Rate Of Change Of Frequency Research Articles

Inertial issues in renewable energy integrated systems and virtual inertia techniques

The global proliferation of renewable energy drastically altered the characteristics of power systems. Integration of clean energy sources reduces the inherent rotational inertia, making the system precarious and susceptible to various disturbances. The major challenges encountered are fast frequency fluctuations, voltage fluctuations, high rate of change of frequency (RoCoF), and frequency nadir. In order to address and adapt to a future low-inertia scenario, it is crucial to understand the effect of inertia on various parameters. This paper introduces a comprehensive review of the fundamental aspects of inertia and challenges that arise due to the reduction in inertia. Researchers have tackled this issue by employing various virtual inertia (VI) emulation techniques, which also have been extensively reviewed in the literature along with their merits, limitations, and recent developments. The impact of RES penetration on system dynamics is analyzed by simulating an IEEE-9 bus system with renewable energy source (RES) in MATLAB/Simulink. Furthermore, a three-phase fault is also introduced, to emphasize the effect of reduced inertia by observing the rotor angle and frequency deviation. The results validate that RES integration and fault location are observed to have a significant impact on stability parameters, making them extremely unstable.

Frequency Stability Constrained BESS Sizing Model for Microgrids

The grid integration of renewable energy sources necessitates using energy storage systems (ESSs) to provide more flexibility and controllability. This paper proposes a frequency stability-constrained battery energy storage system (BESS) sizing model for microgrids formulated as a mixed-integer linear programming (MILP) problem and decomposed using Benders decomposition. The optimal size of BESS is determined as a trade-off between minimizing the operating costs or maximizing the benefits and the high investment costs of BESS. Both the grid-connected and stand-alone operating modes are modeled for the microgrid along with the corresponding generation contingencies. The microgrid scheduling optimization model is built for cost-benefit analysis considering unit commitment and frequency stability (FS) constraints. The transient frequency dynamics are considered using an accurate time-domain model based on the discretized swing equation. The proposed method ensures frequency stability criteria, such as frequency nadir/overshoot, rate of change of frequency (RoCoF), and steady-state frequency, are within their allowable ranges following generation contingencies. Simulation results based on a medium-voltage microgrid test case with historical data of load, PV generation, and market price verify the effectiveness of the proposed method.

Analysis of AC filter detuning characteristics and improvement measures in converter station

Shift of parameters of the double-tuned AC filter component and failure in prompt correction of detuning frequency may affect the filtering effect of the AC filter. Therefore, this paper studies impedance-frequency characteristics of the double-tuned AC filter according to detuned recording data of the A-typed double-tuned AC filter in the Congxi converter station. It analyzes the variation of the impedance-frequency characteristic curves and relative change rate of resonant frequency as there are deviations between actual values and rated values of each filter capacitance and inductance elements in different degrees, and concludes that variation of the parameter of each element in different degrees may cause different deviations of resonant points of the double-tuned AC filter. MATLAB simulation has proved it can reduce the detuning degree and improve the filtering performance of the filter by adjusting the parameters of the variable reactor to change in the opposite direction of the parameters of the resonant capacitor.

Numerical investigation of the effect of bubble properties on the linear resonance frequency shift due to inter-bubble interactions in ultrasonically excited lipid coated microbubbles

Ultrasonically excited microbubbles (MBs) have numerous applications in various fields, such as drug delivery, and imaging. Ultrasonically excited MBs are known to be nonlinear oscillators that generate secondary acoustic emissions in the media when excited by a primary ultrasound wave. The propagation of acoustic waves in the liquid is limited to the speed of sound, resulting in each MB receiving the primary and secondary waves at different times depending on their distance from the ultrasound source and the distance between MBs. These delays are referred to as primary and secondary delays, respectively. A previous study demonstrated that the inclusion of secondary delays in a model describing the interactions between MBs exposed to ultrasound results in an increase in the linear resonance frequency of MBs as they approach each other. This work investigates the impact of various MB properties on the change in linear resonance frequency resulting from changes in inter-bubble distances. The effects of shell properties, including the initial surface tension, surface dilatational viscosity of the shell monolayer, elastic compression modulus of the shell, and the initial radius of the MBs, are examined. MB size is a significant factor influencing the rate of linear resonance frequency increase with increasing concentration. Moreover, it is found that the shell properties of MBs play a negligible role in the rate of change in linear resonance frequency of MBs as the inter-bubble distances change.The findings of this study have implications for various applications of MBs in the biomedical field. By understanding the impact of inter-bubble distances and shell properties on the linear resonance frequency of MBs, the utilization of MBs in applications reliant on their resonant behavior can be optimized.

Modeling of Linearized Generator Inertia Constraints for Unit Commitment

This study presents a novel approach to modeling linearized inertia constraints of generators, considering frequency stability, and applies it to the unit commitment (UC). Specifically, we modeled the average rate of change of frequency (RoCoF) constraint and the minimum frequency constraint using the analytical expression derived from the reduced frequency response (RFR) model. We also considered the load-damping constant as a variable. As the power system has different nonlinear characteristics according to its operating status, the system can be expressed as several different systems. Each subsystem, with its own properties at a given operating point, is modeled as a single-machine system, categorized by pumped storage hydropower (PSH) status. The minimum frequency of each subsystem is determined by its individual machine time constant. We incorporated an additional constraint to ensure the quasi steady-state performance of frequency. This constraint can be omitted when it is not necessary. The proposed concepts have been validated on the Korean Power System. The UC, with the proposed inertia constraints, can secure system inertia and primary frequency response (PFR) that satisfies frequency stability. Our proposed method is more efficient in securing inertia and PFRs and more economical in terms of generation cost compared to existing methods.

A novel reinforcement learning policy optimization based adaptive VSG control technique for improved frequency stabilization in AC microgrids

In this paper, an improved Reinforcement Learning (RL) based approach for adaptive Virtual Synchronous Generator (VSG) control of grid-forming inverters is proposed. High penetration of inverter-based resources causes recurrent frequency stabilization issues. For this matter, a novel model-free Actor–Critic policy optimization technique is proposed to improve frequency transients metrics such as frequency nadir and Rate of Change of Frequency (RoCoF). Stability analysis of the VSG controlled system is conducted through small signal modeling to determine the stability margins of both the virtual inertia parameter J and damping coefficient Dp. The control problem is formulated in RL terms using a new technique for state, action and reward construction that improves the learning process of the agents. The proposed approach’s efficiency is tested for three RL algorithms, namely, Deep Deterministic Policy Gradient (DDPG), Soft Actor–Critic (SAC), and Twin-Delayed DDPG (TD3) with special attention given to the latter. Various performance metrics such as training time and maximum cumulative episodic reward are used to compare the three algorithms. The resulting agent based VSG adaptive controllers are simulated and then compared for power quality and frequency stabilization capabilities. Finally, a comparison between non-adaptive VSG and TD3 based VSG is presented to conclude on the efficiency improvements achieved by the proposed approach.

Frequency response of microgrids with PV power generation and energy storage system (battery and supercapacitor)

Since renewable energy sources (RES) have almost little inertia, an increase in their electricity might harm the power system's ability to run steadily and dependably. Numerous solutions to the issue mentioned above are offered. This paper aims to assess the technological possibility of using energy storage system (ESS) devices built from batteries and supercapacitors to enhance the interia response of sources in microgrids with a large amount of PV power penetration. The microgrid's inertia was altered by varying the penetration level of RES. To obtain a rigid microgrid, batteries and supercapacitors are suggested in this study to enhance frequency stability and droop control is utilized to complete this assessment. The model of the on-grid power network was designed using Simulink in MATLAB to evaluate the high level of RES penetration impact on the frequency stability of the system. Results verify that the microgrid stiffness is significantly enhanced when the suggested storage elements are incorporated. The findings show that the rate of change of frequency (RoCoF) is reduced when the size of the ESS increases and vice versa. The supercapacitor energy storage system (SCESS) can increase the stability of the system's frequency more effectively than the battery energy storage systems (BESS) with a slower time response.

Second-Order Filter-Based Inertia Emulation (SOFIE) for Low Inertia Power Systems

The massive integration of power electronic converters into the power grid has led to a decrease in the mechanical inertia of power systems, causing an increase in the rate of change of frequency (RoCoF) that may lead to stability problems. The scientific community has focused on developing grid-forming control techniques, although their implementation implies a significant change in the firmware of the converter. Grid-supporting approaches, on the other hand, are an interesting alternative to add frequency support to the grid while preserving the original control structure of the converter. This paper proposes three new grid-supporting control techniques based on the dynamic behaviour of a synchronous machine (SM) and its equivalence with a second-order low-pass filter. They endow the converter with the capability of providing synthetic inertia, damping, droop-based <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p/f</i> primary response and virtual reactance. The dynamics of the proposed implementations are compared with a reduced-order synchronous machine by means of time-domain simulations and in-depth state-space-based small signal analyses. Besides, their operation is validated in a nine-bus low-inertia power system. Hardware-in-the-loop (HIL) laboratory results are used to validate experimentally the proposed techniques.

Real-time validation of RoCoF – Enhancing advanced coordinated control strategy for voltage unbalance mitigation implementing demand side management

The absence of rotational masses in converter-interfaced microgrids has led to a reduction in system inertia. As a consequence, the stability of modern microgrids is at risk, especially in the case of unbalanced systems, resulting in significant issues such as an increase in the rate of change of frequency (RoCoF), disturbances in the nominal frequency, and unfavourable voltage unbalances. This research article introduces an advanced concept centered around a virtual synchronous generator designed to enhance RoCoF performance. This is achieved through the implementation of a positive and a negative (PN) - sequence controller scheme in coordination with demand side management to ensure that RoCoF remains within the limit of 2 Hz/s according to IEEE Standard 1547–2018 and the voltage unbalance factor (VUF) adheres to the established standard of 2 % according to IEC 61,000–3–13. The behaviour of the proposed control strategy during transient conditions has also been demonstrated. The framework of the virtual synchronous generator is utilized in this paper to demonstrate the influence of damping coefficient and moment of inertia on the low inertia system's frequency and transient response where it has been established that greater inertia and damping are essential for their enhancement. The study also conducts a small signal stability analysis to assess the effects of various parameters on system stability. Furthermore, the real-time efficacy of the coordinated control methodology based on virtual inertia has been experimentally verified using OPAL-RT simulator. The simulation and experimental results, both provide evidence of the successful performance of the proposed approach in realizing efficient RoCoF enhancement and VUF mitigation.

Estimation of Power System Inertia with the Integration of Converter-Interfaced Generation via MEMD during a Large Disturbance

The decrease in overall inertia in power systems due to the shift from synchronous generator production to renewable energy sources (RESs) presents a significant challenge. This transition affects the system’s stable frequency response, making it highly sensitive to imbalances between production and consumption, particularly during large disturbances. To address this issue, this paper introduces a novel approach using Multivariate Empirical Mode Decomposition (MEMD) for the accurate estimation of power system inertia. This approach involves applying MEMD, a complex signal processing technique, to power system frequency signals. The study utilizes PMU (Phasor Measurement Unit) data and simulated disturbances in the IEEE 39 bus test system to conduct this analysis. MEMD offers substantial advantages in analyzing multivariate data and frequency signals during disturbances, providing accurate estimations of system inertia. This approach enhances the understanding of power system dynamics in the context of renewable energy integration. However, the complexity of this methodology and the requirement for precise data collection are challenges that need to be addressed. The results from this approach show high accuracy in estimating the rate of change of frequency (RoCoF) and system inertia, with minimal deviation from actual values. The findings highlight the significant impact of renewable energy integration on system inertia and emphasize the necessity of accurate inertia estimation in modern power systems.

Active Power Allocation Method of Doubly Fed Induction Generators Based on Rotor Speed

The integration of wind power into a grid on a large scale results in a reduction of the system’s inertia level, causing an impact on the stability of the system frequency. Doubly fed induction generators (DFIG) can optimize active output but lack inertia support under maximum power point tracking control. To make the wind turbine improve the inertia support ability of the system based on virtual inertia control, a method for active power allocation based on the rotor speed of DFIG is proposed. Firstly, the minimum system inertia requirement based on the frequency change rate of the system is established. Active power allocation assumes that the wind farm inertia meets the minimum system inertia requirement. Secondly, the objective is to enhance the inertia support capability and overall active power output of the wind farm, considering the constraint of the minimum system inertia requirement. Based on the rotor speed to establish the inertia allocation weight factor, the weight of the power command is assigned to a single machine to achieve the wind farm active power allocation. Finally, it is verified that the system’s equivalent inertia meets the minimum inertia requirement of the system. Simulations show that the proposed allocation method can adequately elevate the inertia support capability of DFIGs to the system and the rotor kinetic energy utilization.

Enhancing Grid-Forming Converters Control in Hybrid AC/DC Microgrids Using Bidirectional Virtual Inertia Support

This paper presents a new grid-forming strategy for hybrid AC/DC microgrids using bidirectional virtual inertia support designed to address weak grid conditions. The stability of hybrid AC/DC microgrids heavily relies on the AC mains frequency and the DC-link voltage, and deviations in these factors can lead to undesirable outcomes such as load curtailments and power system congestions and blackouts. This paper introduces a unique approach that leverages bidirectional virtual inertia support to enhance the stability and reliability of hybrid AC/DC microgrids under weak grid conditions. The proposed strategy employs virtual inertia as a buffer to mitigate rapid changes in DC-link voltage and AC frequency, thereby enhancing system stability margins. This strategy significantly contributes to a more stable and reliable grid operation by reducing voltage and frequency fluctuations. A standard hybrid AC/DC microgrid configuration is used to implement the bidirectional virtual inertia support, where a bidirectional interlinking converter control is adjusted to deliver inertia support to both the AC and DC subgrids. This converter utilizes the DC grid voltage and AC grid frequency as inputs, effectively managing active power balance and implementing auxiliary functions. Extensive simulations are conducted under weak grid conditions and standalone mode to validate the effectiveness of the proposed strategy. The simulation results demonstrate a remarkable improvement in frequency nadir, rate-of-change-of-frequency (RoCoF), and DC bus voltage deviation in the hybrid AC/DC microgrids. The bidirectional virtual inertia support substantially reduces voltage and frequency fluctuations, enhancing the microgrid stability and resilience. There is an improvement of over 45% and 25% in the frequency deviation and voltage deviation, respectively, achieved through implementing the proposed control strategy.

RoCoF Constrained Unit Commitment Considering Spatial Difference in Frequency Dynamics

The post-disturbance rate of change of frequency (RoCoF) is a critical index for low-inertia power system frequency stability. This paper proposes a RoCoF constrained unit commitment model so as to enhance the frequency stability in operation time-scale, where the spatial difference in frequency dynamics is considered and the RoCoF constraint is enforced for each node. The maximum of node RoCoF is approximated by two terms, i.e., the initial post-disturbance node RoCoF and the maximum of the center of inertia (COI) RoCoF. Analytical expressions of the node initial RoCoF under typical disturbances are derived. Then, a tractable relationship between the node initial RoCoF and the working status of generators is obtained by the piecewise linearization approach. Simulation results carried out on the IEEE 39-bus system demonstrate the proposed model can limit the node RoCoF in an economic and accurate manner. The adaptability to renewable power generation and online application are also discussed.

Online Estimation of Disturbance Size and Frequency Nadir Prediction in Renewable Energy Integrated Power Systems

The displacement of conventional synchronous generation by Inverter-Based Resources (IBRs) poses critical challenges to the frequency stability of Renewable Energy (RE) integrated power systems. An increased shift towards green energy by integrating RE sources that provide little or no inertia results in a high Rate of Change of Frequency (RoCoF) and deteriorated frequency nadir/zenith following a credible system disturbance. Prediction of frequency metrics, such as frequency nadir and RoCoF, immediately after disturbances will help grid operators to take preventive/corrective actions, such as the deployment of faster frequency control, to ensure secure and stable grid operation. This paper presents an easy-to-implement analytical method to estimate disturbance size in a power system immediately following a contingency which is then used for predicting frequency nadir. The proposed estimation method uses active power measurements from a limited number of monitoring nodes and an adaptive bus admittance matrix of the system for the disturbance size estimation. The estimated disturbance size is then used to predict frequency nadir using a Neural Network (NN) based method. The performance and accuracy of the presented approach are evaluated using a standard IEEE 39 bus system and a real-life Gujarat power system in India through extensive simulations in DIgSILENT PowerFactory, considering various cases of disturbance size, type, and location.

P-f Stability of 2030 Nordic Power System due to Non-Synchronous Generation

The Nordic Power System is undergoing significant transformation and development in the coming years. A driving factor for this is the increased dependency on renewable energy sources and high voltage direct current transmission (HVDC). Various stability challenges due to the dynamics of reactive power - voltage (Q-V) balancing and active power - frequency (P-f) balancing seep into the system with such rise of non-synchronous generation (NSG). This paper investigates the projected impact of NSGs on the P-f dynamic performance of Nordic power system in 2030. As NSGs are systems with low inertia, power discrepancies lead to larger oscillations, higher Rate of Change of Frequency (RoCoF) and bigger maximum frequency deviation (MFD) values. To address these issues, Emulated Inertia (EI) control for wind turbines and Synthetic Inertia (SI) control for VSC-HVDC links are proposed in this paper. The simulation is carried out using DIgSILENT PowerFactory 2022 SP1 simulation software. The results obtained confirm the Effectiveness of the proposed EI and SI methods to enhance frequency response and mitigate deviations.

Synergistic adaptive control of virtual inertia and damping coefficient in virtual synchronous generators for standalone microgrid applications

The current control methods for virtual synchronous generators (VSG) in regulating inverter frequency in standalone microgrids at border posts and remote mountainous regions remain suboptimal. This study introduces a small-signal VSG model to elucidate the intrinsic dynamics of the virtual inertia and damping coefficient, along with their coupled interrelationship. A novel VSG control approach is proposed, featuring synergistic adaptive regulation of both virtual inertia and damping coefficient. This approach is designed to optimize the interaction of the virtual inertia and damping coefficient with the frequency difference and rate of frequency variation, within a predefined operational range. Additionally, it adaptively modulates these parameters to mitigate further frequency reductions, taking into account the frequency difference and active power when deviations occur outside the predefined range. The experiments demonstrate that this approach effectively moderates the rate of frequency change, diminishes frequency departure velocity for approximately 4 times the original during disturbances, expedites frequency stabilization post-disturbance, the stabilization time is reduced by at least half of the original and prevents excessive frequency deviations. The implementation of this method significantly enhances the response speed and accuracy of frequency control in standalone microgrids, contributing to improved overall system stability.

Walking and scuba diving assisted amphibious exoskeleton robots: the designing of power assist control and myoelectricity based wearers' fatigue evaluation.

Exoskeleton robots have the potential to augment human motor capabilities. however, current control strategies often require task-specific control laws tailored for different scenarios, which limits the applicability of exoskeletons. In this study, we propose a control strategy for exoskeleton robots that is adaptable across various scenarios. We employ adaptive oscillators (AO) with feedback control to rapidly estimate the wearer's motion phase and subsequently provide torque assistance to the wearer's hip joint based on a TCN-LSTM model. During experiments, we collected surface electromyographic (sEMG) signals from the tibialis anterior, gastrocnemius, and rectus muscles of seven groups of subjects performing treadmill walking and inclined treadmill exercises. We utilized the short-time Fourier transform to extract frequency characteristics of the signals and statistically analyzed the rate of frequency change in each muscle group under different strategies. The results indicate that when wearing the exoskeleton, the overall muscle frequency changes more slowly, suggesting that subjects can maintain activity for a longer duration before fatigue sets in. This control strategy effectively reduces the energetic cost of lower limb work for the wearer and enhances the exoskeleton's versatility in various applications.

Sizing method of a novel hybrid energy storage considering adaptive inertia control

This paper introduces a novel hybrid energy storage system (HESS) with a focus on adaptive inertia control and its sizing methodology. The HESS is built upon the modular multilevel converter (MMC) topology, incorporating hybrid submodules, batteries, and supercapacitors (SC). The sizing method for the hybrid energy storage system in the proposed HESS is discussed, with a specific emphasis on its application in frequency response scenarios. The center of inertia frequency (COIF) is selected to represent the overall system's frequency characteristic. By examining COIF deviation and the Rate of Change of Frequency (ROCOF) during contingency events, the inertia and damping parameters of the HESS are designed. Additionally, an adaptive inertia approach is incorporated to further reduce the SC capacity. The analysis of COIF dynamics under contingency with adaptive inertia is performed, and an analytical expression of COIF dynamics is derived. Subsequently, a sizing method for the SC and battery in the HESS, considering adaptive inertia, is proposed. The effectiveness of the proposed sizing method is verified through simulation results, demonstrating its suitability for optimizing the design of the hybrid energy storage system in the novel HESS configuration.

Appropriate models for designing frequency control schemes in power systems

Frequency response characteristics like frequency nadir and rate of change of frequency (ROCOF) are important in designing frequency control schemes. The so-called Frequency Response Model (FRM), widely used in power system frequency studies, has some limitations in calculating these metrics. This paper evaluates and analyses the performance of FRM and multi-area FRM in calculating performance metrics for small and multi-machine power systems while considering the effect of amplitude and duration of voltage deviations after a disturbance. The capabilities and limitations of FRM and multi-area FRM are inferred by comparing their performance with a detailed model. To overcome the shortcomings of simplified models, a partly-linearized detailed model is suggested that preserves the important nonlinearities in frequency studies but, to consider the impact of the network on the results of frequency studies with reduced computation time, linearizes the models of other system components. Also, based on the two-part characteristic curve of steam and gas power plants, modified models have been suggested for the turbines and included in the proposed model. Numerical results show that the accuracy of the proposed simplifications is close to the detailed model while its computation time is less than 10 % of that of the detailed model.

A Parallel Connected Hybrid Microstrip-Substrate Integrated Waveguide Bandstop Filter

This study presents an original parallel connected hybrid microstrip-substrate integrated waveguide (PCHM-SIW) bandstop filter. A low-pass filter implemented on a microstrip structure and a SIW-based high-pass filter are connected in parallel to each other. In this way, the aim is to obtain a bandstop filter in the novel hybrid design. The parallel connected hybrid microstrip-substrate integrated waveguide (PCHM-SIW) bandstop filter is synthesised, simulated, and produced. The effects of connecting filters in parallel are discussed. It is seen from the results of CST Studio Suite simulation that PCHM-SIW bandstop filter has a bandwidth of 2.85 GHz and a center frequency of 4.26 GHz. The frequency change rate of the center frequency between simulation and measurement is 7.02 % where it is just 3.76 % for the deviation in bandwidth. The results of the simulation and those of the measurement are close to each other. These results converge to ideal analytical results.