# Electrical Power and Communication Analysis

The Electrical Power and Communication Analysis library is aimed to analyze linear AC circuits. The library enables electrical power and communication analysis. A power analysis is performed to calculate the power variations in the system and is typically executed as a transient simulation in the time domain. A signal analysis is performed to verify the signal damping and phase variations and uses the phase vector (also called "phasor") representation. The signal analysis is performed as a steady state analysis. The solution for the circuit is assumed with sinusoidal voltages and currents with constant frequency (one frequency for the whole circuit) and root-means-square value is calculated. Remember that this assumption is only valid if the circuit is linear.

The library contains the following sub-libraries: Interface Elements Basic Elements Ideal Elements Sources Lines Sensors

## General Basics

Some basic equations of the phasor representation shall be denoted in the following. For further reading any basic literature about electrical engineering should be suitable. An overview may be attained from the Wikipedia article about Phasor (sine wave). A sine wave can be represented as the real part of a complex valued function :   where j denotes the complex unit , is the amplitude of the sinusoid, A its root-means-square (rms) value and the phase constant or so called phase angle.

Assuming the angular frequency is known, the complex phasor is enough to represent the sine wave. It can also be written as the sum of its real and imaginary part  Thus given any complex phasor ,

its length and phase angle can be calculated by:  The phase angle \$ is the argument of the complex number  . The function above is often called atan2, thus can be used to calculate .

The complex resistance, also called impedance, is defined by     with and  with and The imaginary part of is called reactance.

The real instantaneous power p(t) is defined by the multiplication of the real parts of voltage and current. The real part of a complex valued function is defined by where is the related conjugate-complex value . Thus the power is defined by      The complex instantaneous power has a time-independent stationary pointer and one with double velocity rotating . The time-independent part is the time mean value of the complex instantaneous power and is called complex apparent power. Where is the apparent power, is the effective power and is the reactive power.