Electric Power – Part 4 – AC Power Equation

Active Power – What is in a name?

We have used a term–‘Active power’–for ‘P’ in Equation 1.  It is really a reflex action since we named ‘Q’ as ‘Reactive power’!  Somehow, the power system engineers like the term ‘Active Power’ in preference to other terms!

In fact, it is not uncommon to refer to ‘P’ as the ‘Real power’ since it is the ‘real part’ of the complex power ‘S’.  By this token, we should be referring to the ‘Reactive power’ as the ‘Imaginary power’!  Thank goodness that such a term did not become popular!

We have the choice of  ‘Active power’,  ‘Real power’,  ‘Average power’ and ‘Useful power’.  Which term is the best?  You be the judge!  The jury is still out!  This shows how important it is to have a standardised terminology that is logical and meaningful.

Can we use S = V* I instead of S = V I*?

In theory, we can use the equation S = V* I to calculate the power in AC.  The conjugation of either the voltage or the current vector gives the correct power factor angle.  In fact, the active power (‘P’) value is not affected at all, since cos(φ) = cos(-φ).  However, the reactive power (‘Q’) value will have the opposite sign compared with Equation 1.

Some older power systems textbooks do use the power flow equation S = V*I.  Fortunately, all new textbooks use the equation S = V I* – for a good reason. 

The definition of the ‘direction of reactive power flow’ depends on the equation used.  The use of S = V I* results in positive values for ‘inductive’ reactive power flowing out of the generator and the ‘inductive’ reactive power flowing into the load.  This is convenient and useful in practice, since power systems loads are mostly inductive loads – namely induction motors.  Hence, the generators supply the required inductive reactive power!

It is necessary to formally define the power flow direction, depending on the equation used for power flow calculation.  We will use Equation 1 for our definitions.

Definition of Active Power flow Direction

The direction of active power (P) is defined as below:

A positive value of ‘P’ obtained from Equation 1, indicates that the active power is flowing in the direction of the assumed current direction.  Conversely, a negative value of ‘P’ obtained from Equation 1, indicates that the active power is flowing in the direction opposite to the assumed current direction.

What is the current direction in AC circuits?

Good question.  The current flows in both directions in AC systems!  It changes direction every half cycle!  However, it is necessary to assign (assume) a current direction when solving AC circuits.  This helps to establish the circuit equations using Kirchhoff’s laws (KVL and KCL) in a consistent manner.  In fact, you would have assigned the current directions when solving AC circuits, even without asking the above question!

The choice of current direction can be arbitrary.  However, in practice, it is convenient to choose the current direction based on the expected active power flow direction.  The active power generally flows from utility generator (source) to load – unless there are solar panels on the roof tops!

Definition of Reactive Power flow Direction

Again, one might ask, what is the relevance of ‘reactive power direction’ since the reactive power is an ‘oscillatory’ power? 

Good question again!  Even though the reactive power is oscillatory (like the AC current flow), the inductive and capacitive reactive power flows have a phase difference of 180 degrees.  In other words, the ‘inductive reactive power’ flows in a direction opposite to ‘capacitive reactive power’.  These flows essentially cancel out each other.  Hence, the direction for reactive power flow is important for reactive power flow calculations.

With the above background, let us now formally define the power flow direction for the reactive power (Q).

A positive value of ‘Q’ obtained from Equation 1, indicates that the ‘inductive’ reactive power (I lags V) is flowing in the direction of the assumed current direction.  Conversely, a negative value of ‘Q’ obtained from Equation 1, indicates that the inductive reactive power is flowing in the direction opposite to the assumed current direction.  In other words, the ‘capacitive’ reactive power (I leads V) is flowing in the assumed current direction.

The Equation 1 implicitly specifies the ‘inductive reactive power’ as the reference.  Hence, when using this equation, the term ‘reactive power’ is synonymous with ‘inductive reactive power’.  We generally avoid the use of the term ‘capacitive reactive power’ in power systems.  Consequently, in power system terminology, a capacitor is considered as a ‘generator’ or ‘source’ of (inductive) reactive power!