@ -49,29 +49,38 @@ When a reactance (either inductive or capacitive) is present in an AC circuit, t
\textbf{Real power} (or true power) is the power that is used to do the work on the load:
$$P = V_{RMS}I_{RMS}\,cos\,\varphi$$
where P is the real power in watts (W), $V_{RMS}$ is the RMS voltage, defined as $V_{peak}/\sqrt{2}$ in Volts (V), $I_{RMS}$ is the RMS current, defined as $I_{peak}/\sqrt{2}$ in Amperes (A) and $\varphi$ is the impedance phase angle - phase difference between voltage and current.
where P is the real power in watts, $V_{RMS}$ is the RMS voltage, defined as $V_{peak}/\sqrt{2}$ in volts, $I_{RMS}$ is the RMS current, defined as $I_{peak}/\sqrt{2}$ in amperes and $\varphi$ is the impedance phase angle - phase difference between voltage and current.
\textbf{Reactive power} on the other hand, is the power that is wasted and not used to do work on the load. Curiously, it is defined as
$$Q = V_{RMS}I_{RMS}\,sin\,\varphi$$
with $Q$ being the reactive power in volt-ampere-reactive (VAR).
with $Q$ being the reactive power in volt-ampere-reactive [var].
\textbf{Apparent power} is the power that is supplied to the circuit. Definition:
$$S = V_{RMS}I_{RMS}$$
where the unit of apparent power $S$ is volt-ampere (VA). It can be seen that it is not phase-angle dependent.
where the unit of apparent power $S$ is volt-ampere [VA]. It can be seen that it is not phase-angle dependent.
The relation all these three quantities are in is defined as
$$ P^2+ Q^2= S^2$$
however, again, nothing in the real world is perfect, and this relation only applies for a perfectly \textbf{sinusoidal waveforms}!
\subsection{Phasor}
\subsection{Phasor and phase difference}
A phasor is a constant complex number representing the complex amplitude (magnitude and phase) of a sinusoidal function of time. It is usually expressed in exponential form. Phasors are used in engineering to simplify computations involving sinusoids, where they can often reduce a differential equation problem to an algebraic one. The origin of the word phasor comes from phase + vector.
Phasor is a vector that represents a sinusoidally varying quantity, as a current or voltage, by means of a line rotating about a point in a plane, the magnitude of the quantity being proportional to the length of the line and the phase of the quantity being equal to the angle between the line and a reference line.
%\subsection{Power factor}
%
%
%\subsection{Measuring electric power with a microcontroller}
\caption{The phase difference between voltage (blue) and current (red), the origin of phase difference of angle $\varphi$}\label{f:ph_diff}
\end{figure}
Considering the figure \ref{f:ph_diff}, the voltage waveform above starts at zero along the horizontal reference axis, but at that same instant of time the current waveform is still negative in value and does not cross this reference axis until 30\textdegree later. Then there exists a Phase difference between the two waveforms as the current cross the horizontal reference axis reaching its maximum peak and zero values after the voltage waveform.
As the two waveforms are no longer “in-phase”, they must therefore be “out-of-phase” by an amount determined by phi, $\varphi$ and in our example this is 30\textdegree. It can now be said, that the two waveforms are now 30\textdegree out-of phase. The current waveform can also be said to be “lagging” behind the voltage waveform by the phase angle $\varphi$\cite{maxfield2011electrical}.
\subsection{Power factor}
also power factor correction
\subsection{Measuring the electric power}
Measuring the electric power makes most sense on the customer appliances. The first reason is, that they generally consume power that is purchased on contract. The energetic company measures all the power used up by the end customer, but customer has no easy way to see how much and how \textit{effectively} is power used by the appliances. The second important reason is that the appliances has a standardised connector (plug) that is guaranteed to fit in all the area using it, which is not a case for example on battery powered devices (batteries has different sizes, connectors and general properties.
@ -109,6 +118,14 @@ the conclusion can be made, that the procedure for measuring the electrical powe
However, as seen in a subsection \ref{ss:ac_power}, this procedure would measure the \textit{apparent} power, which includes the power stored in reactive elements and later returned to the circuit. To have a useful result of a measurement, the \textit{real} power is desired. Thu keeping track of the \textit{phase angle} is needed.
\subsubsection{Measuring electric power with a microcontroller}
some words about sampling too
\newpage
\section{ESP8266 wi-fi node}
since it is used, the whole section should be designated to provide some description about it
\newpage
\section{Embedded system}
An embedded \gls{system} is some combination of \gls{computer}\gls{hw} and \gls{sw}, either fixed in capability or programmable, that is specifically designed for a particular function \cite{ganssle2008embedded}. Industrial machines, automobiles, medical equipment, cameras, household appliances, airplanes, vending machines and toys (as well as the more obvious cellular phone and \gls{pda}) are among the myriad possible hosts of an embedded \gls{system}. Embedded \glspl{system} that are programmable are provided with programming \glspl{interface}, and embedded \glspl{system} programming is a specialized occupation.
Peter Babič
9 years ago
