Frequency Response Of System Research Articles

A Novel Approach to Robust PID Autotuner for Overdamped Systems: Case Study on Liquid Level System

This paper proposes and validates an automatic control tuning methodology based on initial frequency response. This approach facilitates the design of robust PID controllers for overdamped systems characterized by S-shaped step responses. In the prior autotuner, which is inherently robust, the critical frequency value is determined via the relay test, while process frequency response and its derivative at this frequency are found using the sine test. Our novel approach offers a fully automated calculation for these parameters based solely on the step response test (i.e., minimal information from the process), eliminating the need for additional calculations by relay and sine tests. For this aim, it estimates these values employing the first order plus dead time models. Firstly, five step response methods are introduced to ascertain the model parameters. Secondly, three alternative estimation methods for the critical frequency of the system are proposed through (i) solving a nonlinear equation, (ii) employing a linear approximation, and (iii) using a power regression. Lastly, the model parameters are then employed to calculate the system frequency response and its derivative at the critical frequency. The remaining design steps are the same as in the initial robustness-based autotuner. In the simulation studies, two types of overdamped systems are considered. The critical frequency estimation values obtained from three estimation methods are compared to each other. Additionally, the impact of the step response methods and the proposed estimation methods within the novel approach on system response and control signal are investigated. The designed controllers use a new approach to the initial autotuner and are implemented on a two-tank liquid-level system. The experimental outcomes are in accordance with the simulation results, confirming the validity and compatibility of the findings. Quantitative performance metrics are used to evaluate the effectiveness of the designs comprehensively.

Measuring the frequency response of an optical microphone system with a fiber based setup

Abstract This paper presents a measurement method for characterizing the frequency response of an optical microphone system using a purely optical approach. The use of optical methods allows to precisely determine the frequency response of the device from infra-sound up to 100 kHz in a single measurement, without the need of a reference microphone. The presented method relies on the inherently flat frequency characteristics of an optical cavity, allowing the assignment of any frequency-dependent behavior to secondary sources, such as the signal conditioning and data acquisition unit. The frequency characteristic was found to be strongly dependent on the settings of the internal amplifiers and high-pass filters, indicating the necessity of a calibration procedure if a flat frequency response is required.

Artificial intelligence-based system frequency response modeling considering contribution of inverter-based resources

Artificial intelligence-based system frequency response modeling considering contribution of inverter-based resources

Analytical approach in designing PID controller for complex fractional order transfer function

The study focuses on the fractional complex order plant model, which has gained popularity in applied mathematics, physics, and control systems. A significant contribution of this research lies in discussing the physical phenomena associated with complex plant models and their impact on system stability and robustness. The main purpose of the method presented in this paper is to tune the controller parameters to ensure the stability and robustness of the system. There are methods presented in the literature for this purpose. One of these methods is to keep the phase curve in the system frequency response flat within a certain range. However, this process is based on equating the derivative of the phase value to zero at a certain frequency and adds great mathematical complexity to the calculations. In this study, reliable analytical formulas are presented for the same purpose using a graphical approach. Since the fractional complex order plant model represents the most general mathematical form, it enables easy creation of other plant models, including integer order and fractional order plant. The reason why this plant is chosen is that this structure can be named as the universal plant, which all other structures can be built by making little variations. For instance, a transfer function having integer, real and/or complex number coefficients and/or orders can be obtained by proper determination of the parameters of the universal plant. A time delay can also be added towards researcher's desire. The main inspiration comes from studying on an inclusive plant. The method in this paper intends to tune the well‐known classical Proportional Integral Derivative controller. Thus, effectiveness of the integer order controller on various plants will be shown. This approach provides analytical calculation equations for the physical modifications of plants with integer, fractional, and/or complex coefficients and/or orders. The effectiveness of the method is demonstrated visually with different examples that include these different possible situations. The results observed in the changes of the parameters in the transfer functions were also examined. Thus, pros and cons of the variations of integer, fractional, and complex numbers on system parameters have been shown.

Monte Carlo uncertainty quantification method of pneumatic measurement tube frequency response

Abstract The pneumatic tube plays a critical role in the frequency response of the pressure measurement system, which also greatly affects the accuracy of the measurement data. This paper applied the Monte Carlo uncertainty qualification method to the pressure measurement tube system frequency response and studied the effects of four parameters, including tube length, radius, temperature, and source pressure, on uncertainty characteristics for a given tube system configuration. The reported results show the technique's applicability and flexibility and the limitations of GUM. It is found that the frequency response and corresponding uncertainty are not directly related to frequency but are closely related to the natural frequencies. Comparative experimental results show that the longer tube significantly reduces the system's natural frequencies and intensifies the phase lag. In addition, larger tube radius and source pressure result in larger amplitude response peaks. Closed to the natural frequencies, with the increase of the parameter, the uncertainties of frequency response value and the corresponding variation range increase for tube radius and source pressure while decreasing for temperature and tube length.

A primary joint frequency regulation strategy for wind-thermal-storage systems considering frequency regulation deadband

Abstract For the issue of system frequency stability in low-inertia regions, a primary joint frequency regulation strategy for wind-thermal-storage systems considering frequency regulation deadbands is proposed. First, a system frequency response model incorporating wind-storage frequency regulation deadbands is constructed to analyze the dynamic impact of deadband variations on grid frequency. Next, the timing of frequency regulation actions in the wind-storage system is determined by manually setting the frequency regulation deadband. Finally, the effectiveness of the proposed strategy is validated using a large disturbance excitation method.

Spectral element method for random vibration analysis of the vehicle-track coupling system

In this paper, we propose a new random vibration analysis model for the vertical vehicle-track coupling system, which combines the symplectic method and the spectral element method (SEM) to enhance calculation efficiency and accuracy. The model assumed that the vehicle is composed of a multi-rigid body with 10 DOFs, and its motion equation is derived using the traditional frequency analysis method. Tracks are considered periodic structures, and the part between sleeper support points is considered a substructure. The motion equation of the periodic track-substructure is established by spectral element method (SEM), and the propagation of vibration wave between the substructures is calculated by the symplectic method. The frequency responses of the vehicle-track coupling system are calculated by using the German low-interference irregularity spectrum and short-wave irregularity spectrum as excitation. Then, the rationality of this method is verified by comparing it with the results from the traditional symplectic method and simulations using Universal Mechanism software. The comparison shows that this method surpasses the traditional symplectic method in high-frequency accuracy while maintaining high computational efficiency. Although the finite element method also has the capability for high-frequency analysis, this method can calculate the high-frequency vibration of an infinitely long track using just one element, making it more suitable for the efficient analysis of vehicle-track coupling systems. Finally, the model is applied to analyze the distribution characteristics of the vibration response of the coupled system in the frequency domain.

A Static/Dynamic Coupled Harmonic Balance Method for Dry Friction Systems Containing Rigid Body Modes

Abstract A harmonic balance method for underconstrained dry friction systems containing rigid body modes (HBM-RBM) is proposed. This method aims to overcome the encountered obstacle when applying the harmonic balance method to turbine blades damped by underplatform dampers (UPDs). The inspiration for HBM-RBM comes from the free interface modal synthesis method. The key innovation involves deriving the elastic inversion of the singular stiffness matrix through the elimination of rigid body modes. In this way, the general HBM framework can be adopted, and the frequency response of underconstrained dry friction systems can be solved in a static/dynamic coupled manner. The accuracy and efficiency are both verified on a lumped parameter model and a finite element model of turbines with UPDs from a real gas turbine. A comparative study between the HBM-RBM and the commonly adopted way of imposing artificial grounding springs (HBM-AGS) is conducted. Results demonstrate that the HBM-RBM holds a significant advantage over HBM-AGS, as it eliminates the need for artificial grounding springs (AGS) and avoids the necessity for numerous trial cases to determine AGS stiffness.

Minimizing phase delay of feedback control signals for electromagnetic vibrators to reduce measurement uncertainty in ultra-low frequency vibration calibration

Suppressing the distortion of ultra-low frequency (ULF) vibration waveforms produced by an electromagnetic vibrator (EMV) presents significant challenges, leading to considerable measurement uncertainty during vibration calibration. A phase delay minimization method for feedback control signals is proposed to reduce the harmonic distortion of ULF vibration waveforms. The method quantitatively describes the influence law of the active viscoelastic approach on system frequency response characteristics. By selecting appropriate active stiffness and damping coefficients, the method minimizes the phase delay of the feedback control signal, thereby enhancing the disturbance suppression capability of the displacement and velocity composite negative feedback control. Experimental results indicate that harmonic distortion of the vibration waveform is reduced to less than 1.70 % within the ULF frequency range of 0.001 Hz ≤ f ≤ 1 Hz. Furthermore, the amplitude sensitivity calibration uncertainty, which arises from vibration waveform distortion, has been reduced to 0.038 % (k = 1.8), thereby improving the accuracy of vibration calibration.

Towards non-virtual inertia control of renewable energy for frequency regulation: Modeling, analysis and new control scheme

Currently, when renewable generation participates in frequency regulation, the traditional control method is to emulate synchronous generators through virtual inertia control. However, virtual inertia has a time delay, so essentially, it is a fast power response. Meanwhile, virtual inertia control is likely to be affected by frequency fluctuation since it responds to the derivative of frequency. Hence, it’s worth exploring non-virtual inertia control for renewable energy when participating in frequency regulation. For this reason, a novel two-segment droop control scheme for renewable energy frequency regulation is proposed in this research. Firstly, the extended system frequency regulation (SFR) model, which contains virtual inertia with time delay, is built and analytically solved by order decrement based on the Routh approximation method. Afterwards, according to the analytical solution, time delay affects the frequency response of renewable energy. It can also be analytically proved that the non-virtual inertia control, e.g., sole droop control, could replace virtual inertia under the same frequency deviation. Still, more energy may be needed for frequency regulation. Furthermore, a novel two-segment droop control is presented, and to analytically prove its ability to replace virtual inertia, the impulse function balancing principle and the integration by parts algorithm were adopted to address the initial conditions of the differential equation. Based on the analytical expression, it can be analytically proved that a lower frequency deviation can be obtained under the same frequency regulation energy. Accordingly, a parameter-setting method for two-segment droop control was proposed. Finally, the effectiveness of the proposed method is verified by using a two-area system frequency response model, and the results reveal that it can be used to replace virtual inertia and has better performance.

New Safety Feedback Control Design to Guarantee Adequate Frequency Performance in Microgrids

ABSTRACTSafety analysis of power systems is concerned with the system's ability to maintain critical variables within specified limits following a disturbance. Frequency control adequacy has become increasingly important as the system inertia decreases due to the increase in renewable energy penetration. Various controllers for inverters have been proposed to improve the system frequency response and few are capable to ensure the safety of the response. In this article, a diesel‐wind energy system is considered and modeled as a switching system between normal, faulted, and post‐fault modes. A safety feedback controller is designed as a supplementary signal for a wind turbine generator such that the speed of the diesel generator stays within a permissible range in the presence of a finite energy disturbance. Numerical results on the modified 33‐bus microgrid system obtained of the proposed novel approach indicate that the suggested control configuration can guarantee adequate frequency response without excessive conservativeness.

A novel frequency constrained unit commitment considering VSC-HVDC's frequency support in asynchronous interconnected system under renewable energy Source's uncertainty

The increasing share of renewable energy source (RES) poses a challenge to the frequency security of the power system. Frequency constrained unit commitment (FCUC) serves as an effective measure to address this challenge at the operational level. This paper introduces a novel FCUC model applicable to the asynchronous interconnected system connected by voltage source converter based HVDC (VSCHVDC), fully taking into account the frequency support capability of VSCHVDC in order to reduce the demand for synchronous generators' inertia and reserve while ensuring frequency security, thereby lowering operating costs. Additionally, the uncertainty of RES is also considered. The constraint expressions for three frequency indicators are derived based on a system frequency response model that includes frequency support from VSCHVDC. The proposed model optimizes unit commitment, generation and reserve dispatch and VSCHVDC transmission power and frequency response parameters, while addressing RES uncertainty using the distributionally robust chance constrained approach. In response to the highly nonlinear characteristics of the maximum frequency derivation (MFD) constraints, we propose an intelligent sampling-based support vector machine to convexify the MFD constraints and introduce a two-stage decomposition algorithm for solving the model. The effectiveness of the proposed model is demonstrated based on a modified IEEE RTS-79 system.

Advanced frequency control schemes and technical analysis for large-scale PEM and Alkaline electrolyzer plants in renewable-based power systems

Integrating electrolyzers into power systems can significantly contribute to sustainable energy via the generation of green hydrogen while also enhancing frequency stability through effective regulation of the electrolyzers’ operating power. This study gives a comprehensive analysis of large-scale electrolyzer plants when providing frequency support to power systems. First, the authors present a model predictive control (MPC)-based secondary frequency controller, combined with a droop controller as the primary frequency controller and a virtual inertia controller. Additionally, the study introduces a universal system frequency response (U-SFR) modeling approach that enables high accuracy, low computation burden, and reduced initial parameters as a testbed. Finally, an in-depth analysis is conducted, focusing on different technical aspects of large-scale electrolyzer plants when providing frequency support services. Case studies integrating PEM and Alkaline electrolyzers into the modified IEEE 39-bus system with over 50% wind power penetration are conducted. It is found that the proposed U-SFR model achieves high accuracy with lower computational time compared to detailed physical models. Additionally, model predictive controllers improve frequency quality more effectively than PID and PID-FLC methods. PEM electrolyzers are found to be more efficient in providing grid frequency support than alkaline electrolyzers due to their technical characteristics. Finally, smaller hydrogen tanks may frequently breach storage constraints, negatively impacting the system’s frequency response capability.

A Simplified Dynamic Model of DFIG-based Wind Generation for Frequency Support Control Studies

In recent years, wind generation has been fast growing and become one of the major generation resources in power systems. Since the wind generation does not inherently equip with frequency support functions, the power system frequency response degrades as the wind penetration increases. Therefore, frequency support control of wind generation has gained increasing focus. However, the dynamic models of wind generation systems, which are required by the control design and analysis, are commonly very complicated and difficult to obtain, especially for the doubly-fed induction generator based wind turbine (DFIG-WT). In this paper, the authors propose a simplified dynamic model for the DFIG-WT. The proposed analytical model is derived from the detailed model by selectively neglecting very fast dynamics while keeping the critical ones. It is suitable for frequency control studies. The model accuracy is first validated against the detailed DFIG-WT model in Simulink. Then, the wind frequency control function is studied based on the proposed model.

Research on The Influence of Continous Damping Control Shock Absorber on Frequency Response Function of Spindle Coupled Road Simulation Test Bench

When the semi-active suspension is tested based on the 6-DOF spindle coupled road simulation test bench, the traditional test method is no longer applicable, because the continous damping control shock absorber of the original vehicle controller cannot be used and the overall nonlinear of the system is stronger. At present, there are few related engineering applications in the industry. This paper introduces the current reproduction technology of semi-active suspension on the 6-DOF spindle coupled road simulation bench and researches the difference of the system frequency response function by excitation of continous damping control shock absorber with different control current.

Data integrity cyber-attack mitigation using linear quadratic regulator based load frequency control in hybrid power system

Abstract Hybrid power systems are the contemporary solution to meet the stiff climate change targets and also hold future for implementing distributed generation and microgrids. These systems have renewable sources as their key elements which in turn have high level of intermittency due to weather conditions and other reasons. At the same time, these hybrid power systems are also vulnerable to cyber threats owing to the intense adoption of various IoT Technologies (Internet of Things). Load frequency control (LFC) is a formidable task for the system operators under such scenario and robust control strategies are required to achieve the load frequency within tolerable limits. In this work Linear quadratic controller (LQR) has been proposed to address the challenges of hybrid power systems. Two area interconnected power systems are considered in this work with each one having different configuration with respect to source of power generation. Solar, wind, geo-thermal, electric vehicle charging infrastructure and pumped storage power plant are integrated together with conventional thermal power plant for showcasing the LQR based controller under data integrity cyber-attack scenario. The frequency response of the hybrid power system is demonstrated through MATLAB simulations.

Signal Components and Impedance Spectroscopy of Potential p‐Si/n‐CdS/ALD‐ZnO Solar Cells: EIS and SCAPS‐1D Treatments

AbstractA silicon heterojunction (SHJ) solar cell with the attractive and widely used atomic layer deposited (ALD)‐ZnO/n‐CdS/p‐Si configuration is examined in this work to learn more about its electrical properties. Using EIS and SCAPS‐1D, a comprehensive model of the device is created and then simulated. Theoretical aspects of the cell are examined through the use of similar electrical circuit models, focusing on the transmittance spectrum made possible by the ALD‐ZnO layer's low reflectance and high visible transmittance. In this study, the C–V tool is used to study the trap states in the silicon absorber layer under different lighting conditions and wavelengths. The doping concentration and built‐in potential are determined using the Mott–Schottky technique. In addition, the cell's properties are investigated by measuring its G–V, G–F, C–T, and C–F in different real‐world scenarios. As a means of visualizing the electrochemical impedance data, Nyquist plots—sometimes called Cole–Cole plots—are utilized. By utilizing absolute impedance and phase shifts, Bode plots are employed to examine the system's frequency response. Last, the results of the SHJ cell's spectral response measurements are given, which confirm the results of the Nyquist plots.

Unit commitment of power systems considering system inertia constraints and uncertainties

AbstractLarge‐scale integration of renewable energy into the power grid results in a lack of system inertia, posing challenges to the optimal operation and scheduling of systems considering frequency stability. This article proposes a unit commitment model that considers both inertia constraints and the uncertainty of load and renewable energy. First, the time‐domain expression of the system frequency response is calculated based on the aggregated System Frequency Response (SFR) model, considering the system's maximum frequency deviation and the maximum Rate of Change of Frequency (RoCoF) limit. This calculation determines the minimum inertia requirement for the system. Furthermore, inertia constraints suitable for mixed‐integer programming model are derived to address the nonlinearity of conventional frequency constraints. Second, considering the uncertainties of load and wind energy from renewable sources, a unit commitment model with inertia constraints is constructed, and a robust method is used to solve the uncertainties. Finally, the accuracy of the proposed inertia constraints and unit commitment model is validated using case study of IEEE standard test cases and a provincial power grid in China.

Experimentally validated passive nonlinear capacitor in piezoelectric vibration applications

Abstract Piezoelectric vibration isolation and energy harvesting applications have been extensively studied in the literature. The studies include linear and nonlinear approaches. Linear methods are simpler but possess inherent limitations. On the other hand, nonlinear ones could perform better over a broader operating frequency range. Nonlinearity can be introduced in the mechanical domain or electrical domain actively or passively. Since electrical components can be on smaller scales compared to mechanical counterparts, inducing nonlinearity on the mechanical system through the electrical domain can be more practical. Moreover, passive structures require no energy supply and controller therefore they are simpler and more reliable than active ones. In this paper, a novel way to attain passive hardening stiffness was suggested by introducing an electrical component in a shunt circuit for passive nonlinear piezoelectric vibration isolation or energy harvesting applications and the induced structural non-linearity is demonstrated experimentally. A passive nonlinear component is suggested to be a hardening capacitor obtained by the P–N junction. An analytic model is derived for parallel connected macro-fiber composite (MFC) piezoelectric material attached bimorph configuration on a cantilever beam and the model is solved numerically. MFC integrated bimorph model, and P–N junction approximate model are presented. The frequency response of the coupled system is obtained by using numerical models and experiments. Both numerical analysis and experiments validated the hardening stiffness effect of the P–N junction. To the best of the authors’ knowledge, this study is the first study to demonstrate that nonlinear capacitance of P–N junctions can be used to attain nonlinearity in a mechanical system.

Improving primary frequency response in photovoltaic systems using hybrid inertia and intelligent control techniques

Abstract Low inertia poses a significant challenge to the widespread integration of photovoltaic (PV) systems into the grid, particularly affecting frequency stability. This paper addresses this challenge by proposing an advanced hybrid inertia (AHI) approach, characterized by the integration of real and virtual inertia, combined with the application of intelligent control techniques, to enhance the primary frequency response of a PV system. Internal inertia is provided by a synchronous generator (SG) acting as a compensator, while virtual inertia is generated through a real-time deloading strategy in the PV plant. The AHI is implemented on an isolated grid, utilizing various intelligent control techniques to improve frequency stability. The intelligent techniques employed include genetic algorithms (GA) and fuzzy logic controllers (FLC), which do not require mathematical modeling. This allows them to overcome the nonlinear dynamics of the PV plant and the uncertainties associated with climatic changes. These techniques are applied to the nonlinear components on the generator side, including the governor loop, DC-DC converter loop, and power reserve injection management loop. A frequency fluctuation scenario, induced by generating power perturbations in the proposed system, demonstrates and validates the improvement in frequency stability achieved by the HI and intelligent techniques. All tests are conducted using MATLAB Simulink. Various simulation results show a significant improvement in frequency stability through the incorporation of HI and intelligent control techniques.