To find the largest kVA load that can be delivered by the parallel combination of these two transformers without loading any transformer, we need to consider the impedance matching between the transformers.

The impedance of a transformer is typically given in per unit (pu) values, which are relative to the transformer's rated values. In this case, the per unit leakage impedance of the 1000 kVA transformer is (0.01 j0.04) pu and the per unit leakage impedance of the 500 kVA transformer is (0.02 j0.06) pu.

To parallel two transformers, the impedance values of both transformers must be equal. Therefore, we need to find a common per unit impedance value that can be used for both transformers.

Let's assume the common per unit impedance value for both transformers is (x jy) pu.

For the 1000 kVA transformer:
0.01 x 1000 = x
0.04 x 1000 = y

For the 500 kVA transformer:
0.02 x 500 = x
0.06 x 500 = y

Solving the above equations gives us:
x = 10 pu
y = 20 pu

Now, we have a common per unit impedance value of (10 j20) pu that can be used for both transformers.

To find the largest kVA load that can be delivered by the parallel combination without loading any transformer, we need to consider the total impedance of the parallel combination.

The total impedance (Z_total) of the parallel combination is given by the formula:
1/Z_total = 1/Z1 + 1/Z2

Where Z1 and Z2 are the impedances of the individual transformers.

For the 1000 kVA transformer:
Z1 = 0.01 + j0.04 = 0.04 + j0.16 pu

For the 500 kVA transformer:
Z2 = 0.02 + j0.06 = 0.02 + j0.12 pu

Plugging the values into the formula:
1/Z_total = 1/(0.04 + j0.16) + 1/(0.02 + j0.12)

Using complex number division, we can simplify the equation to:
1/Z_total = (0.04 - j0.16) + (0.02 - j0.12)

Adding the real and imaginary parts separately, we get:
1/Z_total = 0.06 - j0.28

Taking the reciprocal of both sides:
Z_total = 1/(0.06 - j0.28)

Using complex number division, we can simplify the equation to:
Z_total = 0.0556 + j0.2593 pu

The largest kVA load that can be delivered by the parallel combination without loading any transformer is given by the formula:
Largest kVA load = Total kVA rating / |Z_total|

Plugging in the values:
Largest kVA load = (1000 + 500) kVA / |0.0556 + j0.2593|

Using the Pythagorean theorem, we get:
Largest kVA load = 1500 kVA / sqrt(0.0556^2 + 0.2593^2)

Calculating the square root and simplifying, we get:
Largest kVA load = 1500 kVA / sqrt(0.