Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov–Galerkin approach with moving Kriging interpolation

A detailed analysis of natural frequencies of laminated composite plates using the meshfree moving Kriging interpolation method is presented. The present formulation is based on the classical plate theory while the moving Kriging interpolation satisfying the delta property is employed to construct the shape functions. Since the advantage of the interpolation functions, the method is more convenient and no special techniques are needed in enforcing the essential boundary conditions. Numerical examples with different shapes of plates are presented and the achieved results are compared with reference solutions available in the literature. Several aspects of the model involving relevant parameters, fiber orientations, lay-up number, length-to-length, stiffness ratios, etc. affected on frequency are analyzed numerically in details. The convergence of the method on the natural frequency is also given. As a consequence, the applicability and the effectiveness of the present method for accurately computing natural frequencies of generally shaped laminates are demonstrated.

An efficient meshfree method for vibration analysis of laminated composite plates

Frequency response analysis (FRA) of transformers as a tool for fault detection and location: A review

Power transformers are a key component of electrical networks, and they are both expensive and difficult to upgrade in a live network. Many utilities monitor the condition of the components that make up a power transformer and use this information to minimize the outage and extend the service life. Routine and diagnostic tests are currently used for condition monitoring and appraising the ageing and defects of the core, windings, bushings and tap changers of power transformers. To accurately assess the remaining life and failure probability, methods have been developed to correlate results from different routine and diagnostic tests. This paper reviews established tests such as dissolved gas analysis, oil characteristic tests, dielectric response, frequency response analysis, partial discharge, infrared thermograph test, turns ratio, power factor, transformer contact resistance, and insulation resistance measurements. It also considers the methods widely used for health index, lifetime estimation, and probability of failure. The authors also highlight the strengths and limitations of currently available methods. This paper summarizes a wide range of techniques drawn from industry and academic sources and contrasts them in a unified frame work.

A review of condition monitoring techniques and diagnostic tests for lifetime estimation of power transformers

The meshfree methods in computational mechanics have been actively proposed and increasingly developed in order to overcome some drawbacks in the conventional numerical methods. Over past three decades meshfree methods have found their way into many different application areas ranging from classical astronomical problems to solid mechanics analysis, fluid flow problems, vibration analysis, heat transfer and optimization to the numerical solution of all kind of (partial) differential equation problems. The present work is an effort to provide a comprehensive review of various Meshfree methods, their classification, underlying methodology, application area along with their advantages and limitations. Key contributions of mesh free techniques to the area of fracture mechanics have been discussed with applications of element free Galerkin method (EFGM) to fracture analysis as primary concern.

Meshfree Methods: A Comprehensive Review of Applications

To diagnose electrical and mechanical failures on the active part of power transformers efficiently, different state-of-the-art testing methods are recommended to be performed since transformers are complex devices Measurement results can be equivalent electrical parameters relating to the windings (resistances, leakage/zero-sequence inductances and capacitances), core magnetic property (via induced voltages and exciting currents) or terminal frequency responses (standard FRA tests) Consequently, it is not easy for normal users to implement all necessary measurements, which require much time and training skills due to use of different specialized testing devices To help users for fast and efficient diagnostics, the paper presents a new method in determining most electrical parameters of the transformer active part based on only the driving-point impedance tests performed by means of a vector-network analyzer More importantly, the method can be applied to give a FRA interpretation based on physical electrical parameters, which is currently requested from relevant standards The physical FRA interpretation is found to be useful in calculating immeasurable series capacitances of windings in transformer bulk, which is still problematic until now Investigation on a large distribution transformer shows that the new method is simple, less time consuming but efficient

A new method for purposes of failure diagnostics and FRA interpretation applicable to power transformers

Further application of an efficient novel meshfree technique based on the moving kriging (MK) interpolation for static and dynamic analyses of two-dimensional piezoelectric structures is presented. The MK scheme is used for constructing the shape functions which satisfy the Kronecker delta property. Hence, the burdensome task of enforcing the essential boundary conditions as in the moving least-squares approximation is avoided. The mechanical displacements, electric potential and natural frequencies of structures are investigated in detail through a series of numerical examples that are to demonstrate the applicability and the efficiency of the proposed method. The results obtained are then compared with those of other available reference solutions with very good agreement.

https://iopscience.iop.org/article/10.1088/0964-1726/20/6/065016/pdf

An efficient meshfree method for analysis of two-dimensional piezoelectric structures

The standard frequency response analysis (FRA) is not fully efficient for diagnostics of mechanical failures in power transformers. The article recommends that physical electrical parameters of the transformers should be analyzed in addition to support the current FRA assessment.

A new diagnostic method to support standard frequency response analysis assessments for diagnostics of transformer winding mechanical failures

The authors of this paper proposed an effective method applied to frequency response interpretation in low frequency range and mechanical failure diagnosis support based on measurements and analysis of a physical lumped component transformer circuit. To extend the interpretation until medium frequencies where mechanical failures influence most, this paper presents a novel approach on determining parameters in a physical distributed component circuit. The most important contribution of this paper is the possibility of determination of electrical parameters in the distributed circuit without knowing detailed knowledge of the transformer construction, which has been a challenge so far. In addition, the application capability of the distributed circuit in diagnosis of several mechanical failures in a distribution transformer is also investigated.

Analysis of physical transformer circuits for frequency response interpretation and mechanical failure diagnosis

The lumped transformer equivalent circuit has been recently adapted based on duality principle and verified for the purposes of transient analysis with reasonable accuracy and frequency response analysis. However such circuit is developed and validated for balanced and unbalanced three-phase excitation. On the other hand, several diagnostic tests such as Frequency Response Analysis (FRA), ratio, short-circuit impedance measurements etc. are performed only under single-phase excitation in open- and short-circuit conditions. Therefore, there is a requirement to develop an equivalent circuit for power transformers under single-phase excitation to analyse relevant tests, which has not been completely investigated until now. The required equivalent circuit should in general include all windings of three phases as suggested by several recent publications since the influence from other non-tested windings to the tested phase winding was confirmed. The paper's main contribution is to introduce a duality-principle-based lumped equivalent circuit for a three-phase two-winding transformer under single-phase excitation at low frequencies for the purpose of impedance and frequency response analyses. More importantly, a method for determining internal, i.e. per-phase, parameters of the circuit based on impedance tests is also proposed. Results show that, thanks to frequency-dependent functions of the parameters and their connection in the circuit, inter-phase effect and quantitative interpretation of several first parallel- and series resonances in frequency response of winding impedances in transformer bulk are now possible. Furthermore, these physical parameters can be useful as input for machine-learning algorithms to diagnose transformer failures.

D. A. K. Pham

Papers

A new method for purposes of failure diagnostics and FRA interpretation applicable to power transformers

An efficient meshfree method for analysis of two-dimensional piezoelectric structures

A new diagnostic method to support standard frequency response analysis assessments for diagnostics of transformer winding mechanical failures

Analysis of physical transformer circuits for frequency response interpretation and mechanical failure diagnosis

Duality-based lumped transformer equivalent circuit at low frequencies under single-phase excitation