Phase-locked Loop Research Articles

Analysis and Implementation of a Frequency Synthesizer Based on Dual Phase-Locked Loops in Cesium Atomic Clock

The frequency synthesizer plays a crucial role in atomic clock technology. In this study, we demonstrate a direct microwave frequency synthesizer for a cesium atomic clock, employing frequency multiplication and a dual-phase-locked loop mode. A mathematical model of the frequency synthesis chain is established to estimate its performance. The phase-settling time and system stability are analyzed and studied in detail, and the obtained results are verified by experiments. An optimized realization of the frequency synthesizer shows that the phase-settling time can be adjusted within the range of 644.5 µs to 1.5 ms. Additionally, we measure the absolute phase noise values to be −63.7 dBc/Hz, −75.7 dBc/Hz, −107.1 dBc/Hz, and −122.5 dBc/Hz at 1 Hz, 10 Hz, 1 kHz, and 10 kHz offset frequencies, respectively.

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.

Modified Extended Complex Kalman Filter for DC Offset and Distortion Rejection in Grid-Tie Transformerless Converters

Proper operation of the grid-tie transformerless converters under unbalanced and distorted conditions entails a precise detection of the frequency and fundamental component of the grid voltage. One of the main problems that could arise during the estimation of grid parameters is the existence of a DC offset generated from measurement and A/D conversion. This undesirable induced DC offset could appear as a part of the reference sinusoidal current of grid-tie converters. Although literature has proposed the use of an extended complex Kalman filter (ECKF) for the estimation of positive and negative sequence voltage components as a promising competitor to phase locked loops, mitigating the effect of possible DC offsets when a Kalman filter is employed remains scarce. This paper proposes a new extended complex Kalman filter to improve the filter stability for estimating the frequency and the fundamental positive and negative symmetrical components of the grid voltages, where DC offset, scaling error, and noise can successfully be rejected. The theoretical findings are experimentally validated.

The Influence of On-Orbit Micro-Vibration on Space Gravitational Wave Detection

Large-aperture space telescopes have played an important role in space gravitational wave detection missions. Overcoming the influence of the space environment on interstellar laser distance measurement and realistic high-concentration laser distance measurement is one of the topics that LISA and Taiji are working hard on. It includes solar temperature, spatial stress relief, pointing shake and tilt, etc. However, when considering the impact of vibration on the telescope, both LISA and Taiji only consider the resonance impact of vibration on structural parts, which greatly ignores the impact of high-frequency micro-vibration on space ranging. This paper first considers space gravitational wave detection. Then, we establish the heterodyne interference model and demodulation algorithm of the optical phase-locked loop, and then introduce the vibration component for theoretical analysis. The results show that, although the resonance effect of low-frequency vibration on the system structure is avoided in space gravitational wave detection, the influence of high-frequency micro-vibration on heterodyne interference cannot be ignored. At the same time, we quantitatively analyze the influence efficiency of amplitude and frequency; in the premise of small amplitudes, the influence of vibration frequency is related to the frequency of the heterodyne signal, which has important guiding significance in engineering.

Assessment of Energy Conversion in Passive Components of Single-Phase Photovoltaic Systems Interconnected to the Grid

This paper presents a mathematical analysis of how energy return in grid-connected single-phase photovoltaic systems affects the sizing of passive components. Energy return affects the size of the link capacitor, making it larger than reported in the literature. One of the main points of this article is that an inverter connected to the grid using a DC–DC converter with an appropriate link capacitor is analyzed. The energy return is caused by the value (in Henry units) of the L-filter, which is also analyzed in this paper. The analysis shows that there is a link between the value of the L-filter and the voltage of the DC bus. The analysis assumes two conditions: (1) the DC bus voltage is always higher than the peak value of the grid sinusoidal voltage, and (2) there is a unity power factor at the connection point between the grid and the L-filter. To operate in an open loop, a compensation phase angle is calculated and introduced in the single-phase inverter modulation; this phase angle compensates the phase shift caused by the L-filter, avoiding the use of a phase-locked-loop (PLL) control system. The L-filter ripple current is evaluated by Fourier analysis, and the DC bus ripple voltage is evaluated by considering the energy returned to the link capacitor. The results of the analyses are compared with existing methods reported in the literature. The results also show that, to minimize the value of the L-filter, the DC voltage must be almost equal to the maximum voltage of the grid. Equations to assess the value of the DC-link capacitor and the L-filter in function of their ripples are developed. The results were verified with simulations in Simulink and experimentally.

The Impact of Phase-Locked Loop (PLL) Architecture on Sub-Synchronous Control Interactions (SSCI) for Direct-Driven Permanent Magnet Synchronous Generator (PMSG)-Based Type 4 Wind Farms

Electric vehicles (EVs) are a promising solution to reduce carbon dioxide (CO2) emissions, but this reduction depends on the fraction of renewable sources used to generate electricity. Wind energy is thus a vital candidate and has experienced a remarkable surge recently, establishing itself as a leading renewable power source worldwide. The research on Direct-Driven Permanent Magnet Synchronous Generator (PMSG)-based type 4 wind farms has indicated that the Phase-locked Loop (PLL) bandwidth significantly impacts Sub-Synchronous Resonance (SSR). However, the influence of PLL architecture on SSR remains unexplored and warrants investigation. Therefore, this paper investigates PLL architectural variations in PLL Loop Filter (LF) to understand their impact on SSR in type 4 wind farms. Specifically, an in-depth analysis of the Notch Filter (NF)-based enhanced PLL is conducted using eigenvalue analysis of the admittance model of a PMSG-based type 4 wind farm. The findings demonstrate that the NF-based enhanced PLL exhibits superior performance and improved passivity in the sub-synchronous frequency range, limiting the risk of SSR below 20 Hz. Additionally, Nyquist plots are employed to assess the impact on system stability resulting in increased stability margins. In the future, it is recommended to further investigate and optimize the PLL to mitigate SSR in wind farms.

Study of Voltage Controlled Oscillator for the Applications in K-band and the Proposal of a Tunable VCO

The advances in wireless technology have made the transfer or sharing of information simple and efficient thereby maximizing its impact to society around the globe. Due to these advances more memory space is required to store such a large transfer of information. This can only be done by reducing the device size which means scaling of MOS transistor to deep submicron levels. The most important part of wireless technology is the wireless trans-receiver. Its role is to transmit or receive the information to (or from) the wireless device. In the wireless trans-receiver, the frequency synthesizer is responsible for generating a stable output frequency which is used further to mix the received signal down to lower frequencies and vice-versa. This stable output frequency is generated by using Phase Locked Loop (PLL). While working at high frequency at the range of 12GHz to 40 GHz, where the operation is carried out at a very high speed and the coverage is done with the multiple beams, the circuits used at high frequency should be compatible with high speed. So, in this paper one very basic component which is the heart of communication system i.e., VCO is studied and the design parameters has been listed in this paper.

Synergetic control for three-level voltage source inverter-based shunt active power filter to improve power quality

The present paper proposes a synergetic control (SC) with Phase-Locked Loop (PLL) technique for a three-phase three-levels neutral point clamped-voltage source inverter-based shunt active power filter (SAPF). This one is devoted to compensating for nonlinear load harmonics and reactive power to improve power quality in distribution power systems. SC strategy is known as a robust control with good performances in transient and steady-state performance. Furthermore, it does not require solving the state equations, nor knowing the poles of the system. The DC voltage, as well as the active filter currents, are controlled using SC strategies. The efficiency of the suggested strategy has been verified through simulation tests using Matlab/Simulink software, where the simulation results are analyzed for two scenarios: a diode bridge rectifier with RL load and RC load. The active power filter demonstrated outstanding performance in reducing harmonics, maintaining a dynamic response, and tracking DC voltage for both RL and RC loads, as revealed by the simulation results. By comparing the suggested control with the traditional control, we found that the former outperforms the latter in all aspects. This sheds light on the effectiveness of the suggested control.

Control for Power Quality Improvement of Solar Photovoltaic-Distributed Static Synchronous Compensator Interfaced with Weak Grid Using Multi-Variable Filter Dual Second-Order Generalized Integrator Phase-Locked Loop

This study proposes a control method for transferring power generated by a solar photovoltaic system. The control algorithm, called MVF-DSOGI-PLL or Multi-Variable Filter Dual Second-Order Generalized Integrator Phase-Locked Loop), accurately estimates symmetrical components, phase angle, and positive sequence voltages of the Common Point of Interface (CPI) in distorted grid conditions. The approach creates a compensatory current to reduce PQ difficulties by extracting the size of the basic current load undergoing operation employing the SOGI method. These systems can operate in either modes of PV-DSTATCOM or DSTATCOM, depending on solar insolation’s availability. The simulation models of the grid-interfaced SPV systems are developed in Matlab/Simulink to evaluate the performances of the suggested control method. The results of simulation demonstrate that the suggested control systems efficiently transfers the power generated by PV arrays to a grid while performing tasks like load balancing, power factor correction (PFC), and harmonics reduction. Furthermore, the MVF-DSOGI-PLL-based control algorithm successfully mitigates PQ issues in distribution networks with weak grids, ensuring that PQ levels remain between a limited set by the IEEE-519 standard. A laboratory prototype of the proposed system is implemented to assess its steady states and dynamic efficient under fluctuating solar insolation, and load imbalance distortions.

A Virtual-Flux State Observer-Based Inductance Identification Method for Model Predictive Control of Grid-Tied Inverters With a Finite Phase Angle Set-Based PLL

To reduce the calculation burden of the conventional finite phase angle set-based phase-locked loop (PLL) and enhance the parameter robustness of the model predictive control for grid-tied inverters (GTIs), an improved finite phase angle set-based PLL and a new inductanceidentification method basedonvirtual-flux state observer (VFSO) are proposed in this paper. First, three improved PLLs are proposed based on the principles of the conventional finite phase angle set-based PLL. Second, the proposed PLLs are further improved by redesigning the cost function, which can search the optimal phase angle within the region of [0, π] instead of [0, 2π], reducing the iteration times. Third, a new VFSO with only one observer parameter is proposed, based on which a new inductance identification method is presented. Fourth, by analyzing the characteristics of the proposed VFSO, it is found that a larger observer gain can improve the dynamic convergence speed of the proposed VFSO, while a smaller one can enhance its robustness against grid frequency deviation. So, an observer gain adaptive method is proposed, aiming to improve both the dynamic and steady state control performance of the proposed inductance identification method. Finally, comparative experimental studies verify the effectiveness of the proposed strategies.

A Derivative-Feedback Based Compensation Control to Enhance the Small-Signal Stability for LCC-HVDC System

The small-signal stability of the LCC-HVDC system connected to the weak AC grid is of great concern. This paper derives the SISO model of the LCC inverter station. On this basis, the influence mechanism of AC system strength on system stability is studied via the Bode stability criterion, and the coupling interaction between different control loops is quantitatively evaluated. Results reveal that, as the AC grid becomes weaker, the system stability margin is diminished characterized by the larger phase lag in the phase-frequency response. Also, the interaction between DC voltage controller (DVC) and phase locked loop (PLL) control loops is intensified. Then, a derivative-feedback based compensation (DFC) control is presented to improve the LCC system stability under the weak AC grid condition. Theoretical analysis and simulation results indicate that the presented DFC control can effectively improve the stability and dynamic performances of the LCC system, which allows the system to operate stably even connected to the extremely weak AC grid.

Intelligent Parameter Identification and Sensorless Control of Permanent Magnet Synchronous Motor

In this paper, a spider monkey optimisation (SMO) algorithm is utilised to identify the parameters of the permanent magnet synchronous motor (PMSM), considering the parameters vary during the motor operation, which affects the sensorless control (SC) performance of the motor. An improved sliding mode observer (SOBS) is proposed for estimating the position and speed of the rotor. First, the SMO algorithm is used to identify the parameters of PMSM. Then, based on the identification results, an improved SOBS is proposed by a piecewise Sigmoid function. Furthermore, the stator position and speed are estimated by extended state observer (ESO) and phase-locked loop (PLL). Finally, a comparison simulation scenario is provided to demonstrate the efficacy of the suggested approach.

Stability enhancement of grid side converter in PV-wind-BESS based microgrid under weak grid conditions

This article revisits the design of a feedforward controller to improve the stability of grid side converter (GSC) in a microgrid system with harmonic reinjection ability, and power transfer capability while integrating into a weak utility grid. The stability and injection/absorption of active power to the utility grid are greatly affected by grid conditions. In addition, the variable grid impedances because of the expanding utilization of renewable energy sources, long distance of transmission lines, power system faults, harmonic pollution, etc., interrupts the grid codes. In these uncertain grid circumstances, coupling between the phase-locked loop (PLL) of the d-q control scheme and the grid impedance might also lead to instability. An enhanced feedforward controller term is implemented during the proposed research to counteract this effect. The proposed controller adapts the changes in grid parameters and makes the system stable by increasing power transfer to the receiving end. Proficiency of the proposed control scheme is validated by comparing it with existing control schemes using simulation tools with different operating modes of the microgrid and weak grid conditions. It is established from the simulation results that the proposed novel feedforward controller gives substantiated results during stable operations and integration while maintaining the IEEE-1204 standards.

Modeling and small-signal stability analysis of doubly-fed induction generator integrated system

Owing to their stability, doubly-fed induction generator (DFIG) integrated systems have gained considerable interest and are the most widely implemented type of wind turbines and due to the increasing escalation of the wind generation penetration rate in power systems. In this study, we investigate a DFIG integrated system comprising four modules: (1) a wind turbine that considers the maximum power point tracking and pitch-angle control, (2) induction generator, (3) rotor/ grid-side converter with the corresponding control strategy, and (4) AC power grid. The detailed small-signal modeling of the entire system is performed by linearizing the dynamic characteristic equation at the steady-state value. Furthermore, a dichotomy method is proposed based on the maximum eigenvalue real part function to obtain the critical value of the parameters. Root-locus analysis is employed to analyze the impact of changes in the phase-locked loop, short-circuit ratio, and blade inertia on the system stability. Lastly, the accuracy of the small-signal model and the real and imaginary parts of the calculated dominant poles in the theoretical analysis are verified using PSCAD/EMTDC.

Synchronization stability and multi-timescale analysis of renewable-dominated power systems.

Synchronization is one of the key issues in three-phase AC power systems. Its characteristics have been dramatically changed with the large-scale integration of power-electronic-based renewable energy, mainly including a permanent magnetic synchronous generator (PMSG) and a double-fed induction generator (DFIG) for wind energy and a photovoltaic (PV) generator for solar energy. In this paper, we review recent progresses on the synchronization stability and multi-timescale properties of the renewable-dominated power system (RDPS), from nodes and network perspectives. All PMSG, DFIG, and PV are studied. In the traditional synchronous generator (SG) dominated power system, its dynamics can be described by the differential-algebraic equations (DAEs), where the dynamic apparatuses are modeled by differential equations and the stationary networks are described by algebraic equations. Unlike the single electromechanical timescale and DAE description for the SG-dominated power system, the RDPS dynamics should be described by the multiscale dynamics of both nodes and networks. For three different timescales, including the AC current control, DC voltage control, and rotor electromechanical timescales, their corresponding models are well established. In addition, for the multiscale network dynamics, the dynamical network within the AC current control timescale, which should be described by differential equations, can also be simplified as algebraic equations. Thus, the RDPS dynamics can be put into a similar DAE diagram for each timescale to the traditional power system dynamics, with which most of power electrical engineers are familiar. It is also found that the phase-locked loop for synchronization plays a crucial role in the whole system dynamics. The differences in the synchronization and multiscale characteristics between the traditional power system and the RDPS are well uncovered and summarized. Therefore, the merit of this paper is to establish a basic physical picture for the stability mechanism in the RDPS, which still lacks systematic studies and is controversial in the field of electrical power engineering.

A Micro-Oven Controlled Dual-Mode Piezoelectric MEMS Resonator With ± 190 ppb Stability Over −40 to 105 °C Temperature Range

This letter presents a dual-mode piezoelectric microelectromechanical system (MEMS) resonator with an in-chip micro-oven for resonator temperature control. The piezoelectric MEMS resonator simultaneously operates in width-extensional (WE) mode with a high temperature turnover point, and torsion-bending (TB) mode with a large temperature coefficient of frequency (TCF) based on a phase-locked loop based system. Exploiting the difference in frequency-temperature characteristics of these two modes, accurate temperature sensing and precise close-loop micro-oven heating control are achieved by phase locking the resonator at its turnover point temperature of WE mode. Measured real-time frequency stability of the reported micro-oven controlled MEMS resonator is ±190 ppb over an extended industrial temperature range of -40 °C to 105 °C, indicating potential applications in high-end timing field, such as macro base stations and instrumentations.

Neural Network Assisted Laser Frequency Locking System

The laser frequency locking system with high robustness, high accuracy, and good anti-noise performance is usually used in laser synchronization and optics communications, continuous-variable quantum key distribution, and ultra-stable laser wavelength stabilization. In such systems, the analog or digital method is usually used to implement feedback control. Digital systems are more widely used than analog systems based on phase-locked loops due to their simplicity, flexibility, and robustness. The proportional- integral-derivative (PID) algorithm is the most typical algorithm well-developed in the digital locking system. However, due to the nonlinearity of the error signal induced by frequency variation, the PID algorithm will have a deviation in compensation for the transient response. This paper demonstrates a neural network assisted laser frequency locking system using predicted values to decrease the nonlinearity. Compared to the PID algorithm locking performance in the same locking system, both the peak-to-peak deviation and the root- mean-square error of the neural network assisted locking system are reduced by half.

Off-Board Bidirectional Electric Vehicle Charger Featuring Reactive Power Compensation and Reduced Total Harmonic Distortion for Enhanced Efficiency and Power Quality

The purpose of this study is to explain a recently developed off-board battery charger system for electric vehicles (EVs) that is capable of supporting grid-to-vehicle (G2V) and vehicle-to-grid (V2G) operations, in addition to adjusting for reactive power. A utility-connected AC-DC cascaded H-bridge (CHB) converter is included into the system design. This converter is responsible for controlling the power exchange that occurs between the grid and the battery while a bidirectional DC-DC converter is located at the rear end of the system. There is galvanic separation between the grid and the user end of the charger, which is included for the purpose of increasing safety. In order to manage electric vehicle power and battery current, the suggested system makes use of an ANFIS controller. This controller adheres to active power orders for both G2V and V2G modes, and it also provides reactive power adjustment when it is necessary. Furthermore, a control algorithm that is based on an adaptive notch filter has been developed in order to estimate network phases and achieve accurate current synchronization without the need for phase-locked loops (PLLs). This has resulted in the simplification of controller design and an improvement in both the steady-state and dynamic performance of the system. The efficiency of the suggested system in regulating reactive power in V2G and G2V scenarios is shown by the experimental results that were achieved in a MATLAB environment.

Analysis of optimized phase locked loop for grid synchronization of solar PV system under grid disturbances

AbstractIn this work, an optimal phase locked loop (PLL) is employed to estimate the fundamental grid frequency and phase angle under grid disturbances, which largely reduces the frequency and phase error. Conventional synchronous reference frame (SRF) offers considerable results for balanced grid conditions but has poor performance under grid disturbances with improper phase detection. In this regard, gravitational search algorithm (GSA)‐based optimization is utilized to optimally tune the proportional and integral (PI) gain values of conventional SRF PLL, which ensures the proper tracking of fundamental phase angle and frequency even during abnormal grid conditions, that is, voltage unbalance, frequency variations, high‐frequency harmonics, and phase variations. Further, integral square error (ISE) criteria, settling time, and overshoot are considered as objective functions to obtain the optimal value of current gain, present in the control loop of a grid‐tied solar photovoltaic (PV) system. The supremacy of the proposed work, compared to SRF and optimal SRF PLL, is tested with MATLAB®/Simulink studies and verified by dSPACE‐1104‐based hardware‐in‐loop (HIL) results for real‐time validation.

Transient synchronous stability analysis and enhancement control strategy of a PLL-based VSC system during asymmetric grid faults

The stability of a voltage source converters (VSC) system based on phase-locked loop (PLL) is very important issue during asymmetric grid faults. This paper establishes a transient synchronous stability model of a dual-sequence PLL-based VSC system during low voltage ride-through by referring to the equivalent rotor swing equation of synchronous generators. Based on the model, the synchronization characteristics of the VSC system under asymmetric grid faults are described, and the interaction mechanisms, as well as the transient instability phenomena of positive and negative sequence PLL during asymmetric faults are explained. Using the equal area criterion, the influences of sequence control switching action, detection delay, and interaction between the positive and negative sequence PLL on the transient synchronous stability of the VSC system are analyzed, respectively. In addition, a transient stability assessment criterion based on the critical fault clearance angle and time and an enhancement control strategy based on the improved positive and negative sequence PLL are proposed. Finally, the analytical results are validated through simulation and experiments.