Orthogonal Signal Generator Research Articles

Frequency Estimators for SOGI FLL: Modeling, Design, and Equivalence for FLL Advancements

Different frequency estimators have been reported for frequency-locked loop (FLL) implementations. One example is the widely employed gradient descent estimator in second-order generalized integrator (SOGI) FLL. Whether this estimator differs from those in some existing FLLs is unknown. Therefore, in this article, gradient descent and two other estimators with amplitude normalization in the stationary and synchronous reference frames are developed for SOGI FLL implementation. By obtaining linear model of SOGI FLL with the three estimators, equivalence of their FLL is established. Thus, it is shown that when the estimator parameters are designed based on the established equivalence, the FLL dynamics is dictated by the SOGI stage. Thus, research involving orthogonal signal generation is crucial to FLL’s rapid advancements. Furthermore, harmonic rejection in SOGI FLL with the estimators is considered where it is shown that SOGI FLL with amplitude normalization in the synchronous reference frame is ideal for applications involving harmonics.

A Robust Half-Cycle Single-Phase Prefiltered Open-Loop Frequency Estimator for Fast Tracking of Amplitude and Phase

This article presents a fast phase-locking and amplitude detection scheme for single-phase applications. The proposed scheme employs a pseudo-rectification process in order to generate even harmonics from the grid signal. The dc-offset component present in the grid signal increases the sensitivity of the pseudo-rectification process, and the design of the prefiltering stage must, therefore, be completely focused on the rejection of dc-offset and the even-harmonics. The application of a half-cycle (HC) prefilter would consequently appear to be a highly attractive option as regards improving the dynamic response time and even harmonic rejection abilities. However, the elimination of the dc-offset component and the estimation of phase and amplitude information is still a very challenging task. The aforementioned issues are addressed by employing an HC comb filter and an HC nonadaptive Lyapunov orthogonal signal generator. The estimation of single-phase grid parameters is thereby made simpler by employing an improved open-loop frequency estimation, which is capable of providing accurate frequency deviation information with good precision. The research shown herein also reveals that the estimation of the amplitude and phase information differs slightly from the usual mathematical notations owing to the pseudo-rectification method adopted in the proposed work. Note that the prefiltering stage is nonadaptive in nature, which may lead to steady-state errors in the amplitude and phase information under off-nominal frequency conditions. An online mathematical correction approach dependent on frequency deviation is, therefore, employed in order to obtain the error-free amplitude and phase information. Finally, the robustness of the current proposal is validated by experimentally comparing several known grid parameter estimation schemes using a real-time controller.

Enhanced controller for a four-leg inverter operating in a stand-alone microgrid with unbalanced loads

<span lang="EN-US">Stand-alone low voltage (LV) microgrids supplying small local loads far from the utility grid are becoming an increasingly popular alternative to a total reliance on the centralized utility grid. In most of LV microgrids, three-phase four-wire distribution systems are used to supply both single- and three-phase loads. Unequal distribution of loads can result in voltage unbalance problems. The use of the four-leg inverter is one of the best solutions for providing a neutral current path and compensating unbalanced load conditions in stand-alone LV microgrids. This paper proposes a fast control technique to compensate unbalanced voltage conditions for a four-leg inverter operating in a stand-alone LV microgrid. The suggested technique provides the current controller’s orthogonal component without introducing any additional dynamics or distortions. The major benefits of the recommended per-phase control technique over conventional orthogonal signal generation (OSG) methods are enhanced steady-state and dynamic performances as well as independency to the system parameters. Several simulation results are provided to confirm the superior performance of the suggested methods.</span>

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.

An Accurate Orthogonal Signal Generator for Voltage Control in Synchronous Reference Frame of Stand-Alone Single-Phase Voltage Source Inverters

An Accurate Orthogonal Signal Generator for Voltage Control in Synchronous Reference Frame of Stand-Alone Single-Phase Voltage Source Inverters

Experimental assessment of Single Phase Grid assisted system using Second Order Generalized Integrator–Frequency Locked Loop

Objectives: To design and develop a simple, robust, and novel SOGI based frequency lock loop approach with DC-offset elimination capability for extracting precise phase angle of the grid voltage. As the additional objective of the work is to utilize the unused capacity of the PV system for providing reactive power support to the grid. Method: The second-order generalized integrator (SOGI)-Frequency Look loop (FLL) is implemented to achieve precise phaseangle for the control system, filtering capability for the adaptive frequency tuning as well as an orthogonal signal generation. The DC blocker is designed to eliminate the dc-offset generated during analog to digital conversion without compromising the dynamics of the system. To achieve the second objective, the virtual two-axis current control is simulated and experimented on in a single-phase grid-assisted system. Synchronous-frame current controllers are designed to inject active power to the grid and also ensure the unity power factor by providing reactive power support to the grid. The developed system is simulated using MATLAB /Simulink and implemented on the experimental stepup. Findings: The precise phase-angle is extracted from the grid voltage during the abnormal grid conditions like frequency shift, distorted by harmonics, and dc-offset. The DC-offset can be eliminated without adopting high-order FLLs by choosing the appropriate control parameter and DC cancellation block (DBC). Novelty: This study presents simple, efficient, novel SOGI based control that provides assurance of power quality as well as injection of active power injection into the grid using the virtual two-axis reference frame power control. The experimental and simulation results confirm that the presented control approach provides fast and accurate phase angle extraction in the grid synchronization with DC-offset cancellation. Keywords: Grid synchronization; STM32F407VG microcontroller; WAIJUNG Blockset; phase detection; Phase Locked Loop (PLL); virtual two axis reference frame power control

Tuning and experimental assessment of second-order generalized integrator –frequency locked loop grid synchronization for single-phase grid assisted system

The phase-locked loop (PLL) is an essential part of the grid-tied system to synchronize control of converter with grid voltage, particularly affects the converter stability as well as performance under weak grid conditions. During abnormality in a grid, its bandwidth ought to be a11dequately brought down to achieve appropriate disturbance rejection capability with a compromise to slower detection speed. The researchers have done intended work in advanced PLLs to improve phase-angle detection speed by modifying the pre/in-loop filtering stage. A most concerning challenge with the PLLs is the means by which to additionally provide superior dynamic performance and reduced settling time without bargaining stability of system along with the capability of disturbance elimination To overcome this challenge, this paper describes the second-order generalized integrator (SOGI-Frequency Look loop (FLL) which offers filtering capability like band-pass filter, low-pass filter, and notch filter for adaptive frequency tuning as well as an orthogonal signal generation for the grid-tied photovoltaic inverter. The impact of control parameters on their dynamic performance in SOGI-FLL is tabulated from a step response of frequency estimation by taking a frequncy shift. Furthermore, Low-cost DSP based STM32F407VGT the microcontroller is employed to implement a SOGI-FLL to test under adverse grid conditions using Waijung Block-set of SIMULINK/MATLAB. The experimental results of SOGI-FLL have proven superior dynamic performance over type-2 PLLs by choosing the appropriate value of the control parameter of SOGI-FLL.

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.

Fractional Order PID PLL Controller Based on Particle Swarm Optimization Algorithm

In this paper, a Fractional Order PID PLL controller based on particle swarm optimization algorithm is proposed for power grid system. The parameters of Fractional Order PID controller are optimized by particle swarm optimization algorithm, so as to control the orthogonal signal generator in PLL, realize accurate phase discrimination and effectively suppress grid harmonics.In this paper, firstly, the mathematical model of PLL is established, and then the PID controller and Fractional Order PID controller are compared and controlled. Finally, the parameters of Fractional Order PID controller are optimized by particle swarm optimization algorithm to achieve the optimal control.In this paper, the simulation of PLL controller is completed based on MATLAB / Simulink. The simulation results show that the Fractional Order PID based on PSO algorithm can automatically find the optimal control parameters, realize the precise control of PLL, and improve the ability of filtering harmonic and dynamic performance of power grid.

A Robust Lyapunov’s Demodulator for Tracking of Single-/Three-Phase Grid Voltage Variables

This article proposes a robust Lyapunov’s demodulator (LD) based on an orthogonal signal generation (OSG) approach for single-/three-phase applications. The LD is not normally capable of rejecting the dc-offset in the grid signal, and an additional estimation loop is, therefore, required, which may affect the dynamic performance. Nevertheless, an application of a harmonically polluted grid voltage signal to the LD may severely affect the steady-state performance of the parameters estimated. These issues are addressed by proposing an enhanced LD-based-OSG in which a moving average filter is incorporated into the LD-OSG structure. The rapid rejection of dc-offset and harmonics is, therefore, easily achieved without any additional loop. The proposed structure can accurately estimate the fundamental in-phase and quadrature components. However, these orthogonal components may suffer from amplitude imbalance and errors in the phase information under off-nominal frequency conditions. Nevertheless, the errors in the amplitude and the phase information are eliminated using an open-loop frequency deviation detector and a feed-forward curve-fitting approach. The dynamic performance of the proposed scheme has been validated by means of numerical and hardware studies whose results show that, with the less sensitivity toward the phase angle jump and good immunity to the fundamental negative sequence, the proposed scheme is a potential technique with which to synchronize single-/three-phase grid-connected power electronic equipment.

Wide Frequency Band Single-Phase Amplitude and Phase Angle Detection Based on Integral and Derivative Actions

Numerous applications, such as the synchronization of distributed energy resources to an existing AC grid, the operation of active power filters or the amplification of signals for Power-Hardware-In-The-Loop (PHIL) systems require a few tasks in common. Amplitude, phase angle and frequency detection are crucial for all these applications and many more. Various techniques are presented for three-phase and single-phase applications but only a few of them are able to identify the signals’ attributes for a wide range of frequencies and amplitudes. Single-phase systems are typically burdensome, considering the challenge to create an internal signal, orthogonal with the input, in order to perform the phase angle detection. This matter is even more critical when the amplitude and frequency of the input signal varies in a wide range. This paper presents an Orthogonal Signal Generator (OSG) based on integral and derivative actions. It includes a detailed design procedure and a design example. The performance of a single-phase wide range amplitude and frequency detector based on the discussed OSG is experimentally validated under steady state and dynamic conditions.

A finite control set model predictive control scheme for single-phase grid-connected inverters

The present article investigates a control scheme for single-phase grid-connected inverter based on the finite control set model predictive control (FCS-MPC) approach. The proposed grid integration scheme provides direct control of the active and reactive power (PQ) injected to the grid from distributed energy resources (DER) composed of a photovoltaic (PV) array as a renewable resource integrated with a battery bank as energy storage. The direct PQ control scheme includes also low voltage ride through (LVRT) capability of the inverter during voltage sag.The optimum inverter switching state is indicated via the employed FCS-MPC algorithm instantaneously such that the actual PQ, injected to the grid, will track the corresponding reference values.During normal operation, the active power, injected to the grid, is set to the maximum possible value, while the reactive power is nil. Under voltage sag, the PQ will be injected to the grid as a function of the percentage of voltage sag based on the existing grid codes and regulations.In single-phase systems, successful application of direct PQ control depends on accurately creating the fictitious orthogonal components of grid current and voltage required for instantaneous power computations. Therefore, the following three different orthogonal signal generation (OSG) methods are utilized in this study in order to create such virtual (quadrature) components: second-order generalized integrator (SOGI), all-pass filter (APF), and quarter cycle phase delay (QCPD). In addition, qualitative and quantitative analyses of the obtained results are involved in this study of the FCS-MPC PQ system in order to compare the three adopted OSG methods. The PSIM® software was utilized in this study for modeling and studying the overall FCS-MPC system and the DER grid integration system.According to the results, the investigated FCS-MPC approach is effective in providing quick response and flexible control of PQ injected to the grid through the use of the three OSG methods. Moreover, the investigated FCS-MPC scheme successfully involves the LVRT option in order to improve the dynamic grid voltage support during the permissible duration of voltage sag following the LVRT profiles and grid codes of many countries.

Single-Phase Phase-Locked Loop Based on Tracking Differentiator

To better capture the phase information of single-phase power grids, a novel single-phase phase-locked loop method is proposed in this paper. The method uses a tracking differentiator as an orthogonal signal generator. Because the generator is sensitive to the input signal’s frequency, the amplitudes of the tracking and differential signals may not be equivalent, causing a failed phase tracking. Therefore, the amplitude correction of the differential signal needs to be done. Then, the corrected differential signal and the tracking signal are both input to the phase detector. To further verify the practical feasibility of the method, the voltage sampling and phase tracking experiments were performed on a digital signal processor-based inverter experimental platform, which is aimed to simulate the grid. The experimental results show that the proposed algorithm has strong dynamic performance and steady-state performance under different states of the power grid, and the phase-locked method has a practical feasibility in single-phase grid-connected applications.

Small-Signal Modeling and Design of Phase-Locked Loops Using Harmonic Signal-Flow Graphs

This article introduces signal-flow graphs for linear time-periodic systems to streamline and visually describe the frequency-domain modeling of complex phase-locked loop (PLL) systems used in grid-connected converters. Small-signal modeling using the proposed graphs is demonstrated for two commonly used single-phase PLL structures: SOGI-PLL and Park-PLL. Loop-gain models are developed for these PLLs to evaluate how an orthogonal signal generator (OSG), which is required in single-phase PLLs using the synchronous reference frame (SRF) architecture, modifies the PLL loop gain compared to that of a three-phase SRF-PLL, which does not require an OSG. It is shown that the OSG in the SOGI-PLL and Park-PLL introduces a significant phase lag in the PLL loop gain, limiting the maximum bandwidth for which either PLL can be designed. Slow-frequency adaptation (SFA) of OSG is proposed to mitigate the influence of the OSG dynamics on the PLL loop gain. Experimental results are presented to validate the developed loop-gain models and show that the proposed SFA-SOGI-PLL and SFA-Park-PLL have better transient performance, they do not suffer from the bandwidth limit, and they preserve the steady-state performance of the standard SOGI-PLL and Park-PLL.

A Fast Instantaneous Power Calculation Algorithm for Single-Phase Rectifiers Based on Arbitrary Phase-Delay Method

The instantaneous power for a three-phase rectifier can be calculated directly in the orthogonal coordinate system via coordinate transformation. However, it is difficult to calculate the instantaneous power directly for a single-phase rectifier due to the lack of another phase. Therefore, an orthogonal signal generator (OSG) is required to create an orthogonal coordinate system. Currently, conventional OSG algorithms suffer from long response time. To remedy this problem, in this paper, an arbitrary phase-delay OSG algorithm is developed and applied to the direct power control (DPC) system in the single-phase rectifiers. First, the instantaneous power theory and DPC are presented. Then, the principle of the arbitrary phase-delay OSG method is introduced and the anti-interference ability of the proposed method is analyzed. Through the dynamic response analysis, the developed algorithm brings faster response, easier implementation, and less computational burden compared with other common OSG algorithms. Finally, the validity and advancement of the proposed algorithm are verified by simulations and hardware-in-the-loop experimental tests. A comparison with conventional OSG algorithms also proves the advantages of the developed method.

Precompensator for Disturbance Signal Elimination in Single-Phase Inverters With Virtual Vector Control

In virtual vector control schemes for single-phase current-regulated voltage source inverters, many methods are proposed to generate a virtual orthogonal feedback current from the real feedback current. However, the generation stage causes mismatch between feedback and command currents, which may deteriorate dynamic current-tracking capability and power quality. A precise scalar model is developed to analyze the phenomenon. Based on this model, the mismatch is presented as a current disturbance signal introduced into the control loop. The mathematical analysis establishes that the current disturbance cannot be eliminated by any orthogonal signal generation (OSG) method. To solve the problem, a current precompensator is mooted. In this paper, the effect of the current precompensator is studied in detail. Furthermore, a voltage precompensator is proposed, which better suits OSG methods than the current precompensator. Experimental results of both the current and voltage precompensator are compared with the conventional solution to substantiate enhanced dynamic performance.

Unbalanced synchronous reference frame control of singe-phase stand-alone inverter

This paper presents harmonic damping schemes of the single-phase stand-alone inverter. The unbalanced synchronous reference frame technique is selected to control fundamental frequency voltage at the point of common coupling. The output voltage and the inductor current of the inverter are transformed to the unbalanced synchronous reference frame in which the proportional-integral regulators are used to force the error signals in the dq axes to zero. This control scheme does not require an orthogonal signal generator, and it is equivalent to the ideal proportional-resonant regulator. Harmonic regulators, orders 3rd, 5th, 7th, and 9th are added to minimize the voltage harmonics caused by the connected nonlinear load. The proposed controller is compared with the commonly-used multi-resonant controller. Simulation and experimental results of a 1.5-kVA inverter with the proposed control scheme exhibited excellent harmonic damping of the output voltage, caused by a highly nonlinear load and fast transient performance, which were better than the conventional resonant controller.

Enhanced orthogonal signal generator for a single‐phase grid‐connected converter

This study presents a new orthogonal signal generation (OSG) technique for the control system of a single-phase grid-connected voltage-source converter (VSC). The existing methods mostly suffer from delay, rely on the system parameters, or require multiple inputs. Among them, the second-order generalised integrator (SOGI) excludes the drawbacks of the other methods and shows better steady-state and dynamic response. The proposed OSG method here includes the advantages of the SOGI technique while demonstrating superior dynamic response and higher disturbance rejection capability. It is structurally simple without adding complexity to the control system. The proposed method is implemented in a DQ -frame current controller and its feasibility and reliability are verified through mathematical analysis, simulation, and experimental results.

Improved Voltage Unbalance and Harmonics Compensation Control Strategy for an Isolated Microgrid

This paper suggests an enhanced control scheme for a four-leg battery energy storage systems (BESS) under unbalanced and nonlinear load conditions operating in the isolated microgrid. Simplicity, tiny steady-state error, fast transient response, and low total harmonic distortion (THD) are the main advantages of the method. Firstly, a new decoupled per-phase model for the three-phase four-leg inverter is presented. It can eliminate the effect of power stage coupling on control design; thus, the three-phase four-leg power inverter can be viewed as three single input single output (SISO) control systems. Then, using an improved orthogonal signal generation method, the per-phase model of the four-leg inverter in the stationary and synchronous frame is derived. As the second step, a per-phase multi-loop control scheme for the four-leg inverter under unbalanced load conditions is suggested. The proposed control strategy has the ability to provide balanced output voltages under unbalanced load conditions by avoiding the need to deal with the symmetrical components. Finally, a multi-resonant harmonic compensator is used to actively prevent low-order harmonic currents to distort the output voltages of the three-phase four-leg grid-forming power converter. Simulations results are also presented to verify the performance of the suggested control strategy.

Design and Implementation of Digital Phase Locked Loop for Single-Phase Grid-Tied PV Inverters

In this article, a synchronous rotating-frame based phase-locked loop (PLL) for a single-phase PV inverter control system is presented. Detailed PLL mathematical model and the digital implementation for a single-phase PV inverter system are presented. A practical solution for transport delay based orthogonal signal generation using first-in-first-out (FIFO) circular buffer is also discussed. Details of implementation for a real-time system using digital signal processor were also described. The performance of the developed PLL was experimentally verified on a developed single-phase PV inverter prototype.