Equation
Base number selection
{\displaystyle {\text{Base number selection}}}
Arbitrarily selecting from ohm's law the two base numbers: base voltage and base current
{\displaystyle {\text{Arbitrarily selecting from ohm's law the two base numbers: base voltage and base current}}}
1
{\displaystyle 1}
We have, Z
=
E
I
{\displaystyle {\text{We have, Z}}={\frac {E}{I}}}
2
{\displaystyle 2}
Base ohms
=
base volts
base amperes
{\displaystyle {\text{Base ohms}}={\frac {\text{base volts}}{\text{base amperes}}}}
3
{\displaystyle 3}
Per-unit volts
=
volts
base volts
{\displaystyle {\text{Per-unit volts}}={\frac {\text{volts}}{\text{base volts}}}}
4
{\displaystyle 4}
Per-unit amperes
=
amperes
base amperes
{\displaystyle {\text{Per-unit amperes}}={\frac {\text{amperes}}{\text{base amperes}}}}
5
{\displaystyle 5}
Per-unit ohms
=
ohms
base ohms
{\displaystyle {\text{Per-unit ohms}}={\frac {\text{ohms}}{\text{base ohms}}}}
Alternatively, choosing base volts and base kva values, we have,
{\displaystyle {\text{Alternatively, choosing base volts and base kva values, we have,}}}
in single-phase systems:
{\displaystyle {\text{in single-phase systems:}}}
6
{\displaystyle 6}
Base amperes
=
base kva * 1000
base volts
{\displaystyle {\text{Base amperes }}={\frac {\text{base kva * 1000}}{\text{base volts}}}}
7
{\displaystyle 7}
Base amperes
=
base kva
base kv
L
−
L
{\displaystyle {\text{Base amperes }}={\frac {\text{base kva}}{{\text{base kv}}_{L-L}}}}
8
{\displaystyle 8}
Base ohms
=
base volts
base amperes
{\displaystyle {\text{Base ohms }}={\frac {\text{base volts}}{\text{base amperes}}}}
and in three-phase systems:
{\displaystyle {\text{and in three-phase systems:}}}
9
{\displaystyle 9}
Base amperes
=
base kva * 1000
3
∗
base volts
{\displaystyle {\text{Base amperes }}={\frac {\text{base kva * 1000}}{{\sqrt {3}}*{\text{base volts}}}}}
10
{\displaystyle 10}
Base amperes
=
base kva
3
∗
base kv
L
−
L
{\displaystyle {\text{Base amperes }}={\frac {\text{base kva}}{{\sqrt {3}}*{\text{base kv}}_{L-L}}}}
11
{\displaystyle 11}
Base ohms
=
base volts
3
∗
base amperes
{\displaystyle {\text{Base ohms }}={\frac {\text{base volts}}{{\sqrt {3}}*{\text{base amperes}}}}}
Working out for convenience per-unit ohms directly, we have
{\displaystyle {\text{Working out for convenience per-unit ohms directly, we have}}}
for single-phase and three-phase systems:
{\displaystyle {\text{for single-phase and three-phase systems:}}}
12
{\displaystyle 12}
Base ohms
=
ohms * base kva
k
v
L
−
L
2
∗
1000
{\displaystyle {\text{Base ohms }}={\frac {\text{ohms * base kva}}{kv_{L-L}^{2}*1000}}}
Short-Circuit Calculation Formulas
{\displaystyle {\text{Short-Circuit Calculation Formulas}}}
Ohms conversions:
{\displaystyle {\text{Ohms conversions:}}}
13
{\displaystyle 13}
Per-unit ohms reactance
=
ohms reactance *
kva base
k
v
L
−
L
2
∗
1000
{\displaystyle {\text{Per-unit ohms reactance}}={\frac {{\text{ohms reactance * }}{\text{kva base}}}{kv_{L-L}^{2}*1000}}}
14
{\displaystyle 14}
Ohms reactance
=
%
reactance
∗
k
v
L
−
L
2
∗
10
kva base
{\displaystyle {\text{Ohms reactance}}={\frac {\%{\text{ reactance}}*kv_{L-L}^{2}*10}{\text{kva base}}}}
15
{\displaystyle 15}
Per-unit ohms reactance
=
per cent ohms reactance
100
{\displaystyle {\text{Per-unit ohms reactance}}={\frac {\text{per cent ohms reactance}}{100}}}
Changing ohms from one kva base to another:
{\displaystyle {\text{Changing ohms from one kva base to another:}}}
16
{\displaystyle 16}
%
ohms reactance on kva base
2
=
kva base
2
kva base
1
∗
%
ohms reactance on base
1
{\displaystyle \%{\text{ ohms reactance on kva base}}_{2}={\frac {{\text{kva base}}_{2}}{{\text{kva base}}_{1}}}*\%{\text{ ohms reactance on base}}_{1}}
17
{\displaystyle 17}
0/1 ohms reactance on kva base
2
=
kva base
2
kva base
1
* 0/1 ohms reactance on base
1
{\displaystyle {\text{0/1 ohms reactance on kva base}}_{2}={\frac {{\text{kva base}}_{2}}{{\text{kva base}}_{1}}}{\text{ * 0/1 ohms reactance on base}}_{1}}
Changing incoming system reactance:
{\displaystyle {\text{Changing incoming system reactance:}}}
a. If system reactance is given in percent, use Eq. 16 to change from one kva base to another.
{\displaystyle {\text{a. If system reactance is given in percent, use Eq. 16 to change from one kva base to another.}}}
b. If system reactance is given in short-circuit symmetrical rms kva or current, convert to per-unit as follows:
{\displaystyle {\text{b. If system reactance is given in short-circuit symmetrical rms kva or current, convert to per-unit as follows:}}}
18
{\displaystyle 18}
0/1 reactance
=
kva base used in reactance in studied calculation
system short-circuit kva
{\displaystyle {\text{0/1 reactance}}={\frac {\text{kva base used in reactance in studied calculation}}{\text{system short-circuit kva}}}}
19
{\displaystyle 19}
0/1 reactance
=
kva base used in reactance in studied calculation
system short-circuit current *
3
* system kv
L
−
L
{\displaystyle {\text{0/1 reactance}}={\frac {\text{kva base used in reactance in studied calculation}}{{\text{system short-circuit current * }}{\sqrt {3}}{\text{ * system kv}}_{L-L}}}}
Calculating approximate motor kva base:
{\displaystyle {\text{Calculating approximate motor kva base:}}}
a. For induction motors and 0.8 power factor synchronous motors
{\displaystyle {\text{a. For induction motors and 0.8 power factor synchronous motors}}}
20
{\displaystyle 20}
kva base
≈
horsepower rating
{\displaystyle {\text{kva base}}\approx {\text{ horsepower rating}}}
b. For unity power factor synchronous motors
{\displaystyle {\text{b. For unity power factor synchronous motors}}}
21
{\displaystyle 21}
kva base
≈
0.8 * horsepower rating
{\displaystyle {\text{kva base}}\approx {\text{ 0.8 * horsepower rating}}}
Converting ohms from one voltage to another:
{\displaystyle {\text{Converting ohms from one voltage to another:}}}
22
{\displaystyle 22}
Ohms on basis of voltage
1
=
(
voltage
1
voltage
2
)
2
* ohms on basis of voltage
2
{\displaystyle {\text{Ohms on basis of voltage}}_{1}=({\frac {{\text{voltage}}_{1}}{{\text{voltage}}_{2}}})^{2}{\text{ * ohms on basis of voltage}}_{2}}
Short-circuit kva and current calculations
{\displaystyle {\text{Short-circuit kva and current calculations}}}
Symmetrical short circuit kva:
{\displaystyle {\text{Symmetrical short circuit kva:}}}
23
{\displaystyle 23}
=
100 * kva base
%
X
{\displaystyle ={\frac {\text{100 * kva base}}{\%{\text{ X}}}}}
24
{\displaystyle 24}
=
kva base
0/1 X
{\displaystyle ={\frac {\text{kva base}}{\text{0/1 X}}}}
25
{\displaystyle 25}
=
3
∗
Voltage
L
−
N
2
ohms reactance
* 1000
{\displaystyle =3*{\frac {{\text{Voltage}}_{L-N}^{2}}{{\text{ohms reactance}}{\text{ * 1000}}}}}
26
{\displaystyle 26}
=
kv
L
−
L
2
* 1000
ohms reactance
{\displaystyle ={\frac {{\text{kv}}_{L-L}^{2}{\text{ * 1000}}}{\text{ohms reactance}}}}
Symmetrical short circuit current:
{\displaystyle {\text{Symmetrical short circuit current:}}}
27
{\displaystyle 27}
=
100 * kva base
%
X
∗
3
∗
kv
L
−
L
{\displaystyle ={\frac {\text{100 * kva base}}{\%{\text{ X}}*{\sqrt {3}}*{\text{kv}}_{L-L}}}}
28
{\displaystyle 28}
=
kva base
0/1 X
∗
3
∗
kv
L
−
L
{\displaystyle ={\frac {\text{kva base}}{{\text{0/1 X}}*{\sqrt {3}}*{\text{kv}}_{L-L}}}}
29
{\displaystyle 29}
=
kv
L
−
L
* 1000
3
∗
ohms reactance
{\displaystyle ={\frac {{\text{kv}}_{L-L}{\text{ * 1000}}}{{\sqrt {3}}*{\text{ohms reactance}}}}}
Asymmetrical short-circuit current and kva:
{\displaystyle {\text{Asymmetrical short-circuit current and kva:}}}
30
{\displaystyle 30}
Asymmetrical short-circuit current = symmetrical current * X/R factor
{\displaystyle {\text{Asymmetrical short-circuit current = symmetrical current * X/R factor }}}
31
{\displaystyle 31}
Asymmetrical short-circuit kva = symmetrical kva * X/R factor
{\displaystyle {\text{Asymmetrical short-circuit kva = symmetrical kva * X/R factor }}}