Query: PLL

title: Design Oriented Transient Stability Analysis of PLL Synchronized Voltage Source Converters
abstract: Differing from synchronous generators, there are lack of physical laws governing the synchronization dynamics of voltage source converters (VSCs) The widely used phase locked loop (PLL) plays a critical role in maintaining the synchronism of current controlled VSCs, whose dynamics are highly affected by the power exchange between VSCs and the grid. This article presents a design oriented analysis on the transient stability of PLL synchronized VSCs, i.e. the synchronization stability of VSCs under large disturbances, by employing the phase portrait approach. Insights into the stabilizing effects of the first and second order PLLs are provided with the quantitative analysis. It is revealed that simply increasing the damping ratio of the second order PLL may fail to stabilize VSCs during severe grid faults, whereas the first order PLL can always guarantee the transient stability of VSCs when equilibrium operation points exist. An adaptive PLL that switches between the second order and the first order PLL during the fault occurring/ clearing transient is proposed for preserving both the transient stability and the phase tracking accuracy. Time domain simulations and experimental tests, considering both the grid fault and the fault recovery, are performed, and the obtained results validate the theoretical findings.

title: Impact of Power Grid Strength and PLL Parameters on Stability of Grid Connected DFIG Wind Farm
abstract: This paper investigates the impact of power grid strength and phase locked loop (PLL) parameters on small signal stability of grid connected doubly fed induction generator (DFIG) based wind farm. Modal analysis of the grid connected DFIG wind turbine under different operating conditions and various power grid strengths are investigated at first. Modal analysis results reveal that the DFIG connected to a weak grid may easily lose stability under the heavy duty operating conditions due to PLL oscillation. The object of this paper is to identify the PLL oscillation mechanism as well as influence factors and propose a damping solution for this oscillation mode. A simplified linear system model of the grid connected DFIG wind turbine is proposed for analyzing the PLL oscillation. Through the complex torque coefficients method and using this model, the oscillation mechanism and influence factors including the power grid strength and the PLL parameters are identified. To suppress this PLL oscillation, a mixed $H_2/H_{\infty robust damping controller is proposed and designed for the DFIG. Electromagnetic transient simulation results of both single DFIG system and multiply DFIG system verify the correctness of the analysis results and effectiveness of the proposed damping controller.

title: Grid Synchronization Stability Analysis and Loop Shaping for PLL Based Power Converters With Different Reactive Power Control
abstract: Power converters may lose synchronization with the remaining network when integrated in a weak power grid. Such an instability phenomenon [known as grid synchronization instability (GSI) features the frequency divergence of phase locked loop (PLL) and oscillations of the converter's power output. In this paper, we focus on the influences of reactive power control (RPC) methods on GSI. We develop a single input single output model to explicitly reveal how the PLL interacts with the other parts of the converter system in terms of grid synchronization. Then, after deriving the open loop transfer function and sensitivity function of the entire converter system, we compare the stability margins for different RPC methods. Furthermore, we elaborate on the interactions among RPC, PLL, and voltage feedforward (VFF) and then demonstrate that different design methods of RPC and VFF will lead to different stability margins. The subsequent stability analysis provides insightful guidelines for coordinating the design of multiple control loops, i.e. RPC, VFF, and PLL. In particular, we demonstrate how the loop shaping of PLL takes effect in increasing the stability margin and eventually preventing the converter from GSI. The validity of the stability analysis is verified through simulations in MATLAB/Simulink.

title: Improved Design of PLL Controller for LCL Type Grid Connected Converter in Weak Grid
abstract: When LCL type converter is attached to weak grid, its current control and phase locked loop (PLL) will interact with each other, via the point of common coupling voltage. Unfortunately, the conventional PLL controller design methods are mainly for PLL independent systems, regardless of the aforesaid interaction. As a consequence, PLL dynamic might deteriorate the grid current control and even leads to instability problem. For this issue, this article proposes an improved design of PLL controller parameters to mitigate the negative effect of PLL on the current control. First, the small signal model of the current control system considering PLL effect is established, and the system stability with the conventional PLL controller design method is analyzed. Then, an improved design of PLL controller parameters is proposed, and the design guideline is given in detail. With the method, not only the dynamic and static response performance of PLL independent system can be maintained, but also the negative influence of PLL dynamic on the current control can be effectively reduced in weak grid. Moreover, the grid current control has a strong robustness to the grid impedance variation. Finally, the proposed method is validated by the simulation and experiment.

title: Symmetrical PLL for SISO Impedance Modeling and Enhanced Stability in Weak Grids
abstract: This paper proposes a symmetrical phase locked loop (PLL) that can eliminate the frequency coupling terms caused by the asymmetric dynamics of conventional PLLs. In the approach, a concept of complex phase angle vector with both real and imaginary phase components is introduced, which enables to control the direct and quadrature axis components with symmetrical dynamics. The small signal impedance model that characterizes the dynamic effect of the symmetrical PLL on the current control loop is also derived, which, differing from the conventional multiple input multiple output impedance matrix, is in a single input single output (SISO) form based on complex transfer functions. This SISO representation allows for a design oriented analysis. Moreover, the undesired sub synchronous oscillation caused by the conventional asymmetrical PLL can be avoided, and the classical SISO impedance shaping can be utilized to cancel the negative resistor behavior caused by PLL; thus can greatly enhance the grid synchronization stability under weak grid conditions. The effectiveness of the theoretical analysis is validated by experimental tests.

title: All Pass Filter Based PLL Systems: Linear Modeling, Analysis, and Comparative Evaluation
abstract: All pass filter (APF) passes all frequency components of a signal without altering their amplitude, but changes their phase. This feature has made the APF a versatile building block in different signal processing applications. The focus of this article is on APF based phase locked loops (PLLs) where the APF is required for creating a \text{90}\circ$ phase shift at the fundamental frequency. Such a phase shift is needed for generating a fictitious orthogonal signal in single phase applications and rejecting the grid voltage imbalance in three phase systems. To the best of authors' knowledge, none of the APF based PLLs have an accurate model yet. This gap in knowledge makes the analysis of these synchronization systems and identifying their advantages/disadvantages compared to state of the art structures complicated. The main objective of this article is to bridge this knowledge gap.

title: Demodulation type single phase PLL with DC offset rejection
abstract: This Letter proposes demodulation type PLL for phase and frequency estimation of single phase system that can reject DC offset. Using results from the adaptive estimation literature, this Letter proposes a linear parametric model based initial phase angle estimation approach. Then by using differentiation and integration operation on the estimated initial phase angle, the frequency is estimated. This avoids the use of any low pass filter unlike conventional demodulation based technique. Moreover, unlike existing demodulation based technique, the proposed technique can completely reject DC offset. Comparative experimental results, provided with state of the art DC offset rejection based enhanced phase locked loop, clearly demonstrate the suitability of the proposed technique.

title: A CMOS 76 81 GHz 2 TX 3 RX FMCW Radar Transceiver Based on Mixed Mode PLL Chirp Generator
abstract: A fully integrated 76 81 GHz frequency modulated, continuous wave (FMCW) radar transceiver (TRX) in a 65 nm CMOS is presented. Two transmitters (TXs) and three receivers (RXs) are integrated for multiple input multiple output (MIMO) processing. A 38.5 GHz mixed mode phase locked loop (PLL) with reconfigurable loop bandwidth and a frequency doubling scheme are employed to generate the reconfigurable FMCW chirp waveforms. The coarse to fine segmented current DAC is utilized to support sawtooth FMCW chirps with fast frequency ramping down capability, and the delay lock loop (DLL) based delay time calibration is used to improve the linearity of the embedded 2 D Vernier time to digital converter (TDC) Passive voltage mode down conversion is utilized to improve the RX linearity against TX leakage and short range interference. A bottom switching Gilbert type modulator in the TX is proposed to realize the bi phase modulation, and the magnetically coupled resonator technique is used to effectively expand the link bandwidth. The measurement results show that the FMCW TRX could generate reconfigurable chirps with the bandwidth from 250 MHz to 4 GHz and the period from 30 \mu \text{s} to 10 ms. The root mean square (rms) frequency error is 110 kHz for a sawtooth chirp with 4 GHz bandwidth and 300 \mu \text{s} period. The TX maximum output power is 13.4 dBm and is adjustable within 3 dB by reconfiguring its low dropout regulator (LDO) voltage. The RX achieves a 15.3 dB noise figure at 600 kHz IF and a 8.5 dBm RF input referred P1dB. The overall power consumption is 921 mW, with two TXs and three RXs powered ON. Based on the proposed TRX chip, prototype hardware and a data process algorithm are developed. Real time experimental results show that the distance and the angular resolution of the MIMO radar achieved are 5 cm and 9deg, respectively.

title: Large Signal Synchronizing Instability of PLL Based VSC Connected to Weak AC Grid
abstract: Similar large signal synchronizing instability that is common in traditional power system also exists in voltage source converter (VSC) dominated power system, which is increasingly reported and investigated. In this paper, the large signal instability of phase locked loop (PLL) synchronized VSC connected to weak ac grid is investigated. First, the influence of high grid impedance on PLL's dynamics is explored and an additional feedback loop is found to be introduced, which deteriorates the performance of PLL. Then an analysis model that is similar as the rotor motion model of synchronous generator (SG) is developed. Based on the developed model, equal area method is employed to carry out the large signal stability analysis. The large signal instability is found to be mainly resulted by the following two factors. One is the nonexistence of equilibrium point, which is similar as that there does not exist intersection between the mechanical power input curve and electromagnetic restoring force curve in SG grid connected system. The other is related with the transition process resulted by insufficient decelerating area, which leads to that the system cannot stably go through the transition from initial point to the existing equilibrium point. The proposed analysis not only contributes to revealing the physical mechanism but also provides guidance for the future improvement measures.

title: Whale optimization algorithm applied to load frequency control of a mixed power system considering nonlinearities and PLL dynamics
abstract: In this work, an attempt has been made to implement a nature inspired stochastic evolutionary algorithm, namely whale optimization algorithm (WOA) for exploring optimum and practical solutions of load frequency control (LFC) problem in power system. The proposed WOA mimics the 'bubble net feeding' strategy of 'humpback whales' in the oceans. The optimization technique is individually applied to a two area thermal power plant and two area hydro thermal gas power plant with AC DC tie line for fine tuning of the controller parameters. The study further houses the consequences of frequency measurement and the dynamics of a phase locked loop (PLL) with power system nonlinearities. To establish the efficacy of WOA, the obtained results are compared with results of success history based adaptive differential evolution (SHADE) krill herd algorithm (KHA) and some other well known control algorithms. Finally, statistical analysis is performed to affirm robustness of the proposed WOA in LFC area.