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# What is the effect of Load Power Factor on efficiency and regulation?

The power factor of the load connected to the power system considerably affects the voltage regulation and efficiency of a transmission line.

## Effect of Load Power Factor on Voltage Regulation

The expression for percentage voltage regulation of a transmission line, when a load of lagging power factor is connected to the system, is given by,

$$\mathrm{\%\:Voltage \:Regulation\:=\:\frac{\mathit{IR}\:cos\:\phi _{\mathit{R}}\:+\:\mathit{IX_{\mathit{L}}}cos\:\phi _{\mathit{R}} }{\mathit{V_{\mathit{R}}}}\:\times \:100\%\:\:\:...\left ( 1 \right )}$$

Where, suffix * R* denotes the receiving end quantities.

Also, the percentage voltage regulation for leading power factor is given by,

$$\mathrm{\%\:Voltage \:Regulation\:=\:\frac{\mathit{IR}\:cos\:\phi _{\mathit{R}}\:-\:\mathit{IX_{\mathit{L}}}cos\:\phi _{\mathit{R}} }{\mathit{V_{\mathit{R}}}}\:\times \:100\%\:\:\:...\left ( 2 \right )}$$

Therefore, from equations (1) and (2), the following points can be concluded −

When the power factor of the load $\mathrm{\left ( cos\:\phi _{\mathit{R}} \right )}$ is lagging or unity or such leading that $\mathit{IR}\:cos\:\phi _{\mathit{R}}\:>\:\mathit{IX_{\mathit{L}}}\:cos\:\phi _{\mathit{R}}$, then the voltage regulation of the transmission line is positive. That means the receiving end voltage $\mathrm{\left ( \mathit{V_{R}} \right )}$ will be less than the sending end voltage $\mathrm{\left ( \mathit{V_{S}} \right )}$.

When the power factor of the load is such leading that $\mathit{IR}\:cos\:\phi _{\mathit{R}}\:<\:\mathit{IX_{\mathit{L}}}\:cos\:\phi _{\mathit{R}}$, then the voltage regulation of the transmission line is negative which means that the receiving end voltage $\mathrm{\left ( \mathit{V_{R}} \right )}$ is more than the sending end voltage $\mathrm{\left ( \mathit{V_{S}} \right )}$.

For a given receiving end voltage $\mathrm{\left ( \mathit{V_{R}} \right )}$ and line current $\left ( \mathit{I} \right )$, the voltage regulation of the transmission line increases with the decrease in load power factor for lagging loads.

For a given receiving end voltage $\mathrm{\left ( \mathit{V_{R}} \right )}$ and line current $\left ( \mathit{I} \right )$, the voltage regulation of the transmission line decreases with the decrease in load power factor for leading loads.

## Effect of Load Power Factor on Transmission Efficiency

The amount of power that is delivered to the load depends upon its power factor. As the expression of electrical power is given by,

For single-phase transmission line,

$$\mathrm{\mathit{P}\:=\:\mathit{V_{\mathit{R}}}\mathit{I}\:cos\:\phi _{\mathit{R}}}$$

$$\mathrm{\therefore \mathit{I}\:=\:\frac{\mathit{P}}{\mathit{V_{\mathit{R}}}cos\:\phi _{\mathit{R}}}\:\:\:...\mathrm{\left ( 3 \right )}}$$

And for three-phase transmission line,

$$\mathrm{\mathit{P}\:=\:3\mathit{V_{\mathit{R}}}\mathit{I}\:cos\:\phi _{\mathit{R}}}$$

$$\mathrm{\therefore \mathit{I}\:=\:\frac{\mathit{P}}{3\mathit{V_{\mathit{R}}}cos\:\phi _{\mathit{R}}}\:\:\:...\mathrm{\left ( 4 \right )}}$$

From the equations (3) and (4), it is clear that, for a given amount of electric power (*P*) to be transmitted and receiving end voltage $\mathrm{\left ( \mathit{V_{R}} \right )}$, the load current $\left ( \mathit{I} \right )$ is inversely proportional to the power factor of the load (cos $\phi _{\mathit{R}}$). Therefore, with the decrease in load power factor, the load current and hence the power losses in the transmission line are increased. Consequently, the transmission efficiency of the line decreases with the decrease in the load power factor and *vice-versa*.

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