@ -35,7 +35,7 @@ The term AC or to give it its full description of Alternating Current, generally
This means then that the AC waveform is a “time-dependent signal” with the most common type of time-dependant signal being that of the Periodic Waveform. The periodic or AC waveform is the resulting product of a rotating electrical generator. Generally, the shape of any periodic waveform can be generated using a fundamental frequency and superimposing it with harmonic signals of varying frequencies and amplitudes but that is out of the waveform fundamentals theory.
Alternating voltages and currents can not be stored in batteries or cells like direct current (DC) can, it is much easier and cheaper to generate these quantities using alternators or waveform generators when they are needed. The type and shape of an AC waveform depends upon the generator or device producing them, but all AC waveforms consist of a zero voltage line that divides the waveform into two symmetrical halves. The main characteristics of an AC waveform are defined as:
Alternating voltages and currents can not be stored in batteries or cells like direct current (DC) can, it is much easier and cheaper to generate these quantities using alternators or waveform generators when they are needed. The type and shape of an AC waveform depends upon the generator or device producing them, but all AC waveforms consist of a zero voltage line that divides the waveform into two symmetrical halves. The main characteristics of an AC waveform \cite{nicolaides1996electrical}are defined as:
\begin{itemize}
\item the \textbf{period (T)} is the length of time in seconds that the waveform takes to repeat itself from start to finish. This can also be called the Periodic Time of the waveform for sine waves, or the Pulse Width for square waves
@ -45,7 +45,7 @@ Alternating voltages and currents can not be stored in batteries or cells like d
\subsection{Power in AC circuits}\label{ss:ac_power}
When a reactance (either inductive or capacitive) is present in an AC circuit, the Ohm's law formula does not apply and different approach must be taken to express and calculate power.
When a reactance (either inductive or capacitive) is present in an AC circuit, the Ohm's law formula does not apply and different approach must be taken to express and calculate power\cite{rawlins2000basic}.
\textbf{Real power} (or true power) is the power that is used to do the work on the load:
$$P = U_{RMS}\cdot I_{RMS}\cdot cos\,\varphi$$
@ -64,7 +64,7 @@ $$ P^2 + Q^2 = S^2 $$
however, again, nothing in the real world is perfect, and this relation only applies for a perfectly \textbf{sinusoidal waveforms}!
\subsection{Phasor and phase shift}
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.
A phasor\cite{2009electrical} 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.
@ -76,7 +76,7 @@ Phasor is a vector that represents a sinusoidally varying quantity, as a current
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 \textit{in-phase}, they must therefore be \textit{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 \textit{lagging} behind the voltage waveform by the phase angle $\varphi$\cite{maxfield2011electrical}. This angle represents the phase shift (also called phase difference) between two sinusoids.
As the two waveforms are no longer \textit{in-phase}, they must therefore be \textit{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 \textit{lagging} behind the voltage waveform by the phase angle $\varphi$.This angle represents the phase shift (also called phase difference) between two sinusoids\cite{maxfield2011electrical}.
\subsection{Power factor and power factor correction}
The power factor is just a specific name for a phase shift between the sinusoids of a current and voltage. So the figure \ref{f:ph_diff} in fact shows the power factor. However, it is not expressed in a plane angle, but rather as a dimensionless number between -1 and 1.
@ -85,7 +85,7 @@ The power factor is defined as $\frac{P}{S}$, as a ratio of the real power over
$$|P| = |S|\,\cdot\,cos\,\varphi$$
If the power factor is 1, it means that current flows only through purely resistive components. This is the best possible outcome. A positive power factor indicates that the current flow is altered by a reactive components. The lower the factor, the higher the effect. A negative power factor means that the device, considered to be power load is in fact a power source (produces more power than consumes).
Now why is power factor important? Every device with a power factor other than 1 returns some power back to the transmission line. Since the transmission lines does have some resistance, this returned power translates to some wasted power in a form of heat. Energetic companies want to minimise the power wasted in the transmission lines to increase their profit, so numerous laws are coming into effect to correct (increase) the power factor.
Now why is power factor important? Every device with a power factor other than 1 returns some power back to the transmission line. Since the transmission lines does have some resistance, this returned power translates to some wasted power in a form of heat. Energetic companies want to minimise the power wasted in the transmission lines to increase their profit, so numerous laws are coming into effect to correct \cite{singh2008electric}(increase) the power factor.
@ -132,13 +132,13 @@ If not handled with care, operating or manipulating with voltage can cause perma
\subsection{Power measuring integrated circuits}
Although it is possible to construct a circuit out of discrete components that would measure the mentioned quantities, and such a solution would probably be the cheapest solution out there, it would be highly impractical due to multiple reasons.
Although it is possible to construct a circuit out of discrete components that would measure \cite{webster2003electrical} the required physical quantities, and such a solution would probably be the cheapest solution out there, it would be highly impractical due to multiple reasons.
The most importantly, the obtained accuracy of the measurements would be dependent on the implementation and used components. It is safe to assume, that without multiple design iterations, the accuracy may be too low to be used in practice.
Another point is that, there is no definitive guide, ready to follow, about how to design such circuit. The reason of this is the vast amount of components available on the market and a lot of design considerations to take into account, depending on the requirements.
A special purpose \glspl{ic} are being developed for the exact purpose of measuring the real, apparent and reactive power, the power factor, and in most cases, gathering some other relevant information.
A special purpose \glspl{ic} are being developed for the exact purpose of measuring the real, apparent and reactive power, the power factor, and in most cases, gathering some other relevant information.
\begin{figure}[ht!]
\centering
@ -146,7 +146,7 @@ A special purpose \glspl{ic} are being developed for the exact purpose of measur
\caption{The simplified block diagram for a power measurement \gls{ic}}\label{f:meas_IC_diag}
\end{figure}
From the block diagram \ref{f:meas_IC_diag}, it can be seen that the power measuring \gls{ic} is just a specialised microcontroller. It takes the data from the sensing circuitry, which in case of voltage can be measured \textit{directly}, provided that the galvanic isolation is included, for the sake safety. The current however, must be measured \textit{indirectly}. There are three common ways of doing so:
From the block diagram \ref{f:meas_IC_diag}, it can be seen that the power measuring \gls{ic} is just a specialised microcontroller. It takes the data from the sensing circuitry, which in case of voltage can be measured \textit{directly}, provided that the galvanic isolation is included, for the sake safety. The current however, must be measured \textit{indirectly}. There are three common ways \cite{srinivasan2015composite}of doing so:
\begin{enumerate}
\item\textbf{shunt resistor} - a resistor with a very small but precise value, that causes a voltage drop with a current passing through it due to the Ohm's law, regardless of frequency. The actual voltage drop is so small, that it can be assumed insignificant. However, the voltage drop is still present and may cause some issues, if not taken into account. The advantage is really low price. External galvanic isolation must be provided.
Peter Babič
9 years ago