An accurate method for leakage inductance calculation of shell-type multi core-segment transformers with circular windings

The leakage field in shell-type transformers is strongly affected by the boundary conditions introduced by the core walls and thus the effect of the core should be considered properly in the leakage inductance calculation. In this paper, a new method for accurate calculation of the leakage inductance of shell-type multi core-segment transformers with circular windings is presented. For this purpose, first, the expressions for self and mutual inductances are derived in cylindrical coordinates considering the core walls as the flux-normal boundary condition. Then, a new approach is proposed for calculating the leakage inductance considering the number and dimensions of the used core segments. The method is developed at first for single and double core-segment transformers (known also as E-core and U-core transformers) and then adopted for shell-type segmented-core transformers. The method is verified by 3-D FEM simulations. The comparisons with the previous analytical methods demonstrate the superiority of the proposed method. A transformer prototype has been built and verification tests have been conducted. The comparisons show that the leakage inductance can be estimated with an error less than 1%, demonstrating a very high accuracy with the proposed method

An Accurate Analytical Method for Leakage Inductance Calculation of Shell-Type Transformers With Rectangular Windings

This paper presents an accurate analytical method for calculating the leakage inductance of shell-type E-core transformers with rectangular windings. For this purpose, first, an expression for calculating the leakage inductance per unit length inside the core window considering the core walls as the flux-normal boundary condition is derived. Then, a new accurate method for determining the Mean Length of Turns (MLT) based on the total stored energy is presented. The MLT is needed for the leakage inductance calculation using 2-D methods. By dividing the MLT into three partial lengths and calculating the corresponding leakage inductances using three different core window arrangements, the effect of core structure on the total leakage inductance is considered. The method is verified by 3-D FEM simulations as well as the leakage inductance measurements on two different fabricated transformer prototypes. The superiority of the method is also confirmed by comparisons with the previous analytical approaches. The proposed method enables the leakage inductance calculation with an error less than 1%, compared to the 3-D FEM results. Using the presented method, the leakage inductance calculations can be performed rapidly and accurately in the design stage without the need for time-consuming 3-D FEM simulations

A Game Theory Approach for Conjunctive Use Optimization Model Based on Virtual Water Concept

In this study to allocate the agricultural and environmental water, considering virtual water concept, a multi-objective optimization model based on NSGA-II is developed. The objectives consist of equity maximization, agricultural benefit maximization for each region, maximization of green water utilization and finally minimization of environmental shortage. Then a cooperative game (Grand Coalition) model is presented by forming all possible coalitions. By the game model including Nucleolus, Proportional Nucleolus, Normal Nucleolus and Shapley methods, the benefit is reallocated based on all Pareto optimal solutions obtained from multi-objective optimization model. Then using two famous fallback bargaining methods, Unanimity and q-Approval, preferable alternative (solution) for each of the cooperative games is determined. Finally, based on the obtained benefit for each selected alternatives, the two most beneficial alternatives are chosen. The proposed methodology applied for water allocation of Minoo-Dasht, Azad-Shahr and Gonbad-Kavoos cities in Golestan province, Iran for a 3-year period as a case study. Also, eight crops including Wheat, Alfalfa, Barley, Bean, Rice, Corn, Soya, and Cotton are selected based on local experts’ recommendations. The models’ results indicated no significant difference between the grand coalition model and the multi-objective optimization model in terms of the average cultivation area (a relative change of 2.1%), while lower agricultural water allocation occurred for the grand coalition model (about 10.35 percent average) compared with the multi-objective optimization model. It is also observed that more agricultural benefit gained by the grand coalition model (32 percent average). Finally, it is found that Wheat and Corn hold the most rates of import and export, respectively, and Rice was the crop which has the least shortage of production to supply food demand

Comparison of Changes in Mandibular Third Molar Angulation Following First/Second Premolar Extraction versus Non-Extraction Orthodontic Treatments

Objective: Extraction of premolars is believed to affect the eruption of third molars. This comparative study aimed to assess the change in angulation of third molars following first/second premolar extraction versus non-extraction orthodontic treatments.Methods: This historical cohort study was conducted on patients assigned to three treatment groups: extraction of mandibular first premolars (group A), extraction of mandibular second premolars (group B) and non-extraction orthodontic treatment (group C). Each group included 30 third molars. Patients were in the age range of 11-19 years and the third molars were in Nolla’s6-8 stage of tooth development. Pre- and post-treatment panoramic radiographs were analyzed.Results: The angle between the long axis of the mandibular third molar and mandibular plane increased by 7 (2.2°) in group A and 5.2° in group B and the increase in both groups was statistically significant (p<0.05). Angular changes in group C were not statistically significant (p>0.05). The angle between the long axes of mandibular first and third molars decreased by 6.83 (0.3°) in group A. This reduction was statistically significant (p<0.05).Conclusion: In extraction orthodontic treatments (versus non-extraction treatments), mandibular third molars tend to straighten up and become upright so the risk of their impaction may be decreased