Second Order Generalized Integrator Research Articles

Model Predictive Control of Transformerless Series Custom Power Device for Voltage Quality Improvement

A single-phase series custom power device (Se-CPD), based on model predictive control (MPC), is presented in this paper to compensate for erratic supply voltage conditions such as voltage sag, swell, and harmonics. The control strategy for Se-CPD encapsulates the generation of reference voltage and optimal switching signals for the voltage source inverter (VSI) of the Se-CPD. The reference voltage extraction from the distorted point of common coupling (PCC) voltage is synthesized using a second-order generalized integrator (SOGI) without any phase delay, unlike the case that uses a low-pass filter (LPF). An MPC realizes the generation of optimal switching signals for Se-CPD with its intuitive and straightforward implementation, without any modulation stage, and considers the converter’s switching characteristics in the MPC algorithm itself. The simulation results, using MATLAB/Simulink and the real-time simulation results using the OPAL-RT OP4510 real-time simulator, are presented to validate the SOGI-MPC’s effectiveness for voltage quality improvement.

A Unified Control of Grid-Interactive Off-Board EV Battery Charger With Improved Power Quality

This article presents a self-tuning filter (STF) and sliding mode control (SMC)-based control algorithm for a grid-interactive off-board electric vehicle (EV) battery charger to power the EV batteries and simultaneously improve the grid power quality. In grid-connected operation (GCO), the charger uses the STF-based control strategy to estimate the fundamental load current and synchronize voltage templates to generate a pure sinusoidal reference current. Compared to the phase-locked loop (PLL) and the second-order generalized integrator (SOGI), the STF-based technique precisely estimates the synchronizing voltage templates during nonideal grid voltage conditions. Therefore, in GCO, the charger reference current ensures the unit power factor in the grid-to-vehicle/vehicle-to-grid (G2V/V2G) operation mode and the harmonic free grid current in the charger-for-grid (C4G) operation mode. Furthermore, the charger operates in the vehicle-to-load (V2L) operation mode during grid outages to maintain an uninterrupted supply to the residential load. The control algorithm also includes a grid synchronization technique to achieve a smooth transition between GCO and V2L. Furthermore, an SMC-based dc-link voltage controller (SMC-DLVC) is proposed to reduce dc-link voltage overshoot with finite-time convergence during external disturbances in all operation modes. The performance of the proposed control algorithm is validated in a 12.6-kVA off-board charger laboratory prototype under ideal/nonideal grid voltage conditions.

A whole control strategy for cascaded H‐bridge rectifiers under distorted grid voltage and unbalanced load

AbstractControl for single‐phase cascaded H‐bridge rectifier (CHBR) under distorted grid voltage is seldom discussed in the existing control methods; a modified direct power control (DPC) scheme is therefore proposed in this paper. A simple power control structure with proportional‐integral control method is first presented, which can discard phase‐locked loop (PLL) and coordinate transformation. Then, an improved fictitious orthogonal algorithm is proposed to provide a better anti‐disturbance ability compared with the traditional second‐order generalized integrator (SOGI). Since the orthogonal component of the grid current runs concurrently with the power reference, it offers an excellent dynamic performance in inner loop. On the other hand, a voltage balancing control (VBC) model by the relationship between the difference of dc‐side voltage square and that of power is established. On this basis, an internal model VBC (IM‐VBC) method is provided to reduce the parameter tuning complexity. With this method, the dynamic performance of voltage balancing on the dc side is improved. Finally, several test results on hardware‐in‐the‐loop (HIL) and scale‐down platform are demonstrated, which validate the effectiveness and superiority of the proposed control strategy.

A THD-Based Fault Protection Method Using MSOGI-FLL Grid Voltage Estimator

The rapid growth of the distributed generators (DGs) integration into the distribution systems (DSs) creates new technical issues; conventional relay settings need to be updated depending on the network topology and operational mode as fault protection a major challenge. This emphasizes the need for new fault protection methods to ensure secure protection and prevent undesirable tripping. Total harmonic distortion (THD) is an important indicator for assessing the quality of the grid. Here, a new protection system based on the THD of the grid voltages is proposed to address fault events in the electrical distribution network. The proposed protection system combines the THD with the estimates of the amplitude voltages and the zero-sequence component for defining an algorithm based on a finite state machine (FSM) for the detection, identification, and isolation of faults in the grid. The algorithm employs communication lines between all the protective devices (PDs) of the system to transmit tripping signals, allowing PDs to be coordinated. A second order generalized integrator (SOGI) and multiple SOGI (MSOGI) are used to obtain the THDs, estimated amplitude voltages, and zero-sequence component, which allows for fast detection with a low computational burden. The protection algorithm performance is evaluated through simulations in MATLAB/Simulink and a comparative study is developed between the proposed protection method and a differential relay (DR) protection system. The proposed method shows its capability to detect and isolate faults during different fault types with different fault resistances in different locations in the proposed network. In all the tested scenarios, the detection time of the faults has been between 7-10 ms. Moreover, this method gave the best solution as it has a higher accuracy and faster response than the conventional DR protection system.

Integrated control algorithm for fast and accurate detection of the voltage sag with low voltage ride-through (LVRT) enhancement for doubly-fed induction generator (DFIG) based wind turbines

Low voltage ride-through (LVRT) is one of the essential aspects of grid codes for integrating doubly-fed induction generators (DFIG) to achieve reliable and uninterrupted electrical power generation. The detection time of the voltage sag is one of the crucial aspects for the LVRT improvement of the DFIG. This paper introduces a second-order generalized integrator (SOGI), quadrature signal generator (QSG) with a frequency locked loop (FLL) based algorithm to detect the symmetrical voltage sag fast and accurately. The proposed SOGI-QSG-FLL-based voltage sag detection algorithm (VSDA) works under a second-order band-pass filter with an alfa-beta stationary reference frame. The proposed VSDA is integrated with the novel feed-forward transient current compensation (FFTCC) scheme with an advanced interval type-2 fuzzy logic-proportional integral (IT2-FLC-PI) controller to enhance the LVRT capability of the DFIG. This FFTCC scheme is activated after the detection of voltage sag by using the proposed VSDA. The proposed FFTCC feeds the uninterrupted active and reactive power to the grid and reduces the torque ripple of the DFIG. The detection time of voltage sag by using the proposed VSDA is compared with existing algorithms. The experimental results are also presented to validate the proposed algorithm.

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.

Improved Cascaded SOGI Control for Islanding-Synchronization in Photovoltaic System

This work presents an improved cascaded second-order generalized integrator (I-CSOGI) controlled photovoltaic system (PVS), which functions as an islanded system during grid interruption without energy storage. Here, a single-stage PVS structure is used, simplifying the control by automatically regulating the PV array operating point and dc-link voltage during the grid outage. The I-CDSOGI algorithm is exercised to determine the sensed voltages angle, frequency, and harmonics free positive sequence components of the sensed voltages and load currents. The advantage of the presented I-CDSOGI over the existing CDSOGI algorithm is that the gain of its frequency-locked loop is changed adaptively. It reduces the spurious change in the frequency during the sudden phase jump, which is experienced by the load voltages during synchronization. Hence, the repeated tripping of the power electronics switches, which isolates the PVS from the local grid, is reduced, and smooth synchronization is achieved. Furthermore, the cascading of two second order generalized integrator (SOGI) blocks eliminates the dc offset from the sensed signals and boosts the overall harmonics rejection capability, which enhances the angle and frequency estimation performance. A comparison is made to showcase the benefits of I-CSOGI compared with the existing SOGI-based methods in the PVS.

A Fast Power Calculation Algorithm for Three-Phase Droop-Controlled-Inverters Using Combined SOGI Filters and Considering Nonlinear Loads

The power calculation is an indispensable element in droop-controlled inverters because the bandwidth of the measured power has a direct impact on the controller performance. This paper proposes a fast and accurate power calculation algorithm based on the combined Second Order Generalized Integrator (SOGI) filters in stationary coordinates for a three-phase system, which takes into consideration the use of nonlinear loads. The power calculation scheme is formed by the two-stage SOGI filters that are employed for obtaining the active and reactive powers required to perform a droop-based inverter operation, respectively. From the two-stage structure, the first SOGI is used as a band-pass filter (BPF) for filtering harmonics and obtaining the fundamental current of the nonlinear load; The second SOGI is used as a low-pass filter (LPF) for extracting the DC-component, which corresponds with the average power. A small-signal model of a two droop-controlled inverters system is built to obtain the dynamical response and stability margin of the system. And compared it with the dynamical behaviour of a standard droop-control method. Next, the proposed power calculation system is designed in order to achieve the same ripple amplitude voltage as that obtained with the standard droop-control method by adjusting the bandwidth gains. Through simulation and hardware in the loop (HIL) validation, the proposed approach presents a faster and more accurate performance when sharing nonlinear loads, and also drives the inverters’ output voltage with lower distortion.

Discrete Multiple Second-Order Generalized Integrator With Low-Pass Filters and Frequency-Locked Loop for DC Rejection

The multiple second-order generalized integrator (MSOGI), which is composed of parallel second-order generalized integrators (SOGI), is widely used in grid synchronization and signal extraction, and it usually suffers from dc offset issue. In continuous domain, low-pass filter (LPF) can be added to SOGI to eliminate the dc offset in its quadrature channel. However, in digital implementation, directly discretized LPF-based methods may not be able to eliminate dc offset and ac discretization error simultaneously, where the steady-state error will also be introduced by the conventional frequency-locked loop (FLL). In this article, a modified impulse invariant method is adopted to discretize SOGIs, which presents zero ac errors and good dynamics, but shows dc offset in both output channels. Then, an LPF is introduced to eliminate the dc offset of the discrete SOGI, forming a discrete SOGI-LPF. And, a discrete MSOGI-LPF (DMSOGI-LPF) is formed by paralleling multiple DSOGI-LPFs, which can extract different frequency components. Furthermore, a discrete FLL is proposed to estimate the frequency of the input signal, which suppresses the influence of the dc offset and achieves good dynamics. Finally, the stability analysis of the proposed method based on discrete linear-time periodic (LTP) model is provided. The effectiveness of the proposed method and its discrete LTP model are validated through experimental results.

Improvements on E-PLL to Mitigate Transient Low-Frequency Oscillations

This paper aims at improving the Enhanced-PLL (E-PLL) to mitigate the transient low-frequency oscillations, which is inherent to single-phase circuits. These improvements resulted in a new PLL configuration, designated here as the Double-Frequency Mitigation SOGI-EPLL, or simply DFM-SOGiEPLL. We integrate the EPLL with a Second-Order Generalized Integrator (SOGI), by modifying the computation of the internal error signals of the phase-and-frequency loop and the amplitude loop. Thus, the proposed DFM-SOGiEPLL is able to extinguish transient low-frequency oscillations, in a short time period, in comparison to the conventional EPLL. A dynamic model approach of both EPLLs, including four different test-cases, was implemented through numerical simulations and hardware experiments to verify the better performance of the proposed one.

A Quadrature Signal-Based Control Strategy for Vienna Rectifier Under Unbalanced Aircraft Grids

In order to eliminate the input current harmonics and dc-link voltage ripples of Vienna rectifier under unbalanced input, a novel control strategy applicable to wide variable frequency (360–800 Hz) aircraft electrical system is proposed in this article. To serve this purpose, current references on natural frame are first derived, which contain quadrature signals of grid voltages. Then, a natural-frame-based control strategy is designed, in which the second-order generalized integrator (SOGI) frequency-locked loop (FLL) is employed for variable frequency grids. Compared with traditional dual-frame control strategy, the proposed strategy reduces the algorithm complexity and has better frequency adaptability. The proposed strategy is suitable for all the unbalanced conditions, which is defined by test procedures DO-160G. Simulation and experimental results verify the effectiveness of the proposed control strategy.

Triple Current Control of Four-Wire Inverter-Interfaced DGs for Correct Fault Type Identification

Inverter-interfaced distributed generators (IIDGs) have fault current signatures that could jeopardize protective relaying. This paper unveils the failure of phase selection methods (PSMs) utilized by commercial relays in the presence of four-wire IIDGs, which adversely impacts the grid resiliency and reliability. A triple current controller (TCC) is proposed to regulate the inverter’s sequence currents during unbalanced faults to ensure accurate fault type identification. The negative- and positive-sequence components are extracted using a decoupled double synchronous reference frame (DDSRF)-based phase-locked loop (PLL). Further, a second-order generalized integrator (SOGI)-based PLL is employed for zero-sequence component synchronization. The negative- and zero-sequence reference currents are generated to force the angles of IIDG sequence currents to behave like those from synchronous generators (SGs) and abide by the inverter’s current limits. Consequently, commercial PSMs can correctly identify the fault type. The proposed TCC scheme pertains to four-wire as well as transformer-less IIDGs. A performance evaluation using time-domain simulations is conducted on a CIGRE benchmark system to confirm the success of the proposed control scheme under different fault conditions.

Shunt active power filtering with reference current generation based on dual second order generalized integrator and LMS algorithm

For reducing the carbon emissions from utility sector, it is important to improve the efficiency of network and electrical loads. Current harmonics are responsible for the degradation of the system as well as load efficiency. The propagation of current harmonics into the grid can be prevented with shunt active power filters (SAPFs). Reference current generation (RCG) is critical for SAPF operation. This paper presents the control of SAPF with RCG based on least mean square (LMS) and dual second order generalized integrator (SOGI). The two SOGIs separately process grid voltage and load current to determine the respective fundamental in-phase component (FPC) and fundamental quadrature component (FQC). FPC and FQC of grid voltage are used to determine the phase angle of fundamental grid voltage. With LMS algorithm the distorted current can be decomposed into fundamental active (FA), fundamental reactive (FR) and harmonic components. However, the dynamic response of LMS based estimation is poor when the same learning rate is used for all components. FQC of load current, estimated with SOGI, can be processed by LMS algorithm to separate FA and FR components. RCG can be implemented with the computed phase angle and FA component. In LMS algorithm, as only two components are to be separated, two different learning rates can be easily specified. This results in faster dynamic response for LMS algorithm and has consequent positive impact on RCG and SAPF operation. Also, the computational complexity is considerably reduced. The performance of SAPF with the proposed extraction algorithm is analyzed for different operating conditions and comparative analysis is carried out.

An Enhanced Time-Delay-Based Reference Current Identification Method for Single-Phase System

This article proposes an enhanced time-delay-based current component identification method for single-phase systems to overcome the absence of filtering and poor grid frequency response of conventional method. The proposed technique integrates a delayed signal cancellation with a time-delay unit, to incorporate a dc offset rejection feature, while maintaining speedy and precise extraction of orthogonal current components. The frequency adaption is also developed through the incorporation of linear interpolation. The dynamic and steady-state performance of the proposed method is analyzed and compared with two advanced second-order generalized integrator (SOGI) based methods, namely, modified SOGI and cascaded SOGI under different operating scenarios. The simulation and experimental results substantiate the advantage of zero steady-state error and lower settling time of the proposed solution while exhibiting comparable overshoot with advanced SOGI-based methods.

A Straightforward Quadrature Signal Generator for Single-Phase SOGI-PLL With Low Susceptibility to Grid Harmonics

Suppressing the negative effects of grid voltage harmonics on the estimated frequency of a phase-locked loop (PLL) is a challenge in literature. This article proposes an easy-to-implement quadrature signal generator (QSG) to attenuate the oscillations on the estimated frequency in single-phase grid-connected inverters, which use second-order generalized integrator (SOGI)-PLL. It is shown that SOGI exerts a stronger filtering effect in generating the quadrature signal than the in-phase signal. Against this background, in this work, a modified integrator is introduced into the path of the in-quadrature signal to generate another in-phase component with much lower harmonic content. The proposed method imposes only a small computational burden on the existing SOGI-PLL compared to the previously presented methods that address the input voltage harmonic problem. Moreover, this method can work properly within the allowable range of grid voltage frequency deviations. The proposed integrator benefits from an error-decaying mechanism to overcome dc drift in pure integrators. The integrator has been designed based on theoretical equations. The validity of the proposed QSG and theoretical equations is evaluated using simulations and experimental studies. A fixed-point representation of the proposed QSG is also provided for implementation on low-cost microcontrollers.

A Modified SOGI-PLL with Adjustable Refiltering for Improved Stability and Reduced Response Time

The controls of most power electronic inverters connected to an electrical power system (EPS) rely on the precise determination of the voltage magnitude, frequency, and phase angle at the point of common coupling. One of the most widely used approaches for measuring these quantities is the phase-locked loop (PLL); however, the precision of this measurement is affected during transients in the EPS and is a function of the type of event and the architecture of the PLL. PLLs based on the second-order generalized integrator (SOGI) are widely used in power converter synchronization, offering an adaptive or fixed-parameter prefilter with low-pass and band-pass characteristics. This article proposes a variant of the SOGI-PLL that offers improved stability and a faster response time. This is accomplished by decoupling the effect of the SOGI’s gains and adding feedback. The modification is carried out in the state space model of the SOGI. Manipulating the attenuation moves the poles of the SOGI to improve the stability. The performance of the proposed PLL is verified and validated under the processor-in-the-loop (PIL) approach.

Compensation of Position Estimation Error in PMSM Sensor-less Control Based on High Frequency Square Wave Injection

The high-frequency square-wave injection method is widely used to estimate rotor position at low speed. However, the accuracy and reliability of the method are greatly affected by the dead-time effect. The specific expression of position error is deduced. On this basis, a dead zone error reduction method based on second-order general integrator (SOGI) is adopted to improve the accuracy of position estimation. Besides, low-pass filter needs to be introduced into the current loop, which will bring delay to the system. Aiming at this problem, a delay compensation algorithm is adopted, which can effectively improve the accuracy of position estimation. Results of simulation verify the effectiveness of the methods and their applicability to PMSM sensorless control systems.

Accurate LTP Model and Stability Analysis of the Second-Order Generalized Integrator-Based Single-Phase Phase-Locked Loop

This article focuses on the modeling and stability analysis of the typical single-phase phase-locked loop (PLL) based on second-order generalized integrator (SOGI). Traditionally, SOGI-based PLL (SOGI-PLL) is linearized as the linear time-invariant (LTI) model for the stability analysis and parameter design. Yet, the PLL has periodical nature due to the periodical variation of the grid voltage. The traditional LTI model for PLL thereby reduces the precision of stability analysis. For addressing this problem, an accurate linear time-periodic (LTP) model of the single-phase SOGI-PLL is proposed in this article. The proposed model can precisely characterize the coupling nature of phase, frequency, and amplitude estimated by SOGI-PLL. A precise stability region of SOGI-PLL, thereby, can be derived from the proposed LTP model. The effectiveness of the proposed LTP model for SOGI-PLL is verified by simulation and experimental tests.

Frequency-Insensitive Rotor Position Estimation Method for Three-Stage Synchronous Machine Based on Indirect High-Frequency Signal Injection

A frequency-insensitive rotor position estimation method for the three-stage synchronous machine (TSM) in the starting procedure is proposed in this article, where the high-frequency signals (HFSs) are injected into the main exciter (ME), and response signals for the rotor position estimation are extracted from the main generator (MG). Due to the specific structure, the frequency of the response HFSs is distorted by the intermediate links of the ME and rotating rectifier, the frequency-response characteristics of the response signals with information of rotor position are analyzed, and the frequency-insensitive demodulation method for the rotor position estimation based on the second-order generalized integrator (SOGI) is given. Finally, the simulation and experiment results are implemented to verify the effectiveness and feasibility of the proposed frequency-insensitive rotor position estimation method for TSM.

LTP Modeling and Stability Assessment of Multiple Second-Order Generalized Integrator-Based Signal Processing/Synchronization Algorithms and Their Close Variants

A second-order generalized integrator (SOGI) is a resonant regulator with a pair of complex-conjugate poles, and therefore, with infinite magnitude at its center frequency. Thanks to this property, one can put together a set of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> SOGIs in an elegant way and decompose a single-phase signal into its constituent frequency components and detect their amplitude and phase angle. Such a configuration, which is often referred to as the multi-SOGI (MSOGI) structure, requires a frequency estimator to adapt the center frequency of SOGIs to frequency changes. This frequency estimation is often provided by interconnecting the MSOGI structure with a basic frequency-locked loop (FLL) or phase-locked loop (PLL). The resulting structures are known as the MSOGI-FLL and MSOGI-PLL. These structures and their close variants are mathematically difficult to analyze probably because of the lack of a linear model for these systems. This article aims to bridge this research gap. First, it is shown how linear time-periodic (LTP) models of the MSOGI-FLL and MSOGI-PLL can be obtained. The model verification, obtaining open-loop harmonic transfer function from the LTP model, and LTP stability assessment of MSOGI-based synchronization systems are the next parts of this article. Finally, some close variants of the MSOGI-FLL/PLL are considered and their modeling and stability assessment are briefly discussed.