PER-UNIT AND BASE IMPEDANCE CALCULATOR

The following calculators compute various base and per unit quantities commonly used in the per unit system of analysis by power system engineers.

Calculator-1


Known variables: Base Three Phase Power, Base Line-to-Line Voltage



           
Base Impedance   Per-Unit Impedance - Given kA  
Input Base Three Phase Power (MVA3ɸ):    Input Source Voltage (kV):   
Input Base Line-to-Line Voltage (KVLL):    Input 3-Phase Short Circuit Current (kA):  
Base Impedance (Ω):   Impedance (Ω):  
  Input Base Three Phase Power (MVA3ɸ):   
  Per-Unit Impedance:  
     
Base Current   Capacitor Bank Per-Unit Impedance - Given KVAR  
Input Base Three Phase Power (MVA3ɸ):    Input Capacitor Bank 3-Phase Rating (KVAR):   
Input Base Line-to-Line Voltage (KVLL):    Input Capacitor Bank Voltage (KVLL):   
Base Current(A):   Capacitor Bank Impedance(Ω):  
    Input Base Line-to-Line Voltage (KVLL):   
  Input Base Three Phase Power (MVA3ɸ):   
   Per-Unit Capacitor Bank Impedance:  
     
Per-Unit Impedance - Base Change     Per-Unit Impedance Calculation for Motors  
Input Given Base Three Phase Power (MVA3ɸ Given):    Input Horse Power(HP):    
Input New Base Three Phase Power (MVA3ɸ New):    Input Rated PF :   
Input Given Base Line-to-Line Voltage (KVLL Given):    Input Rated Efficency:   
Input New Base Line-to-Line Voltage (KVLL New):    Input Rated KVLL :  
Input Given Per-Unit Impedance (Ωgiven):   Rated KVA:  
New Per-Unit Impedance (ΩNew):   Rated Current:  
  Input Motor Sub-tansiant Impedance (X"  in Per Unit) :  
   Base Impedance on Motor Base (Ω):  
    Motor Impedance (Ω):   
Per-Unit Impedance - Given Ohms     Calculation of Motor Impedance on a Different MVA and Voltage Base  
Input Actual Impedance (ΩA):    Input new MVA :  
Input Base Impedance (ΩB):    Input new KVLL :  
Per-Unit Impedance:   Per-Unit Impedance on Specified MVA and KV Base:  
           
           

Formulas and Variables










Change of Base Formula







Capacitor Bank Per-Unit Calculations









Motor Per-Unit Calculations







Where:

ZBASE = Base Impedance
KVLL = Base Voltage (Kilo Volts Line-to-Line)
MVA = Base Power
ABASE = Base Amps
ZPU = Per Unit Impedance
ZPU GIVEN = Given Per Unit Impedance
Z = Impedance of circuit element (i.e. Capacitor, Reactor, Transformer, Cable, etc.)
XC = Capacitor Bank Impedance (ohms)
XC-PU = Capacitor Bank Per Unit Impedance
MVAR = Capacitor Bank 3-Phase Rating
X" = Motor Sub-Transient Reactance
LRM = Locked Rotor Multiplier

Background


The per unit system of calculation is a method whereby system impedances and quantities are normalized across different voltage levels to a common base. By removing the impact of varying voltages, the necessary calculations are simplified.

To use the per unit method, we normalize all the system impedances (and admittances) within the network under consideration to a common base. These normalized impedances are known as per unit impedances. Any per unit impedance will have the same value on both the primary and secondary of a transformer and is independent of voltage level.

A network of per unit impedances can then be solved using standard network analysis.

There are four base quantities: base MVA, base KV, base ohms, and base amperes. When any two of the four are assigned the other two can be derived. It is common practice to assign study base values to MVA and KV. Base amperes and base ohms are then derived for each of the voltage levels in the system. The MVA assigned may be the MVA rating of one of the predominant pieces of system equipment or a more convenient number such as 10 MVA or 100 MVA. Selection of the latter has some advantage of commonality when many studies are made while the former choice means that the impedance or reactance of at least one significant component will not have to be converted to a new base. The nominal line-to-line system voltages are normally used as the base voltages with 3-phase power being used as base power.