Grid Inductance Research Articles

Reactive Current Reshaping With Series Resonance Damping for Three-Phase Buck-Type Dynamic Capacitor

By adding Buck-type AC/AC converter to conventional power capacitor, dynamic capacitor (D-CAP) can be formed to compensate variable rather than fixed reactive power. However, some nonlinear distortion factors, namely grid harmonic voltage, voltage drop of switches and dead-time, would cause harmonics in its compensation current, meanwhile, its capacitance may interact with the grid inductance to cause series resonance. Both nonlinear distortion factors and series resonance would distort the waveform of its compensation current and make the grid current failed to meet the power quality standard IEEE Std.519. This paper focuses on the output current distortion of Buck-type D-CAP in reactive power compensation. For harmonic distortion, through establishing the equivalent circuit of Buck-type D-CAP, the generation of low-order harmonic current is investigated under three nonlinear factors. A current reshaping method to simultaneously diminish the harmonics caused by the three nonlinear distortion factors is thus adopted, which is a feedback control of output current harmonics. Then for series resonance, based on the block diagram of Buck-type D-CAP within the grid, transfer function from grid voltage to the output current is deduced and the corresponding Bode diagram is depicted. An active damping method is therefore suggested to shrink the low-order series resonance peak, by detecting power capacitor's voltage for feedback control. Finally, a combined control, reactive current reshaping with series resonance damping is proposed in this paper for three-phase Buck-type D-CAP. A wide variety of experimental results from a 33kVar/220V laboratory prototype are provided to demonstrate the validity of the combined control.

Improved Current Decoupling Method for Robustness Improvement of LCL-type STATCOM Based on Active Disturbance Rejection Control

When theoretically studying the control method of LCL-type static synchronous compensator (STATCOM), we often ignore the influence of complex power grid on the stability and reactive compensation performance of STATCOM. Improving traditional current decoupling method with PI controller (PI decoupling) in synchronous (dq) reference frame, an original current decoupling method with active disturbance rejection controller (ADRC decoupling) is proposed in this paper. First, the influence of internal and external disturbances on STATCOM with PI decoupling method is analyzed. External disturbances include harmonic grid voltage and grid inductance variation. Internal disturbances come from coupled channels between d axis and q axis, and parameter perturbations of LCL filter. Second, the principle of ADRC decoupling method applied to LCL-type STATCOM is analyzed in detail. Taking advantage of ADRC's capability to estimate and compensate for the “total disturbances”, robustness of STATCOM is improved. Comparing with PI decoupling method, ADRC decoupling method can improve the disturbances rejection performance and stability of LCL-type STATCOM. Finally, results from STATCOM simulation model show the effectiveness and superiority of this original method.

Detection of Series Arcs Using Load Side Voltage Drop for Protection of Low Voltage DC Systems

Low voltage dc distribution grids face issues associated with arc faults, aggravated by the absence of current zero crossing. The focus of this paper is to comprehensively develop a method of series arc fault detection at the load side power electronics, based on the electrode dependent initial voltage drop occurring at the arc initiation. The proposed arc detection algorithm is described along with the structure and time constants of the designed bandpass filter. The operational boundaries of the arc detection algorithm are defined for copper electrodes depending on the set threshold voltage and the system parameters, like grid inductance, resistance, and the load capacitance. Further, the detection time and the zone of guaranteed positive detection are depicted. These are validated through test simulations on the state space model of the system. Finally, experimental validation of the proposed scheme is carried out, wherein, a series arc is generated in the dc circuit and the programmed micro-controller provides a real time signal upon detecting the arcing event. The results on variation in detection time with set threshold voltage are also presented experimentally.

A Unique Pulse Width Modulation to Reduce Leakage Current for Cascaded H-Bridge Inverters in PV and Battery Energy Storage Applications

Cascaded H-bridge (CHB) inverters operate with isolated DC sources, which makes them a favorable topology for hybrid-interfaced applications. Parasitic capacitance of grounded photovoltaics (PV) results in leakage currents that may deteriorate the system performance and raise safety concerns. In order to address this problem, a common-mode equivalent circuit for a multilevel CHB is illustrated. The study reveals that common modulation techniques such as phase shifted pulse width modulation fail to suppress the leakage current. A unique modulation scheme, based on considering the switching states is proposed in order to ensure that the topology conforms to the transformerless inverter regulations and standards such as VDE-0126-1-1. Simulation study results for conventional and proposed modulation methods are presented and analyzed in a symmetrical grid inductance filter circuit.

Benchmarking of Stability and Robustness Against Grid Impedance Variation for <italic>LCL</italic> -Filtered Grid-Interfacing Inverters

This paper comprehensively analyzes the stability of a grid-interfacing inverter with the LCL -filter in the discrete domain, where the LCL-filter, along with the controller, is modeled in a polar coordinate. System open-loop and closed-loop poles are analytically studied and expressed in the z -domain. Through the poles movement and distribution analysis, the relationship between system stability and the ratio of resonance frequency over sampling frequency is mathematically revealed and calculated as well as the system control gain limit. Moreover, this paper demonstrates that a grid-voltage feedforward regulator would significantly alter the inverter stability in a weak power system. By means of Jury stability criterion, the stability status under different filter resonance frequency is given. The selection of resonance frequency and filter parameters makes a considerable difference on system behavior. Finally, to improve the robustness against grid inductance variation, a conservative design recommendation of filter parameters and control gain is given. Through the tests on a laboratory-scale prototype, the theoretical analysis is validated by experimental results.

Robust multisampled capacitor voltage active damping for grid-connected power converters

The derivative feedback of the capacitor voltage is one of the most extended active damping strategies, used to eliminate stability problems in grid-connected power converters with an LCL filter. This strategy is equivalent to the implementation of a virtual impedance in parallel with the filter capacitor. This virtual impedance is strongly affected by the control loop delays and frequency, creating changes in the sign of the emulated virtual resistor, and raising instability regions where the active damping is ineffective. As a consequence, the LCL resonance frequency is restricted to vary, as the effective grid inductance changes, within the active damping stability region. This is an additional restriction imposed on the LCL filter design that can compromise the achievement of an optimised design. For this reason, in this work, a different strategy is presented; by adjusting the delay in the active damping feedback path, it becomes stable within the range where the LCL resonance frequency can be located for a given filter design, achieving a robust damping. Analytical expressions are provided to adjust this delay. To widen the stability region of the capacitor voltage derivative active damping, a multisampled derivative is implemented, overcoming its limitations close to the control Nyquist frequency. Experimental and simulation results validate the active damping strategy presented.

Inverter-Current-Feedback Resonance-Suppression Method for LCL-Type DG System to Reduce Resonance-Frequency Offset and Grid-Inductance Effect

For the LCL-type grid-connected distributed generation system, the grid-current-feedback active damping (GCFAD) methods have a conflict between the resonance-suppression ability and harmonic-currents amplification. For this, an inverter-current-feedback reso-nance-suppression (ICFRS) method without additional sensors is proposed to reduce resonance-frequency offset and grid-inductance effect due to its unattenuated damping characteristic under high-frequency bandwidth. By analyzing two types of equivalent impedance models of ICFRS and GCFAD with a high-pass filter (HPF), GCFAD can suppress the resonance peak well only with a large resonance-frequency offset and might result in a narrow control bandwidth. However, ICFRS can suppress the resonance peak well with smaller resonance-frequency offset and maintain a high power quality compared with GCFAD. Considering the influence of control delay and grid inductance, the positive/negative critical point of an equivalent virtual resistance of ICFRS derived in the interval of [1/6, 1/3) is obtained, and a robust ICFRS is further proposed to improve system stability by maintaining a positive resistance regardless of grid-inductance variation. The stable-state and dynamic properties of the overall system are analyzed in detail in this paper, and its proper control parameters are selected without a complicated trial. Finally, simulation and experimental results verify the validity of the proposed method.

Plug-In Identification Method for an <italic>LCL</italic> Filter of a Grid Converter

This paper proposes a method for estimating two inductances and capacitance of an LCL filter, connected between a converter and a grid. Only the dc-bus voltage and converter phase currents need to be measured. An excitation signal is fed into the converter voltage reference. The fundamental and selected harmonic components are removed from the stored identification data to prevent biases in the parameter estimates. The parameters of the hold-equivalent discrete-time model are estimated recursively. The inductance and capacitance estimates are calculated from the estimated discrete-time parameters using the corresponding closed-form model. The proposed method can be added to the existing converter control algorithms. It can provide the parameter estimates for the converter control. Further, it can be run occasionally during the normal operation in order to obtain an updated grid inductance estimate. Experimental results show that the proposed method yields very good parameter estimates and that it can also detect the changes in the grid inductance.

On Stability of Voltage Source Inverters in Weak Grids

As the number of inverters increases in the power grid, the stability of grid-tied inverters becomes an important concern for the power industry. In particular, a weak grid can lead to voltage fluctuations at the inverter terminals and consequently cause inverter instability. In this paper, impacts of circuit and control parameters on the stability of voltage source inverters are studied using a small-signal state-space model in the synchronously rotating $dq$ -frame of reference. The full-order state-space model developed in this paper is directly extracted from the pulsewidth modulation switching pattern and enables the stability analysis of concurrent variations in the three-phase circuit and control parameters. This paper demonstrates that the full-order model of a grid-tied active (P) and reactive (Q) power (PQ)-controlled voltage source inverter (VSI) can be significantly reduced to a second-order model, preserving the overall system stability in the case of grid impedance variations. This paper also shows that a decrease in the grid inductance does not necessarily improve the stability of grid-tied VSIs. The system stability is a function of both the grid R/X ratio and grid inductance. Despite the grid-side inductor of the LCL filter is in series with the grid impedance, they have different impacts on the stability of a grid-tied PQ-controlled VSI, i.e., an increase in the filter inductance may improve the system stability in a weak grid. These findings are verified through simulated and experimentally obtained data.

Design methodology of a passive damped modified LCL filter for leakage current reduction in grid‐connected transformerless three‐phase PV inverters

Although grid-connected transformerless photovoltaic (PV) inverters present higher efficiency and power density compared with inverters with a transformer, the leakage current caused by the inverter common-mode voltage introduces several problems. Among the techniques to reduce the leakage current, the modified LCL (MLCL) filter with passive damping is an effective and simple solution. However, the classical design of the filter damping resistance is not adequate for ensuring both proper leakage current attenuation and control system stability. Therefore, this study proposes a methodology to design the resistance in a low-loss passive damping structure applied to the MLCL filter. In addition to the conventional specifications for LCL-type filters, this study includes the leakage current limit in the design procedure. Simulation and experimental results for a 10 kW PV inverter show the damping resistance impact on the leakage current. The results related to the efficiency and grid inductance variation are also presented. Therefore, it is possible to conclude that the proposed design methodology is very useful for obtaining a damping resistance that ensures control system stability and a leakage current in conformity with PV standards.

Robust Active Damping Methods for LCL Filter-Based Grid-Connected Converters

Grid-connected converters (GcCs) employ LCL filters instead of simple L filters in order to meet new grid codes and their on-going changes in the near future. Active damping methods, without power losses, are preferred to passive ones for solving the resonance problems of LCL -filter-based GcCs ( LCL -GcCs). However, large changes in the grid inductance (typically under weak grid conditions and in rural areas) may compromise the system stability. Moreover, the delay of digital controllers will change system phase-frequency characteristics and consequently will affect the system stability. In view of this, this paper proposes a systematic design procedure for the active damping of voltage-oriented PI control for LCL- GcCs. The procedure considers active damping methods based on capacitor current feedback and is aimed to ensure stable operation under severe grid inductance variations while taking into account the influence of digital control delay and LCL filter parameters changes on the system stability. Simulation and experimental results are presented and discussed in order to validate the proposed design procedure.

Variable Structure Control for Three-Phase LCL-Filtered Inverters Using a Reduced Converter Model

This paper presents a new concept in active damping techniques using a reduced model of an LCLfiltered grid-connected inverter. The presence of the LCL filter complicates the design of the inverter control scheme, particularly when uncertainties in the system parameters, especially in the grid inductance, are considered. The proposed control algorithm is addressed to overcome such difficulties using a reduced model of the inverter in a state observer. In this proposal, two of the three state variables of the system are obviated from the physical inverter model, and only the inverter-side current is considered. Therefore, the inverter-side current can be estimated emulating the case of an inverter with only one inductor, thus eliminating the resonance problem produced by the LCL filter. Besides, in the case of a distorted grid, the method allows us to estimate the voltages at the point of common coupling free of noise and distortion without using any phase-locked loop based synchronization algorithm. This proposal provides the following features to the closed-loop system: first, robust and simple active damping control under system parameters deviation; second, robustness against grid voltage unbalance and distortion; and third, an important reduction in the computational load of the control algorithm, which allows us to increase the switching frequency. To complete the control scheme, a theoretical stability analysis is developed considering the effect of the observer, the system discretization, and the system parameters deviation. Experimental and comparative evaluation results are presented to validate the effectiveness of the proposed control scheme.

Variable Structure Control in Natural Frame for Three-Phase Grid-Connected Inverters With LCL Filter

This paper presents a variable structure control in natural frame for a three-phase gird-connected voltage-source inverter with LCL filter. The proposed control method is based on modifying the converter model in natural reference frame, preserving the low-frequency state-space variables dynamics. Using this model in a Kalman filter (KF), the system state-space variables are estimated allowing us to design three independent current sliding-mode controllers. The main closed-loop features of the proposed method are: first, robustness against grid inductance variations because the proposed model is independent of the grid inductance; second, the power losses are reduced since physical damping resistors are avoided; third, the control bandwidth can be increased due to the combination of a variable hysteresis comparator with the KF; and fourth, the grid-side current is directly controlled providing high robustness against harmonics in the grid. To complete the control scheme, a theoretical stability analysis is developed. Finally, selected experimental results validate the proposed control strategy and permit illustrating all its appealing features.

Immitance based stability assessment for multi paralleled 3-ø pv inverters connected to grid

The main objective of this work is to analyze and investigation on Immitance Based Stability Assessment for Multi paralleled 3-O PV Inverters connected to Grid is checked by using the Impedance based Stability Criterion (IBSC), The causes for Harmonically stabilized/destabilize the Multi paralleled PV inverter Connected to the grid by varying grid impedance is Analysed by the impedance-based stability criterion.Here Two case studies are Considered with the different grid Inductances to demonstrate the overall system is stable/unstable. The Third case study is projects the overall stability of the System with the constant grid impedance and variable Load Impedance/ Admittance. The Overall System is stable up to grid Inductance 5 mH even though there is change in Load Admittance The stability of the system depending on the grid impedance and not depending on the Load Admittance. The Harmonic content in the grid current of the stable system is in the acceptable limit. It is verified in the Time domain Simulation is provided in MATLAB- Simulink TM .

Robust Stability Analysis of Grid-Connected Converters Based on Parameter-Dependent Lyapunov Functions

This paper deals with the problem of robust stability analysis of grid-connected converters with LCL filters controlled through a digital signal processor and subject to uncertain grid inductance. To model the uncertain continuous-time plant and the digital control gain, a discretization procedure, described in terms of a Taylor series expansion, is employed to determine an accurate discrete-time model. Then, a linear matrix inequality-based condition is proposed to assess the robust stability of the polynomial discrete-time augmented system that includes the filter state variables, the states of resonant controllers and the delay from the digital control implementation. By means of a parameter-dependent Lyapunov function, the proposed strategy has as main advantage to provide theoretical certification of stability of the uncertain continuous-time closed-loop system, circumventing the main disadvantages of previous approaches that employ approximate discretized models, neglecting the errors. Numerical simulations illustrate the benefits of the discretization technique and experimental results validate the proposed approach.

Indirect Sliding Mode Power Control associated to Virtual Resistor based Active Damping Method for LLCL-Filter-based Grid-Connected Converters

LLCL filters are becoming an attractive solution for Grid connected Converters (GcCs) due to their ability to reduce the filter cost and size while meeting new grid codes and power quality requirements. Compared to the conventional LCL filter, the LLCL filter inserts a small inductor in the capacitor branch to compose a series LC circuit that resonates at the GcC switching frequency. The LC branch has a very low impedance at the switching frequency, which can strongly suppress the harmonic current around switching frequency and therefore reduce the filter grid side inductor. However, the LLCL filter resonance phenomenon and the large changes in the grid inductance (typically under weak grid conditions and in rural areas) may compromise the system stability. In order to address these concerns, this paper proposes an Indirect Sliding Mode Power Control associated to Virtual Resistor based Active Damping method (ISMPC-VRAD) for LLCL -filter-based Grid-connected Converters ( LLCL-GcCs ) . The LLCL filter design parameters as well as the ISMPC-VRAD gains are carefully tuned in order to ensure stable operation under severe grid inductance variations while taking into account the influence of LLCL filter parameters changes on the system stability. Simulation results are presented and discussed in order to prove the efficiency and the reliability of the proposed ISMPC-VRAD for LLCL-GcCs as well as the high filtering performances of the designed LLCL-GcCs .

New DPC Look-Up Table Methods for Three-Level AC/DC Converter

This paper presents new look-up table methods for a three-level ac/dc converter supplied from the grid. The nonlinear direct power control (DPC) method, by reason of its drawbacks resulting from the omission of grid inductance voltage drop, has been improved in the DPC- ${\updelta}$ $5\times2$ method by rotating the orientation of coordinates by angle ${\updelta}$ , i.e., the angle between grid voltage vector and set converter voltage vector. The other proposed development involves further improvement of the DPC- ${\updelta}$ $5\times2$ , into which a new optimal division of the current error plane is introduced. The new optimal voltage vector assignment allows us to choose a converter voltage vector using the modified error current vector. The proposed look-up table methods have been tested and compared applying the following criteria: current error, total harmonic distortion (THD) of input current, average transistor switching frequency, and response time on step changes of set current. The experimental results validate the proposed control schemes and show good system performances that were verified according to above criteria.

Stability Analysis and Robust Design of <italic>LCL</italic> With Multituned Traps Filter for Grid-Connected Converters

Utilizing high-order passive filters for the voltage-source converters is becoming attractive in industrial applications due to the excellent attenuation performance, smaller size, and lower cost. The LCL , the multituned traps, and recently the combined LCL with multituned traps ( LCL-mT ) are the most popular high-order filters. However, the increased number of elements and the inherent resonances complicate both filter parameter design and current control loop stabilization, especially, in the presence of parameter uncertainties and wide variations of the grid inductance. Hence, in this paper a straightforward and robust design procedure for the LCL-mT filter is proposed. Compared to the existing methods, the proposed technique is not iterative and satisfies the traditional practical limits on filter parameters, while ensures stability even in the presence of wide grid inductance variations and filter parameter uncertainties. The validity and effectiveness of the proposed method are proved by simulation and experimental results.

Use of Boundary Control With Second-Order Switching Surface to Reduce the System Order for Deadbeat Controller in Grid-Connected Inverter

Deadbeat control is commonly used in grid-connected inverter with L filter, but it faces the challenge of having filter resonance in inverter with LCL filter. Although many active damping techniques have been proposed to tackle such phenomenon, their digital implementation would introduce nonminimum phase characteristics. Furthermore, the plant viewed by the deadbeat controller is of high order, making the system performance be susceptible to the drift of the filter parameters. This paper introduces a new perspective of using boundary control with second-order switching surface to reduce the order of the plant viewed by the deadbeat controller. The structure hybridizes the merits of the deadbeat control in its simplicity and the boundary control in achieving wide control bandwidth. Small-signal dynamic modeling of the boundary control is formulated. The performance sensitivities of the overall system to filter parameters and grid inductance variations are studied with the derived models. An online grid inductance estimation algorithm is proposed to assure sufficient phase margin under an extremely weak-grid condition. A 2-kW, 220-V, 50-Hz prototype with the switching frequency of 8 kHz has been built and evaluated. Its steady-state and transient behavior, and harmonic rejection capability under stiff- and weak-grid conditions are discussed.

Robust optimal current control for grid‐connected three‐phase pulse‐width modulated converters

This study deals with the current control of three-phase inverters connected to the grid by means of LCL filters. The control action is given by the feedback of the filter states, in coordinates αβ0, and of the internal states of resonant controllers. The control gains are computed by means of an optimal linear quadratic regulator that is robust to uncertain and time-varying parameters related to the grid impedance at the point of common coupling. As contributions, one has the detailed proof of a robust discrete linear quadratic control, showing its applicability also for the time-varying case, the experimental validation of the results in terms of the total harmonic distortion and harmonic limits for the grid injected current, according to the IEEE 1547 standard, and the analysis of the ℋ∞ norm of the closed-loop system for several values of grid inductance, indicating a value of grid inductance for which one has best performance for the time-invariant case. For comparison, a conventional state feedback controller is designed and implemented, showing the limitation of the non-robust strategy.