Coverting from abc waveform to qd0, I know I have to take the abc form and multiply by Ks matrix, which I have done bellow. However I am not sure how my answer is suppose to go from my calculation to the last set of 3 equation on the picture from 3.6-5 -3.6-7.
Coverting from abc waveform to qd0, I know I have to take the abc form and multiply by Ks matrix, which I have done bellow. However I am not sure how my answer is suppose to go from my calculation to the last set of 3 equation on the picture from 3.6-5 -3.6-7.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Coverting from abc waveform to qd0, I know I have to take the abc form and multiply by Ks matrix, which I have done bellow. However I am not sure how my answer is suppose to go from my calculation to the last set of 3 equation on the picture from 3.6-5 -3.6-7.
![The image contains mathematical expressions related to transformations in electrical engineering, specifically for phase currents. Here is the transcription of the text:
\[ f_{as} = \sqrt{2} f_s \cos \theta_{ef} \]
\[ f_{bs} = \sqrt{2} f_s \cos \left( \theta_{ef} - \frac{2\pi}{3} \right) \]
\[ f_{cs} = \sqrt{2} f_s \cos \left( \theta_{ef} + \frac{2\pi}{3} \right) \]
...of time and
\[ \frac{d\theta_{ef}}{dt} = \omega_e \]
into the transformation to the arbitrary...
\[ f_{qs} = \sqrt{2} f_s \cos (\theta_{ef} - \theta) \]
\[ f_{ds} = -\sqrt{2} f_s \sin (\theta_{ef} - \theta) \]
\[ f_{0s} = 0 \]
There are no graphs or diagrams in this image, only mathematical equations relevant for educational purposes on the transformation of phase currents in an electrical engineering context.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb010926-0d81-478d-9736-679f94816a5d%2Ff06e5eb1-b534-44fe-9bc9-1a53440e7be4%2Fvzo272f_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains mathematical expressions related to transformations in electrical engineering, specifically for phase currents. Here is the transcription of the text:
\[ f_{as} = \sqrt{2} f_s \cos \theta_{ef} \]
\[ f_{bs} = \sqrt{2} f_s \cos \left( \theta_{ef} - \frac{2\pi}{3} \right) \]
\[ f_{cs} = \sqrt{2} f_s \cos \left( \theta_{ef} + \frac{2\pi}{3} \right) \]
...of time and
\[ \frac{d\theta_{ef}}{dt} = \omega_e \]
into the transformation to the arbitrary...
\[ f_{qs} = \sqrt{2} f_s \cos (\theta_{ef} - \theta) \]
\[ f_{ds} = -\sqrt{2} f_s \sin (\theta_{ef} - \theta) \]
\[ f_{0s} = 0 \]
There are no graphs or diagrams in this image, only mathematical equations relevant for educational purposes on the transformation of phase currents in an electrical engineering context.
![### Matrix Multiplication
#### Initial Matrices
We begin with the multiplication of two matrices:
1. **First Matrix:**
\[
\begin{pmatrix}
\cos(\theta) & \cos\left(\theta - \frac{2\pi}{3}\right) & \cos\left(\theta + \frac{2\pi}{3}\right) \\
\sin(\theta) & \sin\left(\theta - \frac{2\pi}{3}\right) & \sin\left(\theta + \frac{2\pi}{3}\right) \\
\frac{1}{2} & \frac{1}{2} & \frac{1}{2}
\end{pmatrix}
\]
2. **Second Matrix:**
\[
\begin{pmatrix}
\sqrt{2} f \cos(\alpha) \\
\sqrt{2} f \cos\left(\alpha - \frac{2\pi}{3}\right) \\
\sqrt{2} f \cos\left(\alpha + \frac{2\pi}{3}\right)
\end{pmatrix}
\]
#### Matrix Multiplication
To perform matrix multiplication, the elements of the rows of the first matrix are multiplied by the corresponding elements of the columns of the second matrix:
\[
\begin{pmatrix}
\cos(\theta) \sqrt{2} f \cos(\alpha) + \cos\left(\theta - \frac{2\pi}{3}\right) \sqrt{2} f \cos\left(\alpha - \frac{2\pi}{3}\right) + \cos\left(\theta + \frac{2\pi}{3}\right) \sqrt{2} f \cos\left(\alpha + \frac{2\pi}{3}\right) \\
\sin(\theta) \sqrt{2} f \cos(\alpha) + \sin\left(\theta - \frac{2\pi}{3}\right) \sqrt{2} f \cos\left(\alpha - \frac{2\pi}{3}\right) + \sin\left(\theta + \frac{2\pi}{3}\right) \sqrt{2} f \cos\left(\alpha + \frac{2\pi}{3}\right) \\
\frac{1}{2} \sqrt{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb010926-0d81-478d-9736-679f94816a5d%2Ff06e5eb1-b534-44fe-9bc9-1a53440e7be4%2Fucsx75r_processed.png&w=3840&q=75)
Transcribed Image Text:### Matrix Multiplication
#### Initial Matrices
We begin with the multiplication of two matrices:
1. **First Matrix:**
\[
\begin{pmatrix}
\cos(\theta) & \cos\left(\theta - \frac{2\pi}{3}\right) & \cos\left(\theta + \frac{2\pi}{3}\right) \\
\sin(\theta) & \sin\left(\theta - \frac{2\pi}{3}\right) & \sin\left(\theta + \frac{2\pi}{3}\right) \\
\frac{1}{2} & \frac{1}{2} & \frac{1}{2}
\end{pmatrix}
\]
2. **Second Matrix:**
\[
\begin{pmatrix}
\sqrt{2} f \cos(\alpha) \\
\sqrt{2} f \cos\left(\alpha - \frac{2\pi}{3}\right) \\
\sqrt{2} f \cos\left(\alpha + \frac{2\pi}{3}\right)
\end{pmatrix}
\]
#### Matrix Multiplication
To perform matrix multiplication, the elements of the rows of the first matrix are multiplied by the corresponding elements of the columns of the second matrix:
\[
\begin{pmatrix}
\cos(\theta) \sqrt{2} f \cos(\alpha) + \cos\left(\theta - \frac{2\pi}{3}\right) \sqrt{2} f \cos\left(\alpha - \frac{2\pi}{3}\right) + \cos\left(\theta + \frac{2\pi}{3}\right) \sqrt{2} f \cos\left(\alpha + \frac{2\pi}{3}\right) \\
\sin(\theta) \sqrt{2} f \cos(\alpha) + \sin\left(\theta - \frac{2\pi}{3}\right) \sqrt{2} f \cos\left(\alpha - \frac{2\pi}{3}\right) + \sin\left(\theta + \frac{2\pi}{3}\right) \sqrt{2} f \cos\left(\alpha + \frac{2\pi}{3}\right) \\
\frac{1}{2} \sqrt{
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