Frequency Constraints Research Articles

A wind farm planning method considering frequency security constraint based on wind farm participation in primary frequency regulation

Abstract Renewable energy sources such as wind power, connected to the grid on a large scale, reduce the rotational inertia and frequency regulation of the power system. Many studies have included frequency security constraints (FSC) in power system scheduling to ensure system frequency stability, but few studies have included FSC in grid planning. Therefore, this paper establishes a planning model for wind farms that considers the FSC based on the wind turbines’ participation in the primary frequency regulation (PFR) by obtaining the maximum deviation value constraint of the system frequency through the system frequency response (SFR) model. Tests were conducted on the IEE30-node system, and the results show that the proposed model enhances the system frequency response capability and ensures system security.

Relationships between Food Insecurity, Self-Efficacy, and Changes in Body Mass Index among the Youth in Taiwan: Analysis from a Longitudinal Cohort Survey.

Food insecurity is a heightened concern among economically disadvantaged youth, and it may contribute to the atypical body mass index (BMI) patterns frequently observed in this group. Self-efficacy seems to intervene in the negative impacts of contextual restraints. This study investigated the relationship between food insecurity, self-efficacy, and BMI trajectory among economically disadvantaged Taiwanese youth. We utilized three-wave longitudinal data from the Taiwan Database of Children and Youth in Poverty. The Food Insecurity Score (FIS) assessed food insecurity with a 4-item scale measuring reduced meal frequency, hunger, skipping meals, and economic constraints. Moreover, the General Self-Efficacy Scale (GSES) assessed self-efficacy, showcasing the ability to handle stress effectively and envision success scenarios, contributing to positive outcomes. By employing latent growth modeling, we were able to delineate the impacts of baseline food insecurity and self-efficacy on initial BMI and its subsequent growth trajectory. Elevated baseline FIS significantly predicted higher initial BMI (coefficient = 0.420, p = 0.042). Baseline GSES was negatively associated with initial BMI (coefficient = -0.093, p < 0.001) but positively predicted the BMI growth rate (coefficient = 0.023, p = 0.011). Enhancing self-efficacy may be an effective multidisciplinary intervention to address psychosocial and socioeconomic factors when tackling weight problems in vulnerable youth groups.

Stress-driven design of incompressible multi-materials under frequency constraints

This paper presents an efficient and comprehensive numerical approach to address topology optimization challenges within the multi-material framework. The focus encompasses several key aspects: solving various stress-related problems from compressible to incompressible materials, broadening the scope to encompass multi-material systems, adopting a flexible methodology suitable for various elements (triangular, quadrilateral, and polygonal), and expanding to incorporate frequency constraints within the stress-driven system. The core idea to accommodate a broad range of materials, from compressible to nearly incompressible, is to implement a specialized polytopal composite finite element (PCE) technique to mitigate volumetric locking issues often prevalent in nearly incompressible materials. Then, to effectively solve the stress-related multi-material system, a well-known P-norm function integrated with the Moved and Regularized Heaviside function (MRHF) is employed, capitalizing on the correlation between topological phases and material allocation to handle multi-material problems effectively. Additionally, to deal with frequency-related multi-material problems, an extended technique addressing localized mode issues based on the relationship between representative solid and void is also employed. Several numerical examples are tested to validate the method’s efficiency and reliability within a multi-material framework, considering a diverse range of materials from compressible to nearly incompressible.

Robust optimal design of UFLS schemes in island power systems

Since settings of conventional underfrequency load shedding (UFLS) schemes cannot be adjusted in real-time, this paper proposes a novel robust optimal design method of the UFLS scheme for an island power system (IPS) that once fixed, gives an adequate performance in all possible operating conditions in the IPS. The core of the novel robust optimal design method is the implementation of a synthetic data generation algorithm that covers all the feasible generator operating points, which are further classified into a set of large number (but computationally manageable) representative generation dispatches using clustering techniques. A real-world Spanish island will be used to illustrate the method, where the UFLS robust design will be tested and compared with non-robust UFLS designs tuned using generation dispatches of an actual day of operation provided by both standard and frequency-constrained unit commitment algorithms. Results will show that the proposed robust design avoids frequency constraints violations in contingencies and obtains better frequency metrics.

Depth imaging of multicomponent seismic data through the application of 2D full‐waveform inversion to P‐ and SH‐wave data: SEAM II Barrett model study

AbstractWe examine the value of the nine‐component seismic survey by generating the Kirchhoff depth migration images of compressional wave (P‐wave), converted wave (PS‐wave) and horizontally polarized shear wave (SH shear wave) data simulated from the SEAM II Barrett unconventional model. We first utilize full waveform inversion to obtain a P‐wave velocity model from P‐wave data and an S‐wave velocity model from SH‐wave data. Both P‐wave and SH‐wave data are generated with the maximum frequency of 20 Hz while assuming that the subsurface is isotropic. To implement full waveform inversion, we use a two‐dimensional time‐domain finite‐difference method and the L2 norm to measure the data misfit. We use both refractions and reflections in P‐ and SH‐wave data to reconstruct the P‐ and S‐wave velocity models from the surface to the reservoir. The inverted P‐ and S‐wave velocities contain the main features of the model (e.g., major faults and channels) but have some difficulties in estimating high‐frequency velocity variation within the first 300‐m depth of the model due to the frequency constraint. We then use the inverted P‐ and S‐wave velocities to generate Kirchhoff depth migration gathers and images from the P‐, PS‐ and SH‐wave data. The flat P‐ and SH‐wave common‐image offset gathers suggest that SH‐ and P‐wave full waveform inversion can generate adequate S‐ and P‐wave velocities for migration. Flat PS‐wave gathers and the clear PS‐wave migration image are also obtained using the inverted P‐ and S‐wave velocities simultaneously. This result indicates that obtaining S‐wave velocities from SH‐wave data can aid PS‐wave data processing and imaging. Moreover, the SH‐wave images and S‐wave images of the radial component provide better delineation of fault planes and small‐scale geobodies within the reservoir since the wavelength of the S‐wave is smaller compared to P‐wave when similar frequency ranges are recorded. Therefore, our study shows that S‐wave velocities can be successfully constructed by the two‐dimensional full waveform inversion application of the SH‐wave data. The subsequent imaging of multicomponent seismic data improves the delineation of certain unconventional reservoirs compared to the traditional P‐wave imaging.

Selection and integration of adjustable load in multiple scenarios

In the context of the “carbon peaking and carbon neutrality goals”, the new electricity systems are evolving towards source-load friendly interactions. At the same time, the increasing necessity for adjustable loads to participate in the power balance of the new electricity systems is highlighted. Consequently, a large-scale source-grid-load design scheme is proposed. It employs three independent communication channels to facilitate communication between users and intelligent grid-load terminals. Based on analysis of the individual loads and equipment characteristics of each user, principles for user shunt load access principle and adjustable loads are formulated by combining the maximum duration, frequency constraints, and compliance costs. Furthermore, it proposes construction plans for both the customer side in a single distribution room and the customer side distributed across different locations. According to the experimental analysis of 245 users, the response time of the experimental system is less than 600 ms. These advancements enhance the emergency response speed and responsiveness, contributing to the advancement of precise, real-time, and lean management of the demand side of the power grid.

Transient heat conduction in multi-material topology optimization of thermoelastic structures involving dynamic constraints

This work presents a modified solid isotropic material with penalization (SIMP) for conducting dynamic-constrained multi-material topology optimization (MMTO) of thermoelastic structures subjected to transient thermal conduction. The novelty of this study is the multi-material optimization of instantaneous temperature conduction under specific frequency constraints, which has never been studied before. The proposed method has been developed for general models of multi-material interpolations such as thermal stiffness, heat capacity, and thermal stress coefficient. The temperature environment is formulated by applying prescribed mechanical and thermal loads that are exposed over a period of time. In this work, we focus on the objective of minimizing compliance in a transient heat conduction structure while simultaneously imposing constraints on the dynamics. With high temperatures, the stiffness of the optimization results decreases while stability is still guaranteed. The sensitivity of the objective function is subsequently calculated using the discretize-then-differentiate approach for the dynamic problem as well as the adjoint variable method. This study examines the impact of thermal fields and different time increments in conjunction with dynamic criteria. The outcomes of heat conduction result in notable alterations under identical dynamic constraint levels.

Structural seismic response reconstruction method based on multidomain feature-guided generative adversarial neural networks

Structural seismic response reconstruction is important to assess the safety of structures. This study presents a novel multidomain feature-guided generative adversarial neural network model (MWGAN-TF) for reconstructing the seismic responses of structures, which takes into account the joint non-stationarity of the seismic response in the time-frequency statistical domain. It innovatively incorporates time, frequency, and statistical-domain feature constraints into the multiscale generative adversarial neural network, which guides the model to learn the multidomain feature information of the seismic response at different time scales. A statistical indicator (CNCSI) was proposed to evaluate the performance of the model in capturing nonstationary characteristics. The effectiveness of the MWGAN-TF was verified using response data from numerical models of a three-story moment-resisting frame and reinforced concrete frame structures, as well as the field measurement data of an actual building. Thereafter, the effects of different domain feature-guided models on the reconstruction response accuracy are discussed. The results show that embedding multidomain feature constraints can provide a more reliable response reconstruction by improving the ability of the model to capture nonstationary characteristics. Thus, the deep learning paradigm based on multidomain feature guidance outperforms the classical neural network guided only by time-domain features.

Ground-roll attenuation using dual-model self-supervised selective learning with blind horizontal convolutional neural networks

Ground-roll is a coherent noise that we inevitably encounter during seismic data acquisition on land. It broadly conceals the reflected wave signals, reducing the signal-to-noise ratio (SNR) of data. To attenuate ground-roll, various machine learning techniques have been studied. Recently, the label-free self-supervised learning-based techniques have become actively studied, and the ground-roll attenuation method using the two U-Nets and the loss function combining the Fourier and misfit losses has shown high accuracy. However, this method suffers from incomplete separation of ground-roll from desired signals, which is caused by the identity mapping problem of U-Net, and has instability due to the loss function. To mitigate this problem, we propose using the blind horizontal network (BHN) and dual-model self-supervised selective learning (dSSSL). BHN is designed by removing horizontal pixels in the vertically aligned receptive fields to prevent the identity mapping and effectively separate ground-roll from seismic data. For dSSSL, we use the output image from the first network and its residuals with respect to the input to redistribute ground-roll and desired signals. The synthetic data experiment shows that the proposed ground-roll attenuation method improves the accuracy and convergence stability. For the synthetic data, we also investigate the effects of user-defined parameters such as weighting factors and frequency constraints. Furthermore, we compare our method with the widely used f-k filter for the field data acquired in Pohang, South Korea, which indicates that our approach has a performance close to f-k filtering.

A Simple Differential Evolution with Random Mutation and Crossover Constants for Constrained Optimization

The article proposes a simple version of the differential evolution algorithm (abbreviated as sDE) in which the mutation factor and crossover constant are chosen randomly in the range (0,1) during the search for the optimal solution. The sDE is the same as the original version of the differential evolution algorithm, except the user does not have to choose the best values of mutation constant and crossover constant for each optimization problem. Therefore, the optimization process is now very simple as it remains only one parameter (i.e. the population size) in the algorithm, besides the stopping criterion (e.g. number of iterations). It also consumes less computation time than the original differential evolution as it is not necessary to tune the mutation and crossover constants. In this study, the proposed technique is applied to three constrained optimizations, three engineering design problems, and six planar and spatial trusses under frequency constraints. Despite the very simple characteristics of the proposed technique, sDE gives promising results in comparison with other results in the literature.

Modified jaya optimization and TOPSIS for determining the optimal frequency in LF-HVac

This study presents a novel approach of hybrid modified Jaya and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) optimization (MJTO) for efficiently determining the optimal frequency of low-frequency HVac lines. The proposed technique takes frequency constraints and static synchronous compensator (STATCOM) equations into the account. The objective functions in this study are the minimization of power losses, voltage deviation, and voltage stability index of transmission system. This study examines two types of objective functions: the traditional quadratic function and the enhanced quadratic function. These functions are used to incorporate more accurate modeling that considers low frequency. The MJTO is employed for global searching and gradient-free optimization to determine optimal control settings. The Modified Newton-Raphson method is utilized to minimize the mismatch power between power flow (PF) and STATCOM equations. The proposed method utilizes a hybrid technique to handle inequality constraints by preserving feasible solutions while keeping the original objective function intact. The suggested methodology is successfully implemented in extensive benchmark testing of IEEE systems on the 39 Bus and 14 Bus. The optimal solutions obtained are validated by comparing them to recent algorithms as mentioned in literature. The analytical and Statistical results indicates that the proposed optimization strategy is more optimistic for the LF-HVac system.

An Offline–Online Integration Approach for Security Traffic Patrolling With Frequency Constraints

An Offline–Online Integration Approach for Security Traffic Patrolling With Frequency Constraints

Optimal design of truss domes with frequency constraints using seven metaheuristic algorithms incorporating a comprehensive statistical assessment

In this article, seven recently developed metaheuristic algorithms are utilized for optimal design of dome-shaped trusses with natural frequency constraints. These algorithms are social network search, jellyfish search optimizer, equilibrium optimizer, teaching-learning-based optimization, grey wolf optimizer, colliding bodies optimization, and the improved grey wolf optimizer. This study focuses on the assessment and tuning of these algorithms to enhance both computational efficiency and solution quality. In particular, we introduce a hyperparameter tuning procedure that significantly improves the performance of the algorithms to make them more suitable for the solution of structural optimization problems. The performance of the selected algorithms is studied through five benchmark examples for design optimization of dome structures, from small-scale to large-scale cases, with frequency constraints. Many combination scenarios are studied for hyperparameter tuning of the algorithms in each design example in order to provide comprehensive statistical results determining the sufficient number of structural analyses as well as the number of particles to find an efficient condition of each algorithm. Indeed, this study also presents an insight into the efficient setting of hyperparameters for each algorithm, leading to a better solution with lower computational cost. Furthermore, the optimization results provide a comparison of the solutions obtained in the current and previous studies in order to demonstrate the suitability of the selected algorithms.

Hybrid event-triggered control for networked switched Takagi–Sugeno fuzzy systems with aperiodic DoS attacks

This article investigates the event-triggered control problem for networked switched Takagi–Sugeno fuzzy systems (NSTSFSs) with denial of service (DoS) attacks. First, an attack-instant-constrained hybrid event-triggered mechanism (ETM) is proposed, which uses the acknowledgment character (ACK) detection scheme. It can describe the triggering schemes under different attack intervals and modify the triggering frequency based on the performance of the system. Second, a new segmented Lyapunov function is designed that takes into account the asynchronous behavior of system and controller modes, as well as DoS frequency and duration constraints. Then, sufficient conditions are provided to ensure the exponential stability of the system and have an H∞ performance. Furthermore, a collaborative design scheme is proposed to obtain controller gains, the switching law, and event-triggered parameters. Finally, the accuracy and effectiveness of this method are verified through two simulation examples.

Situation-Aware Load Restoration Considering Uncertainty and Correlation

In order to minimize power supply interruption to customers, power system restoration needs to be performed rapidly after a blackout. With the integration of intermittent renewable energy and flexible loads, power system load patterns are becoming more uncertain. The goal of this paper is to tackle the challenging task of developing a secure yet speedy load restoration planning strategy considering load uncertainty. The key is to leverage the real-time measurements of the restored load blocks to refine the statistical knowledge about the unrestored load blocks derived from historical data, such that the load restoration plans can be less conservative without harming security. Specifically, as the restoration process rolls forward and more loads are restored, we use a Kalman filter to update the probability distribution of the unrestored loads using the newly available measurements from the restored loads. With the updated distribution, a rolling-horizon load restoration problem for load-pickup decision making is formulated with given specified confidence levels under frequency, voltage, and power flow constraints. The effectiveness of the proposed method is evaluated through case studies on the IEEE 39-bus test system and the NPCC 140-bus system. Results demonstrate that the proposed method can restore loads more quickly and securely than conventional methods under load uncertainty.

Minimum Energy Demands of Energy Storages for Fast Frequency Response: Formulation, Solution, and Implementation

Energy storage (ES) is a kind of promising but costly fast-frequency-response (FFR) resource in low-inertia power systems. This paper addresses the minimum demand of a power system for energy capacities of ES to providing sufficient frequency support, including the formulation, the optimal solution, and its practical implementation. First, the minimum energy control problem of ESs for providing FFR with transient frequency constraints is formulated and then converted into an optimal frequency trajectory planning counterpart. This transformation makes the transient frequency constraint tractable and allows to identify the optimal frequency trajectory that minimizes energy demand for ESs, which leads to an analytical expression of the system minimum demand for ESs energy capacities to ensure frequency security. Moreover, by unfolding the optimal frequency trajectory, the optimal control strategy of ESs is derived explicitly for the first time. The theoretical result directs to a practical controller implementation, which is referred to as the decentralized optimal energy frequency control (DOEFC). Finally, simulations on the modified IEEE 39- bus system verify our results and demonstrate the superiority of the DOEFC in reducing the energy capacity demand of ESs, defending successive disturbances, and hedging against parameter errors.

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.

Topology optimization of stationary fluid–structure interaction problems considering a natural frequency constraint for vortex-induced vibrations attenuation

Topology optimization applied to fluid–structure interaction problems is challenging because the physical phenomenon in real engineering applications is usually transient and strongly coupled. This leads to costly solutions for the forward and adjoint problems, the computational bottleneck of the topology optimization method. Thus, this paper proposes a topology optimization problem formulated in the steady state with post-processing and verification in the transient state. The objective is to design a stiff structure with lower effects of vibrations induced by the transient fluid vortices. For that, the compliance minimization problem is solved subject to a natural frequency constraint (without any volume constraint). The TOBS-GT (Topology Optimization of Binary Structures with geometry trimming) method is used to solve the problem. To observe the vortex-shedding around the structure, a transient simulation is performed considering an incompressible fluid flow under a laminar regime and the structure subject to large displacements. For topology optimization, the fluid flow is at a steady state and the structure is modeled considering small displacements, i.e., a one-way coupled analysis. The finite element method is used to solve the governing equations and obtain the direct/adjoint sensitivities for the compliance and natural frequency functions. In this approach, the natural frequency of the structure is shifted away from the fluid flow vortex-shedding frequency, avoiding resonance. Numerical examples show that the proposed method can be effectively applied to design 2D structures in FSI problems with lower effects of Flow-Induced Vibration, attenuating the levels of displacement at the analyzed points of the structure.

SABO algorithm for optimum design of truss structures with multiple frequency constraints

In this study, a very recently developed intelligent algorithm called the self-adaptive bonomo optimizer (SABO) algorithm is implemented for the size and shape optimizations of the truss structures with the multiple frequency constraints. The bonomo optimizer (BO) algorithm is a recently developed metaheuristic optimization algorithm that imitates the social behavior and reproductive schemes of the bonobos and this algorithm is successfully applied to solve some challenging and highly nonlinear optimization problems. On the other hand, the BO algorithm suffers from the poor exploration and prematurely converges to the non-optimal solutions, especially when dealing with the multi-dimensional optimization problems. In order to overcome these shortcomings, an improved version of this algorithm, the so-called self-adaptive bonomo optimizer (SABO) algorithm, is utilized to optimize the truss structures subjected to the design constraints. The objective of this study is to minimize the weight of the truss structures with the multiple frequency constraints. Five well-known benchmark problems are considered to verify the robustness and reliability of the SABO algorithm. The design results obtained by the SABO algorithm are compared with those previously reported in the literature.

Predicting the thermal maturity of source rock from well logs and seismic data in basins with low-degree exploration

Vitrinite reflectance (Ro) is a significant geological index that evaluates the thermal maturity of source rock. However, measured Ro data and suitable evaluation methods are lacking, making it difficult to predict the thermal maturity of source rock in basin, especially in those with a low exploration degree. In this study, we propose a novel method for estimating Ro from well logs and seismic data using seismic velocity inversion and the vitrinite reflectance-mudstone porosity (Ro-ϕ) model. First, using a wavelet neural network, acoustic transit time curve was reconstructed from spontaneous potential, gamma rays, resistivity, and density logs, and new curve was used as inputs in a colored inversion to obtain seismic relative velocity. Second, a low-frequency model was established to counteract critical frequency and sequence framework constraints. Third, the seismic absolute velocity was merged by relative and low-frequency velocity components. Finally, Ro distributions were calculated using the Ro-ϕ model. Our findings indicate that the inversion effect improved with low-frequency supplement; compared with the graphic and geochemical method, the Ro-ϕ model predicted Ro in poor-data areas more accurately, with a relative error of <9.5205%. We also propose an explanation for the appearance of highly mature source rocks distributed from dispersion to aggregation in depression-rift transitions: the thick stratum in the downthrow wall of boundary faults promote source rock maturity in the rift period; hence, in an open depression, the source rocks in large subsidence areas are highly mature, particularly near the downthrow wall of a boundary fault, which has the highest maturity owing to the superimposed subsidence of the overlying rifted basin.