Active Power P Active power P (in kW)   - Single phase (1 phase and neutral): P = V I cos φ
  - Single phase (phase to phase): P = U I cos φ
  - Three phase (3 wires or 3 wires + neutral): P = ρίζα3 επί U επί I επί cos φ
Apparent power S Apparent power S (in kVA)   - Single phase (1 phase and neutral): S = V I
  - Single phase (phase to phase): S = U I
  - Three phase (3 wires or 3 wires + neutral): P = ρίζα3 επί U επί I
V = Voltage between phase and neutral
U = Voltage between phases
I = Line current
φ = Phase angle between vectors V and I.
  - For balanced and near-balanced loads on 4-wire systems


Cy Filter star capacitance - Cy Cy = Nc επί (1-P/100)/Un2 επί 2 επί π επί f
Nc = Filter-nominal power
Un = Grid voltage
P = Detuning ratio
f = Grid frequency


E Energy

(in kilowatt-hours, or kWh) is the TOTAL amount of electricity used/produced over a period of time.
ENERGY = POWER x TIME or the equivalent,POWER = ENERGY / TIME
E  =  (100 Watts) x (10 hours)  =  1000 Watt-hours (Wh)  =  1 kilowatt-hour (kWh)   since "kilo" means 1000

Effective Current RMS current  
Effective Voltage same as RMS voltage  


fr Calculation of resonance points - fr fr = 50 επί ρίζα(ST επί 100/Qcεπί uk)
ST =Transformator-nominal power [kVA]
Qc = Nominal power of the capacitor bank [kVAr]
uk = Transformator impedancy [%]    
FRes Filter frequency - fres fres = f/ ρίζα (P/100)
f = Grid frequency
P = Detuning ratio


L Filter inductance – L L = P/100 επί 4 επί π2 επί f2 επί Cy
P = Detuning ratio
f = Grid frequency
Cy = Star capacitance    


Modbus Modbus is a serial communications protocol originally published by Modicon (now Schneider Electric) in 1979 for use with its programmable logic controllers (PLCs). Simple and robust, it has since become a de facto standard communication protocol, and it is now a commonly available means of connecting industrial electronic devices.[1] The main reasons for the use of Modbus in the industrial environment are:

    It has been developed with industrial applications in mind
    It is openly published and royalty-free
    It is easy to deploy and maintain
    It moves raw bits or words without placing many restrictions on vendors

Modbus allows for communication between many (approximately 240) devices connected to the same network, for example a system that measures temperature and humidity and communicates the results to a computer. Modbus is often used to connect a supervisory computer with a remote terminal unit (RTU) in supervisory control and data acquisition (SCADA) systems. Many of the data types are named from its use in driving relays: a single-bit physical output is called a coil, and a single-bit physical input is called a discrete input or a contact.

The development and update of Modbus protocols has been managed by the Modbus Organization since April 2004, when Schneider Electric transferred rights to that organization, signaling a clear commitment to openness. The Modbus Organization is an association formed of independent users and suppliers of Modbus compliant devices that seeks to drive the adoption of the Modbus communication protocol suite, and its evolution to address architectures for distributed automation systems across multiple market segments. Source and more about Modbus here
Modbus ASCII  This is used in serial communication & makes use of ASCII characters for protocol communication. The ASCII format uses a longitudinal redundancy check checksum. Modbus ASCII messages are framed by leading colon (':') and trailing newline (CR/LF).
ModBus RTU This is used in serial communication & makes use of a compact, binary representation of the data for protocol communication. The RTU format follows the commands/data with a cyclic redundancy check checksum as an error check mechanism to ensure the reliability of data. Modbus RTU is the most common implementation available for Modbus. A Modbus RTU message must be transmitted continuously without inter-character hesitations. Modbus messages are framed (separated) by idle (silent) periods. 
 Modbus TCP This is a Modbus variant used for communications over TCP/IP networks, connecting over port 502.[4] It does not require a checksum calculation as lower layers already provide checksum protection.


P Power (measured in Watts, or W) is the instantaneous RATE of using or producing electrical energy  
P Active Power βλέπε Active Power  
PLC Programmable Logic Controller A PLC is a digital computer used for automation of electromechanical processes, such as control of machinery on factory assembly lines, amusement rides, or light fixtures. The abbreviation "PLC" and the term "Programmable Logic Controller" are registered trademarks of the Allen-Bradley Company (Rockwell Automation)[1]. PLCs are used in many industries and machines. Unlike general-purpose computers, the PLC is designed for multiple inputs and output arrangements, extended temperature ranges, immunity to electrical noise, and resistance to vibration and impact. Programs to control machine operation are typically stored in battery-backed-up or non-volatile memory. A PLC is an example of a hard real time system since output results must be produced in response to input conditions within a limited time, otherwise unintended operation will result. Source and more about PLCs  
Power factor  cosΦ = P / S  The power factor is the ratio of kW to kVA. The closer the power factor approaches its maximum possible value of 1, the greater the benefit to consumer and supplier.
PF = P (kW) / S (kVA)
P = Active power
S = Apparent power


Q Reactive power βλέπε Reactive Power
Qc Calculation of the capacitor nominal power - Qc Qc = (1-P/100) επί Ucn2/Un επί Nc
Nc = Filter-nominal power
Un = Grid voltage
Ucn = selected capacitor nominal voltage (Ucn > Uc)
P = Detuning ratio


Reactive Energy kvar Q=ρίζα3 επί U επί I επί sinφ
Reactive Power  

Reactive power Q (in kvar)
- Single phase (1 phase and neutral): P = V I sin φ
- Single phase (phase to phase): Q = U I sin φ
- Three phase (3 wires or 3 wires + neutral): P = ρίζα3 επί U επί I επί sinφ

Real Energy


P= ρίζα3 επί U επί I επί cosφ

RMS Root Mean Square

RMS = Peak voltage / ρίζα2

A measure of the heating effect of the voltage.
A DC voltage or current displayed on an oscilloscope, you will note the line is straight, voltage or current is present at all times. Now compare this to an AC trace on the scope, you will notice that not only does the value of voltage or current sometimes fall to zero, but also it is not always at it's highest 'peak' value. RMS is a way of representing this time when their is reduced output on the wave. RMS is Peak x 0.707. Rms is only applicable to sinusoidal wave forms.
The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean (average) of the squares of the original values (or the square of the function that defines the continuous waveform) more here

 Resonance frequency  fres = 1/(2 επί π επί ρίζα (L επί C) ) The natural frequency, or frequencies, of any physical system or object are the frequencies at which it will vibrate if physically disturbed.

Resonance is the phenomenon that occurs when a physical system is periodically disturbed at the same period of one of its natural frequencies.

Even small amplitude disturbances will then reinforce the energy stored in the system, causing the amplitude of the vibration to increase.

This will continue until the energy loss in the physical system due to non-elastic motion (resistive loss) equals the energy supplied by the disturbing force. In extreme cases, the system will exceed its limits and self-destruct before equilibrium occurs.

The above is true of any physical system
a: Tuning forks disturb the air around the fork, and the air transmits the periodicity of the tuning fork motion to one's ear. In reverse, striking the piano key causes the piano sounding board to vibrate and disturb the surrounding air which reaches the tuning fork and, if the frequency is the same as the natural frequency of the tuning fork, it will start to vibrate in your hand.

As for electromagnetic systems, they are just different physical systems, their energy being stored in the electric and magnetic fields, and their natural frequencies being determined by their physical construction and the relations between that construction and the rates at which their energies may be built up or dissipated.


S Apparent power βλέπε Apparent power 


Uc alculation of the capacitor nominal voltage
(minimum voltage withstand capability) - Uc
Uc = Un επί 100/100-p
Un = Grid voltage
P = Detuning ratio


Vrms Effective Voltage   Vrms = ρίζα2/2 επί Vpk = 0,707 επί Vpk
όπου Vpk = V peak


W Watt



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