Rate Of Change Of Frequency Research Articles

Quantifying the frequency modulation in electrograms during simulated atrial fibrillation in 2D domains

Atrial fibrillation (AF) affects millions of people in the world, causing increased morbidity and mortality. Treatment involves antiarrhythmic drugs and catheter ablation, showing high success for paroxysmal AF but challenges for persistent AF. Experimental evidence suggests reentrant waves and rotors contribute to AF substrates. Ablation procedures rely on electroanatomical maps and electrogram (EGM) signals; however, current methods used in clinical practice lack consideration for time–frequency varying EGM components. The fractional Fourier transform (FrFT) can be adopted to capture time-varying frequency components, thereby enhancing the comprehension of arrhythmogenic substrates during AF for improved ablation strategies. To this end, a FrFT-based algorithm is developed to characterize non-stationary components in EGM signals from simulated AF episodes. The proposed algorithm comprises a pre-processing step to enhance the coarser features of the EGM waveform, a windowing process for dynamic assessment of the EGM, and a FrFT order optimization stage that seeks compact signal representations in fractional Fourier domains. The resulting order is related to the rate of frequency change in the signal, making it a useful indicator for frequency-modulated components. The FrFT-based algorithm is implemented on EGM signals from AF simulations in 2D domains representing a region of the atrial tissue. Consequently, the computed optimum FrFT orders are used to build maps that are spatially correlated to the underlying propagation dynamics of the simulated AF episode. The results evince that the extreme values in the optimum orders map pinpoint the localization of fibrillatory mechanisms, generating EGM activation waveforms with varying frequency content over time.

Study on the Driver Visual Workload in High-Density Interchange-Merging Areas Based on a Field Driving Test.

A visual workload model was constructed to determine and evaluate drivers' visual workload characteristics in high-density interchange-merging areas. Five interchanges were selected, and a real-vehicle driving test was conducted with 47 participants. To address the differences in drivers' visual characteristics in the interchange cluster merging areas, the Criteria Importance Through Intercriteria Correlation (CRITIC) objective weighting method was employed. Six visual parameters were selected to establish a comprehensive evaluation model for the visual workload in high-density interchange-merging areas. The results show that the average scanning frequency and average pupil area change rate are most strongly correlated with the visual workload, whereas the average duration of a single gaze has the lowest weight in the visual workload assessment system. Different driver visual workloads were observed depending on the environment of the interchange-merging areas, and based on these, recommendations are proposed to decrease drivers' workload, thereby increasing road safety.

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.

Optimal Battery Storage Configuration for High-Proportion Renewable Power Systems Considering Minimum Inertia Requirements

With the continuous development of renewable energy worldwide, the issue of frequency stability in power systems has become increasingly serious. Enhancing the inertia level of power systems by configuring battery storage to provide virtual inertia has garnered significant research attention in academia. However, addressing the non-linear characteristics of frequency stability constraints, which complicate model solving, and managing the uncertainties associated with renewable energy and load, are the main challenges in planning energy storage for high-proportion renewable power systems. In this context, this paper proposes a battery storage configuration model for high-proportion renewable power systems that considers minimum inertia requirements and the uncertainties of wind and solar power. First, frequency stability constraints are transformed into minimum inertia constraints, primarily considering the rate of change of frequency (ROCOF) and nadir frequency (NF) indicators during the transformation process. Second, using historical wind and solar data, a time-series probability scenario set is constructed through clustering methods to model the uncertainties of wind and solar power. A stochastic optimization method is then adopted to establish a mixed-integer linear programming (MILP) model for the battery storage configuration of high-proportion renewable power systems, considering minimum inertia requirements and wind-solar uncertainties. Finally, through a modified IEEE-39 bus system, it was verified that the proposed method is more economical in addressing frequency stability issues in power systems with a high proportion of renewable energy compared to traditional scheduling methods.

Comparison between FLL and PLL in frequency estimation to supply distributed virtual inertia

To connect renewable energy sources (e.g. solar or wind) on the grid, an inverter or electronic converter is used. However, a traditional inverter has no inertia in the face of frequency changes. Unlike the inertia of the rotor of a synchronous generator. Frequency variations are a product of the imbalance between the energy generated and the grid loads. If the frequency is too far from its nominal value or if the rate of change of frequency (RoCoF) is high, it can affect the synchronism of the generators that feed the grid. Therefore, power cuts are made in sectors on the grid, thus preventing instability from spreading to other sectors on the grid, which translates into large economic losses. Solutions such as inverters with virtual inertia (or emulated inertia) are a good alternative due to their structural simplicity and low cost, compared to other solutions such as synchronous condensers, for example. For the virtual inertial control strategy, the grid frequency needs to be measured. This article compares the use of a phase-locked loop (PLL) or a frequency-locked loop (FLL) for frequency estimation and its effect on inertia emulation. The proposed control designs are validated through simulations.

Enhancing power system stability with adaptive under frequency load shedding using synchrophasor measurements and empirical mode decomposition

This paper introduces an adaptive under frequency load shedding (AUFLS) scheme based on synchrophasor measurements and Empirical Mode Decomposition (EMD) to enhance power system stability during significant disturbances. The traditional UFLS methods, which rely on fixed frequency thresholds, often lead to unnecessary disconnections and a lack of flexibility. The proposed AUFLS scheme dynamically adapts to the magnitude of disturbances, frequency response, and voltage stability index, resulting in a more efficient and responsive system. Various UFLS techniques are reviewed, highlighting the advantages of adaptive strategies. The novelty of this research lies in the innovative application of the EMD algorithm within the AUFLS framework. This method identifies the center of inertia (CoI) of the rate of change of frequency (RoCoF) from frequency signals and calculates the total active power imbalance due to disturbances. Furthermore, EMD is applied to the voltage angle at each bus to identify and form coherent bus groups. These coefficients are subsequently employed to allocate the required active power shedding within each group to maintain system stability. Voltage stability indices are calculated for each group, and load shedding is distributed among the buses based on normalized voltage stability indices, thereby enhancing the precision of load shedding decisions and the overall stability of the power system. Results demonstrate that the proposed scheme provides satisfactory frequency response while requiring less load shedding compared to traditional methods, making it effective for modern power systems with high penetration of renewable energy sources (RES). The performance of the proposed scheme is assessed using the IEEE 39-bus test system, demonstrating its effectiveness in improving system resilience to frequency disturbances. The research concludes that the AUFLS scheme offers a promising approach for enhancing the resilience of power systems to frequency disturbances.

Research on defense strategies for power system frequency stability under false data injection attacks

The rapid development of cyber-physical power system has highlighted the pressing issue of cyber attacks (CAs) faced by large-scale renewable energy power systems (LREPS). The injection of false data attacks on critical electrical equipment by attackers can lead to abnormal system frequencies, triggering cascade failures and causing widespread blackouts. This paper introduces a tri-level defense model specifically crafted for LREPS, comprising an upper, middle, and lower level (defender-attacker-operator). By promoting collaborative decision-making among these agents, the model aims to mitigate the rate of change of frequency (RoCoF) and effectively withstand CAs. The upper-level employs an economic-inertia optimization strategy, scheduling generator units to maximize system inertia while minimizing generation costs. By leveraging the strong duality theorem, the tri-level model is decomposed into a bi-level model consisting of a master problem and a subproblem, solved using the Benders decomposition method. Furthermore, this paper also considers augmenting the virtual inertia of renewable energy units when defense resources are insufficient, ensuring RoCoF remains within limits after CAs. The effectiveness and superiority of the proposed model and strategy are validated through case studies based on the improved IEEE 118-bus system. The results demonstrate that the model can reduce load shedding caused by the worst-case CAs, enhance system inertia, lower RoCoF, and improve the stability of LREPS.

A hierarchical optimization technique for placement of battery energy storage system to improve grid transient stability

AbstractA battery energy storage system (BESS), due to its very fast dynamic response, plays an essential role in improving the transient frequency stability of a grid. The performance of the BESS varies with the system's installation site. Hence, the optimal location of the BESS is of utmost importance for improving transient frequency stability. Therefore, this paper presents a hierarchical approach for optimizing the BESS placement to improve a grid's transient frequency stability. In most research, frequency nadir and rate of change of frequency (ROCOF) have been considered for studying frequency stability. This paper considers two more parameters, along with frequency nadir and ROCOF, to study the transient frequency stability, settling time, and decay ratio. A novel frequency stability index (FSI) using the four transient frequency parameters has been developed. After a significant disturbance in a benchmarked test system, the FSI was used to identify the optimal location of the BESS for stabilizing the frequency. It has been observed that, after a sudden generator outage, the ROCOF and the frequency nadir improve the best when the BESS is located at the bus closest to the generator experiencing the outage. However, considering the other two parameters as well, the value of the FSI is the minimum; that is, the optimum solution is when the BESS is located at the bus that is the second closest to the generator experiencing the outage. Results of similar studies validate the proposed FSI in indicating the optimal location of the BESS in improving the transient frequency behavior of the system.

Design of osteosynthesis plate for detecting bone union using wire natural frequency

We have developed a novel osteosynthesis plate with bone union detection using a wire's natural frequency (BUDWF) to provide the quantitative result of bone union detection. The concept for detecting bone union is measuring the rate of frequency change. The frequency is measured from sound generated from the wire attached to a modified plate. The plate is modified from a Syncera ADLER B0409.10 and attached with 0.3 mm diameter 316L stainless steel wire. The sound generation mechanism was created by PEEK and installed on the plate to generate the sound. The preliminary experiments were conducted on a Sawbones tibia composite mimic. We used the cut Sawbones to create fracture samples with a 0, 0.5, 1-, 2-, and 5-mm gap representing the fractured bone with different gap sizes and prepared uncut Sawbones as a union sample. These samples were tested five times, and the sound was recorded from a condenser microphone and analyzed. We found that the BUDWF can differentiate samples with a fracture gap above 2 mm from the union sample, as the differences in the rates of frequency change between samples with a fracture gap above 2 mm and union samples were statistically significant. However, there was a limitation that the BUDWF plate was still unable to differentiate the 0 mm fracture gap and the union sample in this study.

Novel Fuzzy Logic Controls to Enhance Dynamic Frequency Control and Pitch Angle Regulation in Variable-Speed Wind Turbines

This study introduced a novel control approach based on fuzzy logic control (FLC) to enhance the frequency regulation capacity of variable-speed wind turbines (VSWTs). The proposed method integrates FLC within droop and inertia control loops. Real-time measurements of the system frequency and the rate of change of frequency (ROCOF) serve as inputs to the FLC, enabling the method to improve the frequency response by VSWTs. In addition, the method employs FLC for pitch angle frequency control, optimizing reserve power for frequency regulation under varying wind speed levels. The innovative aspect of this study lies in the simultaneous application of FLC to pitch angle frequency control and droop/inertia control, leading to the enhanced frequency regulation capability of VSWTs and smoother operation across a range of wind speeds. Compared with traditional methods, the proposed approach provides a comprehensive and effective solution to the challenges associated with frequency regulation in VSWTs. Through simulations across different wind speed scenarios, the proposed control method demonstrated the best performance among various mature methods, highlighting the efficacy of the proposed method on the frequency regulation of VSWTs under different wind speeds. This study’s findings highlight the potential of the proposed FLC-based method to optimize frequency regulation and contribute to more reliable and efficient wind energy systems.

A frequency stability assessment framework for renewable energy rich power grids

The worldwide power grid is undergoing a paradigm shift due to the rise of renewable energy sources. Traditional rotating synchronous generators are being replaced by inverter-based renewable energy sources (RESs), and this trend is expected to persist in the years to come. As a result, the grid’s inertia is decreasing gradually, which presents significant obstacles to maintaining grid frequency stability. Moreover, due to the uncertainties associated with the generation of RESs and load demand, grid inertia has become a stochastic quantity. In this paper, considering the stochastic characteristics of the power generation, load demand profile and grid inertia, a framework to assess grid frequency stability with high penetration of RESs has been presented. This framework first quantifies grid frequency characteristics at different levels of RES penetration using Monte-Carlo simulation (MCS) considering the intermittent nature of RESs and load demand. This is followed by assessment of frequency stability of the power grid using proposed matrices that quantifies the amount of deviation in grid frequency and rate of change of frequency (RoCoF) outside the boundary prescribed by the grid operator. In addition, the proposed framework evaluates the sensitivity of grid frequency stability to RES penetration levels and quantifies the resiliency against contingency. Rigorous case studies on modified IEEE 39 bus test system have been presented to demonstrate the effectiveness of the proposed framework in assessing grid frequency stability.

Voltage suppression strategy for multi-stage frequency regulation of DC-side energy storage batteries in doubly-fed induction generator

When DC-side energy storage batteries participate in frequency regulation, inconsistent inertia requirements exist for frequency deterioration and recovery stages. In addition, the frequency regulation power can lead to the DC overvoltage of the DFIG. To address these issues, this paper proposes a voltage suppression strategy (VSS) during multi-stage frequency regulation with the DC-side energy storage batteries. In the frequency deterioration stage, a SOC segmented feedback inertia control (SSFIC) is developed to reduce the frequency change rate. In the frequency recovery stage, to mitigate transient maximum frequency deviation, a maximum frequency differential inertia control (MFDIC) is constructed by incorporating the transient maximum frequency deviation into inertia control coefficient. In the frequency regulation stage, to decrease the steady state frequency deviation and avoid the secondary frequency drop, an exponential inertia droop control (EIDC) is created by considering the droop coefficient as an exponential function of the frequency change rate. To suppress the DC voltage fluctuation, a DC voltage compensation control (DVCC) is presented to transform the active power of SSFIC, MFDIC and EIDC to the d-axis current compensation increment of GSC. Extensive simulation results have proved that the proposed strategy can successfully enhance the frequency regulation and voltage suppression ability.

Decentralized utilization of distributed energy storage resources for simultaneous frequency regulation in a microgrid

A microgrid has emerged for the transformation from centralized into localized electricity generation, which increases the opportunity for renewable-based distributed generators (DGs) applications such as photovoltaic (PV) and wind as well as small-scale conventional generation units. PV and wind integration provides environmental, technical, and economic benefits. However, the low inertia of the PV system and decoupling due to the presence of the power electronics converter in the wind generation system led to a significant declination in the microgrid's inertia, which causes an excessive frequency nadir and a high rate of change of frequency (ROCOF) in the presence of disturbances. The microgrid's inertia can be enhanced by storing or releasing energy within the microgrid. The wind generation system has intrinsic kinetic energy stored in the rotating parts, while the PV system's sorted energy is improved by introducing an external supercapacitor on the DC link. The aforementioned energy storage elements provide limited energy resources, which should be employed in a proper manner. This article proposes a control scheme to boost the cooperation of wind and PV generation systems for the enhancement of inertia and frequency support. Therefore, the proposed scheme prevents excessive stress on individual generators and improves the utilization of available energy resources. For example, at load increase by 0.5 MW, with frequency support using PV only or wind only, the frequency deviation is enhanced by 44.4 % and 29.5 %, respectively. While for both PV and wind support the frequency simultaneously, the frequency deviation is enhanced by 53.3 %. In addition, with the cooperation of PV and wind, the required energy from PV and wind is reduced by 29.5 % and 13.7 % respectively and the rate of change of frequency is enhanced by 61.9 %. The energy share among PV and wind generation systems is investigated and verified by simulations; tuning formulas are also developed to attain predefined energy support with equal energy sharing among different resources. For instance, with a non-equal energy share strategy and load increases by 0.5 MW, the wind delivers almost 1.6 times the energy delivered from the PV. Hence, more stress occurs on the wind generation compared to PV. While, using equal energy share strategy, the required energy from wind is about 1.03 times the energy delivered from the PV. The proposed control scheme is applied to an AC microgrid that comprises a thermal generation plant, a PV generation system, and a doubly-feed induction generator-based wind generation system. To verify the effectiveness of the proposed scheme, different simulation cases considering load change, wind speed variation, irradiance variations, and weak grid integration are implemented. When compared to individual frequency support, the proposed scheme provides a superior response.

Fast hybrid islanding detection for DGs with inverters using maximum likelihood-based ROCOF and SFS

The present study introduces an unconventional and fast hybrid strategy for islanding detection in Distributed Generators (DGs) based on inverters. The active method utilized in this work is Sandia Frequency Shift (SFS), while the passive method is the Rate Of Change Of Frequency (ROCOF) Relay. The key contribution of this paper is the use of Maximum Likelihood to estimate the ROCOF as opposed to the conventional Phase-Locked-Loop (PLL) method. The objective of this paper is to improve the responsiveness of detection across various conditions by providing fast detection without compromising accuracy. Several simulation investigations, adhering to the anti-islanding test standards of IEEE 1547 and UL1741, have been carried out on a system integrated with the suggested hybrid method. These studies aim to showcase the high sensitivity and specificity of the proposed technique for detecting islanding. In addition, pertinent comparisons are made between the proposed technique and the PLL-based method. The simulation results illustrate that the proposed control system effectively complies with the DG islanding protection requirements. In Furthermore, compared to the PLL, the proposed technique mitigates the common drawbacks associated with other islanding detection techniques by reducing the Non-Detection Zone, enhancing the power quality of the system, and, most significantly, producing fast detection under different conditions. The proposed approach exhibits a response time nearly three times faster than the PLL method, while in less demanding conditions, it provides an instantaneous response.

A quantitative genetic model of background selection in humans.

Across the human genome, there are large-scale fluctuations in genetic diversity caused by the indirect effects of selection. This "linked selection signal" reflects the impact of selection according to the physical placement of functional regions and recombination rates along chromosomes. Previous work has shown that purifying selection acting against the steady influx of new deleterious mutations at functional portions of the genome shapes patterns of genomic variation. To date, statistical efforts to estimate purifying selection parameters from linked selection models have relied on classic Background Selection theory, which is only applicable when new mutations are so deleterious that they cannot fix in the population. Here, we develop a statistical method based on a quantitative genetics view of linked selection, that models how polygenic additive fitness variance distributed along the genome increases the rate of stochastic allele frequency change. By jointly predicting the equilibrium fitness variance and substitution rate due to both strong and weakly deleterious mutations, we estimate the distribution of fitness effects (DFE) and mutation rate across three geographically distinct human samples. While our model can accommodate weaker selection, we find evidence of strong selection operating similarly across all human samples. Although our quantitative genetic model of linked selection fits better than previous models, substitution rates of the most constrained sites disagree with observed divergence levels. We find that a model incorporating selective interference better predicts observed divergence in conserved regions, but overall our results suggest uncertainty remains about the processes generating fitness variation in humans.

Grid Forming Technologies to Improve Rate of Change in Frequency and Frequency Nadir: Analysis-Based Replicated Load Shedding Events

Electric power generation is quickly transitioning toward nontraditional inverter-based resources (IBRs). Prevalent devices today are solar PV, wind generators, and battery energy storage systems (BESS) based on electrochemical packs. These IBRs are interconnected throughout the power system via power electronics inverter bridges, which have sophisticated controls. This paper studies the impacts and benefits resulting from the integration of grid forming (GFM) inverters and energy storage on the stability of power systems via replicating real events of loss of generation units that resulted in large load shedding events. First, the authors tuned the power system dynamic model in Power System Simulator for Engineering (PSSE) to replicate the event records and, upon integrating the IBRs, analyzed the system dynamic responses of the BESS. This was conducted for both GFM and grid following (GFL) modes. Additionally, models for Grid Forming Static Synchronous Compensator (GFM STATCOM), were also created and simulated to allow for quantifying the benefits of this technology and a techno-economic analysis compared with GFM BESSs. The results presented in this paper demonstrate the need for industry standardization in the application of GFM inverters to unleash their benefits to the bulk electric grid. The results also demonstrate that the GFM STATCOM is a very capable system that can augment the bulk system inertia, effectively reducing the occurrence of load shedding events.

VSG Frequency Regulation Strategy for Adaptive Model Predictive Control

When the active power of a Virtual Synchronous Generator (VSG) is unbalanced, the frequency will fluctuate significantly. Based on this, this article proposes an adaptive model predictive control method. By introducing a hyperbolic tangent function to construct an adaptive moment of inertia that includes frequency change and frequency change rate to provide the inertia for the island microgrid system, and the predicted model is updated in real-time; At the same time, model predictive control is used to calculate the optimal power reference value of VSG, strengthening the power support of VSG. The results indicate that under joint control improves the frequency regulation capability of VSG units and further enhances the system frequency performance, and the frequency deviation reduces from 0.15Hz to 0.05Hz, and the frequency change rate reduces from 0.58Hz/s to 0.5Hz/s. It is proved that the proposed control strategy can effectively suppress the maximum frequency offset and maximum frequency change rate during power fluctuations.

Effects of Battery Energy Storage Systems on the Frequency Stability of Weak Grids with a High-Share of Grid-Connected Converters

To achieve an energy sector independent from fossil fuels, a significant increase in the penetration of variable renewable energy sources, such as solar and wind power, is imperative. However, these sources lack the inertia provided by conventional thermo-electric power stations, which is essential for maintaining grid frequency stability. In this study, a grid resembling Madeira Island’s power generation mix was modeled using the Matlab/Simulink platform. The model included solar, wind, hydro, and thermo-electric generation to accurately represent the energy landscape of Madeira Island. Three scenarios were examined: one reflecting the current power generation on Madeira Island, a future scenario with a substantial rise in the percentage of photovoltaic (PV) generation, and the same future scenario but incorporating a battery energy storage system (BESS). Various analyses were conducted to assess the impact on frequency stability during a ground fault and rapid load/generation changes. In the future scenario without a BESS, the thermoelectric power plant generator desynchronized, leading to system collapse in several simulations. However, with the addition of a BESS, a significant improvement in frequency stability was observed. The thermoelectric power plant generator could return to a steady state after each disturbance. Furthermore, both the maximum frequency deviation and the absolute value of the Rate of Change of Frequency (ROCOF) were reduced, indicating enhanced system performance and stability.

A simple estimation method of grid‐forming inverter inertia based on rate of change of frequency

AbstractInertia is the core index of the estimation of power system frequency stability; a simple estimation method of grid‐forming inverter inertia based on the rate of change of frequency (RoCoF) is proposed in this paper. The method records and fits the active power curve by applying RoCoF to obtain the value of the grid‐forming inverter inertia, and it is simpler and higher accuracy compared to existing methods. In addition, the inertia and damping are analysed to support the system, and the relationship equation between the grid frequency slope change and the output active power is derived. Considering the theoretical analyses and influencing factors, the inertia and damping are obtained by using the method of function fitting. The test steps show the simplicity of the proposed test method. Finally, the effectiveness of the proposed method is verified in MATLAB/Simulation and two 1.575‐MW parallel grid‐forming electrochemical energy storage power plants.

Frequency Stability Control Strategy for Voltage Source Converter-Based Multi-Terminal DC Transmission System

The voltage source converter-based multi-terminal DC transmission (VSC-MTDC) system can use additional frequency control to respond to the frequency change of faulty AC system. However, the control coefficient of traditional additional frequency control is mostly fixed, and the control flexibility is insufficient, so it cannot be adjusted adaptively according to the frequency change of the system. Therefore, a frequency control strategy of the VSC-MTDC system based on fuzzy logic control is proposed. Based on the DC voltage slope controller, this strategy introduces an additional frequency controller based on fuzzy logic control, takes the frequency deviation and frequency change rate as the additional controller input, and dynamically adjusts the control quantity through the fuzzy logic control link to realize the adaptive adjustment of the VSC-MTDC system to the AC system’s frequency. Finally, a three-terminal flexible HVDC system is built on the PSCAD/EMTDC simulation platform for simulation verification. The results show that the proposed control strategy can effectively use the flexible DC system to support the frequency of the AC system and significantly improve the frequency stability of the faulty AC system.