubly-fed induction generator (DFIG) of wind generation system is generally located at the end of the distribution power-grid. Under the weak power grid, the grid connection of wind turbines is unstable, and the current quality is poor. Based on DFIG output impedance model, a stability analysis method combined with adaptive control method is proposed in this paper. The DFIG impedance model with power outer-loop is derived based on the virtual synchronous control of DFIG by using adaptive robust control method. Using generalized Nyquist criterion, the impacts of different power grid conditions and control parameters on the system stable operation under virtual synchronous control are analyzed and verified. The proposed control method in this paper is verified by experiments. The proposed control method improves the quality of grid-connected current.

Impedance Characteristics and Harmonic Analysis of LCL-Type Grid-Connected Converter Cluster

This study addresses the output impedance model of the LCL-type grid-connected converter considering the dead-time effects and the digital control delay. The model shows that the digital control delay will affect the accuracy of the output impedance of the grid-connected converter, and the dead-time effects are only equivalent to superimposing a disturbance voltage on the original output impedance model. The derived output impedance model is verified by comparing it with the switching model in the PSIM simulation environment. The harmonic interaction between converter cluster and utility grid is modeled and analyzed based on the output impedance model. A combined harmonic suppression strategy is incorporated into every converter control scheme to suppress the harmonic interaction. Simulation results are presented to demonstrate the correctness of harmonic interaction analysis and the effectiveness of the proposed suppression strategy.

Modeling and Analysis of the Harmonic Interaction between Grid-Connected Inverter Clusters and the Utility Grid

The virtual synchronous generator (VSG) is a promising technology for future utility grids, since it can mimic the output characteristics of a synchronous generator, which provides the necessary inertia to a utility grid. However, the large-scale application of VSGs is limited due to the harmonic interaction between VSGs and the utility grid. Therefore, in order to investigate the stability issue as well as improve the practical application for large-scale power stations, the harmonic interaction mechanism between the VSG cluster and the utility grid is addressed. Firstly, the output impedance model of a single VSG is established, and it is found that the resonance frequency is related to parameters including the output filter, controller, and grid impedance. On this basis, the capacitor current control for a grid-connected inverter based on a VSG is proposed to enhance the resonance suppression. Furthermore, the output impedance of the VSG cluster is established, which reveals the harmonic interaction characteristics between the VSG cluster and the utility grid. In addition, in order to suppress the resonance and improve the stability, an inner-loop control strategy of VSG is introduced. Finally, the simulation and experimental results verified the correctness of the established modeling and analysis of the harmonic interaction between the clustered VSGs and the utility grid. The results show that the proposed impedance model is correct and can predict the resonant point accuracy (which is around 2.3 kHz in the simulation and experimental cases). The total harmonic distortion (THD) can be reduced to 3.2% which meets the requirements of IEEE standard 519.

An improved method of phase-locked loop grid-connected inverter based on capacitor voltage full feedforward

Different from the conventional grid voltage feedforward, the capacitive voltage type full feedforward will not amplify high frequency harmonics, and it can eliminate the capacitor current control and simplify the controller design. However, when the grid impedance is relatively large, the phase-locked loop may increase the current harmonics of the grid-connected inverter, leading to system instability. Therefore, this paper establishes the output impedance model of the grid-connected inverter with full feedforward capacitor voltage including phase-locked loop, and then proposes an improved strategy for adding a low-pass filter in the traditional phase-locked loop, and parameterizes it *Design, so as to achieve the purpose of improving the output impedance phase of the inverter. Finally, the simulation verifies that the inverter using the improved phase-locked loop can effectively improve the quality of the grid current and improve the stability of the inverter system in a weak grid.

Modeling, Analysis, and Control Design of a Single-Stage Boost Inverter

A single-phase, single-stage, differential boost inverter comprises two independently-controlled boost DC-DC converters, with the load connected between their outputs. The net voltage on the load is sinusoidal and has a controllable frequency and magnitude that is larger than that of the DC source. The present work first derives steady-state and small-signal models of the inverter with parasitic elements. The results obtained from the line-to-output transfer function, control-to-output transfer function, open-loop input impedance, and open-loop output impedance models are compared with that of the ones obtained from the experimental testbed. Using the new models, a voltage mode controller is designed in the synchronous reference frame. The regulator design is explored through the use of an example. The results are verified against the small-signal model, then PLECS simulations, and finally a laboratory experiment. The results indicate excellent agreement between the model and experiment during transients in voltage reference, input source voltage, and output load. A sensitivity analysis is performed based on the inverter model considering the parameter variation. Finally, loss and efficiency estimations are provided in this work.

Output impedance modeling and grid-connected stability study of virtual synchronous control-based doubly-fed induction generator wind turbines in weak grids

Virtual synchronous control (VSynC) technology that mimics the behavior of a conventional synchronous generator can be applied in wind turbines (WTs), where it can effectively improve equivalent inertia, damping coefficient, and wind power permeability. Given the unique partial-scale converter structure of a doubly-fed induction generator (DFIG) and its complicated DFIG-grid coupling effect, the grid-connected VSynC-based DFIG WTs have gained little attention. Moreover, under a weak grid condition, some unstable modes of VSynC can interact with the wind power system, which impacts the DFIG’s dynamic characteristics and system stability. To bridge the gap, this study proposes an output impedance model for a VSynC-based DFIG to analyze the grid-connected stability in weak grids. First, the output impedance mathematical model for a VSynC-based DFIG is derived and explained. On the basis of this novel model, the low-frequency characteristics and vital unstable factors of a VSynC-based DFIG are comprehensively investigated. The impact of different VSynC parameters and grid strengths are extensively studied. Finally, the proposed output impedance model is validated by direct current disturbing theory, frequency scanning method, generalized Nyquist criterion, and time-domain simulation (MATLAB/Simulink). All the obtained results are consistent with each other and prove the effectiveness and accuracy of the proposed impedance model.

Impedance stability analysis and impedance remodelling of matrix converter grid‐connected system

Matrix converter has become one of the research hotspots of power electronic converter due to its excellent input and output characteristics and adjustable power factor. To study the stability of the matrix converter grid-connected system, the harmonic linearisation method is adopted to model the positive and negative sequence output impedance models of the matrix converter grid-connected system. The stability of the system is analysed by judging whether the plot of the ratio of the input impedance to the positive and negative sequence output impedance satisfies the Nyquist stability criterion. Also, an impedance remodelling method based on the positive sequence impedance is proposed to improve the stability of the system. Finally, the simulation verification is carried out by MATLAB/Simulink. The simulation results prove the correctness of the theoretical analysis and the feasibility of the impedance remodelling method.

A Reduced RLC Impedance Model for Dynamic Stability Analysis of PI-Controller-Based DC Voltage Control of Generic Source-Load Two-Terminal DC Systems

For the dynamic stability analysis of PI-controller-based dc voltage control of generic source-load two-terminal dc systems, a simpler <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> parallel impedance model has been proposed. First, by ignoring fast inner current control, the output impedance model of the dc voltage control system can be represented as a parallel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> circuit, which gives an intuitive insight into the physical sense of parameters in the dc voltage PI controller. Then, a dynamic impedance ratio is introduced to represent the impact of dc voltage droop control and line impedance on the dc voltage control system. With this ratio, a generalized <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> parallel impedance model appropriate for dynamic stability analysis of the considered dc system has been obtained. By simplifying the higher order dynamic impedance ratio model to a first-order high-pass filter in the dc voltage control timescale, a typical second-order model of the total impedance expression can be obtained, by which the dynamic stability of dc voltage control can be investigated in an analytical way. Furthermore, even including low dynamics of the inner current control of the dc voltage control unit and the constant power load (CPL)-side converter, the generic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> model can still be retained. It should be noted that the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> model can be extended to more complex dc systems. Finally, power system computer aided design (PSCAD)/electromagnetic transients including dc (EMTDC)-based simulation verifications and a small-scale hardware-platform-based experimental validations have been provided.

Impedance modeling, dynamic analysis and damping enhancement for DC microgrid with multiple types of loads

The dc microgrid with multiple types of loads is considered to be a promising solution for integration of distributed generations (DGs). This paper presents the small signal impedance modeling of dc microgrid with multiple types of loads (including resistive loads, constant power loads and induction motor loads) which consists of source-side output impedance model and load-side input impedance model. Afterward, the Nyquist criteria based stability analysis is performed on the deduced small signal impedance models to investigate the interaction influence of different load states on the damping performance and stability boundaries of the dc microgrid system. Besides, a damping enhancement control strategy for dc microgrid is proposed in this paper based on the dual virtual inductive impedances. Since the dual inductive impedance can perform high-frequency attenuation feature during transients or oscillations, enhanced damping performance of the dc microgrid system is presented with the proposed control. Theoretical analysis and simulation cases show the validity and effectiveness of the proposed control strategy.

Output Impedance Modeling and High-Frequency Impedance Shaping Method for Distributed Bidirectional DC–DC Converters in DC Microgrids

Output impedance characteristics of interfaced converters of energy sources are the important indicators to assess the anti-interference ability of the dc microgrids. However, the output impedance is often approximately modeled by neglecting the impacts of delay units. In order to accurately study the anti-interference ability, the output impedance of an energy storage system is modeled with the consideration of the coupling characteristics of the current control gains and the delays caused by digital control and switching. The constraint mechanism of the coupling factors to impact the effective bandwidth of current loop in a load current feedforward system is also revealed. Then, an impedance shaping method is proposed to improve the anti-interference ability by optimally shaping the high-frequency output impedance, and also to improve system performances in terms of increasing the bandwidth of inner loop and the stable margin of outer loop. The simulation and experimental results both clearly validate the correctness and feasibility of the proposed impedance shaping method.

Virtual Capacitance Control for Improving Dynamic Stability of the DFIG-Based Wind Turbines During a Symmetrical Fault in a Weak AC Grid

As the share of wind power in the power system increases, the power grid exhibits the characteristics of a weak grid. The dynamic stability issues of the grid-connected doubly fed induction generator (DFIG)-based wind turbines caused by the interaction between the phase-looked loop (PLL) and rotor current controller (RCC) by high grid impedance have become acute, especially during low-voltage ride-through. In this article, the output impedance model of the DFIG is derived, where the dynamics of the PLL have been first taken into account. In addition, the interaction between the PLL and RCC is analyzed. Furthermore, a novel virtual capacitance control strategy that directly controls the input voltage of the PLL and does not need to change the internal controller parameters and structure is proposed. The proposed control strategy can reduce the effect of the high line impedance by compensating for the PLL output angle deviation. Subsequently, the interaction between the PLL and RCC becomes weaker, and the phase margin of the DFIG system during the severe grid fault increases. Meanwhile, the applicability of the proposed control strategy is presented. Finally, the effectiveness of simulation and experimental results is presented.

Output Impedance Modeling of Single-Phase Grid-Tied Inverters With Capturing the Frequency-Coupling Effect of PLL

The output impedance model for the precise stability analysis on the single-phase grid-tied inverters considering the frequency-coupling effect of the phase-locked loop (PLL) is studied. A multifrequency admittance matrix (MAM) is developed to predict the inverter-grid system stability by applying the generalized Nyquist criterion. Based on the MAM, a novel output impedance model characterized by clear physical meaning is proposed, which reveals that the inverter output impedance $(Z_{op}|_{(Z\text{pcc}, {Im})})$ varies along with the grid impedance $Z_{{\text{pcc}}}$ and the current reference $I_{m}$ . The resonance and the stability problems can be identified by applying the impedance-based stability criterion to the impedance ratio $Z_{op}| _{(Z\text{pcc},\,{Im})}/ Z_{\text{pcc}}$ . The proposed impedance model is further extended to the n -parallel inverter system. It is found that the output impedances of two n -parallel homogeneous-inverter systems are identical if the number n and the total injected current i tot are the same, and the system stability is indicated by the impedance ratio $\frac{1}{\boldsymbol{n}}$ $Z_{op}| _{(n\cdot Z{\text{pcc}},\,{I}{{\rm{avg)}}}}/ Z_{{\text{pcc}}}$ , where $Z_{op}| _{(n\cdot Z{\text{pcc}},\,{I{\text{avg)}}}}$ is the output impedance of one special inverter with the average current i tot / n injected to the grid with $n\cdot Z_{{\text{pcc}}}$ . Further on, the design procedure of the PLL bandwidth $f_{b}$ is elaborated, which guides the selection of $f_{b}$ with the anticipated phase margin. Compared to the conventional impedance model, the developed output impedance is more qualified to precisely identify the harmonic stability problem in the weak grid. The selection of $f_{b}$ and the correctness of the proposed impedance model are experimentally verified by the measured output impedance and the waveforms of the elaborated cases.

Impedance Modeling and DC Bus Voltage Stability Assessment of a Solid-State-Transformer-Enabled Hybrid AC–DC Grid Considering Bidirectional Power Flow

The solid-state-transformer (SST) is a promising technology in the future smart grid. Compared to the line-frequency transformer, the SST has more control flexibilities and the plug and play ability, which allow it to interconnect a hybrid ac–dc multiterminal grid for reliable and flexible power distribution. The dc bus voltage stability of an SST-enabled hybrid ac–dc multiterminal grid is a critical issue due to the dynamic interactions of power converters, which has been investigated in this article. The output impedance modeling method of the dual active bridge (DAB) dc/dc converters considering both the control schemes and bidirectional power flow effect is proposed. Depending on the control strategy and power flow direction, the DAB converters have three different output impedance characteristics at the low-frequency range, which are capacitive, inductive, and resistive. It is found that the dynamic interaction between the inductive impedance and the capacitive impedance of DAB converters could cause instability issues when the system damping ratio is low. A hardware-in-the-loop-based impedance measurement testbed is used to extract the DAB converters’ output impedance, which validates the theoretical derivation. The real-time simulation results are also provided to demonstrate the dc bus voltage instability.