Harmonic Rejection Capability Research Articles

A composite strategy for designing efficient harmonic compensators in grid connected inverters with reduced power

The harmonic controlling schemes are very important for renewable energy applications. The power efficient applications are playing significant role in grid connected inverter applications. The measures like power factor, real & reactive power, voltage at (grid, inverter and converter side), current at (grid, inverter and converter side) are need to be improve for efficient power balancing purpose. The earlier models like liner disturbance controlling LADRC, Proportional-Resonant (PR) Control with Comb Filter (PRC-CF) and PI controlling are outdated. Therefore, PR–NF–STFT-Fuzzy logic controller is proposed to cross over the above limitations. This proposed methodology can improve the PRFI-HC dynamic response, PRFI-HC of inverter current and PRFI-HC voltage. Grid-connected inverters may use the suggested approach to emit high and low frequency harmonics. In the event of many external harmonic's sources, a different analysis statement is provided to indicate the highest achievable individual grid current harmonic. At resonance frequencies, the effect of the series damping resistor on the inverter's harmonic rejection capability is examined. The suggested harmonic structure of the converter is matched by the simulations and testing findings.

Multimode Control for Power Quality Improvement in an Electronically Coupled Distributed Generation Unit Under Grid Connected and Autonomous Modes

This paper develops a new multimode control strategy for power quality (PQ) improvement in distributed generation (DG) units that employs a voltage source converter (VSC) as the electronic interface medium. The devised control strategy seamlessly operates for both the grid connected (GC) and autonomous/stand-alone (SA) modes of microgrid (MG). A novel computationally efficient comb-filter driven discrete time oscillator is developed for current reference generation (CRG) under GC operation. It constitutes a cluster of zeros to introduce notch peaks at integer multiples of the fundamental frequency thereby ensuring improved harmonic rejection capability. Consequently, it ensures unconditionally balanced and sinusoidal grid currents with improved PQ to comply with grid interconnection codes prescribed in the IEEE std-519 and std-1547 even under electrical anomalies. In the SA mode, the CRG scheme is developed in a stationary reference frame with an improved vector proportional integral (VPI) compensator. Despite the uncertainty of load parameters, the proposed VPI guarantees zero steady-state error and superior transient response. A finite state machine-based synchronization framework is proposed to ensure secure and seamless transfer of MG between GC and SA even under disturbances. The practical viability of the proposed multimode control has been demonstrated by applying various switching rules in both GC and SA modes of MG operation.

A synchronization technique for single-phase grid applications

The utility grid disturbances like dc offset and harmonic components can severely affect the estimated variables from the phase-locked loop (PLL), resulting in poor performance of the system relying on it. Therefore, there is an emerging need for well-designed PLL algorithms ensuring robust response against different operating conditions. This paper proposes a simple single-phase PLL algorithm with inherent dc offset and specific harmonic orders rejection capability. Utilizing adaptive time-delay fictitious signal generation. A full mathematical model of the proposed PLL has been provided. The proposed PLL is compared with other filter-based single-phase PLLs, to validate its simplicity and excellent performance.

Sensorless Control of Variable-Speed SCIG Wind Energy Conversion Systems Based on Rotor Flux Estimation Using ROGI-FLL

In this article, a novel sensorless control method for variable-speed squirrel-cage induction generator (SCIG) wind power systems with simple rotor flux estimation is proposed. The rotor flux linkages are estimated using a reduced-order generalized integrator (ROGI)-frequency-locked loop (FLL), which regards the rotor back electromotive forces (EMFs) found from the generator model as its inputs. Based on these rotor flux linkages, the rotor flux angle can be estimated through direct trigonometric relations. Then, to avoid the speed estimation error caused by the FLL under stator frequency variations, the synchronous speed is estimated from the aforementioned rotor flux angle via the derivative. Owing to the excellent harmonic rejection capability of the ROGI, the proposed rotor flux estimation is robust against measured high-frequency ripple components. The analysis of ROGI response in the presence of dc offset in the rotor back EMFs is provided as well, and it shows that the proposed method is not faced with the saturation under those conditions. Performance comparisons between the proposed method and the existing dual second-order generalized integrator (SOGI)-FLL-based method have been conducted via both simulations and experiments, thereby verifying the feasibility of the proposed method.

Moth–Flame-Optimization-Based Parameter Estimation for FCS-MPC-Controlled Grid-Connected Converter With LCL Filter

The ability to model a system with high accuracy plays an important role in finite-control-set model-predictive-control (FCS-MPC)-controlled LCL-interfaced grid-connected converters (LCL-GCCs). However, the effect of aging, unmeasured noise, and temperature change on LCL-GCCs may result in parameter perturbations between the prediction model and the actual system. A model mismatch may occur, which may lead to violations of constraints, worsen the power quality of the grid current, and even threaten the system stability. This article presents a novel nature-inspired optimization paradigm named moth–flame-optimization (MFO), which applies the spiral logarithmic function to simulate the flight of a moth approaching a flame. The method is designed to efficiently identify and update the model parameters, and the fitness function for the state variables is designed and solved iteratively to minimize mismatches with the model. The advantages of the proposed method are its fast convergence and ability to determine parameters with high accuracy. These advantages effectively prevent the algorithm from converging to local optima. To achieve the harmonic rejection capability, a sliding discrete Fourier transform (SDFT) algorithm is also proposed to predict the harmonic at each sampling interval; thus, the harmonics are considered in the cost function. Experimental comparisons under different scenarios validate the effectiveness of the proposed SDFT-based MFO–MPC method.

A coordinated virtual impedance control scheme for three phase four leg inverters of electric vehicle to grid (V2G)

The three-phase four-leg (3p4L) inverter can be utilized to interface electric vehicles (EVs) with the distribution networks. Vehicle to grid (V2G) inverters are employed to charge EVs from the utility grid as well as compensating harmonics and unbalanced voltages & currents on demand. Motivated by this scenario, this paper proposes a coordinated virtual impedance control scheme for a vehicle to grid three phase four leg (V2G 3p4L) inverter. The proposed control scheme achieves simultaneously multifunctional objectives consisting of effective and good harmonic rejection capability, power sharing among V2G 3p4L inverter units with a smaller error, reactive power/voltage support during load power changes and balanced/unbalanced voltage sag conditions. An independently neutral current control approach is proposed for the fourth leg of the V2G 3p4L inverter to regulate the DC-link along with neutral current control capability. Besides, the proposed control scheme achieves grid connected mode (GCM) or standalone mode (SAM) operation capability as well as fulfilling smooth transition between operation modes without reconstructing control structure. Compared to well-known control schemes in the literature, synchronization during operation modes is also achieved without transients in voltage and current. Comprehensive tests under various scenarios validate the excellence of the proposed control scheme over existing methods.

Lyapunov based harmonic compensation and charging with three phase shunt active power filter in electrical vehicle applications

With the increasing proliferation of high-tech loads and electrical vehicle (EV) charging stations, shunt active power filters (SAPFs) are contemplated to play a growingly substantial role in power distribution and delivery. In this regard, this paper proposes a Lyapunov based harmonic compensation and charging with the operation of three-phase SAPF as interface EV applications and the electric grid. The proposed control algorithm provides effective harmonics mitigation capability under various non-linear loads (NLLs) groups and grid disturbances. A noteworthy contribution of this paper is that a Lyapunov based proportional integral with anti-windup (PI with AW) control is proposed to regulate oscillations of the DC-link voltage without increasing DC-link capacitor size. The proposed control algorithm offers comprehensive solutions with several improvements, novelties and features as: (i) keeping the total harmonic distortion (THD) of source currents below recommended IEEE-519 limits, (ii) extraction of reference current and voltage signals based on Lyapunov estimator (LE) with effective and good harmonic rejection capability, (iii) achieving good dynamic performance with utilizing a Lyapunov based PI with AW control for the DC-link capacitor voltage and (iv) eliminating the necessity of any high-pass or low-pass filters with utilizing LE based orthogonal signal generation (OSG). Besides, comparative analyses with previous studies are handled to examine improvements provided by the proposed control algorithm. The feasibility and effectiveness of the proposed control algorithm are confirmed by PSCAD/EMTDC environment and DSP based PIL quasi-real time results.

Control of three wire DSTATCOM using cascaded delayed signal cancellation effect

ABSTRACT In this paper demonstration of three-wire distributed static compensator (DSTATCOM) for compensating disturbed ac main currents with a Frequency Locked Loop (FLL). An improvement with delayed signal cancellation (DSC) technique to a standard FLL is used. An improvement has been observed in the quality of grid current waveform in terms of distortion to 2.2% from load current distortion of 23.4% by applying DSC in cascaded mode. The standard FLL capability to extract fundamental from disturbed load current has increased with cascaded DSC operators. In order to provide fast, accurate, and precise fundamental extraction with a satisfactory dynamic response without any stability struggle, delay factors of 4 and 24 are cascaded and unified with the FLL in the recognized cascaded αβ delayed signal cancellation (Cαβ-DSCFLL).The dynamic response of the Cαβ-DSCFLL is taking three fundamental cycles to settle the system and it shows satisfactory harmonic rejection capability. A small signal model is provided for the FLL structure through which gain estimation and stability analysis is made. An optimization algorithm named JAYA algorithm which is an algorithm designed to perform a specific task, parameterless optimization framework is used for estimating the PI controller gains in modes for correcting of power factor and regulating zero voltage. An optimization problem is formulated with errors by DC as well as AC bus voltages. JAYA optimization algorithm is used for estimating gains. The disturbance removal capability of the recognized Cαβ-DSCFLL is better when compared with the other conventional ones. The efficacy of the recognized FLL has been demonstrated with experimental results on the laboratory proto type. Reactive power mitigation and removal of grid current harmonics in both modes of DSTATCOM with nonlinear load are achieved with recognized FLL and optimized gains. In realizing the recognized control algorithm, the dSPACE-1104 controller is used to generate gate pulses for DSTATCOM.

Improving Harmonic Rejection Capability of OSG Based on n-th Order Bandpass Filter for Single-Phase System

The second-order generalized integrator based orthogonal signal generator (SOGI-OSG) is commonly used to produce direct and quadrature axis ( dq-axes) signals in stationary reference frame for single-phase systems. Fast and robust OSG with harmonic rejection capability is required for parallel operation of power generation systems. The frequency response function (FRF) of classical OSG does not show robustness towards DC offset and grid harmonic disturbances compared to the direct signal of SOGI. This paper presents OSGs based on n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> order bandpass filter with a phase shifter using a scaled Q factor as a design variable. The frequency and time-domain performance analysis will be performed based on the scaled Q factor to simplify the design process of the proposed OSGs. The -3dB frequency and settling step time will be matched in higher order OSGs selecting a scaled Q factor. The proposed method will show enhanced harmonic rejection ratio of an additional -20dB with increasing OSG order with tradeoff in computational burden.

A fast three-phase synchronization technique with parallel structure

For many grid-connected equipment, the phase and frequency of grid voltage are crucial synchronization information. A phase-locked loop (PLL) is usually employed to obtain the information. In distorted grid, adding additional filter is a convenient and effective approach to enhance the harmonic rejection capability of the PLL. Most filters cannot simultaneously block the inter-harmonics, sub-harmonics and other order harmonics. Adaptive notch filter (ANF) can accomplish such task, since multiple ANFs can be flexibly cascaded. Generally, ANFs works as an in-loop filter in a PLL. When the notch frequency of an ANF is very low or multiple ANFs are cascaded in the control loop, the slowing down of the PLL response speed may be unacceptable in some applications. To deal with this problem, this paper proposes a parallel structure for the ANF-PLL to improve the response speed. In the proposed structure, a group of ANFs are placed in a front-stage synchronous reference frame and work as a prefilter, and a conventional ANF-PLL is used as a parallel frequency feedback loop (FFL). The effectiveness of this technique is verified through experimental results.

A prefilter to improve the performance of transfer delay-based synchronization technique under distorted grid conditions

The transfer delay-based adaptive frequency-locked loop (TD-AFLL) is a recently proposed synchronization technique. It has fast respond speed in ideal grid, but the performance degrades significantly in distorted grid. In this paper, a prefilter is proposed to enhance the robustness and harmonic rejection of the TD-AFLL. A fixed-coefficient bandpass filter (FCBF) is selected as the prefilter, which benefits from a simple structure and avoids the influence of frequency feedback dynamic of the TD-AFLL. Compare with standard TD-AFLL, the proposed FLL exhibits stronger harmonic rejection capability. Experimental results verify the effectiveness and advantages of the proposed technique.

Improved Fundamental Frequency Estimator for Three-Phase Application

This letter reports a digital signal processing based frequency estimation technique that relies on the storage of fundamental three-phase grid voltage samples. Unlike phase-locked loop algorithms, the proposed algorithm does not require the phase error information when estimating the grid frequency. Moreover, only four consecutive samples of the fundamental orthogonal components are required in order to estimate the deviation in the grid frequency. The proposed scheme is facilitated with an inherent nonadaptive comb filtering behavior in order to reject the dc offset and harmonics while attaining a good immunity to voltage sag and the fundamental negative sequence component. Additionally, the off-nominal harmonic rejection capability of the proposed frequency estimator is enhanced by using a postfiltering method. The experimental validations reported in this study demonstrate that the proposed frequency estimator is suitable for three-phase grid applications.

An accurate and robust adaptive notch filter-based phase-locked loop

The use of an adaptive notch filter (ANF) is one of the most popular methods to block harmonics in a phase-locked loop (PLL). Existing ANFs suffer from drawbacks such as a low harmonic rejection capability, complex structure or instability. To improve the performance of ANF-based PLLs, an enhanced ANF (EANF) is proposed in this paper. Its structure, filtering characteristics and frequency-adaptive method are analyzed. Multiple EANFs can be easily cascaded and achieve adaptation through a common frequency feedback loop (FFL). A small signal model is provided, and its control parameters are tuned through the symmetrical optimum method. The harmonic rejection capability and stability of the proposed method are confirmed through simulation and experimental results.

Two-Sample PLL With Harmonic Filtering Capability Applicable to Single-Phase Grid-Connected Converters

The two-sample phase locked loop (2S PLL) in single-phase digitally controlled grid-connected power converters provide synchronization with a minimal computational burden. However, the distortion of the grid voltage deteriorates the performance of the 2S quadrature signal generator. To solve this issue, this article introduces a harmonic filtering (HF) structure based on observers of the input voltage for the fundamental and selected harmonics. The stability and sensitivity of the 2S PLL with HF is analyzed. In comparison with second-order generalized integrator (SOGI)-based HF, the observers provide a narrower bandpass, and the subsequent deterioration of the response time is compensated by adapting the filter gains dynamically. The results obtained, both in simulation and experimentally, validate the proposal and compare its performance with other widely adopted PLLs providing harmonic rejection capability. The computational burden is analyzed and in the case of the proposals depends on the number of observers and the use or not of the adaptive strategy based on steepest descent.

Comparative Study of Discrete PI and PR Controls for Single-Phase UPS Inverter

This paper presents a comparative study of discrete proportional integral (PI) and proportional resonant (PR) current control for single-phase uninterruptible power supply (UPS) inverters. There is an increasing requirement for current and voltage-controlled UPS inverters with very low or zero steady-state error, improved transient response and lower total harmonic distortion (THD). The most promising type of current regulator for single-phase inverters is PR control because it can introduce an infinite gain at a selected resonance frequency such as the fundamental frequency to eliminate the steady-state error, which cannot be achieved by well-known proportional integral (PI) control. Note that PI control has limitations in terms of the steady-state magnitude and phase errors. In addition, PI control also has limited harmonic rejection capability, unlike the PR control, also can compensate for low-order harmonics. Imperfections in the current and voltage control scheme results in higher harmonic distortion of the output current and voltage. In this paper, performance of PR control parameters ($K_{p}$ , $K_{i}$ , and $\omega _{c}$ ) and filter parameters ($L_{f}$ and $C_{f}$ ) are optimally tuned to obtain a very low THD current with reduced output voltage ripple and steady-state error. The analysis, design and implementation of both PI and PR current control in single-phase UPS inverter applications through simulations and experiments are also presented in this paper. The performance of both of these control schemes are analyzed in terms of steady-state response, transient response, and level of current harmonics.

An Open-Loop Fundamental and Harmonic Phasor Estimator for Single-Phase Voltage Signals

This article proposes a novel technique for fundamental and selective harmonic phasor estimation of a single-phase voltage signal based on open-loop voltage signal processing approach, under adverse distorted conditions. At heart, a modified fast discrete Stockwell transform (FDST) is used for the phasor estimation. The performance of the FDST is improved by incorporating a new frequency-dependent Gaussian window for capturing the time-localized variations of individual frequency component. The modified window has four parameters, which are selected based on the statistical properties of the given input voltage signal. Furthermore, under off-nominal frequency conditions the spectral leakage problem, faced by the S-transform, is avoided by proposing a modified sample value adjustment based preprocessing stage. Various static and dynamic tests were considered according to the IEEE Standard 1159, IEEE Standard C37.118.1a-2014, and EN-50160 standards under harmonics and interharmonics scenarios. The performance of the proposed method is validated using synthetic voltage signals, simulated voltage signals on 6-bus microgrid model developed in power system computer aided design (PSCAD), and hardware implementation on dSPACE 1103. The rigorous test cases reveal that the proposed phasor measurement unit has a good adaptability to grid frequency drifts, a good harmonic and dc-offset rejection capability, and a very good steady state as well as dynamic response.

Analysis and Control of Weak Grid Interfaced Autonomous Solar Water Pumping System for Industrial and Commercial Applications

The limited hours of availability and fluctuating behavior of solar insolation severely impact the reliability of solar photovoltaic (PV) integrated system. This article proposes a new topology of grid interactive solar water pumping (SWP) system to deal with the issue of frequent variation in insolation, related to solar power generation. Such intermittency affects the system performance and makes it unreliable for industrial and commercial applications. In contrary to the conventional voltage source converter, the proposed topology utilizes a reduced switch Vienna rectifier for utility grid integration. Although utility grid integration appears to be a viable solution, however, as most of the grid in underdeveloped and developing countries are generally weak, such integration faces the additional power quality challenges, like voltage sag, voltage swell, dc offset, harmonics distortion, etc. To deal with the problems associated with weak grid condition, a novel mix multiresonant generalized integrator (MMRGI) control structure is proposed in this article. Along with the selective harmonic elimination capability, the proposed MMRGI structure offers a high dc offset and higher-order harmonic rejection capability. The proposed control approach is also capable of effectively extracting the balanced positive sequence components from unbalanced distorted grid voltages, thereby, keeping the grid currents balanced. The proposed system uses a sensor-less vector control technique to drive the permanent magnet synchronous motor used for rotating the pump. A perturb and observe algorithm is used for optimum power harvesting from the solar PV array. A prototype of proposed system is developed and performance is investigated experimentally using a digital signal processor DS1202.

Spectral analysis for the generalized least squares phase-shifting algorithms with harmonic robustness.

We introduce the frequency transfer function (FTF) formalism for generalized least squares phase-shifting algorithms (GLS-PSAs), whose phase shifts are nonuniformly spaced. The GLS-PSA's impulsive response is found by computing the Moore-Penrose pseudoinverse. FTF theory allows analyzing these GLS-PSAs spectrally, as well as easily finding figures of merit such as signal-to-noise ratio (SNR) and harmonic rejection capabilities. We show simulations depicting that the SNR slightly decreases as the harmonic rejection robustness improves.

A comprehensive control system for multi-parallel grid-connected inverters with LCL filter in weak grid condition

Active damping methods are used for resonance damping in grid-connected inverters with LCL filter. In microgrids, parallel grid-connected inverters are coupled due to grid impedance introducing multiple resonances. In general, such coupling effect is not taken into account for modeling and controller design. For single grid-connected inverter, despite good performance, the system tends to become instable with parallel connection of other inverters. Moreover, the grid injected current can be distorted by the grid voltage harmonics. In traditional control system, grid voltage is used as a feedforward signal to achieve harmonic rejection capability by boosting the inverter output impedance. However, this method introduces negative phase angle which could lead to control system instability. In this paper, the control system design for multi-parallel grid-connected inverters using active damping is clarified. Inverters with different characteristics are also modeled in a weak grid as a multivariable system while coupling effect with a wide variation of grid impedance is taken into account. An improved grid voltage feedforward method is proposed to eliminate negative aspects of the traditional method. The simulation results in MATLAB/SIMULINK software demonstrate the effectiveness of the proposed control system.

A Hybrid Filtering Technique-Based PLL Targeting Fast and Robust Tracking Performance under Distorted Grid Conditions

In most grid-connected power converter applications, the phase-locked loop (PLL) is probably the most widespread grid synchronization technique, owing to its simple implementation. However, its phase-tracking performance tends to worsen when the grid voltage is under unbalanced and distorted conditions. Many filtering techniques are utilized to solve this problem, however, at the cost of slowing down the transient response. It is a major challenge for PLL to achieve a satisfactory dynamic performance without degrading its filtering capability. To tackle this challenge, a hybrid filtering technique is proposed in this paper. Our idea is to eliminate the fundamental frequency negative sequence (FFNS) and other harmonic sequences at the prefiltering stage and inner loop of PLL, respectively. Second-order generalized integrators (SOGIs) are used to remove FFNS before the Park transformation. This makes moving average filters (MAFs) eliminate other harmonics with a narrowed window length, which means the time delay that is caused by MAFs is reduced. The entire hybrid filtering technique is included in a quasi-type-1 PLL structure (QT1-PLL), which can provide a rapid dynamic behavior. The small-signal model of the proposed PLL is established. Based on this model, the parameter design guidelines targeting the fast transient response are given. Comprehensive experiments are carried out to confirm the effectiveness of our method. The results show that the settling time of the proposed PLL is less than one grid cycle, which is shorter than most of the widespread PLLs. The harmonic rejection capability is also better than other methods, under both nominal and adverse grid conditions.