Electrical Power Import and Export

Import and export power in power systems normally refers to the tranfer of power between interconnected power systems. Power generators or utilities that have excess power available will export some of that power to a connected system that imports it. In large, interconnected systems like those in the U.S. and Canada in which groups of utilities form regional or provincial grids and those grids are connected together to form national grids, power can be moved freely from one location to another, even when the exporter and importer are physically separated by great distances and are connected only through the transmission grid. Power transfer is monitored and the system power flow controlled by regional system operators.

Although reactive power is a necessary consideration in importing and exporting power for maintaining voltage and system stability (and is more complex in interconnected systems) it is equally important in isolated systems.

The normal power triangle applies.

Direction of flow of Active and Reactive Power

Even though the AC current flows alternatively in both the directions, the direction of AC current is always rendered positive in the direction of power flow. In power balance calculations at any node in the power system, by a convention adopted by most of the utilities, the outgoing power from the node is taken as positive and incoming power as negative. Let us consider a dummy node N with voltage V and power P with current I flowing from left to right, as below.

......P→.... V.....I →

----------lNl-------

.......I1.......... I2...

.......P1......... P2...

.......Q1......... Q2...

By the convention stated earlier,

P1 = - P, and P2 = + P

I1 = - I, and I2 = + I

Hence at node N, I1 + I2 = 0 and P1 + P2 = 0

I2, i.e., (I) lags V by, say, angle Ø. So, P2 = |V|.|I2|. Cos Ø = V I Cos Ø

I1, i.e. (-I) lags V by angle 180+Ø, and so, P1 = |V|.|I1|.Cos(180+Ø) = - VI Cos Ø

Let us try to do the same thing with reactive power Q (lag, say). Here we have an additional concept of lagging and leading reactive power. As mentioned earlier, lagging reactive power is taken as positive, by convention adopted by most of the utilities.

I2 lags V by, say, angle Ø. So, Q2 = |V|.|I2|. Sin Ø = V I Sin Ø

I1 lags V by, angle 180+Ø. And so, Q1 = |V|.|I1|. Sin (180+Ø) = - V I Sin Ø

Now, we are ready to view the quadrant principle of power factor as below:

Quadrant-2................................ Quadrant-1

Phase angle 90 to 180 Deg (lag).......Phase angle 0 to 90 Deg (lag)

Power Factor: 0 to -1 (lag) .............Power Factor: 1 to 0 (lag)

Active Power P is Negative ..............Active Power P is Positive

Lagging Reactive Q is Positive ..........Lagging Reactive Q is Positive

Quadrant-3................................. Quadrant-4

Phase angle 90 to 180 Deg (lead).......Phase angle 0 to 90 Deg (Lead)

Power Factor: 0 to -1 (lead).............Power Factor: 1 to 0 (lead)

Active Power P is Negative...............Active Power P is Positive

Lagging Reactive Q is Negative..........Lagging Reactive Q is Nagative

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Hope the above has answered your query. If you want further clarification, please contact me at lvnaga@yahoo.com.

L V Nagarajan, 6th Nov 2008

Dear sir, I have some basic doubts sir. 1) In our discussion angle of I2 is phi and angle of I1 is (180+phi) my doubt is angle of I1 is (180+phi) or (180-phi) 2)In 1st quadrant and 2nd quadrant u take PF as lagging. But what I assume previously not in this case, (Generally) is , a) I take voltage as reference (let,positive X-axis) b)If current vector rotates clockwise means it lags c)If current vector rotates anti-clockwise means it leads Based on my assumption,1st quadrant and 2nd quadrant angle was leading. 3)lagging reactive Q is negative means leading reactive power positive. 4)Any power i.e. reactive power or active power positive means,power exports. Please correct me if my assumption was wrong. Thanks and regards gova

Dear LV.nagarajan sir,

the answer u sent for my post in this forum is correct and nice.This is I realized after discussing with my seniors and friends.

please ignore my reply.

and thanks to bluestones for his valueable information.

regards

gova