Weibull Probability Density Function Research Articles

A novel derivative search political optimization algorithm for multi-area economic dispatch incorporating renewable energy

Multi-area economic dispatch (MAED) incorporating renewable energy has become an important issue in the power system optimization. Existing intelligent optimization algorithms often suffer from poor solution accuracy or slow convergence when dealing with MAED problems. In this paper, a novel derivative search-based political optimization (DSPO) algorithm is proposed to handle the MAED problem incorporating renewable energy including wind and solar energy. In the renewable energy modeling, the Weibull and log-normal probability density functions are used to calculate available wind and solar power respectively. In order to improve the search performance, DSPO adopts two strategies: leader guide strategy and derivative search mechanism. The former adds the leader’s global optimal information which can direct candidate solutions to more promising regions and speed up convergence. The latter derives neighborhood solutions around some high-quality solutions to improve the exploitation ability. The DSPO algorithm is applied to solve four MAED problems which take into account valve point effect, prohibited operating zone, power loss and so on. The simulation results show that the DSPO algorithm achieves the overall best results in terms of convergence speed, solution accuracy and stability when compared with several well-established algorithms.

Bayesian approach for modeling diameter distributions of patula pine (Pinus patula Schiede ex Schltdl. & Cham.) stands in Southern Mexico

Characterization of the diameter distribution of forest stands managed for timber production provides accurate estimates of existing wood volume by diameter class and area unit. It provides the basis for determining the stand's ecological and economic value, its structure, the potential for ecosystem services, and appropriate management practices. Patula pine is one of the most important conifers in southern Mexico and requires biometric tools to improve management strategies. This study aimed to use the Bayesian approach to estimate the parameters of Johnson's SB (JSB) and Weibull (W) probability density functions (pdf) and to model the diameter distribution of patula pine stands in southern Mexico. We used data from 462 diameter distributions derived from 66 permanent 400 m2 sampling plots. The results indicated that the Bayesian approach was appropriate for estimating the JSB and W pdf parameters. Due to the similarity between the nonparametric tests and the goodness-of-fit statistics of the functions, the graphical analysis helped to select the W function as the better option to adequately model the diameter distribution of the analyzed stands. The equations developed for parameter prediction of the W function with stand variables allowed us to characterize and project the theoretical distribution of diameter classes in a simple accurate way with variables easily obtained from forest inventories. The Bayesian approach proved to be an effective method for estimating the pdf parameters used. This allowed for the correct characterization of the observed diameter distribution, and its implementation was easy for executing the procedure. Diameter distribution models are a powerful tool for forest inventory and management of patula pine stands analyzed in southern Mexico.

A survey of the high-cycle fatigue performance of additively manufactured alloy 718

This paper presents a survey of the published high-cycle fatigue (hcf) data for the nickel–iron superalloy alloy 718 fabricated by additive manufacture. Approximately 680 fatigue data points were collected from the published literature and the reported data are presented in the form of stress versus cycles to failure curves for load ratios of R = −1, 0 and 0.1. Following this, curves showing estimated survival probabilities of 0.5, 0.95 and 0.99 are constructed using a statistical analysis based on the Weibull probability density function. Finally, a comparison between the fatigue performance of additively manufactured and wrought alloy 718 under fully reversed loading conditions ( R = −1) is provided.

A percolation model of unsaturated hydraulic conductivity using three-parameter Weibull distribution

Accurate estimation of unsaturated hydraulic conductivity, K(Sw), is crucial for modeling water and solute transport in variably-saturated soils. In this study, a new model for the estimation of K(Sw) based on percolation theory and critical path analysis is presented, in which the pore-throat size distribution is described by the three-parameter Weibull probability density function. To evaluate the performance of the proposed K(Sw) model, two datasets including more than three hundred samples are analyzed. The first dataset includes 240 pore-network simulations, while the second dataset consists of 101 soil samples from the UNSODA database. For the pore-network simulations, for which both pore-throat size distributions and capillary pressure curves are available, we estimate K(Sw) from the capillary pressure curve with RMSLE = 0.54 slightly better than the estimations obtained from the pore-throat size distribution with RMSLE = 0.6. For the soil samples, since only the capillary pressure curve is measured, we estimate K(Sw) from the capillary pressure curve and evaluate three previously proposed approaches for determining the exponent, α, in Poiseuille's law. We find that RMSLE = 0.98 for α = 3, RMSLE = 0.87 for α = 2(4 − D) − (3 − D)/(2D − 3), and RMSLE = 1.06 for α = 4 − 0.74D, in which D is the fractal dimension characterizing the pore space. Comparing the results with previous studies in which the power-law probability density function was used to characterize capillary pressure curve and pore sizes shows that the proposed three-parameter Weibull distribution, in conjunction with the CPA analysis, may more accurately estimate K(Sw) for a wide variety of soils ranging from very fine to very coarse textures.

Gradient pyramid mechanism and Nelder-Mead simplex enhanced Colony Predation Algorithm for optimal power flow problems

The escalating human energy demand, particularly in the realm of electricity consumption, imposes a substantial burden on power system planning, resulting in the emergence of the optimal power flow (OPF) problem. To address this challenge, researchers have implemented a Flexible AC Transmission System (FACTS) in modern power systems to optimize network congestion. This paper presents a new application of the Colony Predation Algorithm (CPA) in the domain of Optimal Power Flow (OPF) through the introduction of an enhanced Colony Predation Algorithm (PNMCPA). PNMCPA incorporates the gradient pyramid mechanism and the Nelder-Mead simplex (NMs), marking the first utilization of CPA in the OPF field. The proposed approach presents a novel hierarchical gradient pyramid mechanism that combines the approximate gradient descent method with the construction of a pyramid fall rate, thereby optimizing the population as a whole within a framework that enhances population diversity. Additionally, the NMs algorithm is employed to optimize the optimal set of solutions for the population, thereby accelerating the convergence efficiency of the algorithm. The primary objective of this study is to optimize multiple factors, including the generation cost and transmission loss of the power system when multiple FACT components are present. Utilizing the Weibull probability density function, the model captures the uncertain and unstable nature of wind energy resources, encompassing direct, penalty, and standby costs. The proposed algorithm is applied to the IEEE30 bus test system, and the experimental results demonstrate that PNMCPA achieves a final optimization cost of 806.0132 $/h, surpassing other optimization algorithms. Concerning the power loss matter within the bus system, the PNMCPA algorithm significantly effectively mitigates total power loss, reducing from 1.44 MW to 1.41 MW instead of the initial CPA and substantially enhancing convergence speed. Empirical simulation outcomes clearly endorse PNMCPA as a highly efficient approach to tackling optimal power flow problems in the presence of multiple FACTS devices. The significant advancements presented in this paper mark a significant contribution to the field, offering a novel and superior solution to optimize power systems in the face of escalating energy demands.

Optimal power flow of thermal-wind-solar power system using enhanced Kepler optimization algorithm: Case study of a large-scale practical power system

In the current century, electrical networks have witnessed great developments and continuous increases in the demand for fossil fuels based energy, leading to an excessive rise in the total production cost (TPC), as well as the pollutant (toxic) gases emitted by thermal plants. Under this circumstances, energy supply from different resources became necessary, such as renewable energy sources (RES) as an alternative solution. This latter, however, characterized with uncertainty nature in its operation principle, especially when operator system wants to define the optimal contribution of each resource in an effort to ensure economic and enhanced reliability of grid. This paper presents an Enhanced version of Kepler optimization algorithm (EKOA) to solve the problem of stochastic optimal power flow (SOPF) in a most efficient way incorporating wind power generators and solar photovoltaic with different objective functions, the stochastic nature of wind speed and solar is modeled using Weibull and lognormal probability density functions respectively. To prove the effectiveness of the proposed EKOA, various case studies were carried out on two test systems IEEE 30-bus system and Algerian power system 114-bus, obtained results were evaluated in comparison with those obtained using the original KOA and other methods published in the literatures. Thus, shows the effectiveness and superiority of the efficient EKOA over other optimizers to solve complex problem. The incorporation of RES resulted in a significant 2.39% decrease in production cost, showcasing EKOA’s efficiency with a $780/h, compared to KOA’s $781/h, for IEEE 30-bus system. For the DZA 114-bus system revealed even more substantial reductions, with EKOA achieving an impressive 12.6% reduction, and KOA following closely with a 12.4% decrease in production cost.

An optimal power flow solution for a power system integrated with renewable generation

<abstract> <p>Integrating Green Renewable Energy Sources (GRES) as substitutes for fossil fuel-based energy sources is essential for reducing harmful emissions. The GRES are intermittent and their integration into the conventional IEEE 30 bus configuration increases the complexity and nonlinearity of the system. The Grey Wolf optimizer (GWO) has excellent exploration capability but needs exploitation capability to enhance its convergence speed. Adding particle swarm optimization (PSO) with excellent convergence capability to GWO leads to the development of a novel algorithm, namely a Grey Wolf particle swarm optimization (GWPSO) algorithm with excellent exploration and exploitation capabilities. This study utilizes the advantages of the GWPSO algorithm to solve the optimal power flow (OPF) problem for adaptive IEEE 30 bus systems, including thermal, solar photovoltaic (SP), wind turbine (WT), and small hydropower (SHP) sources. Weibull, Lognormal, and Gumbel probability density functions (PDFs) are employed to forecast the output power of WT, SP, and SHP power sources after evaluating 8000 Monte Carlo possibilities, respectively. The multi-objective green economic optimal solution consisted of 11 control variables to reduce the cost, power losses, and harmful emissions. The proposed method to address the OPF problem is validated using an adaptive IEEE bus system. The proposed GWPSO algorithm is evaluated by comparing it with PSO and GWO optimization algorithms in terms of achieving an optimal green economic solution for the adaptive IEEE 30 bus system. This evaluation is conducted within the confines of the same test system using identical system constraints and control variables. The integration of a small SHP with WT and SP sources, along with the proposed GWPSO algorithm, led to a yearly cost reduction ranging from <bold>$\$$19,368</bold> to <bold>$\$$30,081</bold>. Simulation findings endorsed that the proposed GWPSO algorithm executes fruitfully compared to alternative algorithms regarding a consistent convergence curve and robustness, proving its potential as a viable choice for achieving cost-effective solutions in power systems incorporating GRES.</p> </abstract>

CAVOA: A chaotic optimization algorithm for optimal power flow with facts devices and stochastic wind power generation

AbstractThe study proposes a modified version of African Vultures Optimization Algorithm (AVOA) to address the optimal power flow (OPF) issue. The developed optimizer is called Chaotic AVOA (CAVOA). Prior to applying CAVOA to the problem at hand, its accuracy is evaluated using 23 benchmark functions. The production powers of WTs that are interrupted are predicted using Weibull probability density functions (PDFs). Two additional costs, namely penalty cost and reserve cost, are incorporated into the goal function of the OPF. The simulation results of CAVOA are compared with those of the original AVOA to solve the OPF. The proposed OPF technique and its solution methodology are verified on the IEEE 30‐bus test system, taking into account the flexible alternating current transmission systems (FACTS) devices, which have several benefits such as reducing active power transmission loss, regulating power flow, and improving voltage stability/profile. The research's simulation results demonstrate that CAVOA is more effective in identifying the OPF's optimal solution by reducing the overall power cost and power losses. The results indicate that the CAVOA algorithm outperforms AVOA as a metaheuristic optimization algorithm due to its superior capability in addressing challenging OPF problems with a minimal convergence rate. For example, when comparing the two algorithms, CAVOA achieved a significant improvement. It successfully reduced the cost function by approximately 0.023% in Case I and 0.035% in Case II, while also decreasing power loss by 2.57% in Case II and 0.57% in Case I. Additionally, CAVOA exhibited a remarkable reduction of 5.36% in voltage deviation compared to AVOA in Case I. Furthermore, in Case III, CAVOA demonstrated a decrease of 0.64% in gross cost when compared to AVOA.

Contingency Assessment for Power System Integrated with Wind Power

Electric demand in the last few years has widely increased, especially in Iraq, where there is a significant difference between the generation and the load in almost all months of the year, particularly in the summer season. One of the important aspects where the operational engineers must take appropriate action in case of an unforeseen catastrophe is power system security. Consequently, the security of the power system depends on the contingency analysis. In order to investigate the impact of wind power on the contingency analysis, three wind farms (WFs) are selected based on the wind's speed availability in Iraq, which are Shaikh Saad, Al-Dujaili, and Al-Fajar. In addition, the wind speeds for these locations are analysed using the Weibull and Rayleigh probability density functions. In this regard, this paper studied and analysed the impact of integrating wind power on the operation of the 132 kV Iraqi grid systems (zone 18). The results show that when line outage contingencies occur (single- and double-line outages), the risk of power flow violations based on the MVA rating will be reduced when integrating wind energy with a 100% integration rate with the Iraqi grid system. Matlab, a programming language, and the Power System Simulator for Engineering (PSS/E) software (Version 32) are used to simulate the proposed approach of integrating wind power into the grid.

Statistical distribution of micro and macro pores in acrylic bone cement- effect of amount of antibiotic content

Aseptic loosening due to mechanical failure of bone cement is considered to be a leading cause of revision of joint replacement systems. Detailed quantified information on the number, size and distribution pattern of pores can help to obtain a deeper understanding of the bone cement's fatigue behavior. The objective of this study was to provide statistical descriptions for the pore distribution characteristics of laboratory bone cement specimens with different amounts of antibiotic contents. For four groups of bone cement (Palacos) specimens, containing 0.3, 0.6, 1.2 and 2.4 wt/wt% of telavancin antibiotic, seven samples per group were micro computed tomography scanned (38.97 μm voxel size). The images were first preprocessed in Mimics and then analyzed in Dragonfly, with the level of threshold being set such that single-pixel pores become visible. The normalized pore volume data of the specimens were then used to extract the logarithmic histograms of the pore densities for antibiotic groups, as well as their three-parameter Weibull probability density functions. Statistical comparison of the pore distribution data of the antibiotic groups using the Mann–Whitney non-parametric test revealed a significantly larger porosity (p < 0.05) in groups with larger added antibiotic contents (2.4 and 0.6 wt/wt% vs 0.3 wt/wt%). Further analysis revealed that this effect was associated with the significantly larger frequency of micropores of 0.1–0.5 mm diameter (p < 0.05) in groups with larger antibiotic content (2.4 wt/wt% vs and 0.6 and 0.3 wt/wt%), implying that the elution of the added antibiotic produces micropores in this diameter range mainly. Based on this observation and the fatigue test results in the literature, it was suggested that micropore clusters have a detrimental effect on the mechanical properties of bone cement and play a major role in initiating fatigue cracks in highly antibiotic added specimens.

Fire-mediated biomass loss of woody species seedlings causing demographic bottleneck in the Terai Forests of Central Nepal

Forest fire produces varying ecological effects determining vegetation patterns in ecosystems. Plant community assemblages in forests are altered by fire influencing growth and development. Some plant communities are suppressed and some are encouraged to develop due to fire. Little empirical evidence exists revealing the condition of fire-mediated loss of small-sized individuals, and response of fire to demographic structure of woody plant species in Nepal. The aim of this research, therefore, is to quantify fire-mediated biomass loss of small-sized individuals of woody species (seedlings), and investigate the associated impacts on the demographic structure of plants in the Terai forests of central Nepal. Impacts on small-sized individuals of woody plant species were evaluated based on evidence from 25 sites with 50, 1 m × 1 m subplots for seedlings nested in 10 m × 10 m plots (n = 50) for saplings and adults. Of the 50 sampling plots, 25 represented fire-affected and the remaining 25 represented control plots. Mean density of resprouting and newly grown seedlings developed in one year after the surface fire was 46,800 ± 4071 inds. ha−1. Shorea robusta Gaertn. was the most abundant species regenerated with seedlings in the control forest sites. The estimated average yearly loss of above ground biomass (AGB) for woody plant seedlings in the forest due to surface fire was 1,651.5 ± 360.2 kg ha−1. Of the total fire-affected AGB of S. robusta, 700.0 kg ha−1 was the immediate burnt loss and 322.5 kg ha−1 was dead AGB left unburnt. Similarly, among the other most abundant species, higher proportion of immediate fresh AGB loss was observed for Mallotus philippensis (Lam.) Müll.-Arg. and Casearia graveolens Dalzell. compared to dead AGB left unburnt. The Weibull probability density function shows the existence of saplings recruitment bottleneck in the fire-prone forest sites, i.e., growth of seedlings to saplings was restricted. Surface fire impacted the development of DBH class > 0–5 cm saplings. Surface fires are one of the potential environmental filters of the plant species regeneration and composition in the forests of lowland Terai Nepal. These demographic variations and bottlenecks should be considered while formulating management actions to conserve vegetation assemblages in fire-mediated ecosystems.

Optimal power flow with distributed energy sources using whale optimization algorithm

&lt;span lang="EN-US"&gt;Renewable energy generation is increasingly attractive since it is &lt;br /&gt; non-polluting and viable. Recently, the technical and economic performance of power system networks has been enhanced by integrating renewable energy sources (RES). This work focuses on the size of solar and wind production by replacing the thermal generation to decrease cost and losses on a big electrical power system. The Weibull and Lognormal probability density functions are used to calculate the deliverable power of wind and solar energy, to be integrated into the power system. Due to the uncertain and intermittent conditions of these sources, their integration complicates the optimal power flow problem. This paper proposes an optimal power flow (OPF) using the whale optimization algorithm (WOA), to solve for the stochastic wind and solar power integrated power system. In this paper, the ideal capacity of RES along with thermal generators has been determined by considering total generation cost as an objective function. The proposed methodology is tested on the IEEE-30 system to ensure its usefulness. Obtained results show the effectiveness of WOA when compared with other algorithms like non-dominated sorting genetic algorithm (NSGA-II), grey wolf optimization (GWO) and particle swarm optimization-GWO (PSO-GWO).&lt;/span&gt;

Accuracy of wind speed forecasting based on joint probability prediction of the parameters of the Weibull probability density function

This work aims to evaluate different error estimations of the shape and scale parameters of the Weibull probability density function of wind speed measured at the Fujairah site over a 1-year period. This study estimates trends in the variation of Weibull parameters using moving averages and Markov series methods. The focus is on the scale and shape factors, which are evaluated by mapping monthly mean wind speeds into a Weibull probability distribution function. Due to the imprecise nature of these factors, multiple data simulations are used to predict Weibull factors based on data measuring interpolations. A procedural algorithm is proposed to select the overall best forecast based on several estimation methods that evaluate raised prediction errors. A probabilistic analysis is followed to predict future wind speed and wind energy based on variations in the scale and shape factors. This study focuses on the scale factor variation as it is found to be more dominant than the Weibull shape factor. The forecasted wind speed is checked with the measured value in future months and found to be within trend values. The results suggest that the proposed algorithm provides an accurate and reliable method for predicting future wind speed and energy output.

Assessment of the wind energy potential and economic viability of selected sites along Nigeria’s coastal and offshore locations

Wind energy is a promising sector in the power generation industry because it is renewable and globally available. In this research work, the wind energy potential and the economic viability of using wind turbines to generate electricity in some selected sites along Nigeria’s coastline and offshore locations were evaluated. Using the statistical two-parameter Weibull probability density function method, wind speed data retrieved from an indigenous oceanography company and global information system (GIS) were analyzed for wind energy harvest. The energy output, unit cost of electricity generated by three commercially available wind turbine models (3 MW, 4 MW, and 6 MW), net present value (NPV), and payback period were evaluated. Levelized cost of electricity (LCOE) sensitivity to the discount rate, foundation cost, and turbine lifespan were also examined. The findings from the study showed that the offshore sites have four times greater wind power potential than the coastal sites. The offshore sites can be categorized as “class IIIb” wind sites, making the locations suitable for wind energy harvest. The techno-economic analysis showed that the net gains from investing in a 60-MW wind farm in the region can be as high as $62,000,000.00, while the project payback time can be as low as 5.74 years. Two of the offshore sites are recommended for the development of an offshore wind farm in the country because of their relatively low LCOE (0.04 $/kWh), higher NPV, and lower investment payback time. The Vesta-117 model wind turbine is the most suitable wind turbine system and recommended for use in the region because of its low cut-in speed (3 m/s). Sensitivity analysis showed that the LCOE of offshore-01 was reduced by 31% when the lifespan of the V117 turbine was increased from 20 to 25 years. The results also showed that reductions in the discount rate and foundation cost positively affect the LCOE.

Storage Optimization (r, Q) Strategy under Condition-Based Maintenance of Key Equipment of Coal-Fired Power Units in Carbon Neutrality Era

For the safe, stable, and economic operation of thermal power units in new power systems, the condition-based maintenance mode and storage strategy of key equipment and materials for power generation enterprises were selected. According to the storage linkage demand of condition-based maintenance, a Weibull probability density function was used to calculate spare parts demand, and an intelligent storage optimization model with an availability constraint was established. The application cases of spare parts cost and availability of high-value key equipment and low-value key equipment of coal-fired thermal power units were analyzed, respectively, and the influence of different life spans and the number of covered units on the model were expounded. The results show that the cost of spare parts borne by a single unit is greatly reduced via the optimization of an intelligent inventory (r, Q) strategy on the premise that the availability of units is not less than 99.5%.

Equilibrium optimiser for the economic load dispatch problem with multiple fuel option and renewable sources

The integration of thermal units with renewable sources leads to a highly nonlinear and difficult Economic Load Dispatch (ELD) problem. However, dependency of wind speed and solar irradiance, renewable sources like wind-solar plants cannot guarantee their output. It has been possible to anticipate the wind speed and solar irradiation by Weibull and beta probability density functions. Wind and solar energy output powers have been estimated using the 2-m point estimation method. The renewable-based ELD problem has a solution thanks to the equilibrium optimizer (EO) technique. Finding the answer in a relatively short amount of computing time is made possible by the method's exploration and exploitation stages. The suggested technique has been validated in three, five, six, fifteen, and huge 160 thermal units linked to renewable energy sources by meeting restrictions such generator operating restrictions, valve point loading impact, and numerous fuel possibilities.

Stiffness sensing by smooth muscle cells: Continuum mechanics modeling of the acto-myosin role

Aortic smooth muscle cells (SMCs) play a vital role in maintaining homeostasis in the aorta by sensing and responding to mechanical stimuli. However, the mechanisms that underlie the ability of SMCs to sense and respond to stiffness change in their environment are still partially unclear. In this study, we focus on the role of acto-myosin contractility in stiffness sensing and introduce a novel continuum mechanics approach based on the principles of thermal strains. Each stress fiber satisfies a universal stress-strain relationship driven by a Young's modulus, a contraction coefficient scaling the fictitious thermal strain, a maximum contraction stress and a softening parameter describing the sliding effects between actin and myosin filaments. To account for the inherent variability of cellular responses, large populations of SMCs are modeled with the finite-element method, each cell having a random number and a random arrangement of stress fibers. Moreover, the level of myosin activation in each stress fiber satisfies a Weibull probability density function. Model predictions are compared to traction force measurements on different SMC lineages. It is demonstrated that the model not only predicts well the effects of substrate stiffness on cellular traction, but it can also successfully approximate the statistical variations of cellular tractions induced by intercellular variability. Finally, stresses in the nuclear envelope and in the nucleus are computed with the model, showing that the variations of cytoskeletal forces induced by substrate stiffness directly induce deformations of the nucleus which can potentially alter gene expression. The predictability of the model combined to its relative simplicity are promising assets for further investigation of stiffness sensing in 3D environments. Eventually, this could contribute to decipher the effects of mechanosensitivity impairment, which are known to be at the root of aortic aneurysms.

A Novel Adaptive Manta-Ray Foraging Optimization for Stochastic ORPD Considering Uncertainties of Wind Power and Load Demand

The optimal control of reactive powers in electrical systems can improve a system’s performance and security; this can be provided by the optimal reactive power dispatch (ORPD). Under the high penetration of renewable energy resources (RERs) such as wind turbines (WTs), the ORPD problem solution has become a challenging and complex task due to the fluctuations and uncertainties of generated power from WTs. In this regard, this paper solved the conventional ORPD and the stochastic ORPD (SORPD) at uncertainties of the generated power from WTs and the load demand. An Adaptive Manta-Ray Foraging Optimization (AMRFO) was presented based on three modifications, including the fitness distance balance selection (FDB), Quasi Oppositional based learning (QOBL), and an adaptive Levy Flight (ALF). The ORPD and SORPD were solved to reduce the power loss (PLoss) and the total expected PLoss (TEPL), the voltage deviations (VD) and the total expected VD (TEVD). The normal and Weibull probability density functions (PDFs), along with the scenario reduction method and the Monte Carlo simulation (MCS), were utilized for uncertainty representations. The performance and validity of the suggested AMRFO were compared to other optimizers, including SCSO, WOA, DO, AHA, and the conventional MRFO on the IEEE 30-bus system and standard benchmark functions. These simulation results confirm the supremacy of the suggested AMRFO for the ORPD and SORPD solution compared to the other reported techniques.

Developing Weibull-based diameter distributions for the major coniferous species in Heilongjiang Province, China

Diameter distribution models play an important role in forest inventories, growth prediction, and management. The Weibull probability density function is widely used in forestry. Although a number of methods have been proposed to predict or recover the Weibull distribution, their applicability and predictive performance for the major tree species of China remain to be determined. Trees in sample plots of three even-aged coniferous species (Larix olgensis, Pinus sylvestris and Pinus koraiensis) were measured both in un-thinned and thinned stands to develop parameter prediction models for the Weibull probability density function. Ordinary least squares (OLS) and maximum likelihood regression (MLER), as well as cumulative distribution function regression (CDFR) were used, and their performance compared. The results show that MLER and CDFR were better than OLS in predicting diameter distributions of tree plantations. CDFR produced the best results in terms of fitting statistics. Based on the error statistics calculated for different age groups, CDFR was considered the most suitable method for developing prediction models for Weibull parameters in coniferous plantations.

A vertical and horizontal crossover sine cosine algorithm with pattern search for optimal power flow in power systems

Most of the energy consumption is now being used to supply human demand for electricity, which has increased the burden of power system planning to some extent, and thus, researchers proposed solutions to the optimal power flow (OPF) problem. In such a background, flexible AC transmission system (FACTS) devices are widely used in modern power systems to alleviate human power demand and improve network congestion problems. This research proposes a better-quality sine cosine algorithm (CPSCA) based on a crossover mechanism and pattern search algorithm for optimizing multiple objectives, such as system generation cost and transmission losses when we have multiple types of FACTS devices in the power system. The proposed method uses sine and cosine theory and evolutionary strategy to continuously sample and update the framework and improve the quality of the solutions. The method uses a class of vertical and horizontal crossover operators and pattern-shifting techniques to find the optimal solution set. In addition, the Weibull probability density function was used in this study to model uncertainty in wind energy, while direct costs, penalty costs, and standby costs were considered in constructing the target model. Various types of FACTS devices, such as thyristor-controlled series compensators, thyristor-controlled phase shifters, and static reactive power compensators, are also inserted into the model as power in the target optimization problem. The proposed algorithm has experimented on an IEEE30 bus test system. Based on the experimental results, CPSCA achieves an optimal total cost of 806.0225 $/h. In terms of power loss of the bus system, CPSCA reduces the total power loss value from 2.042 MW to 1.41 MW compared to the original sine cosine algorithm, which is a 31% improvement and has an optimal power loss value. Therefore, the simulation results demonstrate that the proposed algorithm is an effective technique for optimizing the optimal power flow of the entire power system and FACTS equipment.