Determination of DG allocation with modal participation factor to enhance voltage stability

Abstract

Distributed generation (DG) has become increasingly popular in many power systems across the world. It is an effective approach to facilitate the usage of renewable resources for power generation purpose. However, the installation of DGs in a power system may change the pattern of the power flow and cause various complexities in the system. How to plan DGs to best utilize renewable energy source while maintaining system security is an important problem. In this paper, an eigenvalue based analysis method is proposed for DG location planning with detailed case studies.

Modal Participation Factors And Their Potential Applications In Aerospace: A Review

“…u o =u st R (14) To compare the output of this method with respect to others, a steady-state modal participation fraction L i st is defined in (15). This fractional number allows to compare the relative amplitudes of the modal responses q i for a given design and loading condition.…”

“…The modal steady-state L i st , transition L , modal effective mass L and free-free L participation fractions are compute using equations (15), (17), (24) and (29), respectively, and the results are shown in figure 3. This figure gives an idea of the difference in magnitude obtained with each method, however the results should be interpreted independently.…”

“…However, the results obtained using equation (32) are in disagreement with those of the modal strain energy, which indicates that the internal load is dominated by the first elastic mode. Using the steady and the transient modal response participation factors, the peak in plane shear force was recovered using equation (19) with (15) and (17), respectively. Table I shows a comparison and percentage error between the recovered load and the actual peak load computed using MSC NASTRAN [53].…”

“…A simple search of the words "modal participation factor" in the open literature quickly reveals that several variants of this concept exist. For instance, in electrical engineering [15][16][17][18] the term MPF refers to the product between the left and the right eigenvectors; other researchers [19][20][21][22] used simple definitions for MPF such as the same term to refer to the components of the eigenvector matrix. On the other hand, [23][24][25][26][27][28] defined different convenient mathematical forms as modal participation factor suitable to their specific applications.…”

High Fidelity and Efficient Computations of Dynamic Loads for Multidisciplinary Design Optimization of Flexible Transport Aircraft

“…A simple search of the words "modal participation factor" will quickly reveal that several variants of this concept exist and that it is used interchangeably with the term "modal contribution factors". For example, in electrical engineering [79][80][81][82] the term refers to the product between the left and the right…”