Grid Inductance Research Articles

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.

Offset free generalized model predictive control for 3-phase LCL-filter based grid-tied inverters

This paper presents a Generalized Model Predictive Control (GPC) in the natural reference frame for a 3-phase LCL-filter based grid-tied inverter. The proposed controller can track the sinusoidal reference without steady-state phase and amplitude offsets. This is achieved by parameterizing the control law matrices with considering the future reference trajectory.To cope with the LCL filter resonance, traditional controllers need a damping method. The proposed controller has inherent damping against the LCL filter resonance and extra sensors are avoided. The controller parameters are selected by a sensitivity analysis that guarantees the closed-loop stability.The proposed controller provides high accuracy in controlling active and reactive currents, robustness against grid inductance variations, low real-time computation, and a fixed switching frequency. The simulation and experimental results prove the performance of the controller in tracking the grid-side reference currents.

2DOF-based current controller for single-phase grid-connected voltage source inverter applications

This paper presents the design of a discrete-time control scheme for the current injected into the grid by a single-phase voltage source inverter (VSI). The VSI is connected to the grid by means of an LCL filter that attenuates the switching harmonics present in the output waveform of the inverter. The current control is based on a resonant regulator implemented in a Two-Degrees-Of-Freedom (2DOF) scheme that allows the location of all the poles to be defined in the closed loop of the system without the need for observers and measuring only the current injected into the grid. This control scheme, therefore, allows the attenuation of the resonance frequency of the LCL filter and requires no additional damping methods with which to mitigate the resonance phenomenon. The design parameters can be obtained using a fairly straightforward mathematical approach that involves only operations with real numbers. The simulation and experimental results obtained show that the control scheme performs correctly even considering changes in the grid inductance.

Observer-Based Single-Sensor Control Schemes for LCL-Filtered Grid-Following Inverters

In the single-sensor grid-following control of <i>LCL</i>-type grid-connected inverters, extended-observers, which behave as &#x201C;virtual sensors,&#x201D; are typically employed for active damping, disturbance rejection, current tracking, and grid synchronization. However, most of the existing observer-based single-sensor control schemes choose grid current as the system measurement and output, and the performance of other combinations is still unclear. Hence, in this article, with the help of impedance modeling and Nyquist stability criterion, a systematic comparative assessment for selecting different measurements and controlled outputs is introduced. In this comparison, the sub- and super-synchronous oscillation issues induced by grid faults, lower current reference, high phase-locked loop (PLL) bandwidth and large grid inductance, are investigated. In addition, two easily overlooked interval stability corollaries are proved, facilitating the system stability analysis. Finally, the correctness of the theoretical analysis is verified by a series of steady-state and transient experimental tests.

A Current Controller Gain Characterization of Weak Grid Coupled Solar Inverter Through Impedance Interaction Modeling

The interface inverters arbitrate the network impedance based on the source characteristics for efficient solar energy harvesting. The wide impedance arbitration capability of the interface inverter defines the wide operational integrity with the ac network. In the weak grid scenario, the uncompensated grid inductance beyond point of common coupling (PCC) offers the negative damping for power oscillations at the PCC tugs the system toward instability. In this article, the negative damping influence due to interactions between the system impedance (filter inductance and grid power injection resistance) and ac network impedance (grid inductance) on the inverter closed-loop controller is characterized by observing the natural phase deviations in real and imaginary axis. Through distinguished system’s natural response, a novel second-order system impedance model is derived, and proposed current controller gain characterization aiming to achieve positive damping to mitigate the PCC’s oscillations. Further tuning of the controller based on the natural response of the derived impedance model accomplishes the enhanced grid injected power quality. The efficacy of the derived system impedance model along with coherence of current controller gain is demonstrated on hardware for enhanced power quality under the stable operating region.

Adaptive super-twisting sliding mode for DC-AC converters in very weak grids

ABSTRACT This paper presents the design of a direct-type adaptive control structure for current regulation of a single-phase grid-tied Voltage-Source Inverter (VSI) with an LCL filter under very weak grid condition. The initial content of this work was previously published, where the controller was presented and its discrete-time stability proof was provided. Power converters connected to weak grids bring challenges to the control system, since the grid can change abruptly from a strong to a very weak condition , degrading system power quality. This study evaluates the feasibility of a RMRAC-based robust adaptive Super-Twisting Sliding Mode controller for current control of VSI when the grid inductance changes substantially, from 0 mH (strong grid) to 10 mH (very weak grid). To show the benefits of the control strategy and its robustness, hardware-in-the-loop (HIL) simulation results are presented, comparing its performance with two other controllers..

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 Online Inductance Identification of Traction Network and Adaptive Control Method for Cascaded H-Bridge Converter

The grid-tied cascaded H-bridge (CHB) converter may become unstable, especially for the traction onboard application where the grid impedance may gradually vary as the train moves. In order to overcome this weakness, a small-signal stability-based adaptive control strategy is proposed in this article, where the parameter of the current-inner-loop controller is adaptively regulated according to the online grid inductance identification (GII) result. In the proposed control structure, there is only one control parameter needed to be regulated online, which is based on the estimated value of the grid inductance. In this article, the grid inductance is estimated by injecting the specific harmonic current. With the corresponding harmonic current regulator, stable and sustained harmonic current can be injected, which is beneficial to mitigate the fierce fluctuation of the GII result. The GII algorithm is made up of three parts, including the analog low-pass filter, the sliding discrete Fourier transform, and the digital composite filter, which can suppress the switching noise, the low-frequency grid harmonics, and the grid frequency deviation. With the proposed adaptive control strategy, the CHB can ensure small-signal stability wherever it is connected. All these theoretical analyses are verified by the experiment.

A Grid Inductance Detection Method Based on the Oscillation Characteristic of Inverter Terminal Voltage

In grid-connected photovoltaic (PV) systems, grid inductance greatly influences the performance of grid-connected inverters. However, the grid inductance usually varies with the changes of the grid operation conditions. Therefore, accurate grid inductance detection is one of the key technologies to achieve an adaptive control of the grid-connected inverters under different operation conditions. In this article, an equivalent circuit model of a grid-connected PV system which includes the controller, filter, and grid impedance is established. The oscillation characteristic of the inverter terminal voltage caused by the sudden change of the inverter output power is analyzed. The oscillation mechanism of the inverter terminal voltage caused by the interaction of the controller, filter, and grid impedance is investigated. A grid inductance detection method based on the oscillation characteristic of the inverter terminal voltage is proposed. The main advantage of the proposed method is that it does not need complicated signal processing and calculation procedures. A 10-kW grid-connected PV system was built for both simulations and the experimental setup. Finally, simulation and experimental results validate the correctness and effectiveness of the proposed method.

Robust Decoupled Outer-Control Design for Single VSC and HVDC Grid With Controller Weak AC System Interconnection

With the increase in number of VSC based HVDC systems, it is inevitable that there would be interconnections with weak ac grids. The paper presents the analytical basis for identifying coupling in the power loops which is dependent on grid inductance and operating point by utilizing the impedance based modeling technique. The formulation is used to define an inverse-based decoupling outer-loop controller for VSC-HVDC system. The concept is extended to HVDC grids and it is shown that the gains obtained using simple inverse may lead to instability. Robust controller tuning with pole-placement and minimization of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> norm is presented for HVDC grids, which form a restricted feedback system. The results show that the proposed method of decoupling results in effective decoupling of the power loops over a large range of grid inductance values as compared to that with traditional vector control. The system stability is also maintained over a large range of grid inductance values and PLL gains when a sudden variation of parameters is considered. The stability margins can be enhanced by pole-placement. The observations from the small-signal models are confirmed using detailed time-domain simulations. The proposal is expected to be useful in controller design for single VSC as well as HVDC grids, especially, during planing stage.

Cascaded control for LCL filter based grid‐tied system with reduced sensors

This work implements a cascaded control for the LCL filter-based grid-connected neutral point clamped (NPC) inverter with the reduced sensor. The conventional three-loop control requires two current sensors for the inverter side, two voltage sensors for the voltage side, and two current sensors for the grid side in total for sensing. This work proposes a novel cascaded control scheme that allows a considerable reduction of grid-side current sensors and capacitor-side voltage sensors. Only two inverter-side current sensors are required for the same. The sensing point is implemented by the proposed estimation algorithm. As an outcome, the hardware complexity, weight, size, and implementation cost of the system are downsized. A comparative assessment is performed between the conventional technique and the proposed methodology. The system is analysed for grid inductance and LCL filter parametric variations in order to assure the robustness and stability of the system. In addition, the system is also investigated for the influence of digital control delay. The implemented system offers enhanced system stability and improved dynamic performance. In order to meet grid regulation, it offers an economical solution. The proposed system is justified by simulated results on the MATLAB/Simulink platform and verified by the experimental results.

Influences on the LVRT behavior of DFIG wind turbine systems

Grid faults introduce highly dynamic electrical and mechanical loads to a wind turbine (WT). Especially WTs with a direct grid connection like the doubly-fed induction generator (DFIG) are strongly affected. The behavior of a WT during grid faults can be tested in low voltage ride through tests (LVRT). But there are numerous influencing factors on the behavior of the DFIG during a LVRT which have not yet been fully investigated. The pre-fault operating point of the DFIG, the grid inductance, the pre-fault phase angle of the grid voltage, the fall time of the voltage as well as the start and end values of the voltage drop affect the electromagnetic torque and the short circuit current of the generator. Therefore, many LVRT test results for DFIGs are neither comparable nor representative. In this paper it is shown that the peaks of electromagnetic torque and currents during LVRTs can be reduced. A low pre-fault torque and rotational speed, a high grid inductance and a slow voltage drop can minimize the impact of a grid fault. The rotational speed is especially critical because it influences the slip of the DFIG and, thus, has an influence on the dynamics of the fault.

Enhanced dynamic performance of grid feeding distributed generation under variable grid inductance

&lt;p&gt;Controlling weak grid-connected systems is very challenging. In transient, frequency and voltage oscillations may lead to voltage and/or frequency stability problems and finally lead to system collapse. During steady-state operation and at the point of common coupling (PCC), voltage degradation and grid voltage background harmonics restrict the inverter's functionality, reduce the power flow capability and cause poor power quality. With weak grid connection, grid impedance variance will contaminate the voltage waveform by harmonics and augment the resonance, destabilizing the inverter operation. In this paper, complete mathematical modeling is carried out and state feedback-plus-integral control is implemented to support the stabilization of the system. The proposed controller is adopted to provide a smooth transient under sudden load change by controlling the injected grid current under different grid inductance values. Furthermore, the proposed control is used to reduce the order and size of the inverter output filter while maintaining system stability. The proposed control has been compared with the conventional proportional integral (PI) controller under different scenarios to validate its effectiveness and to strengthen its implementation as a simple controller for distributed generator applications.&lt;/p&gt;

A Generic Robust Model-Based Estimator for Active Damping of Single-Phase GridTied Inverters

This paper presents the design and analysis of a signal estimator with improved robustness applied in the active damping (AD) of a single-phase grid-tied inverter with LCL low-pass filter. The proposed estimator is based on the mathematical model of the LCL filter, with resistors in series with the converter-side inductor and capacitor for improving robustness. The implementation method is also capable of estimate multiple filter signals. The control strategy presented uses a virtual resistor based AD, that suppresses the resonance ensuring stability and robustness, helping comply with power quality standards, such as IEEE 1547 and IEC 61727. The signal necessary for achieving the AD is obtained through the estimator, dismissing the use of additional sensors. The current control structure uses grid-side current feedback with proportional-resonant controller and harmonic compensation. The system is designed by the root locus approach to achieve stability despite grid parameter variance. The estimator and overall system is analyzed through mathematical modeling, computational simulation and experimental setup. The results show that the estimator presented is capable of providing the necessary AD feedback signal, even with grid inductance variation.

Model Predictive Control of H7 Transformerless Inverter Powered by PV

Transformerless inverters have become an important integration of the modern photovoltaic (PV) grid-tied systems. Unfortunately, it has a general safety problem regarding the earth leakage current that must be less than the recommended standards. Lately, the H7 transformerless inverter, which is a three-phase inverter with an additional switch on the DC side, is introduced to mitigate the earth leakage current. Different modulation techniques and controllers are proposed to optimize its performance. This paper proposed the application of model predictive control (MPC) to grid-connected H7 transformerless inverter supplied by the PV power system. In modeling the system, the grid inductance has been taken into consideration. The inverter is linked with the PV through a boost converter. It is found that the boost converter inductance value has a great effect on the leakage current. Matlab's simulations for the proposed system are carried out. The performance of the proposed system controlled by MPC is compared to that controlled by the proportional-integral (PI) controller. The results show that the MPC gives the system greater benefits than the PI controller. The effects of the boost-converter inductance on the earth leakage current are studied. Also, the design of the boost-converter inductance is introduced.

A Generalized Analytical Tuning Approach for Model Predictive Controlled Grid-Tied Converters Under Wide Range of Grid Inductance Variation

In medium-high power applications, the LCL is the preferred filter topology to attain efficient power conversion. The filter provides a high damping attenuation of -60 dB/decade above the resonance frequency at the cost of a higher order plant, complex parameter design, and, increased vulnerability to un-modeled disturbances. Recently, model predictive control applied to power electronic converters has experienced great interest from researchers. The technique is tailored to the control of complex MIMO systems such as the LCL filter as it allows simultaneous regulation of several state-variables via a user defined cost function. However, the tuning of weighting factors (WFs) within the cost function is not trivial, and in most cases employs an empirical procedure. This paper presents an analytical procedure for tuning of WFs for indirect model predictive current controlled grid-tied converters. The method is based on using analytical closed-form expressions, that relate closed-loop poles of the filter with WFs via physical plant parameters. The presented expressions generalize the tuning of WFs to any arbitrary LCL design. The proposed method is validated by hardware-in-the-loop simulations conducted on PLECS RTBOX 3. Through experimental testing, it is shown that the controller is robust against a wide range of grid impedance variation.

Robust Control of GTIs under wide grid impedance ranges: An approach combining metaheuristics and LMIs

This paper provides a new design procedure for robust state feedback current controllers suitable for grid-tied inverters under wide grid impedance ranges. The proposed procedure is based on the combination of particle swarm optimization and linear matrix inequalities. The control gains, designed offline, are obtained through the minimization of a novel objective function that takes into account the grid current tracking error in the stationary reference frame, limits for the control signal, and robust stability. Linear matrix inequalities are used in the design stage to theoretically certify the closed-loop robust stability systematically and efficiently, based on a polytopic model of the grid-tied inverter, which avoids the need for exhaustive and time-consuming a posteriori tests. Real-time simulations and experimental results are presented, attesting that the closed-loop system with control gains provided by the proposed procedure is robustly stable for wide ranges in the grid inductances. Moreover, the grid currents exhibit an optimized transient performance and steady-state responses in compliance with harmonic distortion limits from IEEE 1547 Std., even encompassing operation from stiff to weak grid conditions and in the presence of distorted grid voltages. To provide a comparison, results based on other well-established state feedback design techniques are also presented, highlighting the superior performance obtained with the proposed procedure.

Robust Active Damping Strategy for DFIG Wind Turbines

Doubly fed induction generators (DFIGs) with an LCL filter are widely used for wind power generation. In these energy conversion systems, there is an interaction between the grid-side converter (GSC) and the rotor-side converter (RSC) control loops, the generator and the LCL filter that must be properly modeled. Such interaction between the GSC and the RSC proves to have a significant influence on the stability. Several active damping (AD) methods for grid-connected converters with an LCL filter have been proposed, nevertheless, the application of these techniques to a DFIG wind turbine is not straightforward, as revealed in this article. To achieve a robust damping irrespective of the grid inductance, this article proposes an AD strategy based on the capacitor current feedback and the adjustment of the control delays to emulate a virtual impedance, in parallel with the filter capacitor, with a dominant resistive component in the range of possible resonance frequencies. This work also proves that, by applying the AD strategy in both converters simultaneously, the damping of the system resonant poles is maximized when a specific value of the grid inductance is considered. Experimental results show the interaction between the GSC and the RSC and validate the proposed AD strategy.

Performance Improvement of a Grid-connected Voltage Source Converter Controlled by Parabolic PWM Current Control Scheme

Parabolic carrier PWM method is considered as one of the direct current control methods which has been proposed for the voltage-source converters (VSCs). This method has an excellent dynamic response. Besides, it proposes a constant switching frequency by employing a pair of parabolic PWM carriers. However, it suffers from some drawbacks and limitations. The major drawback of this method is its sensitivity to the inductance variations. In other words, in grid-connected applications the exact value of grid inductance should be exactly known to achieve a proper performance from this method. Moreover, it is essential that during each switching cycle the voltage at the point of common coupling remains constant. In grid connected applications such as active power filter these drawbacks may lead to operate at variable or non-expected frequencies. Therefore, this paper concerns the suggestions to deal with the situation. In this paper, by applying the conventional method the aforementioned problems are examined in a grid-connected active power filter. It is shown analytically that by using the proposed method, problems of sensitivity to inductance changes and also necessity to constant voltage at point of common coupling in a switching period will be solved. Finally, simulation and experimental results are presented.

Harmonic stability analysis of multi-paralleled 3-phase PV inverters tied to grid

In this paper the harmonic stability is investigated for multi paralleled three-phase photovoltaic inverters connected to grid. The causes to harmonically stabilize/destabilize the multi-paralleled PV inverters when tied to the grid isanalysed by the impedance-based stability criterion (IBSC). In this paper stability of the system is investigated by varying the grid inductance with constant grid resistance and also by varying load impedance while maintaining grid inductance constant. Stability of the multiple three phase inverters tied to the grid with different grid impedance, inductance value inparticular are analyzed. Overall system is stable up to grid inductance of5mH even though there is change in load admittance. It is concluded that system stability depends only on grid impedance. It is verified with Matlab Simulations.