Power System Frequency Research Articles

Mechanism Analysis of Low-Frequency Oscillation Caused by VSG from the Perspective of Vector Motion

Virtual synchronous generators (VSGs) have attracted widespread attention due to their advantage in supporting voltage and frequency of power systems. However, relevant studies have shown that a VSG has similar low-frequency oscillation as synchronous generators, which is more likely to occur under strong grid conditions. In this paper, the linearized mathematical model of a VSG is established by using small-signal analysis; based on this, the physical process of low-frequency oscillation of a VSG is explained from the perspective of vector motion. Firstly, the amplitude and phase motion of the current vector of a VSG under small disturbance are analyzed, then the mechanism of negative damping caused by terminal voltage control is revealed, and the reason why a VSG is more prone to instability under strong grid conditions is explained. Based on these, the influence of control and grid strength on the low-frequency oscillation of a VSG is analyzed. Studies show that the amplitude motion of the output current is the main cause of negative damping, and the oscillation can be suppressed by optimizing the value of key parameters.

Diffusion Augmented Complex Inverse Square Root for Adaptive Frequency Estimation over Distributed Networks

Using adaptive filtering to estimate the frequency of power systems has become a popular trend. In recent years, however, few studies have been performed on adaptive frequency estimations in non-stationary noise environments. In this paper, we propose the distributed complex inverse square root algorithm and distributed augmented complex inverse square root algorithm for the frequency estimation of power systems based on the widely linear model and the inverse square root cost function, where the function can restrain both positive and negative large errors, based on its symmetry. Moreover, the wireless sensor networks support monitoring and adaptation for the frequency estimation in the distributed networks, and the proposed approach can ensure good robustness of the balanced or unbalanced three-phase power system with the help of a local complex-value voltage signal generated by Clark’s transformation. In addition, the bound of step size is driven by the global vectors, and that low computation complexity do not hinder those performances. The results of several experiments demonstrate that our algorithms can effectively estimate the frequency in impulsive noise environments.

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.

Apply Honey Barger Algorithm to double integral sliding mode observer for stable load frequency in multi-area power system

A randomness of load demand and plant uncertainties causes frequency deviation in linked power plants. Based on the double-integral sliding mode observer (DISMO) integrated Honey Badger algorithm (HBA), a novel LFC for a multi-area power plant (MAPP) is introduced in this article. The main aim is to minimize frequency offset, finite time, and aggregate instability of controllable loads subject to the balance of the power on the MAPP. Firstly, the suggested observer is developed to ensure an exact estimation of the actual signal for the controller input signal. Secondly, a double-integral sliding surface (DISS) is introduced based on estimated signals the designed observer gains. Then, a new SMC rule is designed to ensure finite time reachability and eliminate the chattering and oscillating troubles. Thirdly, in this regard, the proposed sliding surface is designed with four selected parameters. Regarding this, to maximize the ability of the suggested SMCer, the optimized controller parameters are determined by HBA. The robustness of the suggested scheme is examined by various case studies on the LFC models in a single-area power plant (SAPP) and MAPP under different load disturbances and parameter uncertainties.

A new optimal 3° of freedom fractional order proportion integral derivative controller with model predictive controller for frequency regulation in high penetrated renewable based interconnected system

The increasing use of renewable energy sources (RESs) in conventional power systems is making them more complex. RES, such as solar and wind energy, reduce system inertia, affecting power system (PS) stability and frequency aberrations. Thus, the modern PS faces new concerns that arise from integrating RESs and struggles to manage frequency and stability, which can cause power outages and blackouts and lower industry production. The intelligent control mechanism is critical to the PS's operation to ensure frequency under its complicated structure. This study suggests a new best 3-DoF fractional order proportional integral derivative-model predictive controller (3DoF-FOPIDN-MPC) for controlling frequency when there is a lot of load going on quickly. The 3DoF-FOPID controls the outer loop using the area control error (ACE) signal, while MPC controls the inner loop using the output signal from the 3DoF-FOPIDN and the area's total power output response. For optimal controller functionality, the salp swarm algorithm (SSA) extracts optimized controller settings. To validate the suggested controller, it is tested under various load-changing scenarios and compared to state-of-the-art controllers. For 1 % and 3 % load changes, the suggested controller settles in 1.1 s and 1.78 s, respectively.

Convex-Hull Pricing of Ancillary Services for Power System Frequency Regulation With Renewables and Carbon-Capture-Utilization-and-Storage Systems

Convex-Hull Pricing of Ancillary Services for Power System Frequency Regulation With Renewables and Carbon-Capture-Utilization-and-Storage Systems

High proportion of new energy power system frequency and voltage support and regulation technology based on doubly fed induction generator

Abstract With the increasing proportion of new energy in power systems, issues regarding system voltage, inertia, and primary frequency regulation have become increasingly severe. In response to control and grid safety issues, a high proportion of new energy power system frequency and voltage support and regulation technology based on a doubly fed induction generator (DFIG) is proposed. The voltage-magnetic link equation of DFIG is theoretically derived, and the control principles of active and reactive power of DFIG are proposed. The support and regulation characteristics of improving the voltage of new energy substations are studied. Verification is conducted through large-scale grid simulation and on-site measurements.

An analytical approach for power system frequency stability evaluation

AbstractRecent years have seen high penetration of renewable energies, which have significantly reduced the inertia of bulk power systems. As a result, the frequency behaviour of power systems is becoming more complex. To resolve this technical challenge, there is a particularly strong interest in developing analytical solutions for frequency dynamics studies. This study first describes a second‐order frequency dynamics model for power systems with renewable energies. A non‐linear perturbation approach is suggested to drive the analytical solution of the model. It is shown that, under many circumstances, frequency dynamics can be effectively approximated using a linear model. Subsequently, the article describes a fourth‐order linear frequency dynamics model that takes into account governor‐turbines. A polynomial eigenvalue method is proposed to identify the dominant and non‐dominant modes of the solution of the four‐order model. It is demonstrated that the dominant mode has a decisive impact on frequency behaviour, while the non‐dominant modes influence the relative frequency oscillations only. Finally, the study derives the analytical expressions of the standard frequency performance metrics and examines the impact of damping and inertia parameters. The introduced results are verified using two test systems, demonstrating the accuracy and effectiveness of the suggested method.

Complex-Valued Minimum Total Error Entropy Adaptive Algorithm With Fiducial Point for Power System Frequency Estimation

Complex-Valued Minimum Total Error Entropy Adaptive Algorithm With Fiducial Point for Power System Frequency Estimation

An Investigation of the Third Harmonic Power Line Emission in the Topside Ionosphere During the Recent Solar Minimum Period

AbstractPower line harmonic radiation (PLHR) events are radiated by electric power systems on the ground at harmonics of the base power system frequency (50 or 60 Hz, depending on the region). We analyze the global third harmonics PLHR at 150 and 180 Hz using electric field data collected by China Seismo‐Electromagnetic Satellite during the recent solar minimum between January 2019 and December 2022. The average frequency spectrum over industrialized areas shows that the third harmonic has a high occurrence rate in the U.S. region, as well as in western China and northern India, but is very low in the European region. In particular, in the China region and the U.S. region, more than 11,000 and 24,000 dayside and nightside third harmonic PLHR events have been detected from 2019 to 2022, respectively. Compared to the 150 Hz PLHR occurrence rate detected above the China region, the 180 Hz PLHR occurrence rate above the U.S. region is higher, which reveals a significant regional difference. In addition, both at nighttime and daytime, the PLHR electric field intensities at 180 Hz are higher than that at 60 Hz above the U.S. region, which is also different from the result above the China region.

Trade-off between frequency stability and renewable generation – Studying virtual inertia from solar PV and operating stability constraints

The significant increase in solar PV and wind capacity worldwide has raised growing concerns about power system frequency stability in several countries. One reason for this is that these renewable technologies offer almost no inertial response. However, there are some options available to address this issue. Renewables could now offer virtual inertia. Also, power system operators could impose frequency stability constraints as part of the generation Unit Commitment (UC). These options could potentially have a large impact on renewable generation and hence also on energy costs and system emissions. In this paper, we study two key options improving stability, inertia from solar PV generators supplied by virtual synchronous machines, and frequency stability constraints as part of the UC. We assess N-1 generation contingencies for the interconnected power systems of Chile, Argentina, and Peru. We found that the option of virtual inertia reduces the violation of the RoCoF in hours of high solar generation, without affecting renewable generation. On the other hand, frequency stability constraints ensure non-violation of all stability parameters but reduce renewable generation by 12 %. This reduction increases total operating costs by about 35 %, even when the constraints are combined with virtual inertia and battery support.

Robust Fuzzy-PID Technique for the Automatic Generation Control of Interconnected Power System with Integrated Renewable Energy Sources

This paper proposes a robust hybrid fuzzy PID controller, with the PID gain values tuned using the particle swarm optimization (PSO) technique for the automatic generation control (AGC) of the two-area hybrid power system. PSO Algorithm is applied to reduce the integral of time-weighted absolute error (ITAE) of the frequency and tie-line power variations of the two-area interconnected power system. The suggested method’s efficacy is examined on an interconnected two-area power system with Area 1 containing thermal reheat plants, hydropower plants, and diesel generating units, and Area 2 comprising thermal reheat plants and renewable energy sources (RES): wind energy conversion system, solar photovoltaic system, and electric vehicles. The thermal reheat power plants are modelled taking into consideration the governor dead band (GDB) and the generation rate constraints (GRC). The performance of the presented controller is compared with the genetic algorithm-optimized PID AGC and the PSO-optimised PID AGC. The simulation outcomes show superior results of the proposed controller against other controllers. Further, sensitivity analysis reflects that the proposed technique provides better dynamic response and robustness than the other techniques.

Cyber‐attack and defense method for load frequency control in smart grid systems with electric vehicles

AbstractThe latest advancements in Vehicle‐to‐Grid (V2G) technology enable Electric Vehicles (EVs) to contribute to Frequency Regulation (FR), mitigating the impact of uncertain power fluctuations in renewable resources. However, diverse cyber‐attacks pose threats to the Load Frequency Control (LFC) system and smart grid infrastructure, compromising their accuracy and reliability. This research paper focuses on the effects of cyber‐attacks on frequency regulation in a smart grid system that relies on a communication network. The study proposes a two‐area system and a modified IEEE‐39 bus three‐area system, incorporating intermittent solar photovoltaic and wind turbine sources, traditional conventional sources, and electric vehicles. To ensure frequency stabilization and tie‐line power, the researchers introduce a cascade FOPIDN‐(1+TD) controller. Its parameters are optimized using a novel Quasi Opposition Arithmetic Optimization Algorithm (QOAOA). The proposed approach's dynamic response is compared with other commonly used controllers, demonstrating its effectiveness in maintaining stability. The article focuses on the LFC system and presents a novel approach involving a cyber‐physical model. It introduces a method for detecting and defending against cyber‐attacks using deep learning, specifically utilizing the Long‐Short‐Term‐Memory (LSTM) network. The effectiveness of the proposed defense strategy is demonstrated through experiments conducted on both a two‐area interconnected power system and the IEEE‐39 bus system. The outcomes indicate that the suggested defense mechanism effectively maintains acceptable levels of power system frequency and tie‐line power during cyber‐attacks. Additionally, the validity of the controller's performance is verified through real‐time analysis using Hardware‐In‐The‐Loop (HIL) simulation with the OPAL‐RT platform.

A New Electric Arc Furnace Model Based on Current Waveform Synthesis From Distributions of DFT Amplitudes and Power System Frequency

A New Electric Arc Furnace Model Based on Current Waveform Synthesis From Distributions of DFT Amplitudes and Power System Frequency

Research on Mathematical Model of Energy Storage Assisted Wind Turbine Frequency Regulation Control Strategy

Abstract This paper proposes an improved frequency regulation strategy for the Doubly-Fed Induction Generator (DFIG) to mitigate the impact of wind power integration on system frequency. An energy storage system is used on the wind side to participate in the frequency regulation. The influence of wind power integration on the power system frequency is analyzed and an improved frequency control strategy for the DFIG is proposed. A control strategy for energy storage devices to support wind turbine frequency control is proposed. An energy storage device model is established that considers power correction based on the state of charge to avoid excessive charging and discharging. According to the operating state of the DFIG, a control strategy for the frequency regulation of the energy storage device is proposed. According to different wind speeds, a control strategy is proposed for the participation of the joint wind storage system in the frequency regulation. This control strategy can provide frequency support to the system when the wind turbine cannot participate in frequency regulation according to the different operating conditions of the wind turbine. After the wind turbine uses the improved frequency control strategy, it accelerates the recovery of the DFIG rotor speed while avoiding a secondary drop in the system frequency. In addition, when the energy storage device has a poor state of charge and the system frequency is good, it charges to restore the state of charge.

Impact of ABT based control strategies on ALFC and AVR in DFIG-integrated interconnected power systems

To maintain a stable electricity supply in interconnected power grids, effective frequency and voltage regulation are required. Interconnected power systems use Automatic Load Frequency Control (ALFC) and Automatic Voltage Regulator (AVR) for this purpose. The integration of renewable sources, such as Doubly Fed Induction Generators (DFIGs), creates challenges for such control loops. This study investigates the impact of using various Frequency-Linked Pricing (FLP)-based operating strategies under Availability-Based Tariff (ABT) on combined ALFC and AVR in a two-area interconnected power system with DFIGs. FLP-based operating strategies under ABT react to frequency changes through price signals, which can act faster compared to traditional AGC methods that rely on communication between control centers. This quicker response helps maintain frequency and voltage during load disturbances. Most of the earlier research focused mostly on using only a single type of FLP-based operating strategy under ABT within the ALFC loop, neglecting the combined ALFC-AVR interaction. This work addresses this gap by evaluating three FLP-based operating strategies under ABT along with the traditional approach for their impact on frequency and voltage under step load disturbance. Simulation studies conducted in MATLAB 2022a demonstrate the effectiveness of the proposed strategies, providing valuable insights for improving frequency and voltage control in modern power systems. The investigation reveals that the strategy that considers the difference between the actual and reference values of the unscheduled interchange (UI) charge and the marginal cost of generation to produce the control command outperforms the other strategies and restores the frequency and voltage to their nominal values.

Estimation of aggregated inertia constant and load damping: A PMU-based analytical approach

A precise, straightforward, and efficient data-driven methodology is introduced to estimate the most important aggregated generation-load parameters of the power system frequency response model i.e., the inertia constant and the load damping. The estimation method depends on defining specific base systems characterized by particular frequency features. A sensitivity analysis is carried out to determine the most suitable base system for each real-time application. The data collected from PMUs is then compared to the attributes of the base system to make accurate estimations of the parameters of interest. The effectiveness of the proposed methodologies is assessed using datasets that include both simulated data from the New York-New England benchmark and actual measurements collected from six historical power system disturbances within a national power grid.

VSG-LFC on multi-area power system under unsecured communication channel using hybrid trigger mechanism

This paper studies the frequency fluctuation problems of a multi-area power system with renewable energy sources (RESs) under denial-of-service (DoS) attacks. (i) Due to the decoupling of the RESs from power system using electronic devices, the RESs have no natural frequency response capability, which result in decreasing of entire power system equivalent inertia with large penetration of RESs. (ii) DoS attacks cause the insecurity of network communication, which can vanish data transmission and yield data packet dropout. To address the above issues, a virtual synchronous generator (VSG) incorporated with load frequency control (LFC) method (VSG-LFC) is proposed by introducing a hybrid-triggered mechanism (HTM) to (i) reduce the system sensitivity to the penetration level of RESs; (ii) compromise between frequency regulation performance and the reasonable usage of network resource under unsecured communication environments. Then, a switched system model is constructed considering non-identical DoS attack situations. Furthermore, theoretical analyses using Lyapunov functional related methods are carry out for asymptotical mean-square stability with H∞ performance on frequency regulation. Simulation evaluations of power system verify the effectiveness of this development. It shows that in a two-area power system frequency derivation performance indicators (IAE, ITAT, ISE) in Area1 are reduced by (82.996%, 86.273%, 85.823%) and in Area2 are reduces by (77.996%, 83.613%, 82.315%).

Quantum model prediction for frequency regulation of novel power systems which includes a high proportion of energy storage

As the proportion of renewable energy generation continues to increase, the participation of new energy stations with high-proportion energy storage in power system frequency regulation is of significant importance for stable and secure operation of the new power system. To address this issue, an energy storage control method based on quantum walks and model predictive control (MPC) has been proposed. First, historical frequency deviation signals and energy storage charge–discharge state signals are collected. Simulation data are generated through amplitude encoding and quantum walks, followed by quantum decoding. Subsequently, the decoded data are inputted into the MPC framework for real-time control, with parameters of the predictive model continuously adjusted through a feedback loop. Finally, a novel power system frequency regulation model with high-proportion new energy storage stations is constructed on the MATLAB/Simulink platform. Simulation verification is conducted with the proportional–integral–derivative (PID) and MPC methods as comparative approaches. Simulation results under step disturbances and random disturbances demonstrate that the proposed method exhibits stronger robustness and better control accuracy.

Capacitor virtual inertia control and equivalent inertia analysis for a grid-forming wind generation system

A grid-forming wind generation system exhibits exceptional grid frequency support abilities. The DC capacitor of the grid-forming wind generation system, which is characterized by rapid response and high sensitivity to minor disturbances, can provide short-term inertia support for the power system. This paper proposes the capacitor virtual inertia control for the grid-forming wind generation system, coupling the DC capacitor voltage with the power system frequency, which enables the DC capacitor to participate in the system frequency response process and reduces the rate of change of the system frequency during the disturbance. To analyze the inertia of the wind power generation system, this paper establishes an equivalent Philips–Heffron model for the grid-forming wind generation system and uses the equivalent inertia constant to quantify the inertia of the wind power generation system. The effectiveness of the proposed control strategy and the reasonableness of the inertia assessment method are verified through simulations in the single-turbine system and the IEEE four-machine two-area system.