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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Alpha–beta transformation ： ウィキペディア英語版 Alpha–beta transformation In electrical engineering, the alpha-beta ($\backslash alpha\backslash beta\backslash gamma$) transformation (also known as the Clarke transformation) is a mathematical transformation employed to simplify the analysis of three-phase circuits. Conceptually it is similar to the dqo transformation. One very useful application of the $\backslash alpha\backslash beta\backslash gamma$ transformation is the generation of the reference signal used for space vector modulation control of three-phase inverters. ==Definition== The $\backslash alpha\backslash beta\backslash gamma$ transform applied to three-phase currents, as used by Edith Clarke, is : 0 & \frac & -\frac \\ \frac & \frac & \frac \\ \end\begini_a(t)\\i_b(t)\\i_c(t)\end where $i\_(t)$ is a generic three-phase current sequence and $i\_(t)$ is the corresponding current sequence given by the transformation $T$. The inverse transform is: : -\frac & \frac & 1\\ -\frac & -\frac & 1\end \begini_\alpha(t)\\i_\beta(t)\\i_\gamma(t)\end. The above Clarke's transformation preserves the amplitude of the electrical variables which it is applied to. Indeed, consider a three-phase symmetric, direct, current sequence :$$ \begin i_a(t)=&\sqrtI\cos\theta(t),\\ i_b(t)=&\sqrtI\cos\left(\theta(t)-\frac23\pi\right),\\ i_c(t)=&\sqrtI\cos\left(\theta(t)+\frac23\pi\right), \end where $I$ is the RMS of $i\_a(t)$, $i\_b(t)$, $i\_c(t)$ and $\backslash theta(t)$ is the generic time-varying angle that can also be set to $\backslash omega\; t$ without loss of generality. Then, by applying $T$ to the current sequence, it results :$$ \begin i_=&\sqrt2 I\cos\theta(t),\\ i_=&\sqrt2 I\sin\theta(t),\\ i_=&0, \end where the last equation holds since we have considered balanced currents. As it is shown in the above, the amplitudes of the currents in the $\backslash alpha\backslash beta\backslash gamma$ reference frame are the same of that in the natural reference frame. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Alpha–beta transformation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.