Transient Frequency Response Research Articles

A Novel VSG with Adaptive Virtual Inertia and Adaptive Damping Coefficient to Improve Transient Frequency Response of Microgrids

This paper proposes a combined adaptive virtual Inertia and adaptive damping control of a virtual synchronous generator (AID-VSG) to improve the dynamic frequency response of microgrids. In the proposed control scheme, the VSG’s virtual inertia and damping coefficients adapt themselves during the transients to, respectively, reduce frequency deviations and increase the oscillations’ damping. In addition, as an important feature, the proposed AID-VSG is suitable for distributed control scheme applications and is designed to not rely on phase-locked loop (PLL) measurements, which avoids PLL stability issues on weak grids. The control parameters of the proposed AID-VSG are tuned by the particle swarm optimization (PSO) algorithm to minimize the overshoot and settling time of the microgrid’s frequency during an islanding event. The AID-VSG is validated by a comparative analysis with three existing VSG control schemes, also tuned by the stated optimization algorithm. The performance of each compared VSG strategy is evaluated through the simulation of a set of 10,000 initial conditions, using the islanded microgrid’s nonlinear model. The best response among the VSG strategies was achieved by the proposed AID-VSG control for both the optimization problem and the set of initial conditions’ simulations.

Enhancement of frequency transient response using fuzzy-PID controller considering high penetration of doubly fed induction generators

In modern power systems, renewable-based power plant such as wind power system is integrated significantly. Among numerous types of wind power systems doubly fed induction generators (DFIG) is becoming favorable in the last few years. However, adding a wind power plant could give a new challenge to the power system, especially in frequency stability. Hence, it is important to control the frequency of the power system to be able to find its initial condition in every condition. Generally, the frequency of the power system can be controlled by using automatic generation control (AGC). AGC is used to maintain the balance between generating capacity and the load by adding integral control to the governor. However, with more and more wind power systems in the grid conventional AGC is unsuitable. Hence, it is important to have an advanced AGC based on the artificial intelligence method. This paper proposed the application of fuzzy-proportional integrator derivative (fuzzy-PID) for AGC in power systems considering the high penetration of wind power systems. From the simulation results, it is found that the proposed method can reduce the overshoot and accelerate the settling time of frequency better than using conventional AGC.

Transient frequency response test and measurement error prediction of DCTV based on adaptive inertial weight improved ACO

AbstractA temporary frequency response test and measurement error prediction method of direct current voltage transformer (DCTV) based on artificial intelligence (AI) is proposed. Firstly, the frequency characteristic of direct current (DC) side voltage of DCTV is analyzed. On this basis, a DCTV transient Frequency Response testing method based on transient alternating current (AC) & DC superposition was developed. Then, the method of voltage sudden change and phase correction is used to achieve transient process DCTV response time testing. Finally, the ant colony optimization (ACO) algorithm was improved by combining an adaptive inertia weight improvement strategy, achieving accurate prediction of the Measurement Error of DCTV. The proposed AI based DCTV transient Frequency Response testing and Measurement Error prediction method were compared and analyzed with the other three methods through simulation experiments. Compared to the other three comparison methods, the maximum transformation error in the evaluation indicators of mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE) decreased by 0.006, 0.0119, and 0.0085, respectively, while the maximum phase error decreased by 0.2794, 0.3004, and 0.2823, respectively.

Exploring Transient Voltage and Frequency Responses in Low Inertia Power Systems: A Comparative Study of Grid Following and Grid Forming Battery Energy Storage Systems

Exploring Transient Voltage and Frequency Responses in Low Inertia Power Systems: A Comparative Study of Grid Following and Grid Forming Battery Energy Storage Systems

Hybrid Model-Based BESS Sizing and Control for Wind Energy Ramp Rate Control

This paper presents a hybrid model constituting dynamic smoothing technique and particle swarm optimization techniques to optimally size and control battery energy storage systems for wind energy ramp rate control and power system frequency performance enhancement. In today’s modern power system, a high-proportion renewable energy grid is inevitable. This high-proportion renewable energy grid is a power system with abundant integration of renewable energy resources under the presence of energy storage tools. Energy storage tools are integrated into such power systems to balance the fluctuation and intermittence of renewable energy sources. One of the requirements in a high-proportion renewable energy grid is the fractional power balance between generation and load. One of the requirements set by power system regulators is the generation variation between two time points. A power producer is mandated to satisfy the ramp rate requirement set by the grid owner. This paper proposes dynamic smoothing techniques for initial size determination and particle swarm optimization based on optimal sizing and control of battery energy storage systems for ramp rate control and frequency regulation performance of a power system integrated with a large percentage of wind energy systems. Wind energy data taken from Zhangjiakou wind farm in China are used. The results indicate that the battery energy storage system improves the ramp rate characteristics of the wind farm. In addition, the virtual inertia capability of the battery energy storage system enabled the transient and steady-state frequency response of the test power system to improve significantly.

Retooling results of a massive database of home theater measurements

In 2010 the first results of a large-scale measurement program on home theaters was reported in an AES presentation. More than 1,000 rooms were measured for impulse response from each of a minimum of six loudspeakers to at least four (usually more) listening locations. However, computer processing capacity limited the initial report to 275 rooms. Room acoustics and sound system information was reported: RT and its std. dev. with frequency, room volume statistics for those rooms, and transient and steady-state frequency response for some example rooms were shown. From these few rooms an important item of interest emerged: the Schroeder frequency did not show as a boundary of response deviations between lower and higher frequencies—the average deviation from the average response was more constant with frequency than expected. This work will be briefly reviewd. Now in 2022 a new look at this data plus that which was gathered in the intervening years may be studied with much more advanced math tools such as machine learning so much more can be understood. This presentation is interim describing work to be done and soliciting comments from practitioners.

Metamaterial based piezoelectric acoustic energy harvesting: Electromechanical coupled modeling and experimental validation

Piezoelectric energy harvesting technology utilizing acoustic metamaterials investigated by experiment and simulation improves the sound energy density and conversion efficiency. A fully coupled electromechanical model in both the mechanical and electric domains is crucial for accurate prediction and optimization of acoustic metamaterial based on sound energy harvesting. Based on the Kirchhoff thin plate theory, constitutive laws of isotropic aluminum substrate and transversely isotropic piezoelectric bimorph, the electromechanical coupled governing equation in the mechanical domain is deduced for a two-dimensional acoustic metamaterial based piezoelectric energy harvester. Each piezoelectric layer is represented as a current source in series with its internal capacitance for derivation of the electromechanical coupled governing equation in the electrical domain via Gauss’s law and Kirchhoff’s laws. With generalized boundary conditions, modal analysis is performed using the Galerkin method and Kelvin-Kirchhoff condition. The general transient response and frequency response functions are obtained under the excitation of sound waves and the reaction forces of the silicone rubbers. The time-history, power spectrum and phase portrait of the measured harvested voltage at 90 fixed frequencies agree well with the model predictions. The theoretical maximal harvested power is 3.09 mW, with the optimal resistance of 28180 Ω and inductance of 0.28H connected in parallel. Near the resonant frequency, the utilization rate of converting sound energy into electrical power is maximized. The proposed electromechanical coupled model can be used as a basis for further topology design and optimization and underlying physics for experimental study.

Steady-state and transient vibration analysis of a thermally loaded power law-based functionally graded rotor system with induced porosities

The dynamic analysis of a power law-based functionally graded (FG) rotor-bearing system with induced porosities for non-uniform porosity distributions has been performed using the finite element method. A novel porous rotor element considering the effects of transverse shear deformation, gyroscopic moments, translational and rotational inertial has been developed for non-uniform porosity distributions based on the Timoshenko beam theory. Material properties are graded based on the power law along the radial direction of the FG shaft. The nonlinear temperature distribution law has been considered in conjunction with the power law to vary the temperature across the cross-section of the FG shaft. Material is graded in such a way that the stainless steel is comprised at the core of the FG shaft and the outer periphery of the FG shaft is made of Zirconia. The steady-state and transient time and frequency responses of a thermally loaded porous FG rotor-bearing system have been computed for both types of uneven porosity distribution using the Houbolt time marching technique and Fast Fourier Transform, respectively. The free vibration analysis has also been performed on the porous FG rotor-bearing system for various parameters such as power law index, the volume fraction of porosity and porosity distribution under different thermal gradients. The reduction of critical speed with increased amplitude is observed from the steady-state and transient frequency responses with an increase in volume fraction of porosity and temperature gradients

Steady State and Transient Vibration Analysis of an Exponentially Graded Rotor Bearing System Having a Slant Crack

The dynamic behaviour of a slant-cracked exponentially graded (EG) rotor-bearing system has been investigated using the finite element method for flexural vibrations. A two nodded EG rotor element has been developed based on the Timoshenko beam theory. Local flexibility coefficients (LFCs) of a slant-cracked EG shaft element have been derived using fracture mechanics concepts to develop the stiffness matrix of a cracked EG element. The steady-state and transient vibration responses of cracked and uncracked rotor systems have been simulated using the Houbolt time marching method. When a crack is present in the shaft, the subharmonic frequency peaks are centred on operating speed in the steady-state frequency responses, whereas on critical speed in the transient frequency responses at an interval frequency corresponding to the torsional frequency. It has been found that the crack parameters such as crack depth and location, temperature gradients and torsional frequencies have a significant influence on natural frequencies and dynamic responses, which could be implemented for efficient rotor crack detection methodologies.

A piezo stack energy harvester with frequency up-conversion for rail track vibration

To enable predictive and preventive maintenance in rail transportation systems, energy harvesting is a promising powering method. Piezoelectric energy harvesters have great powering potential, but so far the power harvested by piezoelectric railway generators is low. To explore the capability, this work presents a piezo stack energy harvester with frequency up-conversion method consisting of both the inertial mass system and the piezo stack transducer system from rail track vibration energy harvesting. The frequency up-conversion method uses the impact between the inertial mass system and the piezo stack transducer system to enable the piezoelectric transducer to operate at the transient resonant frequency response in spite that the input vibration frequency is much lower than the transducer one to achieve high-power generation. A theoretical model considering the impact between the two systems is established to describe the motion of the energy harvester. Numerical simulation and finite element analysis are conducted to model the proposed energy harvester and compared with experimental results to validate the proposed method. The time-dependent reactions, the frequency response characteristics, and the influence factors on output such as impedance, initial interval, acceleration, signal waveform are studied to evaluate the energy harvesting performance. In the experiments, the proposed energy harvester outputs a maximum power of 495.74 mW and an average power of 43.58 mW at an input rms acceleration of 0.7 g applied at 18 Hz with an optimum load impedance of 150 Ω, exhibiting good performance in comparison with the state-of-the-art piezoelectric energy harvesters applied on the rail track.

Impact localization with a weighted spectral cross correlation method

The impact localization is a typical inverse problem to identify the damage source of structures. To overcome the positioning problems of the low resolution caused by sparse reference points, a weighted spectral cross-correlation (WSCC) method is proposed. First, a mathematical model with a series of Fiber Bragg Grating (FBG) sensors is built to generate a database of transient frequency responses of each reference point when random shock happens. Second, to identify the spectrum difference between the impact point and the reference point, a cross correlation model is built by mean and normalization operations on the frequency domain. Third, to figure out the impact point among the adjacent reference points, bicubic spline interpolation is realized by subdividing the grid of the WSCC. To validate the accuracy of our suggested method, an impact localization system is designed with a multi FBG sensor network and a composite laminate. The experimental result shows that the error of our suggested method is almost ten times lower than that of other traditional methods. The weighted spectral cross-correlation has advantages in the field of structural health monitoring.

One-Parameter Controlled Non-Dissipative Unconditionally Stable Explicit Structure-Dependent Integration Methods with No Overshoot

Although many families of integration methods have been successfully developed with desired numerical properties, such as second order accuracy, unconditional stability and numerical dissipation, they are generally implicit methods. Thus, an iterative procedure is often involved for each time step in conducting time integration. Many computational efforts will be consumed by implicit methods when compared to explicit methods. In general, the structure-dependent integration methods (SDIMs) are very computationally efficient for solving a general structural dynamic problem. A new family of SDIM is proposed. It exhibits the desired numerical properties of second order accuracy, unconditional stability, explicit formulation and no overshoot. The numerical properties are controlled by a single free parameter. The proposed family method generally has no adverse disadvantage of unusual overshoot in high frequency transient responses that have been found in the currently available implicit integration methods, such as the WBZ-α method, HHT-α method and generalized-α method. Although this family method has unconditional stability for the linear elastic and stiffness softening systems, it becomes conditionally stable for stiffness hardening systems. This can be controlled by a stability amplification factor and its unconditional stability is successfully extended to stiffness hardening systems. The computational efficiency of the proposed method proves that engineers can do the accurate nonlinear analysis very quickly.

Deep learning identifies leak in water pipeline system using transient frequency response

Pipeline leak identification method using transient frequency response (TFR) has been researched in the past two decades. To extend this method to a more general water pipeline system with hydraulic uncertainties, this work (1) introduces deep learning (DL) into the TFR-based leak identification framework and (2) develops extended TFR equations in matrix form for DL learning set generation. In this framework, TFR equations are firstly solved in a pre-calibrated hydraulic model of the system to extract frequency response function (FRF) for the training set preparation. Then the simulated FRFs are fed to train fully linear DenseNet (FL-DenseNet) for feature recognition. Finally, the measured FRF of the system is fed to the trained FL-DenseNet to identify a leak to a pipe in the suspected leak area. A study on a hypothetical small system shows that the proposed framework has robustness against uncertainties of friction coefficient, wave speed, and leak flow. A significant advantage is also observed over the existing method with an inaccurate model. Then the framework is applied to a larger network. Over 90% of the synthetic leaks are identified in 5 of the 149 pipes. These results presented in the paper indicate the potential of applying this framework to a water pipeline system.

Efficient leak detection in single and branched polymeric pipeline systems by transient wave analysis

The widespread use of plastic pipes in different fluid conveyance systems has greatly driven the recent development and application of transient-based methods (TBMs) for leak detection in viscoelastic/polymeric pipelines. Current TBMs for viscoelastic pipe leak detection are usually achieved by a two-step procedure, namely viscoelastic parameters identification and leak detection, which requires the pre-knowledge of intact system states (i.e., non-leak) for comparative analysis. This paper presents an efficient single-step frequency domain inverse transient analysis (FDITA) method for simultaneous identifications of viscoelastic parameters and leaks in plastic pipes, so as to enhance the applicability and accuracy of TBMs. Both the single and branched polymeric pipe systems are applied for the method development and application. To this end, analytical solutions of single and branched systems from the transfer matrix method are firstly derived to represent the transient frequency responses of viscoelastic pipelines with leaks. A global optimized nonlinear curve fitting method is then employed to identify both viscoelastic parameters and potential leaks by knowing/measuring other system and flow conditions. Extensive experimental validations and numerical applications of both single and branched pipe systems demonstrate the very good efficiency and accuracy of the developed method for leak detection in different viscoelastic pipe systems. Furthermore, the mechanism of transient wave-leak-viscoelasticity is analysed based on these application results and theoretical evidence. Finally, a sensitivity analysis is performed to quantify and discuss the advantages and potential limitations of the developed method in the paper.

MPC-Based Arctan Droop Control Strategy of the Parallel Inverter System in an Islanded AC Microgrid

Distributed generations (DG) are one of the upcoming technologies recently used by many electric utilities in all corners of the world. Most of those DG form the microgrid (MG) to serve local loads and can be connected to the grid. This DG’s technology is enabled by utilizing renewable energy sources (REs) that are ecofriendly; however, these REs are intermittent by their nature, so controlling a power electronic device interfaced with them to be connected to the grid is another challenge. Many researchers have worked on the inverters’ control in MG. This study also elaborates on the control strategy for inverters adapted to REs for proper control of voltage and frequency used in an islanded microgrid. The study proposes a hybrid control strategy made of the virtual impedance droop control with arctan function and model predictive control. Extensive simulations have been carried out to validate the proposed control strategy’s effectiveness in terms of rapid transient response and stabilization of voltage, frequency, and power equitability among the microsources in the islanded microgrid.

Distributed layered control and stability analysis of islanded networked-microgrids

Networked-microgrid (NMG) system has a much more complex structure with larger control difficulties and complicated dynamic behaviors. This paper firstly proposes a layered distributed control framework for NMG system, which is comprised of two layers: individual MG control layer and NMG control layer. The NMG control layer generates the voltage/frequency reference for the MG control layer. Particularly, to improve the system transient frequency response, each MG layer controller is designed to provide virtual inertia to the whole system. Secondly, a small-signal model for a generalized single-bus NMG system is derived to analyze the impact of coupling among MGs and various parameters on NMG dynamic stability. It reveals that the coupling relationship among MGs will weaken the stability of the whole NMG system while the proper control parameters can facilitate the stability. Besides, the delay effect on NMG system stability is also analyzed. Lastly, the proposed control framework and analytical result are verified by time-domain simulations under various cases considering various cases of load change, different virtual inertia and communication delay.

An Improved Synchronization Stability Method of Virtual Synchronous Generators Based on Frequency Feedforward on Reactive Power Control Loop

The synchronization stability of the virtual synchronous generator (VSG) under grid fault is an important issue for maintaining stable operation in the power system. Existing work has pointed out a low-pass filter (LPF) with a sufficiently low cutoff frequency in the reactive power control loop (RPCL) can improve the transient stability. Yet, the underlying mechanism was unknown. Moreover, as a key index of VSG and precondition of synchronization stability, the frequency response is rarely studied. In this article, based on the linearized model for qualitative analysis, combined with the nonlinear model for quantitative analysis, the underlying mechanism of improving synchronization stability using an LPF in the RPCL is revealed. Furthermore, to avoid increasing the system order and solve the conflict between transient stability and frequency response, an improved synchronization stability method is proposed by feedforwarding the frequency difference between the VSG and grid to the RPCL. The frequency response is also acquired based on the combined linearized and nonlinear model, which shows that the frequency feedforward method can further enhance the frequency stability. How to design the coefficient of the frequency feedforward path with different inertia requirements is also presented. Finally, this method is verified by experimental results.

A New Approach to the Fault Location Problem: Using the Fault’s Transient Intermediate Frequency Response

The fault location problem has been tackled mainly through impedance-based techniques, the travelling wave principle and more recently machine learning algorithms. These techniques require both current and voltage measurement. In the case of impedance-based methods they can provide multiples solutions. In the case of the travelling wave approach it usually requires high sampling frequency measurements together with sophisticated identification algorithms. Machine learning techniques require training data and re-tuning for different grid topologies. This paper proposes a new fault location method based on the fault’s transient intermediate frequency response of the system immediately after a fault occurs. The transient response is characterized by the travelling wave phenomenon together with intermediate frequencies of oscillation, which are dependent on the faulted section and the fault location. In the proposed fault location solution, an offline methodology identifies these intermediate frequencies and their dependency on the fault location is fitted using a polynomial regression. The online fault location is performed using those polynomial regressions together with voltage measurements from the system and simple signal processing techniques. The full method is tested with an EMT simulation in PSCAD, using the exact frequency dependent model for underground cables.

Research on Reduced-Order Modeling of Droop Controlled Inverter Suitable for Analysis of Transient Characteristics

Under the background of a large number of converters connected to the power grid, the converter’s weak overcurrent capability and poor anti-interference ability bring challenges and hidden dangers to the transient safe and stable operation of the power grid. It is urgent to carry out the transient characteristics analysis of the converter. Numerical simulation calculation is an important means to study transient characteristics. However, numerical simulation is time-consuming and poor in generality, which greatly limits the study of transient characteristics of systems with multiple converters. In this paper, the vertical control is the object, and the inverter reduced-order simplified model suitable for different transient stability problems is studied. First, a full-order model of the droop control inverter is established, and the singular perturbation method is used to complete the extraction of system characteristic roots and the analysis of participating factors. Then, according to the droop control of the inverter’s power angle, voltage, and frequency transient response process, accuracy and rapidity are selected as the goals, and a reduced-order simplified model suitable for different transient stability analysis is obtained. The transient characteristic analysis of the numerical simulation of the converter system provides a reduced order reference.

New Second-Order Sliding Mode Control Design for Load Frequency Control of a Power System

The implementation of the sliding mode control (SMC) for load frequency control of power networks becomes difficult due to the chattering phenomenon of high-frequency switching. This chattering problem in SMC is extremely dangerous for actuators used in power systems. In this paper, a continuous control strategy by combining a second-order mode and integral siding surface is proposed as a possible solution to this problem. The proposed second-order integral sliding mode control (SOISMC) law not only rejects chattering phenomenon in control input, but also guarantees the robustness of the multi-area power network, which has an effect on parametric uncertainties such as the load variations and the matched or mismatched parameter uncertainties. Moreover, the reporting of the simulation indicates that the proposed controller upholds the quality requirement by controlling with operating conditions in the larger range, rejects disturbance, reduces the transient response of frequency, eliminates the overshoot problem, and can better address load uncertainties compared to several previous control methods. The simulation results also show that the proposed SOISMC can be used for practical multi-area power network to lessen high parameter uncertainties and load disturbances.