*Preamble*

*From the last two blogs (Electric Power – Parts 2 & 3), we know that the AC power flow consists of two components. *

* **The first is the ‘Average’ power flow over one cycle, which is associated with the energy conversion or the ‘Useful’ power flow. *

* **The second is the ‘Oscillatory’ power flow due to energy storage elements, namely inductances and capacitances. The ‘Oscillatory’ power flow is not relevant for the transfer of ‘Useful’ power. However, ‘Oscillatory’ power uses up the available capacity of the power system. Hence, it is an important factor in the operation of a power system. *

* **Due to some quirk of history, the ‘Oscillatory’ power is called the ‘*__Reactive__’ power! Consequently, the ‘Average’ or ‘Useful’ power flow is called the ‘__Active__’ power. The term ‘Active’ power is more commonly used in practice, and the term ‘Average’ power is rarely used!

*The above alternative terms for power have caused a lot of confusion in the power system community. We have no choice but to accept them and move on.*

*We ***derived** the equation for ‘Average’ power (P) in Part 2 of this series as given below:

* P = E I cos(φ) watts ( where E = E*_{m }/ √2 and I = I_{m }/ √2 )

*We*** defined** the equation for ‘Reactive’ power (Q) in Part 3 of this series as given below:

* Q = E I sin(φ) vars*

*Note that the ‘root mean square (rms)’ values of voltage (E) and current (I) are used for the calculation of AC power.*

*In previous blogs, we used the above equations for power calculations. This resulted in some confusion regarding the calculation of phase angle difference (φ). In addition, the above equations do not adequately specify the direction of power flow.*

* **In this blog, we shall derive a more versatile equation for power in *__complex form__, namely **S **= **V I***, which resolves the above issues.

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