Lots of updates
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@ -1,6 +1,8 @@
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Chapter 1.
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Chapter 2.
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[]
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[5
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Chapter 3.
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@ -115,5 +115,42 @@ The term, $a_0 \over 2$ is the \emph{DC offset} of the signal. While the values
|
||||
$$f(t) = A_0 + \sum_{n=1}^\infty A_n \cos(n \omega t + \varphi_n)$$
|
||||
where $A_n = \sqrt{a_n^2 + b_n^2}$ and $\varphi_n = -\arctan\lt({b_n \over a_n}\rt)$
|
||||
|
||||
\chapter{Three-Phase Power}
|
||||
\section{Y and $\Delta$ Configurations of AC Voltage Sources}
|
||||
\subsection{The Y Configuration}
|
||||
The Y configuration is shaped like the letter Y with a neutral connection in the center.
|
||||
$$V_a = V_an = V_s \sin(\omega t)$$
|
||||
$V_b$ lags by 120$^\circ$.
|
||||
$$V_b = V_bn = V_s \sin(\omega t - {2\pi \over 3})$$
|
||||
$V_c$ lags by 240$^\circ$.
|
||||
$$V_c = V_cn = V_s \sin(\omega t - {4\pi \over 3})$$
|
||||
|
||||
\subsection{The $\Delta$ Configuration}
|
||||
The $\Delta$ configuration is shaped like the letter $\Delta$ with no neutral connection.
|
||||
$$V_ab = V_a - V_b = V_s \lt[\sin(\omega t) - \sin(\omega t - {2\pi \over 3})\rt] = \sqrt{3} V_s \sin(\omega t + {\pi \over 6})$$
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||||
$$V_bc = V_b - V_c = \sqrt{3}V_s \sin(\omega t - {\pi \over 2})$$
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||||
$$V_ca = V_c - V_a = \sqrt{3}V_S \sin(\omega t + {5\pi \over 6})$$
|
||||
|
||||
\subsection{Y Configuration Power}
|
||||
If a Y configuration of AC sources is connected to a Y configuration of resistors, the power through to each load resistor is:
|
||||
$$P_a = {V_s^2 \over 2R_a} \lt[1 - \cos(2\omega t)\rt]$$
|
||||
$$P_b = {V_s^2 \over 2R_a} \lt[1 - \cos(2\omega t - {4\pi \over 3})\rt]$$
|
||||
$$P_c = {V_s^2 \over 2R_c} \lt[1 - \cos(2\omega t + {4\pi \over 3})\rt]$$
|
||||
The total power transfer is:
|
||||
$$P = 3{V_s^2 \over 2R}$$
|
||||
where $R = R_a = R_b = R_c$.
|
||||
\\
|
||||
\\
|
||||
\noindent
|
||||
One benefit of using three-phase is constant power from the source. Another advantage of using three-phase power is that any harmonics divisible by either 2 or 3 cancel out. The first harmonic after the fundamental is the 5$^\text{th}$ harmonic, followed by the 7$^\text{th}$, 11$^\text{th}$, and 13$^\text{th}$. Harmonics are non-zero for $6n \pm 1, n \in \mathbb{Z}$.
|
||||
|
||||
\chapter{Silicon Controlled Rectifier (SCR)}
|
||||
The SCR will be off even when $V_{AC} > 0$ until a pulse is applied to the gate. Once the pulse is applied, the device will stay on as long as $i_F > 0$.
|
||||
|
||||
\nt
|
||||
{
|
||||
The voltage across the SCR can go negative as long as the current remains positive.
|
||||
}
|
||||
|
||||
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||||
\end{document}
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@ -4,4 +4,10 @@
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||||
\contentsline {section}{\numberline {1.3}Full Bridge with Resistive Load and Inductive Filter}{3}{section.1.3}%
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||||
\contentsline {section}{\numberline {1.4}Periodic Steady State}{3}{section.1.4}%
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||||
\contentsline {section}{\numberline {1.5}Trigonometric Fourier Series}{4}{section.1.5}%
|
||||
\contentsline {chapter}{\numberline {2}Three-Phase Power}{5}{chapter.2}%
|
||||
\contentsline {section}{\numberline {2.1}Y and $\Delta $ Configurations of AC Voltage Sources}{5}{section.2.1}%
|
||||
\contentsline {subsection}{\numberline {2.1.1}The Y Configuration}{5}{subsection.2.1.1}%
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||||
\contentsline {subsection}{\numberline {2.1.2}The $\Delta $ Configuration}{5}{subsection.2.1.2}%
|
||||
\contentsline {subsection}{\numberline {2.1.3}Y Configuration Power}{5}{subsection.2.1.3}%
|
||||
\contentsline {chapter}{\numberline {3}Silicon Controlled Rectifier (SCR)}{7}{chapter.3}%
|
||||
\contentsfinish
|
||||
|
||||
Reference in New Issue
Block a user