Equivalent Output Impedance Research Articles

Improved scheme of grid-connected inverters based on virtual PCC and impedance remodeling with enhanced steady-state and dynamic performance

The issue of low-frequency oscillation (LFO) becomes more prominent when considering the phase-locked loop (PLL) impact of grid-connected inverter (GCI) under weak grid. Impedance analysis shows that the frequency interaction point outside the capacitive negative damping region can effectively avoid the oscillation. Therefore, a modified PLL scheme is designed to shape the characteristics of the GCI output impedances, which effectively tracks the grid phase through the virtual point of common coupling and adjusts the phase- frequency characteristic of the GCI equivalent output impedance towards an increasing phase angle. On this basis, the impedance remodeling strategy is used to improve the system, which further broadens the feasible range of stable operation and ensures the phase margin of the GCI. The comparison results indicate that proposed scheme demonstrates enhanced capability in suppressing LFO and exhibits a wider range of adaptability to grid impedance. Experimental validation has verified the accuracy of the theoretical analysis, leading to the conclusion that the GCI with proposed scheme possesses superior dynamic performance.

Stability Analysis and Robust Parameter Design of DC-Voltage Loop for Three-Phase Grid-Connected PV Inverter Under Weak Grid Condition

In the grid-connected inverter, both the PLL (phase-locked loop) and DVL (DC-voltage loop) can lead to the frequency coupling in the weak grid. Instabilities caused by PLL frequency coupling have been widely discussed. For DVL, past studies have analyzed the effect of DVL parameters on the degree of frequency coupling, but it is quite unclear how DVL parameters affect the inverter stability and how DVL can be designed under the weak grid. Hence, by fully considering the abovementioned frequency coupling, an accurate admittance model of PV (photovoltaic) grid-connected inverter is established in this study. By deriving the modified admittance matrix, the effects of grid impedance and DVL parameters on the frequency coupling are clearly studied. In addition, by modeling the equivalent inverter output impedance, the impact of DVL on the inverter stability under the weak grid is revealed. As proved, the increase of DVL bandwidth <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vbw</sub> and grid impedance will aggravate the frequency coupling, but the current distortion does not necessarily increase. Meanwhile, the increase of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vbw</sub> helps to improve the inverter stability under the weak grid. Accordingly, a novel design for DVL in the weak grid is proposed. Experiments verify the correctness of the analysis and design.

Impedance remodeling control strategy of grid-connected inverter with inertia-damping phase-locked loop under extremely weak grid

The operation of the grid-connected inverter (GCI) in weak grid conditions presents a risk of instability due to the presence of high grid impedance and the negative impedance effect of the phase-locked loop (PLL). In response to this issue, this paper introduces an impedance remodeling control strategy for the GCI utilizing the inertia-damping phase-locked loop (ID-PLL). Firstly, the proposed ID-PLL exhibits certain inertia and damping properties in comparison to the traditional PLL (T-PLL), resulting in an enhanced phase margin of the GCI system's equivalent output impedance. Consequently, the adaptation range of the grid impedance increases from 12mH (SCR = 3.00) to 24mH (SCR = 1.37). Next, from the perspective of impedance analysis, this study remodels the PLL impedance and inverter control loop impedance, further improving the amplitude and phase margin of the system's output impedance. As a result, the adaptation range of the grid impedance extends to 33mH (SCR = 1.00), and the transition of grid-connected currents becomes smooth and free of overshoot. Finally, the effectiveness of the proposed control strategy is validated through theoretical analysis and experimental verification.

Reconfigured passivity‐based control strategy of LCL‐type grid‐connected inverter under complex grid conditions

SummaryLCL‐type grid‐connected inverters have seen extensive use of the passivity‐based control (PBC) system. However, traditional PBC systems rarely take time delay into account while designing the system or doing a stability study. Therefore, utilizing Lyapunov's criterion to conclude that the system is stable is not accurate. The analysis revealed that the differential terms of PBC loops with the Euler–Lagrange (EL) mathematical model could induce instability considered control delay for LCL‐type grid‐connected inverter system. Compared with traditional EL‐PBC method, this paper proposed a reconstructed EL‐PBC scheme by properly optimizing the noise term. Then, the equivalent output impedance of the grid‐connected inverter system with proposed controller is analyzed with frequency domain passivity theory. The controller parameters are also optimized to ensure both the internal stability of LCL‐type grid‐connected inverter and the risk of interactive resonance in complex weak and nonideal grid. Results from simulation and experimentation support the modified control structure's efficacy and performance.

Analysis and Optimization Strategy of Active Power Dynamic Response for VSG under a Weak Grid

A virtual synchronous generator (VSG) has a good adaptability to the weak grid but its grid-connected active power (GCAP) has the problem of a slow dynamic response under the active power command step. An optimization strategy of the GCAP dynamic response for the VSG based on the virtual negative impedance combined with the active power transient damping control algorithm is proposed in this paper. The optimization strategy first uses the virtual negative impedance control method to reduce the VSG equivalent output impedance and the GCAP dynamic response time of the VSG. Then, the transient damping as well as the inhibition ability of the GCAP dynamic oscillation for the VSG are enhanced by the active power transient damping control algorithm. The Matlab/Simulink simulation software is used to study the GCAP dynamic response performances of the VSG in the condition of the active power command step, and the experimental test platform of a VSG grid-connected system is established. The simulation and experimental results jointly verify the feasibility and superiority of the proposed strategy in improving the GCAP dynamic response characteristics of the VSG under a weak grid.

Adaptive fuzzy-based stability control and series impedance correction for the grid-tied inverter

The regenerative braking in the tram allows the energy to be returned to the power grid through a power inverter. Since the inverter location between the tram and the power grid is not fixed, resulting in a wide variety of impedance networks at grid coupling points, posing a severe threat to the stable operation of the grid-tied inverter (GTI). By independently changing the loop characteristics of the GTI, the adaptive fuzzy PI controller (AFPIC) can adjust according to different impedance network parameters. It is challenging to fulfill the stability margin requirements of GTI under high network impedance since the PI controller has phase lag characteristics. A correction method of series virtual impedance is proposed, which connects the inductive link in a series configuration with the inverter output impedance, correcting the inverter equivalent output impedance from resistance-capacitance to resistance-inductance and improving the system stability margin. Feedforward control is adopted to improve the system's gain in the low-frequency band. Finally, the specific series impedance parameters are obtained by determining the maximum network impedance and setting the minimum phase margin of 45°. The realization of virtual impedance is simulated by conversion to an equivalent control block diagram, and the effectiveness and feasibility of the proposed method are verified by simulation and a 1 kW experimental prototype.

Virtual composite impedance circulating current suppression strategy with adaptive adjustment capability

AbstractIn the process of accessing distributed power sources in microgrid, there will be serious coupling between active power and reactive power, which will lead to significant changes in the inverter outlet voltage and impedance and increase the circulating current phenomenon. The generation of circulating current will accelerate the aging of devices, reduce the inverter efficiency, and threaten the stable operation of the system. In this paper, the mechanism of circulating current generation is analysed, the basic characteristics of circulating current are studied, and an inverter parallel circulating current suppression strategy with adaptive virtual composite impedance and droop control dynamic adjustment algorithm is proposed. The virtual impedance setting can weaken the influence of line difference on system stability, make the system equivalent output impedance resistive, weaken the inductive device characteristics and reduce the circulating current amplitude; the adaptive droop algorithm implantation dynamically correlates the control power with the droop coefficient, enhance the power decoupling accuracy and weaken the circulating current influenced by power changes. The simulation platform and experimental setup established by the large‐scale simulation software PSCAD/EMTDC are used to study the basic scenarios of the inverter under two conditions of equal and unequal capacity, and the rationality of the proposed control strategy is tested.

Analysis of multi-converter network impedance using MIMO stability criterion for multi-loop systems

This work presents a novel method of simplifying multi-converter systems containing complex grid-forming and grid-following controllers for stability analyses. Analysis is conducted via the equivalent converter output impedance. Important points for impedance-based stability analysis of larger networks are considered, including impedance rotations, proper combination of sources and correctly obtaining a minimum system realisation with appropriate tolerances. The proposed method is used to conduct a sensitivity analysis of different grid-forming and grid-following converter control parameters to determine tuning recommendations for the modern electricity network. To achieve this, complex control structures including power/voltage control, negative sequence regulation and synchronous machine emulation are included. Network stability is found to be sensitive to current control, active power control and frequency-based components such as PLLs. However, voltage control exhibits a smaller effect on stability for a range of short circuit ratios. Some recommendations are provided on when the simplified method can be utilised and how to ensure correct application.

Frequency coordination and harmonic suppression strategy based on composite virtual impedance in hybrid energy storage system

Under the traditional droop control, hybrid energy storage system cannot take advantage of the respective merits of battery and supercapacitor for frequency coordination, which shortens system life. Because of the single-phase inverter load, the second harmonic current is generated in the front-stage converter when the output power pulsates at twice the output voltage frequency. This paper proposes a strategy for frequency coordination and second harmonic current suppression based on composite virtual impedance. Under this strategy, the system equivalent output impedance exhibits resistance and inductance in low-frequency part, dominated by the battery side. The battery reacts slowly to absorb the low-frequency power fluctuations and provide the energy required by load at steady state. It is capacitive in the high-frequency range, with the supercapacitor side dominating. The supercapacitor quickly absorbs the high-frequency part of power fluctuation to suppress the impact of load mutation on DC bus and improve system dynamics. Meanwhile, the strategy realises that the inductor branch impedance is significantly larger than the capacitor branch impedance at double frequency, suppressing the second harmonic current and increasing the system efficiency. Experimentation confirms the effectiveness of the control strategy.

Distributed secondary controller to ensure proportional sharing of reactive power in AC microgrid

In an ac microgrid, reactive power sharing accuracy is affected due to unequal values of interconnecting cable impedances. To resolve this issue, secondary controllers are used to compensate the effect of cable impedances. Various types of secondary controllers are suggested in the literature which includes linear proportional plus integral (PI) controllers to minimize the difference in reactive power sharing created by conventional E−Q droop law. The reference value of the PI controller is the average value of reactive powers supplied by the sources. When the PI controller is used to minimize the difference between the actual and reference value of reactive power, the difference between the algebraic sum of reactive powers supplied by the sources and the reactive powers demanded by the loads has a nonzero value. Therefore, the performance of these controllers becomes poor in the case of ac microgrid having sources of unequal ratings. To resolve this issue, a proportional reactive power-sharing (PRPS) controller-based distributed secondary controller is proposed in this paper. The PRPS controller modifies the droop gain of the E−Q droop control loop of each source in such a way that each source supplies reactive power equal to its proportional value of reactive power. The proportional value of reactive power supplied by each source is the power when the equivalent output impedance of all sources as seen by the loads are identical. The key advantage offered by the proposed controller is the accurate reactive power-sharing in the case of ac microgrid having sources of unequal ratings. The proposed controller ensures zero value of the difference between the algebraic sum of reactive powers supplied by the sources and the reactive powers demanded by the loads. This ensures accurate sharing of reactive power among the sources. The validation of the proposed controller is carried out for islanded mode of operation of ac microgrid. Further, the proposed controller requires of low bandwidth communication for its implementation. The effect of the proposed controller on the stability of the system is demonstrated using reduced order small-signal model. The effect of communication delay on the performance of the system is analyzed with the help of roots locus plots. To validate the efficacy of the proposed controller, detailed simulation studies are carried out in Matlab/Simulink.

Distributed Control Scheme for Accurate Power Sharing and Fixed Frequency Operation in Islanded Microgrids

Global Positioning System (GPS) based control has recently been reported as a replacement of droop control to achieve fixed frequency operation in islanded microgrids. This article presents the perspective that the power sharing performance of a general microgrid synchronized by GPS is essentially determined by equivalent output impedance. A novel adaptive virtual impedance control approach, which implements different values of virtual resistance for d- and q-axis, is proposed accordingly. The virtual resistance concept is implemented comprising a basic local implementation for output impedance shaping, and a sparse resistance tuning network for the compensation of mismatched feeder impedance, which demands no knowledge of actual output impedance. The resistance tuning network utilizes the consensus protocol and only requires neighboring interactions among DG units. A complete tuning of output resistance for a given load condition results in accurate active and reactive power sharing even after communication is interrupted and will still outperform conventional droop control methods if load changes during the interruption. Small-signal analysis based on delay differential equations model of the overall microgrid is performed to investigate the adverse impact of communication delays on system stability. The efficacy of the proposed approach is validated by both simulation and experimentation.

Power Sharing Control Strategy of High-Frequency Chain Matrix Converter Parallel System Based on Adaptive Virtual Impedance

In the high frequency link matrix converter parallel system, the impedance parameters on each line are unequal so that the output power of each converter is not equal. To solve this problem, the reason why the power cannot be divided equally under the droop control strategy is analyzed, and a power sharing strategy based on adaptive virtual impedance is proposed. This strategy introduces virtual impedance in a voltage-current dual-loop system with droop control, and uses the converter’s power information and output power factor to adaptively adjust the amplitude and phase of the virtual impedance, so that different branches have the same equivalent output impedance to compensate The voltage drop on the line impedance, while adding the droop control fine-tuning compensation link, so as to realize the load power sharing. Simulation results show that the proposed strategy can effectively improve the accuracy of output power sharing and ensure the stability of the system output voltage amplitude.

Precise Reactive Power-Voltage Droop Control of Parallel Virtual Synchronous Generators That Considers Line Impedance

Problems such as high power coupling, low distribution accuracy, and insufficient reactive power-voltage droop accuracy occur when distributed generators are operated in parallel due to the influence of line impedance. The precise control of output reactive power and voltage is difficult to achieve using traditional virtual synchronous generator (VSG) control. Taking this into consideration, this study proposes a virtual synchronous generator reactive power-voltage integrated control strategy that considers line parameters to solve this problem. First, the impedance voltage drop of the line is compensated for in accordance with local information control to ensure the consistency of the control voltage in parallel operation of distributed generators and to realize the precise droop control of reactive power and the voltage of the point of common coupling (UPCC). Second, virtual negative impedance control is added to change the equivalent output impedance characteristics of the system and achieve power decoupling. On this basis, the active frequency and reactive voltage decoupling control effect of the improved control strategy is quantified and analyzed using the relative gain matrix. The accuracy of reactive power distribution and droop control is theoretically derived and analyzed by establishing a small-signal model of a two-machine parallel system. Finally, the accuracy and effectiveness of the proposed integrated control strategy are verified via a simulation model and an experimental platform for parallel operation. Results show that the proposed integrated control strategy can effectively solve the problems of power decoupling and accurate distribution, reduce system loop current, and realize accurate reactive power-voltage droop. Compared with the traditional VSG control strategy, the dynamic deviation of UPCC is reduced by at least 40% when a large-scale load disturbance occurs.

Impedance Reshaping Control Strategy for Improving Resonance Suppression Performance of a Series-Compensated Grid-Connected System

In the series-compensated grid-connected system (SCGCS), there is an impedance interaction between the inverter impedance and the grid impedance that is prone to cause resonance in the SCGCS. In this paper, firstly, considering the effects of the phase-locked loop (PLL), current-loop, and frequency coupling, the broadband impedance model of the SCGCS is established. The stability of the SCGCS is analyzed by the impedance-based Nyquist stability criterion. It is found from the stability analysis that the impedance interaction between the inverter impedance and the grid impedance is the leading cause of the resonance. An impedance reshaping based resonance suppression method is proposed to suppress the resonance. The phase characteristics of the inverter equivalent output impedance are reshaped from the perspective of impedance. The phase margin at the intersection frequency of the inverter impedance and the grid impedance is improved. The proposed resonance suppression approach mainly consists of reshaping the current loop impedance and the novel phase-locked loop impedance. Finally, simulations and experiments are used to verify the feasibility of the resonance analysis and the effectiveness of the proposed control strategy.

Coordinated Control Strategy of Virtual Synchronous Generator Based on Adaptive Moment of Inertia and Virtual Impedance

The application of virtual synchronous generators in the power system eases the pressure on the grid caused by penetration of lots of power electronic devices, but worsens the dynamic frequency stability of the grid. Meanwhile, in order to solve the problem of power coupling in low-voltage micro-grid systems, most measures introduced virtual impedance technology to adjust the equivalent output impedance of the system. Therefore, most studies have adopted the adaptive control strategy of the moment of inertia, to improve the dynamic frequency adjustment of the grid. However, it will cause the frequency response speed reduction problem. In order to deal with the contradiction between the moment of inertia and frequency response speed, the voltage phasor relationship of the micro-source - grid system under signal disturbance in the introduction of virtual impedance is analyzed. Then an adaptive virtual impedance control strategy is proposed to accelerate the active power adjustment process of the virtual synchronous generator system, which helps to complete the first frequency modulation and improve the inertia adjustment ability. Finally, combining these two control strategies, a coordinated adaptive moment of inertia and virtual impedance control strategy is proposed. From the perspective of the moment of inertia and virtual impedance, the proposed method fully exploits the control advantages of the virtual synchronous generator system and achieves the purpose of adjusting the inertia of the virtual synchronous generator system while considering the acceleration of the frequency response speed. The comprehensive simulation results verify the feasibility and effectiveness of the proposed method.

Application of Improved Droop Control Based on Grid Impedance in Photovoltaic Grid-Connected Power Generation system

When the power grid impedance mutates, the output power of the grid-connected photovoltaic power generation system controlled by drooping will become very unstable. To solve this problem, an improved droop control algorithm based on network impedance detection is proposed. Taking photovoltaic grid-connected power generation system as the research object, the influence of power grid impedance on traditional droop control is firstly expounded by introducing power grid impedance value into traditional droop control. Then the method of real-time network impedance extraction is introduced. Furthermore, according to the bandwidth and phase angle constraints of the equivalent output impedance phase frequency characteristics of the photovoltaic grid-connected inverter, the controller parameters are updated in real time to achieve the purpose of adaptive network impedance mutation. Finally, the proposed method is tested and verified by real-time simulation in the loop respectively. The results show that the proposed method is correct.

Analysis of the influence of virtual impedance on the stability of Parallel Voltage Inverters with Different Voltage Levels

Using virtual impedance technology to optimize the double closed-loop control structure can improve the equivalent output impedance of the inverter to be inductive, improve the power distribution accuracy of traditional sensibility droop control strategy in low-voltage microgrid, and effectively restrain the circulation. But rarely consider the impact of virtual impedance on system stability. Therefore, Derive the transfer function of the three loop control structure including virtual impedance, line impedance and common point voltage, establish a parallel models of inverters with different voltage levels considering virtual complex impedance and simplify the model using Thevenin’s equivalent. According to the Nyquist stability criterion Analyze the effect of virtual impedance on system stability under various operating conditions. The analysis results show that the multi-inverter parallel system can maintain stable operation after adding the virtual impedance.

Optimization Control Strategy for Islanded Parallel Virtual Synchronous Generators

Virtual Synchronous Generators (VSGs) can reduce the frequency and power oscillation in the grid. For parallel multi-VSGs in island microgrid, the differences of equivalent output impedance and line impedance affect the orderly sharing of reactive power and restraining of circulating current greatly. The power sharing and circulating current characteristics of VSGs are analyzed in this paper. To solve this problem, an optimization control method for parallel VSGs is proposed, which included the inner voltage and current loop and the outer reactive power loop. In the inner voltage and current loop, a virtual complex impedance including a resistive component and an inductive component is introduced. It reduces the coupling between active power and reactive power, and it reduces the disorderly distribution of power due to impedance differences. In the reactive power loop, the output voltage feedback and integrator links are adopted, which reduce the deviation of output voltage and restrain circulating current. The effects on the equivalent output impedance in the different control parameters and virtual complex impedance are analyzed, the effects on system stability in the different resistive components of virtual complex impedance are analyzed, and the proper parameters are selected. Simulation and experimental results show the correctness and validity of the proposed control method.

Curvature-Based Average Modeling of Switched-Capacitor Converters

A precise, curvature-based, average modeling technique for switched-capacitor (SC) dc–dc converters is proposed. The generalized modeling technique provides a comprehensive characterization of the converter at steady-state, across the full range of practical operating conditions. An expression for the equivalent output impedance is obtained, which relates the slow- and fast-switching limit impedances to the total output impedance. This expression can be used to accurately compute the output voltage without deriving the converter’s state equations and precisely weighs the contribution of each floating capacitor and parasitic resistance on the output impedance. The modeling technique is applied to a unity-gain SC converter, a multiphase binary converter, and a nonsymmetrical parallel–series converter, and the results are compared with existing steady-state models. The accuracy of the model is validated through simulations and experimental measurements.

Parallel Control Method of Microgrid Inverter Based on Adaptive Droop Control

Energy is the driving force of social and economic development. With the gradual depletion of conventional energy and the increasingly prominent ecological and environmental problems, the power industry needs to find a sustainable development path. Parallel control of microgrid inverters based on adaptive droop control is an important part of future intelligent and sustainable power systems. However, with the continuous increase of power generation equipment capacity and the continuous increase of load power consumption, the form of power supply by a single inverter can no longer meet the requirements. Therefore, parallel connection of multiple inverters has been widely used in the microgrid. In this paper, a set of parallel control methods for microgrid inverters based on adaptive droop control is established. This paper is based on the inductance of the inverter’s terminal impedance, and the amplitude of the inverter terminal voltage is positively correlated with the output reactive power and has a strong correlation It is concluded that the microgrid based on adaptive droop control has the ability to automatically adjust the voltage and frequency of the microgrid. Properly reducing the droop coefficient can improve the primary frequency modulation capability of the microgrid. In this paper, an improved resistive control equation is used in a parallel system, a multi-loop control structure with a quasi-resonant controller is used for the inverter in the parallel system, and a virtual complex impedance is added to perform small signal analysis on the improved resistive control equation The overall performance of the parallel system is analyzed, and the effect of different control coefficients on the system performance is clarified. The experimental research results show that when analyzing the effect of the inductance coefficient value on the equivalent output impedance in the virtual complex impedance, the value of KL is 1 At this time, the equivalent output impedance becomes resistive again, and the property is stronger than when KL is 0.05.