Virtual Impedance Research Articles

New Framework of RoCoF-FD for Wideband Stability Evaluation in Renewable Energy Generators With Virtual Impedance Control

This research proposes a new perspective for identification of wideband stability in virtual synchronous generator (VSG) with virtual impedance control strategy. At first, the drawback of magnitude-phase-motion-equation (MPME) of grid-forming VSG system is briefly discussed. Then, based on the derived MPME model, a RoCoF-FD framework, which includes two most important indices of frequency performance, e.g., rate of change of frequency (RoCoF) and frequency nadir/deviation (FN/FD), is established to illustrate the interaction between RoCoF and FD based on feedback effect. Moreover, the vector analysis can quantitatively sketch the dynamics of RoCoF impacted by the FD via the loop of feedback effect. In addition, the secure operation regions are defined for the VSG system. It is found that system has a higher risk of oscillation instability when ratio of grid resistance divided by grid inductance gets smaller. However, greater ratio will lessen grid strength/stiffness, which will trigger aperiodic loss of synchronization. To cope with such issues, an adjustable-parameter virtual impedance control strategy (APVICS), based on principle of energy conservation, is proposed to dampen oscillation as well as avoid loss of synchronization of the system, thereby enhance damping behaviors and grid stiffness. Finally, theoretical analysis is validated experimentally.

A Novel Model Predictive Controller for Distributed Generation in Isolated Microgrids—Part II: Model Predictive Controller Implementation

To realize operation automation in remote islanded microgrids, a model predictive control (MPC)-based distributed generation (DG) controller is proposed in Part 2 of this article. The developed data-driven predictive model in Part 1 of this article is implemented in Part 2 to realize the proposed MPC controller. The controller does not incorporate any tunable coefficients, and thus, is not sensitive to the system variations. Kalman filter-based state observer rejects measurement noises and updates the system model under varying system operation. The KWIK optimizer is used to solve the MPC's constrained quadratic programming problem as it ensures a guaranteed convergence. The proposed controller is smaller in size and does not require any intra-DG communication network. It also ensures proportional reactive power sharing despite feeder line impedance mismatch without requiring a secondary controller and a virtual impedance loop. The developed MPC controller is validated through case and sensitivity studies, showing excellent performance when compared with existing methods.

Optimization of Voltage Dynamic Performance at Inverter Output with Machine Learning and Intelligent Virtual Impedance

With the continuous improvement of industrial production and manufacturing level, all kinds of equipment are developing in the direction of refinement and precision, especially the equipment manufacturing industry such as automobile manufacturing, equipment, integrated circuits, chip manufacturing, and other semiconductor industries. An intelligent virtual resistance control strategy based on machine research is proposed for rational power distribution and cycle suppression when multiple inverters are operated in parallel in low-voltage microgrids. Based on this, the control strategy of temporary power reduction of inverters is improved to improve the parallel inverter power distribution accuracy and ensure the reliable dynamic response of the constrained current in the circuit between parallel inverters. Finally, a multi-inverter parallel system model is established to verify the correctness and effectiveness of the proposed control strategy. The voltage waveform under nonlinear load conditions is improved and high-frequency harmonics are suppressed, which has obvious advantages compared with the general virtual impedance design method.

Analysis and Improvement of Large-Disturbance Stability for Grid-Connected VSG Based on Output Impedance Optimization

Except for the benefits of mimicking synchronous generators, virtual synchronous generators (VSGs) still face particular small- and large-disturbance stability problems in practical applications. Therein, the large-disturbance stability is a much more dramatic and intractable problem, such as a short circuit or line tripping. Accordingly, this article explores this challenging problem from the perspective of output impedance optimization for VSGs. First, focusing on the potential risk of overcurrent during the electromagnetic process, the dynamic performances of different virtual impedance control structures used in VSGs are comparatively analyzed, and the output impedance boundary for suppressing the transient current is derived. Then, the output impedance boundaries for maintaining electromechanical transient stability are discussed in depth by using Lyapunov stability theory, which provides novel virtual impedance optimal design guidelines exclusively for the large-disturbance stability. Furthermore, a large-disturbance stability enhancement strategy based on adaptive virtual impedance control is proposed, which can limit the electromagnetic transient current and improves the electromechanical transient stability simultaneously. Finally, experiments validate the accuracy of the theoretical analysis and the effectiveness of the proposed strategy.

A Direct Actual-Power Control Scheme for Current-Fed Dual-Active-Bridge DC/DC Converter Based on Virtual Impedance Estimation

High dynamic performance is an essential requirement for the dual-active-bridge (DAB) dc/dc converters. As dc voltage sources, they should maintain the desired output voltage instantly under all working conditions. However, the previous literature mainly focus on the dynamic control of the voltage-fed DAB converters, and the existing control schemes for the current-fed DAB converters achieve limited dynamic performance. Aiming at improving the dynamic performance, a direct actual-power control (DAPC) scheme based on virtual impedance estimation (VIE) is proposed for the current-fed DAB converters in this article. The proposed DAPC scheme is based on a parallel structure instead of the series structure of existing control schemes, and it realizes fast dynamic control through combining actual power control with the VIE method. The proposed DAPC scheme can obtain the fastest transient response for the output voltage without voltage overshoot in transient conditions, such as load step change, input voltage fluctuation, and the desired output voltage step change. Besides, a leakage inductor precharging method is integrated into the DAPC scheme to avoid the current mismatching. Finally, the proposed DAPC schemes are compared with two existing control schemes and tested in a scale-down experimental prototype. Experimental results verify the effectiveness of the proposed DAPC scheme.

Enhanced Control Strategy Based on Virtual Impedance Loops to Achieve the Sharing of Imbalance and Harmonic in 3-Phase 4-Wire Isolated Microgrids

An improved distributed control strategy for imbalance and harmonic sharing in 4-leg droop controlled power converters for 3-phase 4-wire isolated Microgrids is presented in this letter. The proposed control scheme improves a previous one proposed by some of the authors of this letter in the sense that both negative and zero current sequence components are independently controlled. A numerical comparison between the previous method [1] and the presented in this letter shows that, for the studied case, the negative sequence powers shared among the 4-leg converters using the method [1] are: 1638 VA, 2309 VA, 1760 VA, 2610 VA and 1344 VA (these powers are unequally shared). In contrast, with the improved method, all of these powers are equally shared at 1945VA, showing the effectiveness of the proposal. Similar behaviour was verified for zero-sequence powers, which, for the method [1], varied from 1588 VA to 2547 VA, while the proposed approach produced equal sharing of zero-sequence powers (2072 VA) among all the converters.

A Power Adaptive Impedance Reshaping Strategy for Cascaded DC System With Buck-Type Constant Power Load

It is well-known that the low-frequency negative input impedance of the constant power load (CPL) is the major cause of the cascaded system instability, and the heavier the power, the worse the stability. In this article, a power adaptive load-side parallel virtual impedance (PALPVI) control strategy is proposed to improve the stability of the cascaded dc system with buck-type CPL. First, a parallel impedance with power adaptability is derived followed up with the derivation of the corresponding compensation controller transfer function to realize it virtually. Considering that the compensation controller is highly dependent on the circuit parameters and needs extra current sensors to acquire the power information, a simplification of the compensation controller is made based on the open-loop characteristics of the buck-type CPL. The final PALPVI control strategy does not require the circuit parameters or any current sensor and has almost no side effect on the dynamic performance. Finally, a 48–24–12 V cascaded dc system is fabricated to verify the feasibility and effectiveness of the proposed PALPVI control strategy.

An algorithm for power flow analysis in isolated hybrid energy microgrid considering DG droop model and virtual impedance control loop

Power flow analysis (PF) is an essential tool for secure and efficient operation in power systems. For isolated microgrid (IMG) with only local distributed generators (DGs), there is no slack bus that enables the microgrid to have a constant frequency. So, the bus admittance matrix (Ybus) is not fixed. Also, IMG usually has droop-controlled DGs (DCDG) whose voltage and power are frequency-dependent. These factors make PF a challenging task for IMG that cannot be accomplished through the classic PF techniques. This paper proposes a substantial modification to the well-established Newton–Raphson PF algorithm, called (ENR), to fit the IMG. A new formulation of the Jacobian matrix is developed to accommodate the different control characteristics of DGs as well as the frequency variation. Droop control, maximum power point tracking, and constant power control are considered as DG control types with complete models. Moreover, the virtual impedance concept and its control loop are integrated into the DCDG control scheme to guarantee the stable operation regardless the microgrid X/R ratio. Further, the ENR convergence speed is improved by introducing acceleration factors for voltage angle, magnitude, and frequency. The optimal acceleration factors are determined using a modified PSO method. The ENR is applied to a 45-bus IMG with 12 renewable and dispatchable DGs based on a modified version of the IEEE 33-bus test system. Results are compared to time-domain simulations and also to recent literature. The accuracy and high speed of the ENR are verified.

Adaptive Droop Controller for a Hybrid 375 Vdc/48 Vdc/400 Vac AC/DC Microgrid

This article studies the sharing control scheme for a hybrid 48 V/375 V/400Vac ac/dc microgrid, based on classical droop control and a novel approach for secondary control. In this article, both the dc and ac grids are controlled by a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P/V$</tex-math></inline-formula> droop strategy. At the ac grid, this assumes a main resistive component in the distribution line impedance. The droop control voltage error in steady state is compensated by a novel and simple secondary control approach. The proposed control strategy is based on the calculation of the optimum power flow in each operating point and the real-time modification of the droop characteristics of the converters involved in the power flow calculation. The proposed control is also capable of eliminating the induced voltage drop when using virtual impedance and incorporating any power sharing criteria for the converters contributing to the power production, being this flexibility one of its more important characteristics.

Constrained Predictive Control Based on a Large-Signal Model for a Three-Phase Inverter Connected to a Microgrid

Small-signal models are mostly used to model and design inverter-dominated microgrids. Conversely, this article proposes a large-signal model for grid-forming inverters connected to a microgrid based on the active and reactive power dynamic equations. In this work, it is proposed to use this nonlinear model to develop a constrained predictive control for the inverters connected to a microgrid. The main features of this proposed control are follows: first, direct voltage control (in amplitude and frequency) is not necessary; second, stability is guaranteed under a wide range of line impedances (hence, the virtual impedance is not needed); third, the proposed control can operate with unbalanced and nonlinear loads. Moreover, a theoretical stability analysis is presented. Selected experimental results show that the proposed control operates satisfactorily in case of a load step change, a load imbalance, and nonlinear loads.

Impedance-Based Adaptively Reshaping Method for Enhancing Nonlinear Load Sharing and Voltage Quality in Islanded Microgrids With Virtual Synchronous Generator

For the distributed generation units (DGs) using virtual synchronous generator (VSG) control algorithm connected to the islanded microgrid with high penetration of nonlinear load, there is always a trade-off between harmonics sharing accuracy and voltage quality when using conventional harmonics sharing methods. To address this issue, an impedance-based adaptively reshaping method is proposed in this paper, which is based on harmonic current feedforward compensation control and impedance reshaping factor adaptive control, assigning a variable harmonic impedance reshaping factor for each VSG to improve the controllability of VSG harmonic impedance, thus simultaneously enhancing nonlinear load sharing and voltage quality. Moreover, a droop-based methodology for impedance reshaping factor tuning is presented to adaptively reshape harmonic impedance for each VSG without acquiring the line parameters in advance. The proposed method also enjoys the advantage of avoiding introducing additional virtual harmonic impedance, and thus it is immune from the inverter closed-loop gain throughout the dominant harmonic frequencies. Furthermore, the stability analysis and the key control parameter design are discussed in detail. Finally, the effectiveness of the proposed method is verified by simulation and experimental results.

Low-Frequency Oscillation Analysis of Virtual-Inertia-Controlled DC Microgrids Based on Multi-Timescale Impedance Model

Virtual inertia and damping control (VIDC) improves the stability of DC microgrid (DC-MG). However, the potential positive feedback aggravates low-frequency oscillation induced by the interaction insides control loops, which is explained and solved in this paper. The multi-timescale impedance modelling framework is established to clarify stability mechanism of VIDC and the low-frequency oscillation of VIDC controlled DC-MG. Control loops of different timescales are visualized as independent <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">loop virtual impedance</i> (LVI) elements to form an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">impedance circuit</i> considering the constant power load (CPL), rather than an all-in-one impedance as the external dynamic representation of power converters. Concrete impedance analysis is performed on LVI to reveal the impedance-shaping effect of control loops intuitively, the physical impedance nature of control parameters and the interaction among different timescale, which illustrates the stability mechanism of VIDC. The low-frequency oscillation ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> impedance interaction) in voltage- and inertia-loop is elaborated by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> circuits of LVIs. The potential instability factors, resulting in poor damping against voltage oscillation, are also revealed. Thus, dynamic stability enhancement method is further proposed to compensate for the negative damping caused by positive feedbacks of VIDC and CPL, and super-capacitor is added to alleviate rapid voltage changes. Accordingly, the passivity property of system impedance is strengthened and the stability can be evaluated by Nyquist plot. Finally, the simulation and experiment results have validated the low-frequency oscillation analysis and stability enhancement method.

Improvement of Fault Current Calculation and Static Security Risk for Droop Control of the Inverter-Interfaced DG of Grid-Connected and Isolated Microgrids

The contribution current of an inverter-interfaced distributed generator unit during a fault is one of the significant challenges for two modes: grid-connected and isolated AC microgrid. For this challenge, this article is aimed to study two methods of fault current calculation for two modes: grid-connected and isolated microgrids. These methods include a virtual equivalent impedance and a proposed method. The proposed method is a new technique for calculating the fault current contribution depending on the droop control of inverter-interfaced DG. The proposed method can control the contribution short-circuit current of DG within its limit (2 p.u.) where it is dependent on the voltage value of the DG bus to calculate the short circuit current of DG by using the control criterion. Static security risk and load shedding are calculated after fault clearance using an operation scenario in which the distribution system will be divided into small subsystems and is then grid-connected and isolated due to the removal of the faulted bus by protection devices. The proposed technique is applied to a standard IEEE 33-bus distribution network with five DGs. The results show that the contribution current of inverter-interfaced DG during the fault has more effects than the fault current of the nearest faulted bus to the DG bus. The proposed technique improves the calculated fault current value by about 30% for the grid-connected microgrid and by about 50% for the isolated microgrid from its value of the virtual impedance method. The static security risk is improved after load shedding. The static security risk improved by about 0.025%.

Decentralized Virtual Impedance- Conventional Droop Control for Power Sharing for Inverter-Based Distributed Energy Resources of a Microgrid

The work presents the power-sharing in a standalone low voltage AC microgrid consisting of three parallel grid supporting inverters using a virtual impedance-based droop system. Typically, isolated microgrids suffer unique challenges regarding voltage, current, frequency regulation, power flow control, and power-sharing due to the absence of a stiff AC grid source. This work investigated the power flow and sharing technical challenges using three inverter-based distributed energy sources, three static loads, and one dynamic load. These distributed energy sources are interconnected with the loads using low voltage line impedance within the microgrid to implement the uneven power distribution. Furthermore, a distributed grid supporting control utilizing virtual impedance is proposed in this work to improve power-sharing. The microgrid model is developed with the MATLAB Simulink environment and validated using the Opal RT OP4510 simulator. The proposed technique ensured improved power-sharing and mitigated the effect of voltage drops introduced through a virtual impedance using combined positive and negative virtual.

A Decentralized Current Sharing Strategy for Islanded Resistive Microgrids Based on Iterative Virtual Impedance Regulation

The output impedances of inverters can be reshaped to improve current sharing accuracy in islanded microgrids. This article proposes a decentralized current sharing strategy based on iterative virtual impedance regulation (IVIR). The whole IVIR process is decomposed into several continuous iterations. During each iteration, three stages are involved. In the first stage, a virtual impedance increment is generated with the integral of the inverter uniform output currents. Then, an impedance compensation is introduced to restore the voltage magnitude in the second stage. In the third stage, the current sharing error is evaluated. Based on this iterative regulation, the impedance mismatches are eliminated with small virtual impedances, all the balanced, unbalanced, and harmonic current components are distributed accurately, and good voltage quality maintains. The proposed control strategy requires neither communication nor grid impedance knowledge. Simulation and experimental results are presented to verify the effectiveness of the proposed strategy.

Multi-Time scale control framework of hybrid energy storage system via robust control and virtual impedance

Aiming at the problems of the strong randomness and fluctuation of the output power in photovoltaic power generation system, a multi-time scale control framework of hybrid energy storage system is proposed. Firstly, the complementary characteristics of charge/discharge between lithium battery and supercapacitor is analyzed. Then, The models of lithium battery energy storage unit and supercapacitor energy storage unit are established, respectively. Considering the different time scales of the output power response of lithium battery and supercapacitor, a short-time scale control framework is designed for supercapacitor energy storage unit based on the robust control, so that the bus voltage of system can be stable when the output power of photovoltaic power generation system changes or the load changes rapidly. At the same time, a long-time scale control framework is designed for lithium battery energy storage unit based on the virtual impedance, so that the voltage of the supercapacitor can be maintained within set value when the output power of the photovoltaic power generation system is stable. Therefore, the multi-time scale control framework can not only realize the large current charging/discharging for lithium battery and the power tracking at low frequency, but also realize the small current charging/discharging for supercapacitor and the power tracking at high frequency. Finally, the effectiveness of the proposed framework is verified by the simulation platform of photovoltaic power generation system.

Impedance-Based Analysis and Stability Improvement of DFIG System Within PLL Bandwidth

In this article, we analyze the negative impact of phase-locked loop (PLL) on the stability of the doubly fed induction generators system. The small-signal disturbance of PLL mainly affects the coordinate transformation of the rotor current and introduces a negative resistance within PLL bandwidth. Two impedance reshaping methods are carried out to weaken this negative resistance. A virtual impedance in the conventional current control is added to the first reshaping method. The second reshaping method completely removes the coordinate transformation of the rotor current by switching the control target from current to power. The difference between these two reshaping methods is analyzed based on the equivalent single-input single-output impedance model. The experimental results validate the effectiveness of these two reshaping methods and the superiority of the second reshaping method at a lower short-circuit ratio.

Small-Signal Modeling and Controller Parameters Tuning of Grid-Forming VSCs With Adaptive Virtual Impedance-Based Current Limitation

The adaptive virtual impedance (VI) control emerges as an attractive solution to limit the current of grid-forming voltage-source converters (GFM-VSCs) during grid faults. Yet, the adaptive VI-based current limitation relies on the detection of the current magnitude, which introduces nonlinear dynamics that challenges the controller parameters tuning of GFM-VSCs. This article develops the small-signal model of GFM-VSCs with adaptive VI-based current limitation, from which, the dynamic impact of the adaptive VI is explicitly revealed. Considering such impact, a holistic controller parameters tuning method for GFM-VSC is proposed to guarantee the small-signal stability of the system. Simulation and experimental tests are performed to verify the effectiveness of the theoretical analysis and the proposed parameters tuning method.

High-Frequency Damping Analysis and Compensation Method Above Half PWM Sampling Frequency for Train Grid-Connected Converter

There are serious harmonic overvoltage phenomena in the electric railway system caused by the high-frequency resonance or instability issues, which is rooted in the region not only below, but also above half the PWM sampling frequency. To effectively evaluate the high-frequency admittance of train and further suppress the harmful high-frequency instability issue, a multi-frequency averaging model combining sampling sideband components is developed. Compared with the single-frequency model, the multi-frequency model is more accurate in the region near sampling frequency. After simplification, it is found that the time delay of digital control system is the cause of high-frequency negative damping. However, the time delay may make the traditional virtual impedance method fail in the high-frequency domain. Therefore, a virtual-impedance-controller (VIC) with variable damping characteristic is proposed to reshape the train admittance. The proposed VIC has the same structure as PID control. The detailed design method is given to offset the influence of time delay. The multiple high-frequency negative damping regions of train can be eliminated simultaneously by using multiple parallel VICs. The proposed method is applicable when changing the switching frequency. Hardware-in-the-loop test and low-power physical experiments validate the effectiveness of the proposed VIC strategy.

An approach to arranging primary and secondary control of the operating parameters in microgrids featuring inverter-connected generator sets

Various low-power generator sets (GS) are mainly integrated into microgrids by means of inverters coupled with energy storage systems (ESS). ESSs are connected either to the DC busbars of GSs or to the AC busbars of the microgrid, in this case they are equipped with individual inverters. Use of ESS helps balance power in cases of load surge / loadshedding when the microgrid is islanded. This paper overviews approaches to arranging primary and secondary control of the operating parameters of microgrids. It discusses the technical challenges of, and possible solutions for, implementing primary and secondary control in low- and medium-voltage distribution grids featuring inverter-connected GSs. Calculations of electromechanical transients show that inverter-connected GSs have advantages over conventional GSs when used microgrids that are weakly connected to the power system (the external grid) or islanded. In a microgrid featuring inverter-connected GSs, active and reactive power need to be controlled separately as in power systems featuring conventional GSs; implementation of such controls must be adjusted for the parametric and topological characteristics of low- and medium-voltage distribution grids. To address the issues of linked control, this paper proposes a comprehensive approach that adjusts microgrid design for the specifics of inverter-connected GSs, improves inductance, and incorporates algorithmic solutions. It details upon the virtual impedance algorithm, which extends the common principle of droop speed control. Its implementation helps load the GSs and the ESS with adjustments for their installed capacity; it can also simulate the mechanical constant of GS inertia. Primary control has a low margin that mainly comes from the ESS; thus, backups available to secondary control must be used to compensate for the deviations in operating parameters; this is a key challenge of secondary frequency and voltage control in microgrids. When primary and secondary voltage and frequency controls have been duly implemented in a microgrid, its GSs, the ESS, and electricity delivery to the loads within the microgrid can all operate reliably in a variety of operating situations.