Search Results (18)

The frequency linearity of a frequency-swept light signal is critical for ensuring the precision of Frequency-Modulated Continuous-Wave (FMCW) laser ranging systems. A two-stage nonlinearity correction mechanism for frequency-swept light is proposed, combining both data-driven and principle-based approaches. In the main correction stage utilizing an electro-optic phase-locked loop (EO-PLL), high temporal resolution phase detection is achieved. To address the failure of the EO-PLL caused by a bandwidth limitation of the digital loop filter (DLF), a novel pre-correction mechanism is developed based on a data-driven approach. In this mechanism, the neural network (NN) model establishes a mapping relationship between the input and output of the real laser-modulation system, which effectively simulates this physical system and avoids the risk of trial-and-error damage. Afterwards, the Soft Actor–Critic (SAC) model interacts with the NN model and trains a decision-making agent to determine the optimal modulation strategy for the nonlinearity pre-correction of the frequency-swept light. During the training process of the SAC agent, both the modulation strategy and the accuracy of evaluating the strategy’s effectiveness are optimized. Moreover, in contrast to the basic Actor–Critic model, the SAC model enhances the exploration of modulation possibilities by maximizing entropy expectation of random strategy, thereby improving the robustness of the pre-correction mechanism. Finally, the frequency-swept characteristic analysis experiment proves that integrating NN-SAC with EO-PLL enables frequency locking under the reduced bandwidth of the DLF. Additionally, through actual ranging experiments, it is also demonstrated that the proposed mechanism significantly enhances ranging precision, repeatability, and stability. Therefore, by integrating data-driven and principle-based approaches, this investigation offers an innovative perspective for the nonlinearity correction of FMCW laser ranging and, furthermore, electro-optic control scenarios. Full article

As large-scale renewable energy sources are increasingly integrated into AC grids via voltage source converters (VSCs), the transient synchronization stability of phase-locked loop (PLL)-based VSCs during fault ride-through is gaining more attention. Most existing studies assume that the positive and negative sequence separation and current control dynamics are much faster than the PLL dynamics, thereby neglecting their impact on the transient synchronization stability of the system. However, when the PLL bandwidth is relatively large, ignoring the positive and negative sequence separation and current control dynamics may result in incorrect stability assessments. To address this issue, this paper first considers the multiple control loop coupling, including positive and negative sequence separation, current control, and PLL, to construct a full-order nonlinear mathematical model of the VSC grid-connected system under asymmetric fault conditions. Based on this, the phase trajectory method is employed to analyze the transient synchronization stability of the system. Additionally, this full-order mathematical model is used to determine the PLL bandwidth boundary beyond which the effects of positive and negative sequence separation and current control dynamics cannot be neglected. Finally, PSCAD/EMTDC simulation results validate the effectiveness of the theoretical analysis presented in this paper. Full article

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. Full article

Determining the loop noise bandwidth and the coherent integration time is essential and important for the design of a reliable digital phase-locked loop (DPLL) in global navigation satellite system (GNSS) receivers. In general, designers set such parameters approximately by utilizing the well-known fact that the DPLL is stable if the normalized bandwidth, which is the product of the integration time and the noise bandwidth, is much less than one. However, actual limit points are not fixed at exactly one, and they vary with the loop filter order and implementation method. Furthermore, a lower limit on the normalized bandwidth may exist. This paper presents theoretical upper and lower limits for the normalized bandwidth of DPLL in GNSS receivers. The upper limit was obtained by examining the stability of DPLL with a special emphasis on the digital integration methods. The stability was investigated in terms of z-plane root loci with and without the consideration of the computational delay, which is a delay induced by the calculation of the discriminator and the loop filter. The lower limit was analyzed using the DPLL measurement error composed of the thermal noise, oscillator phase noise, and dynamic stress error. By utilizing the carrier-to-noise density ratio threshold which indicates the crossing point between the measurement error and the corresponding threshold, the lower limit of the normalized bandwidth is obtained. Full article

This paper studies the stability impact of the alternate voltage controller’s (AVC) low-pass filter (LPF) in a wind turbine’s grid-connected voltage source converter (VSC). A small-signal model of the grid-connected converter is designed with a grid-following synchronization control. More specifically, the non-linear state-space model of the grid-connected converter was developed, including the dynamics of both the inner and outer control loops of the converter, the dynamics of the elements of the electrical system, as well as the digital time delay. An eigenvalue-based stability analysis gives insight into the stability impacts of the outer-loop controllers. It is proven that the cutoff frequency of the AVC’s LPF affects the phase-locked loop (PLL) and AVC bandwidths of instability, as well as the corresponding critical oscillation frequencies. This phenomenon is observed in both weak and strong grids. Consequently, the small-signal stability regions of the PLL and AVC bandwidth can be identified for the range of the AVC’s LPF cutoff frequency under study. The stability regions of the PLL and AVC, which are obtained from the small-signal model, as well as the determined critical oscillation frequencies, are validated through time domain simulations and fast-Fourier transformation (FFT) analysis. Full article

This paper proposes a systematic control design method for active damping control of grid-connected voltage source converters (VSCs). The proposed control method considers the conventional cascaded control loops and improves them by including additional states feedback-based active damping. In such a way, all control gains are lumped into one control gain matrix based on the proposed formulation. The lumping of all control gains into one matrix leads to a linear optimization problem, so different techniques can be used to calculate control gains. This work calculates them by using a simple but effective optimal control theorem as a noteworthy feature. The proposed control method can overcome the challenges of designing multiple control loops, evaluating wide time scale dynamics, and tuning required control parameters. Moreover, direct relationships between the proposed tuning parameters and system well-known stability and performance indicators such as maximum damping factor, minimum damping ratio, and the control efforts are identified, providing good physical insight. Finally, the proposed control structure and optimal gain calculations ensure power converter robustness against uncertainties in the grid’s short-circuit ratio (SCR) and different operating-point conditions. When the grid’s SCR changes from 10 (strong grid condition) to 1 (ultra-weak grid condition), the system under the proposed control method maintains good stability margins and simultaneously provides a fast dynamic response by facilitating the implementation of a high-bandwidth phase-locked loop (PLL). The performance of the proposed control strategy was investigated analytically and practically by conducting eigenvalue analysis, simulations, and experiments. Full article

With the integration of renewable energy sources into the power grid, a number of power electronic converters need to be connected together in parallel. Due to this interconnection among the power converters with a common DC bus, the equivalent impedance of the DC network, i.e., DC network impedance (DCNI) of these parallel converters, may vary and can cause oscillations in the DC link voltage (DCLV). In the literature, impedance models of grid-tied converters (GCs) based on the AC side are well reported without including these variations in DCNI. In addition, the dynamics of a phase-locked loop (PLL) play a significant role in GC system stability. To evaluate these stability issues, this paper proposes small signal impedance models viewing from the DC side of a three-phase GC operating under different control modes considering the PLL dynamics and the DCNI variations. Using the proposed DC impedance models (DCIM), DCLV stability analysis is evaluated for a GC. It is verified through bode plots that the interaction between the proposed DCIM and DCNI leads to unstable operation of the closed-loop converter near the PLL bandwidth when the phase difference between DCIM and DCNI is more than 180 degrees. Finally, the analytically developed models are validated using hardware in-the-loop (HIL) testing. Full article

This paper proposes an effective algorithm; this algorithm is updating the phase-locked loop (PLL) gains according to the value of the short circuit ratio that will decrease the weak grid effect in the PLL controllers to reduce problems related to renewable energy sources and connect to the point of common coupling (PCC). Based on system parameters estimation, the proposed algorithm enhances the system stability for the distribution networks. The standard IEEE 33-bus test system is used to investigate the proposed algorithm’s effectiveness and superiority. An extensive mathematical effort is exerted to get the system’s small-signal stability (SSS) model. The tuning of the phase-locked loop and the current control loop are choosing to dynamically change according to the system variables to ensure the same system stability margin, whatever the change in the loading conditions. The MATLAB/Simulink model is used to validate the algorithm and simulate the test system. Full article

A sub-/super-synchronous interaction (sub-/super-SCI) can occur between a voltage source converter-based high-voltage direct current (VSC-HVDC) and the permanent magnet synchronous generator (PMSG)-based wind farms with long AC transmission lines. However, the influencing factors have not been properly analyzed. In this paper, these are deconstructed and mathematically analyzed from detailed small-signal impedance equations in the dq-frame and the corresponding Bode stability criterion. Distinguishing conclusions from existing papers are obtained by studying the controllers’ bandwidths instead of their coefficients. The impacts of AC line impedance on system stability are also investigated. From the analysis of their compositions in impedance structure, the VSC-HVDC bandwidths and the wind farm phase-locked loop (PLL) bandwidth and power ratio, and the AC line impedance have various influences on the system stability. Meanwhile, the wind farm outer DC voltage and inner current control bandwidths have little impact on system stability. The results of these studies show that the magnitude in the axes q-axes impedance interaction is the essential factor for system instability. Our studies also show system stability is more sensitive to the HVDC bandwidths than the wind converter PLL bandwidth. The simulation results verify our theory conclusions. Full article

This paper presents a robust multi-input multi-output (MIMO) state-feedback control scheme for a photovoltaic (PV) inverter connected to a weak grid. For a weak grid, the point of common coupling (PCC) voltage is very sensitive to the power disturbances and it is dynamically coupled to the PLL dynamics. So far, most of the control methods do not take into accounts these couplings. Therefore, in this paper, the MIMO controller was designed taking into account the dynamics of the phase-locked loop (PLL) and coupling effects between PCC voltage and the active power to enhance the system’s robustness. As result, the robust performance of the PV inverter interfaced to a weak grid was yielded. In addition, the sensitivity of the system to PLL was eliminated, allowing the use of larger PLL bandwidth even in a very weak grid. Based on the eigenvalues analysis method, a comparative study between the proposed control method and the conventional vector control method was performed. The proposed method is verified with simulations in PLECS and real-time simulations in the RT Box. The results show that the proposed MIMO control method preserves the system stability robustness against any change of grid strength, generated power and PLL bandwidth. Full article

This paper proposes an accurate quantitative segmentation method by analyzing the probability distribution of tracking variance and strict derivation based on the tracking loop theory. The segmentation points are taken as characteristics of phase lock loop (PLL) and frequency lock loop (FLL) performances, and the two factors that cause the performance difference are discriminator gain and filtering coefficient, which denote proportional and integration coefficients, respectively. The filtering coefficients lead to a difference of 2.5 dB-Hz between the FLL and PLL. Moreover, through the analysis of the normalized bandwidth and phase margin, it is found that the integration time and bandwidth need a dynamic balance to achieve the best performance. Finally, the simulation results and real data are in good agreement with the theoretical analysis results. The minimum mean error rate of the deviation between the real data and the theoretical data is only 1.8%. In the proposed method, the influence of external hardware factors on the tracking loop is removed, and the loop design factors are modeled directly. Instead of testing the denoising performance based on the ranging and angle measuring error after location calculation, the filter coefficient is proposed to evaluate the processing performance of the tracking loop objectively and directly at the theoretical level, which proposes a new performance evaluation method at the theoretical level. The results presented in this study provide theoretical support for the design of a new-type tracking loop with enhanced performances. Full article

Global navigation satellite system (GNSS) receivers use tracking loops to lock onto GNSS signals. Fixed loop settings limit the tracking performance against noise, receiver dynamics, and the current scenario. Adaptive tracking loops adjust these settings to achieve optimal performance for a given scenario. This paper evaluates the performance and complexity of state-of-the-art adaptive scalar tracking techniques used in modern digital GNSS receivers. Ideally, a tracking channel should be adjusted to both noisy and dynamic environments for optimal performance, defined by tracking precision and loop robustness. The difference between the average tracking jitter of the discriminator’s output and the square-root Cramér-Rao bound (CRB) indicates the loops’ tracking capability. The ability to maintain lock characterizes the robustness in highly dynamic scenarios. From a system perspective, the average lock indicator is chosen as a metric to measure the performance in terms of precision, whereas the average number of visible satellites being tracked indicates the system’s robustness against dynamics. The average of these metrics’ product at different noise levels leads to a reliable system performance metric. Adaptive tracking techniques, such as the fast adaptive bandwidth (FAB), the fuzzy logic (FL), and the loop-bandwidth control algorithm (LBCA), facilitate a trade-off for optimal performance. These adaptive tracking techniques are implemented in an open software interface GNSS hardware receiver. All three methods steer a third-order adaptive phase locked loop (PLL) and are tested in simulated scenarios emulating static and high-dynamic vehicular conditions. The measured tracking performance, system performance, and time complexity of each algorithm present a detailed analysis of the adaptive techniques. The results show that the LBCA with a piece-wise linear approximation is above the other adaptive loop-bandwidth tracking techniques while preserving the best performance and lowest time complexity. This technique achieves superior static and dynamic system performance being 1.5 times more complex than the traditional tracking loop. Full article

The DC-link voltage control (DVC) timescale (i.e., the frequency dynamics covering converter outer controls) instabilities in wind generation have gained increased attention recently. This paper presents DVC timescale modeling and stability analysis for multi doubly-fed induction generators (DFIGs) connected to weak AC grids. A reduced-order, small-signal model of a grid-tied multi-DFIG system, designed for DVC dynamics analysis, is firstly proposed. The model allows for the dynamic interactions among the DC-link voltage control, active power control (APC), terminal voltage control (TVC) and phase-locked loop (PLL). Eigenvalue and participation factor analyses are conducted to explore the potential instabilities and correlated critical factors for such a multi-machine system. The sensitivity studies find that instability can occur at high levels of power generations or low short-circuit ratio (SCR) conditions. In addition, the dominant mode is identified to be highly related to the PLL, and its modal damping is decreased when the bandwidths of PLLs in different generators are close. Detailed model-based time domain simulations verified the analysis above. Full article

This paper proposes a low-complexity small signal model for a 3-leg converter connected to a balanced three-phase, three-wire weak grid and synchronised to this grid using a PLL implemented in a synchronous rotating d-q axis. A thorough analysis of the system stability as a function of the PLL bandwidth and the short circuit ratio (SCR) of the grid is performed based on a linearised model. By using the proposed model, an improved design process is proposed for the commonly used dq-PLL that accounts for the potential stability issues which may occur in weak grids. Using the proposed approach, it is possible to optimise the PLL design to find the fastest PLL that can operate stably considering the SCR of the grid. In addition, the proposed model is very simple, resulting in a straightforward design tool that could also be used for online stability monitoring. The method is validated through simulations and experimental results from a 5kW laboratory system. Full article

This article presents an in-situ comparative analysis and power quality tests of a newly developed photovoltaic charging system for e-bikes. The various control methods of the inverter are modeled and a single-phase grid-connected inverter is tested under different conditions. Models are constituted for two current control methods; the proportional resonance and the synchronous rotating frames. In order to determine the influence of the control parameters, the system is analyzed analytically in the time domain as well as in the frequency domain by simulation. The tests indicated the resonance instability of the photovoltaic inverter. The passivity impedance-based stability criterion is applied in order to analyze the phenomenon of resonance instability. In conclusion, the phase-locked loop (PLL) bandwidth and control parameters of the current loop have a major effect on the output admittance of the inverter, which should be adjusted to make the system stable. Full article