LINE LOSS CALCULATION: SAMPLE PROBLEM 3

PROBLEM: A 15MW, 132kV, 80% power factor three phase load is to be served by a transmission line having conductors whose resistance is 0.5ohm/km. if the losses on the line shall not exceed 4.5%, how long must this line be?

SOLUTION:
To better understand the problem,let us first draw the figure that the problem would like to emphasize.

Unlike the previous sample problem, here we are asked to do the reverse. We need to solve for the ideal length of the transmission line for it to have a loss not more than 4.5% of the power generated. The following are the given data;

15MW of Load
132kV voltage at 80% power factor
0.5 ohms per kilometer resisitance of the conductors.

With the given data above, we first need to calculate the line current that passes through the conductors using the formula;

LINE CURRENT = (KW LOAD) / (SQRT(3)*LINEVOLTAGE*POWERFACTOR

= (15,000,000) / (SQRT(3)*132,000*0.8)

LINE CURRENT = 82 A

θL = arccos (0.8) = 36.87 degrees

After solving for the transmission line current, we now need to look for the total sending power by using the formula;

POWER GENERATED = POWER LOAD + POWERLOSS

But it was said in the problem that POWERLOSS must not exceed 4.5% of the Power Generated. Therefore;

POWER GENERATED = POWER LOAD + 0.045*POWER GENERATED

POWER GENERATED = 15 + 0.045*POWER GENERATED

POWER GENERATED = 15.706MW

Power Loss therefore is 4.5% of Power Generated, or,

Ploss = 0.045*(15.706) = 706kW

Ploss = 3*Isquared R

R = Ploss/(3*Isquared) = 706,000 / (3*82squared) = 35 ohms

Solving for Line Length,

LENGTH OF LINE = TOTAL OHMS / OHMS PER KM

LENGTH OF LINE = 35 OHMS / 0.5 OHMS PER KM

LENGTH OF LINE = 70 KILOMETERS

Reference: 1001 Solved Problems in Electrical Engineering by Romeo Rojas Jr.

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