Question

(a) How many Mvars of shunt capacitors are required to increase the power factor on a 10 MVA load from 0.85 to 0.9 lagging? (b) How manyMvars of shunt capacitors are required to increase the power factor on a 10 MVA load from 0.90 to 0.95 lagging? (c) Which requires more reactive power, improving a low power-factor load or a high power-factor load?

Short answer

1. $1.151Mvar$of shunt capacitors are required to increase to power factor on a 10 MVA load from 0.85 to 0.90 lagging.
2. $1.401Mvar$of shunt capacitors are required to increase to power factor on a 10 MVA load from 0.90 to 0.95 lagging.
3. By improving the high power factor load requires more reactive power.

Step-by-step solution

Determine Mvars of shunt capacitors are required to increase the power factor on a 10 MVA load from 0.85 to 0.9 lagging.

(a)

The$S_L$is the total power absorbed by the load, that is$S_L=10MVA$

Write the expression for the power factor angle of the load for power factor of$0.85$.

$$\begin{gathered} {\theta }_L={\cos }^{-1}\left(0.85\right) \\ =31{.79}^0 \end{gathered}$$

Write the expression for reactive power absorbed by the load.

$$\begin{gathered} {\mathbf{Q}}_{\mathbf{L}}\mathbf{=}{\mathbf{S}}_{\mathbf{L}}\mathbf{sin}\left(\mathbf{31}\mathbf{.}\mathbf{79}°\right) \\ =\left(10\right)\left(0.5268\right) \\ =5.268Mvar \end{gathered}$$

Write the expression for the real power absorbed by the load.

$\begin{array}{rcl}{P}_L& =& \left(10\right)\left(0.85\right)\\ & =& 8.5MW\\ & & \end{array}$

Write the expression for the power factor angle of source for power factor of $0.9$.

$\begin{array}{rcl}{\theta }_s& =& {\cos }^{-1}\left(0.9\right)\\ & =& 25.{84}^O\\ & & \end{array}$

The shunt capacitors should not change the actual power that the source delivers to the load.

$P_S=8.5MW$

Write the expression for reactive power delivered by the load.

$\begin{array}{rcl}{Q}_S& =& S_S\sin \left(25.{84}^{\circ }\right)\\ & =& \left(\frac{P_S}{p.f}\right)\sin \left(25.{84}^{\circ }\right)\\ & =& \left(\frac{8.5}{0.9}\right)\left(0.4359\right)\\ & =& 4.116Mvar\\ & & \end{array}$

Write the expression for reactive power delivered by the shunt capacitors.

$\begin{array}{rcl}{\mathbf{Q}}_{\mathbf{C}}& \mathbf{=}& {\mathbf{Q}}_{\mathbf{L}}\mathbf{-}{\mathbf{Q}}_{\mathbf{S}}\\ & =& 5.268-4.117\\ & =& 1.151Mvar\\ & & \end{array}$

Therefore,$1.151Mvar$ of shunt capacitors are required to increase to power factor on a 10 MVA load from 0.85 to 0.90 lagging.

Determine Mvars of shunt capacitors are required to increase the power factor on a 10 MVA load from 0.90 to 0.95 lagging

(b)

The$S_L$is the total power absorbed by the load, that is$S_L=10MVA$

Write the expression for the power factor angle of the load for power factor of $0.9$.

$\begin{array}{rcl}{\theta }_L& =& {\cos }^{-1}\left(0.9\right)\\ & =& 25.{84}^{\circ }\\ & & \end{array}$

Write the expression for reactive power absorbed by the load.

$\begin{array}{rcl}{Q}_L& =& S_L{\theta }_L\\ & =& \left(10\right)\sin \left(25.{84}^{\circ }\right)\\ & =& \left(10\right)\left(0.4359\right)\\ & =& 4.359Mvar\\ & & \\ & & \end{array}$

Write the expression for the real power absorbed by the load.

$\begin{array}{rcl}{P}_L& =& S_L\cos \theta \\ & =& \left(10\right)\left(0.9\right)\\ & =& 9MW\\ & & \end{array}$

Write the expression for the power factor angle of source for power factor of $0.95$.

role="math" localid="1656470459665" $\begin{array}{rcl}{\theta }_s& =& {\cos }^{-1}\left(0.95\right)\\ & =& 18.{19}^{\circ }\\ & & \end{array}$

The shunt capacitors should not change the actual power that the source delivers to the load.

$P_S=9MW$

Write the expression for reactive power delivered by the load.

$\begin{array}{rcl}{Q}_S& =& S_S\sin {\theta }_s\\ & =& \left(\frac{P_S}{p.f}\right)\sin \left(18.{19}^{\circ }\right)\\ & =& \left(\frac{9}{0.95}\right)\left(0.3121\right)\\ & =& 2.958Mvar\\ & & \end{array}$

Write the expression for reactive power delivered by the shunt capacitors

$\begin{array}{rcl}{Q}_C& =& Q_L-Q_S\\ & =& 4.359-2.958\\ & =& 1.401Mvar\\ & & \end{array}$

Therefore,$1.401Mvar$ of shunt capacitors are required to increase to power factor on a 10 MVA load from 0.90 to 0.95 lagging.

Determine which requires more reactive power, improving a low power-factor load or a high power-factor load

(c)

By comparing the results of (a), which require that the power factor be increased from 0.85 to 0.90 lagging on a 10 MVA load. As a result of (b), a 10 MVA load's power factor should be increased from 0.90 to 0.95 lagging.

Therefore, it can be concluded that increasing the reactive power is necessary to improve the high power factor load.