Phase-locked Loop Control Research Articles

A Microgrid Stability Improvement Method by Applying Virtual Adaptive Resistor Paralleling with a Grid-Connected Inverter

An increase in renewable energy generation in the microgrid can cause voltage oscillation problems. To address this issue, an equivalent circuit of the microgrid was established, including a synchronous generator, grid-connected inverter, and constant power load. Then, the impact of different renewable energy generation ratios, different direct current (DC) voltage loops, and phase-locked loop control bandwidths of the grid-connected inverter on microgrid stability were analyzed. The results indicate that an increase in the renewable energy generation ratio leads to a decrease in the stability margin of the microgrid. A microgrid stability improvement method involving the parallel connection of a virtual resistor with the grid-connected inverter was proposed. The resistance value of the virtual resistor was obtained through an adaptive algorithm. This method ensures the stable operation of the microgrid under different renewable energy generation ratios.

Impact of PLL and non-PLL vector current control techniques on grid connected inverter

In the micro-grids, all the Distributed Power Generation Systems (DPGS) and loads are interconnected across the Point of Common Coupling (PCC). The stability and harmonics of the grid connected inverters are significantly impacted by uncertainties in the renewable energy sources based DPGS. The performance of these grid connected inverters across the PCC depends on the Phase-Locked Loop (PLL) used to track the grid angle and power control structures used to control the power fed to grid. These power control structures can be either PLL based or PLL less systems. The PLL based Vector Current Control Direct Quadrature (VCC DQ) control and PLL less Non-PLL Vector Control (NPVC) techniques are compared along with their controller design and bode plots. Also, the small signal models of grid connected inverter with PLL are presented from which the converter impedance is derived to show the effect of PLL on the system using bode plots. The impact of the PLL based and PLL less control techniques on the grid connected inverter are presented with analytical equations along with simulation and hardware results. A 6 kW grid connected inverter simulation model and 150 W hardware prototype is developed using TI F28379D processor to compare the performance of both with and without PLL control techniques.

Identification of secondary resonances of nonlinear systems using phase-locked loop testing

One unique feature of nonlinear dynamical systems is the existence of superharmonic and subharmonic resonances in addition to primary resonances. In this study, an effective vibration testing methodology is introduced for the experimental identification of these secondary resonances. The proposed method relies on phase-locked loop control combined with adaptive filters for online Fourier decomposition. To this end, the monotonic evolution of the phase lag around secondary resonances is exploited for their identification. The method is demonstrated using two systems featuring cubic nonlinearities, namely a numerical Duffing oscillator and a physical experiment comprising a clamped–clamped thin beam. The obtained results highlight that the control scheme can accurately characterize secondary resonances as well as track their backbone curves. A particularly salient feature of the developed algorithm is that, starting from the rest position, it facilitates an automatic and smooth dynamic state transfer toward one point of a subharmonic isolated branch, hence, inducing branch switching experimentally.

Green energy solution for grid integrated solar PV system for water storage towers

In India, water storage towers are present almost everywhere, especially across small towns to rural areas. The storage tanks either utilize diesel powered or utility grid fed induction motor (IM) water pumps. The large spaces available with water storage towers can be utilized to plant solar PV panel for large storage towers water pumping operation, hence, making a switch from diesel or grid run storage towers to solar operated storage towers. This paper presents a robust control of grid integrated solar PV-based water pump system with efficient and smooth transition between standalone and grid interfaced modes. A smart DC link voltage control is presented for distributed generation system (DGS), which provides full control on DC link voltage for both modes of operation at all dynamic load conditions. An enhanced phase-locked loop (EPLL) control is utilized for grid source converter (GSC) in grid control operation, making it flexible to different grid scenarios and power quality. It works for harmonics suppression, load balancing and grid side converter control. An enhanced phase-locked loop (EPLL) is implemented for synchronization control algorithm, which provides an accurate estimation of voltage angle even during frequency ramps and exhibiting superior performance particularly in terms of robustness against DC offsets. The primary requirement for smooth operation of grid-tied solar PV system is effective power management between different sources. The issues of power management and power quality, are discussed in this work, and solutions are presented. The implemented control algorithms are tested successfully for dynamic solar insolation, varying load conditions, unbalance in load, sudden grid outage condition. The system appropriateness is validated by experimental results.

Speed Sensor-less Control of Induction Motor based on Super-helical Sliding Mold

Background: With the continuous progress of technology and the development of shield enterprises, higher requirements are put forward for speed estimation and system stability in the sensorless control system of induction motors in shield machines. Method: In order to solve the problems of velocity observation error and sliding mode vibration of the induction motor velocity observation method based on sliding mold observer, an improved superhelical sliding mold observer is proposed by combining the currently known invention patents and the information based on the induction motor control. Result: The open square of the current error value is introduced into the continuous function of the sliding variable of the observer, and two different functions are used in the boundary layer to replace the sign function, which reduces the sliding mode noise and vibration problems, and the stability of the observer is proved by the Lyapunov stability theory. After that, a phase-locked loop alternative model-referenced adaptive algorithm is used as the rotational speed observation link, which solves the problem that the conventional model-referenced adaptive algorithm relies on the current-modeled magnetic chain observer. Conclusion: The improved super-helical sliding mode observer and phase-locked loop control method effectively reduce the system vibration and speed estimation error of the motor under different speeds and loading conditions, and the observed currents are smoother, which improves the stability of the system. Simulation and experimental results under different working conditions show the effectiveness of the proposed method.

A novel approach of fatigue testing and evaluation of electronic systems based on phase tracking

This paper presents an experimental approach to perform fatigue testing of a lightly damped electronic assembly subjected to harmonic excitation. By leveraging the power of the phase locked loop control algorithm, our proposed work aims to accurately track the phase of the system. This innovative approach enables precise measurement of the drop in resonant frequency due to fatigue, enhancing overall damage prediction. The proposed approach exploits the characteristics of the materials that the phase at the resonance is constant and for a lightly damped system, the value is close to pi/2. In the event that the test article experiences fatigue, and the resonant frequency undergoes a change, the controller will promptly adapt to the new frequency while upholding a constant phase, ensuring the uninterrupted continuity of the testing process. The proposed approach is demonstrated by using the Ball Grid Array (BGA) electronic package as an example, where the test setup, data acquisition, and data monitoring for identifying the interconnect failure are presented. Failure analysis of the test article shows that the primary failure mode is the solder joint failure at the Intermetallic (IMC) layer. A finite element model is developed and correlated with experimental modal analysis to accurately estimate maximum stress and deflection in solder joints. By utilizing the obtained results, one can create a more accurate SN curve for the tested material. This will allow for a better understanding of the material's fatigue behavior and enable more precise predictions of its durability in real-world applications.

Repetition Frequency Control of a Mid-Infrared Ultrashort Pulse Laser

In this study, a method for controlling the repetition frequency of a mid-infrared ultrashort pulse laser with a central wavelength of 2.8 µm is developed. A ring cavity that is insensitive to the polarization state of the laser light emitted from the fiber end was constructed to stabilize the oscillation of the mid-infrared ultrashort pulse laser. More oscillation conditions for the ultrashort pulse laser based on nonlinear polarization rotation are found than the conventional method. To confirm that the pulse oscillation is mode-locked, ultrashort pulse oscillation was confirmed by an autocorrelator. The pulse repetition frequency of this robust ultrashort pulse laser was controlled. The control method was based on the phase-locked loop (PLL) control. A wedge window was inserted into the cavity and mounted on a linear stage driven by a piezoelectric transducer. By driving the piezoelectric transducer, the position of the wedge window changed, and the resulting optical path length also changed. The repetition frequency was controlled based on this principle. Optical path length control by the wedge window and temperature control provides an Allan deviation of approximately 1 mHz.

A Decoupling Control Method for Converting DIDO Sequence Admittance Model of Grid-Tied Converter System Into SISO

This paper proposes a decoupling control method to eliminate frequency coupling in three-phase grid-tied system. Firstly, the admittance model of three-phase <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -type three-phase grid-tied converter (GTC) considering DC-bus voltage control (DVC) loop and phase-locked loop (PLL) is established in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -domain frame, and the influence of asymmetrical DVC and PLL control structure on frequency coupling oscillation is analyzed. Then decoupling factors are added to the DVC loop and current control (CC) loop to achieve that the off-diagonal elements of the sequence admittance matrix of the GTC are 0, which means the frequency coupling in the GTC is eliminated. Therefore, the GTC system can be regarded as a single input single output (SISO) system, and the stability can be analyzed by the classic Nyquist criterion in the sequence-domain frame. Compared with the double input double output (DIDO) system, the resulted SISO system convenient for calculating the stability margin of the system and guiding parameter design. In addition, the SISO system is easier to be analyzed on the oscillation and resonance mechanism, and the analysis results can be used to optimize the design of the converter controller, grid planning and operation. Finally, simulation and experiment verify the feasibility and effectiveness of the proposed decoupling control method.

Small-Signal Modeling and Stability Analysis of a Grid-Following Inverter with Inertia Emulation

Power-converter-based energy-harvesting and storage systems are becoming more prevalent in the electrical grid, replacing conventional synchronous generators. Consequently, grid inertia is diminishing, and to address this, inverter-based energy conversion systems are required by grid codes to provide frequency control support to the main grid. This is undertaken to increase the equivalent inertia of the system and reduce frequency variations. This type of control is necessary and designed for handling large system transients. However, it also impacts the small-signal stability of the grid-connected converters. To investigate this issue, this paper addresses the influence of synthetic inertia control on the output admittance of a grid-following inverter and its interaction with the grid equivalent impedance. A synchronous reference frame dynamic model of the grid-following inverter closed-loop system is obtained and linearized at an operating point to analyze the small-signal stability of the low-switching frequency inverter. The models are validated through numerical simulations. The analysis verifies the interactions of the internal control loops, such as the AC current control with voltage feedforward, DC-link voltage control with power-feedforward, phase-locked loop, and AC voltage control with inertial control. Additionally, the interactions between the output admittance of the inverter and the grid impedance are verified using the generalized Nyquist criterion. The stability regions are validated through simulations, and the results show that the system gain margin is reduced for increasing values of synthetic inertia gain and lower grid short-circuit ratios. Furthermore, there is a limit in the voltage and power-feedforward bandwidth to avoid degrading the system stability when utilizing the synthetic inertia control.

Stability analysis of hybrid synchronization controller based grid forming control

Synchronization units are vital for the stable operation of grid-tied converters in generation and transmission. There are two main synchronization units, i.e., phase-locked loop (PLL) and power synchronization controller (PSC), with the corresponding drawbacks in weak and strong grid respectively. Recently, the hybrid synchronization controller (HSC) is proposed in order to make up the deficiencies of PLL and PSC in weak and strong grid respectively. This paper deduces the detailed impedance characteristics of PSC and HSC and compares their cons and pros to show the stability mechanism of HSC. Moreover, two types of HSCs are also presented and compared in this article with slight difference in structure. It is found that the impedance of Type II based HSC has smaller amplitude and better phase margin than PSC around fundamental frequency, while Type I based HSC has larger amplitude and less phase margin than PSC. Type II based HSC can improve the stability and Type I based HSC can worsen the stability compared with PSC. Realtime experiments are carried out to verify this.

Performance analysis of modeling scale on multiband oscillations in grid-connected wind farm

Grid-connected permanent magnet synchronous generator (PMSG) wind farms may be susceptible to oscillation when connected to weak grids. This paper explores the root causes of the oscillations from two perspectives: the model and the oscillation frequency band. First, the small signal model of PMSG wind farm grid-side system is established, and the small disturbance comparison with the PMSGA full-order electromagnetic transient model in MATLAB/Simulink is carried out. Then, we calculatue the eigenvalues of the small signal model and use model analysis techniques such as participation factors calculation and root locus method to identify the critical factors that cause the oscillation modes to be dominant. Finally, time-domain simulation is used to verify the theoretical analysis. Two dominant modes are identified: the subsynchronous oscillation mode and the low-frequency oscillation mode. The subsynchronous oscillation mode is closely related to the direct current (DC) voltage control and the dynamics of DC link. The low-frequency oscillation is significantly weakened with the decrease in grid strength, and it is closely related to the phase-locked loop (PLL) control. The conclusions can provide a reference for tuning the control parameters of PMSG converter.

An Advance Control of Grid Integrated Wind Turbine Driven DFIG-Battery System with Grid Power Shaping Under Gust Wind Variation

There has been an increase in wind power penetration into the utility grid. The wind speed variations exhibit undesirable oscillations that influence power quality and system reliability. Therefore, the grid operation is challenging in this scenario. Battery energy storage system (BESS) smooths out wind power production and reduces fluctuations. However BESSs low power density and high capacity requirements to compensate for fluctuation limit its implementation for high-power applications. This paper introduces a wind energy conversion system (WECS) based on a doubly fed induction generator (DFIG) incorporating a vanadium redox flow battery (VRFB) in the DC-link, which supports grid power smoothing and power balance even under varying wind speed. Real-site wind data was used to develop a technique for designing the VRFB. The rotor side converter (RSC) employs an off-maximum power point tracking to keep the VRFB operation within the limit and deliver consistent power to the grid. An improved phase lock loop control is designed for DFIG that suppresses DC offset at the input and allows RSC and grid side converter (GSC) to perform appropriately even under grid disturbances. The GSC control is designed with an improved DC-link voltage control by adopting an anti-windup fractional-order proportional-integral (AWFOPI) controller, which can improve transient response. A sparrow search algorithm is adopted to tune the AWFOPI controller. Matlab Simulink is used to simulate the system. Test results show that the system performs well under various operating conditions and is satisfactory. It has also been tested on the OPAL-RT real-time simulator test bench.

Control Loop Stability Criterion and Interaction Law Analysis for Grid-Connected Inverter in Weak Grid

The study of stability criterion and interaction analysis for grid-connected inverter under weak grid is of great value. Different from traditional impedance stability criterion, this paper proposes control loop stability criterion for grid-connected inverter from the perspective of controller bandwidth overlap. Firstly, the system d-q overall small-signal model G0 considering phase-locked loop (PLL) of grid-connected inverter under weak grid is given and split into three multiplied independent parts: grid impedance, phase-locked loop and current controller. Then using the equivalent loop ratio expression obtained by combining PLL and grid impedance together and then divided by the current controller, the control loop stability criterion is proposed. The proposed stability criterion can not only maintain the independence of each single loop, but also can analyze the overall system stability. So, further analysis of the interaction law among the three parts under this control loop stability criterion is carried out by deducing the expression of the bandwidth ratio n of the PLL and current controller. And it is found that under the weak grid, the interaction between the links will be generated when the bandwidth ratio is greater than the threshold of n. This phenomenon can be represented by the overlapping area of amplitude-frequency curves in the bode diagram for G0. And the weaker the grid or the closer the bandwidth of PLL is to current controller, the larger the overlapping area of amplitude-frequency curves, and the more likely it is to lead the closed-loop gain to infinity. Furthermore, when the bandwidth of the current controller is fixed, the threshold of n varies in the regions of less than 1 as well as more than 1 with the change of the grid strength. Therefore, the system can remain stable no matter what the bandwidth ratio of the phase-locked loop to the current controller is greater or less than 1. Accuracy of the proposed control loop stability criterion and interaction analysis is verified through simulation and experimental results.

Nonlinear Dynamics of the Primary Oscillation Circuit of a Mems Gyroscope Under the Action of Phase-locked Loop and Automatic Gain Control Systems

In this work, we study the dynamics of primary oscillations of a high-Q micromechanical resonator - a sensitive element of an RR-type MEMS gyroscope - under the action of various implementations of a phase-locked loop system operating in conjunction with an automatic gain control system for an electrostatic drive. The study of the dynamics of the object is carried out both numerically and analytically - using the averaging method. Conditions for the stability of a stationary regime in a linear approximation are obtained. The questions of accuracy of various methods of numerical solution of differential equations of the circuit of primary oscillations are considered. The influence of the mechanical nonlinearity of the resonator on the dynamics of the resonator and the control system has been studied. An implementation of a low-order PLL circuit that does not contain a double-frequency spurious signal at the output of the phase detector is proposed. The output characteristics of control systems (speed, capture bandwidth, etc.) are analyzed and qualitative conclusions are drawn about the features of the interaction between the dynamics of a mechanical oscillatory link and the PLL-ARC circuit.

Comparative Stability Analysis and Improvement of Grid-Following Converters Using Novel Interpretation of Linear Time-Periodic Theory

This article presents a comparative stability investigation of grid-following (GFL) converters with different advanced phase-locked loops (PLLs) and current control schemes based on linear time-periodic (LTP) theory. First, a time-domain physical interpretation of the LTP theory is proposed, which inspires an iterative LTP eigenvalue computation algorithm. A measure for the influence of the frequency coupling effect on each eigenvalue is defined to demonstrate the necessity of applying the LTP theory. Then, eigenvalue-based stability analysis is carried out to gain insights into dynamic characteristics of two implementations of GFL converters, namely, dual synchronous reference frame PLL (DSRF-PLL) and proportional integral (PI) current control, and dual second-order generalized integrator PLL (DSOGI-PLL) and proportional resonant (PR) current control. The effects of the PLL bandwidth, the current control time constant, the grid strength, and imbalance on the system stability are evaluated. In addition, a damping loop is proposed to improve the stability margin of GFL converters connected to weak grids. Finally, MATLAB/Simulink simulations and experimental measurements validate the correctness of the proposed modeling method and stability assessment results.

Small-Signal Stability Boundary of Heterogeneous Multi-Converter Power Systems Dominated By the Phase-Locked Loops’ Dynamics

While renewable resources are increasingly integrated into the electric power system, the small-signal instability risk may be induced by grid-following converters using phase-locked loops (PLLs) for grid synchronization, especially in low short-circuit strength systems. The stability analysis complexity is further increased in such a heterogeneous multi-converter system (HMCS), where multiple converters may have different PLLs’ control parameters provided by various vendors. To understand how the different PLLs’ dynamics collectively affect the small-signal stability of the HMCS, we transform the HMCS into an equivalent homogeneous multi-converter system for the small-signal stability analysis. Then, we analytically derives the small-signal stability boundary condition of the HMCS dominated by the PLLs’ dynamics (HMCS-DPLL). The derived stability boundary allows us to obtain analytical results about how the small-signal stability of the HMCS-DPLL is collectively affected by network structure, converter operating conditions, and different PLLs’ control parameters. Based on the stability boundary condition, a computationally efficient method is also proposed to identify the design rationality of PLL control parameters as well as the small-signal stability and stability margin of the HMCS-DPLL. The analytical results and proposed method are validated by modal analysis and electromagnetic transient simulation with the full-order models on a 9-converter heterogeneous system.

Stability analysis and parameter coordination of the grid-connected wind farm with heterogeneous PMSGs

Improper setting of phase-locked loop (PLL) control parameters is one of the key factors for the adverse dynamic interaction between wind turbine generators, resulting in the oscillation instability of wind power systems. In this study, considering the spatial distribution characteristics and dynamic heterogeneity of multiple PMSGs, the PLL-induced instability mechanism of the grid-connected PMSG wind farm is studied and a stability criterion is proposed to guide the parameter coordination of the PLL for multiple PMSGs. First, based on the dynamic equivalent modeling method of the homogeneous multi-agent system, a reduced-order model of the homogeneous wind farm dominated by PLL is proposed. The parameter region of PLL control to ensure stability was analytically examined based on the proposed stability criterion. Then, the stability of heterogeneous wind farm is analyzed by constructing an equivalent homogeneous wind farm that has the same dominant oscillation mode as the heterogeneous wind farm; that is, the stability is equivalent. Furthermore, the stability criterion of the heterogeneous wind farm is deduced, and the parameter coordination method of PLL control for multiple PMSGs is proposed. Modal analysis and nonlinear simulation were conducted to confirm the accuracy of the theoretical analysis.

Frequency support strategy for single-Stage grid-Connected photovoltaic generation with active power reserves

Large-scale photovoltaic (PV) generation grid connection causes lack of inertia and insufficient frequency regulation capacity of power system. To solve this problem, this study proposed the active power-frequency droop control (APFDC) and virtual inertia control (VIC) for single-stage PV generation. PV generation is able to participate in the grid frequency regulation by improving the control system of voltage source converter (VSC). The effect of control parameters on the inertia characteristic of PV generation is analyzed. On this basis, the distribution mechanism of unbalanced active power among PV generators with inertia control strategy is revealed. The simulation results indicated that PV generation can be controlled by setting the control strategy of the voltage source converter (VSC) to reduce or increase the active power; it also takes part in the frequency regulation of the system. The inertia provided by PV generation is controllable and frequency-dependent, increases with the increase in control gain, the decrease in the time constant of VIC, and the decrease in phase-locked loop (PLL) control bandwidth.

A PLL-less Vector Control technique for the single-phase Grid connected inverters

The control of single-phase Grid connected inverters by Vector Current Control Direct Quadrature (VCC DQ) method is a well-known technique. However, the presence of a Phase-Locked Loop (PLL) affects the dynamic response of the system. This paper proposes a PLL-less Vector Control (PLVC) method in which a single-phase Grid connected inverter is controlled without any PLL. Hence it reduces the complexity and computational burden during implementation on the Digital Signal Processor (DSP) controller as well as the natural coupling of PLL and current controller. The mathematical modeling and controller design for the PLVC method is described. A 5 kW single-phase Grid connected inverter simulation model and a 150 W hardware prototype with TI F28379D processor are developed and tested under steady-state at rated power condition and dynamic conditions like instant variation in the reference powers. Also, the robustness of the controller is tested under adverse conditions voltage sag, swell at the instant of distinct phase angles and frequency deviation also.

Stability analysis of Three-phase Grid-Connected inverter under the weak grids with asymmetrical grid impedance by LTP theory in time domain

The Grid-connected inverter (GCI) often operates in the weak grid with asymmetrical grid impedance due to the unbalanced and single-phase loads. However, the time-periodic dynamic behavior effect of the Phase-Locked Loop (PLL) on the GCI operating in an asymmetrical system is not investigated in the time domain. This paper explores the influence of the asymmetrical grid impedance on the stability of the weak grid with GCI. Firstly, GCI's complete harmonic state-space (HSS) model considering PLL under the asymmetrical network is established. Secondly, in view of the developed HSS model, the predominant parameters are determined through the eigenvalues of the system state matrix, along with the participation factors. Afterward, with eigenvalue locus analysis, the stability boundaries of the system's critical parameters involving the current reference, current controller, and PLL controller are determined under different grid impedance asymmetrical indexes. It is found that the stability region of system parameters is narrowed with increasing impedance asymmetrical index. Lastly, simulations and experiments are carried out to verify the effectiveness of the proposed HSS model and the theoretical analysis results.Index terms— Grid-connected inverter, asymmetrical grid impedance, Phase Lock Loop, harmonic state-space model, stability boundaries, participation factors.