iii 3. APPROXIMATION OF STABILITY BOUNDARY 3.1 Linear Analysis around the UEP 3.2 Coefficient of Curvature 23 3.3 Approximation of the Manifold of the UEP 25 3.4 Display of Boundary 3.5 Potential Energy 3.6 Computation of Distance 27 3.7 Computational Steps 2S 3.8 Summary 4. NUMERICAL RESULTS 4.1 11 Generator Test System 31 4.2 Simulation of Stress in a System 33 4.3 UEP Angles and System Eigenvalues 4.3.1 Effect of loading of critical generators 4.3.2 Effect of fault location and postfault network 35 4.4 Nonlinear Interaction Coefficients, h2r 4.4.1 Effect of loading of critical generators 4.5 r Coefficients 4.5.1 Effect of loading of critical generators 4.5.2 Effect of fault location and postfault network 4.6 Shape of Manifold Near the UEP and Size of the Region of Stability. 4.6.1 Effect of loading of critical generators 4.7 Trajectory Behavior Near the Boundary of the Region of Stability. . 4.7.1 Behavior of system trajectory near the UEP iv 4.7.2 How the faulted trajectory leaves the boundary 4.8 Potential Energy and Distance of Manifold from the Postfault SEP. 53 4.8.1 Effect of loading of critical generators 4.8.2 Effect of fault location 4.9 Equilibrium Points When System is Stressed 4.10 Summary 5. MODE OF SYSTEM INSTABILITY
Online purchases can support environmental sustainability by reducing the number of shopping trips. The purpose of this article is to understand how online convenience may be used to increase online purchase intention and therefore contribute to environmental sustainability. Employing a snowball sampling technique data from 226 Chinese respondents were used with Least Squares Structural Equation Modelling (PLS-SEM) to test the research hypotheses. Findings suggest that customers with experience have a strong effect on the relationship between service convenience and customer satisfaction. It is also found that satisfied customers desired to stay longer and are willing to pay more. From a theoretical point of view, this study fills several gapes by extending previous work that investigates the impact of online convenience on customer satisfaction and behavioral intention by revealing the novelty impact on the willingness to pay and desire to stay. From a managerial standpoint, the findings help managers considering doing businesses or planning to do businesses in China and for companies committed to reducing their carbon footprint in understanding how they can use online convenience to stimulate online purchases among their clients and consequently becoming more environmentally friendly and socially responsible.
The delivery of products to the end consumer has been widely considered in the e-commerce sector as new challenges to reach customers and provide them with timely and efficient delivery have surfaced. Less focus has been given to information about delivery efficiency that impacts online shoppers’ relations with e-retailers. This study’s research model builds on the extended unified theory of acceptance and use of technology (UTAUT-2) by adding the critical e-commerce variables of delivery efficiency, cost-saving efficiency, and online purchase experience (shopping satisfaction and subsequent willingness to pay). The conceptual model was tested, and samples were collected using an online survey hosted on Google Forms using e-mail in Bangladesh. The findings show that consumers’ willingness to pay is enhanced by satisfaction with online shopping and delivery efficiency. The study also contributes insights into how cost-saving efficiency affects online customer satisfaction and the intention to repurchase. Also, by applying hierarchical regression analysis, this study contributes to understanding how e-retailers can provide a functional online experience for customers. Finally, our findings offer guidelines to e-retailers regarding increasing shopping satisfaction, the intention to repurchase, and the willingness to pay more.
The objective of this work is to approximate the stability boundary of a power system without any integration using the normal form of the vector fields. This involves two steps: 1) first t o test which unstable equilibrium point (UEP) lies on the stability boundary, and 2) the second step is to approximate the boundary by the second order approximated manifolds. The approximation is accomplished using the normal forms of vector fields. T h e stability boundary and its behavior under stressed system conditions are examined. T h e method is applied to an 11 generator test system. W"() X E?
I. I N T R O D U C T I O N A . Sfability BoundaryThe region of stability of a stable equilibrium point (SEP) is the region within which a system trajectory starting will converge to the SEP. This region is bounded by the union of the stable manifolds of the unstable equilibrium points (UEP's) on the boundary [1, 21. For an autonomous system, this is mathematically stated as follows:where the vector field f maps RN into RN and is continuously differentiable. In our present formulation f is of type C". A point, x is called an equzlibrium point or a fixed point of equation (1) if f(i) = 0. T h e solution curve of equation (1) starting at t = 0 is called a trajectory, and is denoted by $(x, .). Let 2 be a hyperbolic equilibrium point. Its stable and unstable mamfolds, Ws(x) and W"( i) , are defined as W"2) = ( 2 : 4(x1 t ) -+ x as t -+ C O } (2) Figure 1: Eigenspace and local invariant manifolds of a nonlinear system B. Approxzmation of the Invariant Manifolds at the Direct stability analysis involves calculation of a value of critical potential energy against which transient stability assessment is made. T h e UEP of interest is called the controlling UEP and its computation is one of the key steps in power system transient stability assessment by the transient energy function (TEF) method [3]. Thus,we can assume that computation of (at least some of) the UEP's on the stability boundary is feasible.Normal form of vector fields [4] provides the means by which a differential equation may be transformed into a "simplified" form by eliminating higher-order terms. This is done using a nonlinear variable transformation performed on the Taylor series expansion of the power sysUEPs 1 (3) tem's nonlinear differential equations. In this work only second-order terms are used, giving a second order approximation of the nonlinear system, W"(2) = {.c : q 5 ( X l t ) + 2 as t --+ -02
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