Three Phase Power Factor Formulas & Terms

USEFUL FORMULAS
(Three Phase)

POWER FACTOR
and the
POWER TRIANGLE

Power Losses due to the transmission of current can be significantly lowered with the improvement of Power Factor. This benefit is mainly realized where there are long conductor runs to motors or electrical distribution systems are heavily loaded. Known as I²R losses, the formula for calculating the reduction of these losses is shown as follows:

$$( \hspace{3 pt}Loss \hspace{3 pt}Reduction \hspace{3 pt}= 100 – 100 \hspace{3 pt}* \begin{pmatrix} \frac{Original \hspace{3 pt}PF}{Improved \hspace{3 pt}PF}\end{pmatrix}^{2})$$

Capacitors can increase the system voltage. This increase is beneficial in electrical systems where voltage drops are a problem. The calculation is shown as follows:

$$( \hspace{3 pt}Voltage \hspace{3 pt}Rise \hspace{3 pt}=frac{Capacitor \hspace{3 pt}KVAR \hspace{3 pt}x \hspace{3 pt} \hspace{3 pt} Transformer \hspace{3 pt} Reactance}{Transformer \hspace{3 pt}KVA} )$$

Legend
A	Amps
V	Volts
KV	Kilovolts (1000 volts)
KW	Kilowatts (1000 watts)
KVA	Kilovolt-Ampere
KVAR	Kilovolt-Ampere-Reactance
PF	Power Factor
C	Capacitance (in microfarads)
f	Frequency
p	PI – 3.1415927
1mF	1 x 10-6 farads (MFD)

$$(KW \hspace{3 pt}= \hspace{3 pt} \frac{V * A * sqrt{3} * PF}{1000})$$

$$(KVA \hspace{3 pt}= \hspace{3 pt} \frac{V * A * sqrt{3}}{1000})$$

$$(KVAR \hspace{3 pt}= \hspace{3 pt} \frac{(2PF)C(KV)^{2}}{1000})$$

$$(C \hspace{3 pt}= \hspace{3 pt} \frac{KVAR * 1000}{(2PF)(KV)^{2}})$$

$$(Line \hspace{3 pt}Amps \hspace{3 pt}= \hspace{3 pt} \frac{KVA * 1000}{sqrt{3} V})$$

$$(Capacitor \hspace{3 pt}Amps \hspace{3 pt}= \hspace{3 pt} \frac{KVAR * 1000}{sqrt{3} V})$$

$$(Capacitor \hspace{3 pt}Amps \hspace{3 pt}= \hspace{3 pt} \frac{(2PF)CV * 10^{-6}}{sqrt{3} V})$$

$$(PF \hspace{3 pt}= \hspace{3 pt} \frac{KW}{KVA})$$

$$(KW \hspace{3 pt}= \hspace{3 pt}KVA * PF)$$

$$(KVA \hspace{3 pt}= \hspace{3 pt}sqrt{KW^{2} + KVAR^{2}})$$