Problem $5$: Real World Problem $-20\backslash \%$

Power factor $($PF$)$ is an important consideration when designing and building factories and other facilities that consume a large amount of power. A $120$ MW factory with a power factor of $0\mathrm{.}6$ consumes $160$ MVAR of reactive power, and draws $\backslash (66\mathrm{.}7\backslash \%\backslash )$ more current than is necessary. Therefore, it is critical to design power systems with high power factors to avoid over$-$stressing our energy infrastructure.

One of the difficulties in managing power factor is that a lot of equipment is powered by induction motors, machines that consume a lot of reactive power. Therefore, a factory with a large number of induction motors will have a low lagging power factor. One solution is to attach a large capacitor in parallel with the motor as capacitors supply reactive power $\backslash (\{\}^\{1\}\backslash ).$

$\backslash (\{\}^\{1\}\backslash )$ You can think of this as consuming leading reactive power if it helps.