Grid Impedance Uncertainty Research Articles

-Synthesis-Based Generalized Robust Framework for Grid-Following and Grid-Forming Inverters

Grid-following and grid-forming inverters are integral components of microgrids and for integration of renewable energy sources with the grid. For grid following (GFL) inverters, which need to emulate controllable current sources, a significant challenge is to address the large uncertainty of the grid impedance. For grid forming (GFM) inverters, which need to emulate a controllable voltage source, large uncertainty due to varying loads has to be addressed. This article presents a generalized control framework by leveraging the voltage-current duality in the plant dynamic model of GFL and GFM inverters. The modeling of uncertainties is also generalized under the control framework by quantifying the uncertainties in grid impedance parameters and the uncertainties in equivalent loading parameters for GFL and GFM inverters, respectively. Based on the generalized control framework, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\mu}$</tex-math></inline-formula> -synthesis-based robust control design methodology is proposed for both GFL and GFM inverters. The control objectives, while designing the proposed optimal controllers, are reference tracking, disturbance rejection, and harmonic compensation capability with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${i})$</tex-math></inline-formula> sufficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${LCL}$</tex-math></inline-formula> resonance damping under large variations of grid impedance uncertainty for GFL inverters and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${ii})$</tex-math></inline-formula> with enhanced dynamic response under large variations of equivalent loading uncertainty for GFM inverters. A combined system-in-the-loop, controller hardware-in-the-loop, and power hardware-in-the-loop based experimental validation on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {10}$</tex-math></inline-formula> -kVA microgrid system with two physical inverter systems is conducted in order to evaluate the efficacy and viability of the proposed controllers.

Adaptive Control of Grid-Connected Inverters With Nonlinear LC Filters

Distributed generation is an effective solution to clean, reliable, and cost-efficient energy supply. In this framework, inverters play a key role as energy converters. Accordingly, this article investigates the utilization of nonlinear inductive–capacitive (LC) filters for grid-connected inverters. Nonlinear LC filters are made of inductors with nonlinear B–H curves, which makes them have a smaller volume, less dissipation loss, and lower cost. The main drawback of using these filters, however, is their nonlinear current-dependent characteristics. To harness the undesirable impacts of nonlinear filters on the system performance, an adaptive observer-based control scheme is developed in this article. The proposed controller is based on a concurrent estimation of nonlinear inductor values, capacitor voltages, and grid-side currents. Based on its fast adaptation to plant changes, this scheme provides an improved stability margin and an inherent resonant damping characteristic under grid impedance uncertainty. Compared with the conventional approaches, this method requires no extra sensors. A comparative simulation and experimental analysis, based on a three-phase 7-kW inverter, is provided to validate the efficacy of the proposed control strategy.

Modified Passivity-Based Control for LCL-Filtered Grid-Tied Inverter with Output Admittance Reshaping

As a nonlinear control method, the Euler–Lagrange- (EL-) based passivity-based control (PBC) has been studied for grid-tied converters based on energy function to achieve better performance. However, the EL-based PBC method is dependent on an accurate mathematical model. In the traditional EL-based PBC research for LCL-filtered grid-tied inverter, the effect of the digital control delay is rarely considered and the stability under the grid impedance uncertainties is not discussed, especially in the capacitive grid or complex weak grid. To address these concerns, this study proposes a modified EL-based PBC method based on the output admittance reshaping for LCL-filtered grid-tied inverters. The system’ passive region is expanded by adding capacitor current feedback loop up to the Nyquist frequency. The potential resonance is thus eliminated irrespective of the grid impedance. Additionally, the stable region and control parameters design methods of the modified EL-based PBC method with inverter-side control are also carried out. To verify the correctness of the theoretical analysis, both simulation and experimental results are investigated from a 3 kW grid-tied inverter prototype.

A robust adaptive One Sample Ahead Preview controller for grid-injected currents of a grid-tied power converter with an LCL filter

This paper presents the development of a discrete-time Robust Adaptive One Sample Ahead Preview controller, based on the combination of a Robust Model Reference Adaptive Controller (RMRAC) with the One Sample Ahead Preview controller (OSAP), which is a particular case of the Deadbeat controller. This control structure is applied to grid-side current control of a grid-tied voltage-source inverter (VSI) with an LCL filter. The developed controller is robust enough to be designed considering the LCL filter as a first order model, which is commonly modelled as a third order transfer function, considering the neglected dynamics as unmodelled dynamics on controller design thanks to its adaptive identifier, which is a modified Gradient algorithm. Furthermore, the controller can deal properly with grid impedance uncertainties, which change the resonance peak frequency of the LCL filter, which affects the controller performance and can induce the closed-loop to instability, by incorporation of a majorant signal and the σ-function into the adaptive law, turning it robust. In addition, the predictive nature of the controller, which aims to regulate the current tracking in the minimum time possible (one sample) impacts straightforwardly in the reduction of harmonic distortion on grid-injected currents, improving energy quality, because the transient regime is reduced thanks to the fast dynamics of the adaptive predictive control strategy. To corroborate the controller’s performance and discuss its robustness, Hardware-in-the-Loop and experimental results using a grid-tied 5.5 kW VSI with an LCL filter are presented

Robust multivariable control design for HVDC systems considering AC grid impedance uncertainties

High-voltage direct current (HVDC) transmission system based on modular multilevel converter (MMC) technology is considered as an attractive solution for the interconnection of two AC grids to enhance the security of supply. Several studies have concluded that the AC grid impedance is a key parameter for the control system design of the MMC. Such important design parameter, however, is subject to wide variations due to the time-varying nature of AC grid and the future modifications and expansions. Therefore, the grid impedance has to be considered as an uncertain parameter during control design stage. To this end, this paper suggests a robust multivariable controller which is able to maintain system stability and performance for an extended range of grid impedance uncertainties. To ensure that the controller operates robustly in a wide range of grid impedances, structured singular value of the system (known as μ) is minimized via an iterative procedure. In such procedure, the uncertainties are separated from the nominal linear model of the system and the weighing functions are tuned to fulfill the robustness criteria defined by the small-gain theorem. The effectiveness of the suggested controller and the design procedure is validated by means of simulation results.

Adaptive Grid Impedance Shaping Approach Applied for Grid-Forming Power Converters

This paper proposes an adaptive grid impedance shaping approach, implemented through a variable structure virtual impedance control strategy (VS-VIS), to improve the power flow control of grid-forming power converters (GF-PC). In this strategy, an equivalent grid impedance estimator (EGIE) evaluates the feeder X/R ratio to determine the required virtual impedance to reach the grid shaping objective. Besides, the virtual impedance definition also considers the converter power rating to ensure the system&#x2019;s feasibility. A virtual negative resistance series interconnected with a positive virtual reactance implements the virtual impedance. Moreover, the required virtual impedance is only updated when the X/R ratio extrapolates deviation limits determined by allowed grid voltages boundaries specified by the standards. Besides, the virtual reactance is split into two parts that use the conventional and sliding mode (SMC) approaches. The first implements the main part of required virtual reactance, while the second provides a fine-tuning action matching the X/R control objectives and compensating grid impedance uncertainties. This grid-shaping method provides a smooth compensation increasing the GF-PC resilience under grid impedance variation. These features constitute a novelty compared to the shaping methods presented in the literature. Experimental tests obtained from a GF-PC laboratory setup demonstrate the effectiveness and robustness of the proposed grid impedance shaping method.

Robust L Approximation of an LCL Filter Type Grid-Connected Inverter Using Active Disturbance Rejection Control under Grid Impedance Uncertainty

High-order filters, such as LCL, are more commonly employed in grid-connected inverters (GcIs) as an interference element for the better attenuation of switching harmonics. However, LCL filters may have resonance poles and antiresonance zeros in the frequency response with inverter side current. This may affect the stability of the system and limit the control bandwidth with the simple single-loop PI control. This becomes severe with the introduction of grid impedance due to the large distance between renewable energy sources and the power grid. To mitigate this effect, active damping and sensorless damping is preferred with pre-information about grid impedance. In this paper, linear active disturbance rejection control (ADRC) is introduced, first to L filter type GcI and later extended to LCL filter type GcIs with minimum modification. From the frequency analysis, it is shown that the characteristics of the proposed control scheme remain the same even with a change in filter order and grid impedance. The resonance poles and antiresonance zeros in the LCL filter are compensated via the pole–zero cancelation technique. In addition to this, the preserve bandwidth, simple control design, and decoupled current control are also achieved with the proposed method. The robustness of the proposed method is compared with the single-loop PI control under different filter types and grid impedance uncertainty through MATLAB simulation and experimental outcomes.

Virtual State Damping for Resonance Suppression and Robustness Improvement in LCL-Type Distributed Generation Inverters

This article proposes a Virtual State Damping (VSD) plugin to output current controllers of distributed generation (DG) inverters. The VSD is designed to suppress the resonance usually present in LCL-type grid-connected DG systems, providing robustness to the control system against grid impedance uncertainties or variations. Typical active damping techniques apply an equivalence impedance model to design their structures. The proposed VSD has the advantage of not needing to take such analysis into account for its design, i.e., it is not dependent on the LCL filter's physical model. The VSD structure applies the model reference theory, and it does not require additional sensors for its implementation. The paper also presents the VSD design methodology and stability analysis. Real-time domain emulation (RTDE) results and 5kW lab-prototype experimental results demonstrate the effectiveness of the proposed technique.

Active Disturbance Rejection Control Based Single Current Feedback Resonance Damping Strategy for LCL-Type Grid-Connected Inverter

The LCL-type grid-connected inverter (GCI) is widely adopted between distributed generation (DG) and power grid to realize DC/AC power conversion. However, the underdamped LCL filter will cause a resonance phenomenon near the control stability boundary, which may lead to instability of the GCI system. The traditional passive damping method will cause power loss, while the active damping method may have the need for additional sensors or be sensitive to parameter changes. In this article, a control scheme based on active disturbance rejection control (ADRC) is proposed for the LCL-type GCI, and the systematic parameter design method is presented through root locus analysis. With the proposed strategy, only the grid-injected current is sensed to achieve the objectives of grid-injected current direct control and robust resonance damping for the LCL-type GCI. In the design process, the influence of digital control delay and grid impedance uncertainty on system stability is explicitly analyzed in detail. Through this, the GCI can work stably over a wide range of the typical inductive-resistive grid impedance. In addition, it is found that the proposed strategy also has good adaptability to the filter parameter perturbation. Simulation and experimental results validate the theoretical analysis in this paper.

Grid Impedance Estimation by Measuring Only the Current Injected to the Grid by a VSI With $LCL$ Filter

A strategy for grid impedance estimation is proposed in this article. The strategy is based on the use of an observer suitable to implement the control and synchronization of a voltage-source inverter with an LCL filter, by measuring only the current that the system injects to the grid. The estimation is done based on the modification of the original structure of the observer, together with the implementation of a grid current injection strategy, which allows the observer to adapt in the presence of grid impedance uncertainty. The proposed strategy provides an accurate estimate of the grid impedance inductive and resistive components, suitable for control purposes. The validity and effectiveness of the proposed strategy are demonstrated by simulation and experimental results.

Observer-based second-order sliding mode control for grid-connected VSI with LCL-type filter under weak grid

LCL-type grid-connected voltage source inverters (VSI) have been widely used in distributed generation systems. However, due to the inherent LCL resonance, it brings a stability challenge to the control system. To address this issue, a sliding mode observer-based second-order sliding mode control method is proposed to achieve arbitrary poles placement, which can ensure desired resonance damping and dynamic performance even under weak grid operation. With the help of sliding mode observer (SMO), only the grid current and grid voltage are sensed to realize system stable operation and grid synchronization, which reduces the cost of system. To improve the robustness and dynamic response of LCL-filtered grid-connected inverters under weak grid operation, a super-twisting algorithm (STA) second order sliding mode control (SOSMC) is proposed. Due to the existence of grid impedance in weak grid, the sliding surface would drift, which increases the track error of grid current. To solve this problem, an integral term is added to the sliding surface function. The systematic design approach of SOSMC is presented, and the stability of system under the grid impedance uncertainties as well as external disturbances is proved by Lyapunov theory. Simulation results are finally presented to validate the effectiveness of the proposed control strategy.

Design of a novel robust current controller for grid-connected inverter against grid impedance variations

In this paper, a simple low order robust current controller with capacitor-current-feedback active damping is developed to reject grid impedance variations. Two control parameters among five are identified as the parameters that affect the system’s stability significantly. Thus, the goal of the robust controller design is to fix the three control parameters, varying only the other two, and to determine the robust stability region in the two-parameter plane by using D-decomposition method under the specified uncertainty region. The D-decomposition method maps the roots of closed-loop characteristic polynomials onto the graphic control parameter plane since certain relationship exists between the value of the control parameters and the value of the characteristic roots. By constraining all the closed-loop poles inside the unity circle in z-plane, the two control parameters are then the solutions to the characteristic polynomials which mathematically determines the robust stability region. Any parameters selected from this region can reject the specified grid impedance uncertainty. A robust performance region (settling time and damping ratio) is further determined inside the robust stability region, thus achieving robust stability, fast response and high quality current injection. All the analytical studies and simulation results verified the control design. The developed simple low order robust controller has been proven to be able to guarantee robust stability and achieve desired robust performance with the specified grid impedance uncertainty.

Resonance damping for an LCL filter type grid-connected inverter with active disturbance rejection control under grid impedance uncertainty

Higher-order filters, like LCL, are more commonly employed in grid-connected inverters (GCIs) as an interface element for the better attenuation of switching harmonics. However, the LCL filter has resonance poles which may degrade the performance of control without damping. Among the different damping techniques, notch filter (less expensive) and derivative filtered capacitor voltage (insensitive to parameter variation) based damping is recommended where the resonance pole is canceled with zero. However, notch filter requires prior information about grid impedance and remain sensitive to parameter variations. On other hand, derivative filtered capacitor voltage based active damping may not achieve higher stability margin depending on the filter parameters. In this paper, reduced-order extended state observer based linear active disturbance rejection control is introduced to the LCL filter type GCI. With the proposed method, the resonance poles in the LCL filter are compensated via pole-zero cancelation and it remains effective under grid impedance, and filter parameters uncertainties without control tuning. In addition, it is found that the proposed method achieves higher stability margins, dynamic performance, simple, less reliant on the system modeling, and highly decoupled current control. The stability and performance of the proposed method are compared with the single-loop PI control without/with notch filter based damping and dual loop with capacitor voltage based active damping under filter parameters and grid impedance variations via simulation and experimental results.

Robust Vector Control of a Very Weak-Grid-Connected Voltage-Source Converter Considering the Phase-Locked Loop Dynamics

Conventional vector-controlled voltage-source converters (VSC) suffer from stability and performance problems when integrated into very weak ac grids (high-impedance grids). This is attributed to the increased coupling between the converter and grid dynamics, via the phase-locked loop (PLL), at the very weak-grid condition. In the current literature, the impact of the PLL is usually ignored when the converter controllers are designed. While this approach can be accepted under stiff grid conditions, it yields unmodeled dynamics that destabilize the converter under weak-grid conditions and high-power injection levels. To overcome this limitation, this paper presents a robust vector-controlled VSC that facilitates full converter power injection at weak and very weak-grid conditions (i.e., when the short-circuit capacity ratio is one). To realize the controller, first, a detailed dynamic model for the ac-bus voltage dynamics, including the PLL dynamics, is developed and validated in this paper. Second, the model is used to optimally design a robust ac-bus voltage controller to stabilize the dynamics under operating point variation and grid impedance uncertainty. Because the developed model includes the PLL dynamics, the developed controller inherently stabilizes the negative impact of the PLL on the converter stability. A theoretical analysis and comparative simulation and experimental results are provided to show the effectiveness of the proposed controller.

A Synchronous Reference Frame Robust Predictive Current Control for Three-Phase Grid-Connected Inverters

This paper presents a new predictive current control for three-phase grid-connected inverters in the synchronous reference frame. The control combines a deadbeat control law with a diagonal Luenberger observer to estimate the future value of the grid currents. It provides a decoupled control of the active and reactive power and offers robustness against the computational delay inherent in the digital implementation and against filter and grid-impedance uncertainties. This control exhibits a very fast current response while widely improving the gain and phase margins of the traditional predictive controllers.

Design and Implementation of a Robust Current Controller for VSI Connected to the Grid Through an LCL Filter

This paper describes the design and implementation of a discrete controller for grid-connected voltage-source inverters with an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> filter usually found in wind power generation systems. First, a theorem that relates the controllability of the discrete dynamic equation of the inverter with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> filter and the sampling frequency is derived. Then, a condition to obtain a partial state feedback controller robust to grid impedance uncertainties and based on linear matrix inequalities is proposed. This controller guarantees the stability and damping of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> filter resonance for a large set of grid conditions without requiring self-tuning procedures. Finally, an internal model controller is added to ensure asymptotic reference tracking and disturbance rejection, significantly reducing the impact of grid background voltage distortion on the output currents. Experimental results are presented to support the theoretical analysis and to demonstrate the system performance.