Environmental Engineering Reference

In-Depth Information

In the case of full wind farm output at unity power factor, the per-unit export is

P
¼
20
0
:
660
=
100
¼
0
:
132

Q
¼
0

The voltage rise may now be estimated using (2.24), assuming an initial wind

farm voltage of
V
g
¼
1
:
0:

RP
þ
XQ

V
g

0
:
551
0
:
132

1
:
0

D
V

¼

¼
0
:
0727

Setting wind farm voltage to 1.0727, and performing two further iterations gives

V
g
¼
1
:
0681

It may be noted that this value for wind farm voltage implies a variation of

6.8% for a gust causing generation to increase from minimum (
V
g
¼
1.0) to max-

imum. Line losses may be obtained from line current:

P
¼
VI
cos
f
¼
1
:
0681
I
1
:
0
¼
0
:
132

∴
I
¼
0
:
1236

∴
I
2
R
¼
0
:
0084

To summarize: the wind farm voltage is 6.81% above nominal, which is out-

side the range recommended above. The line losses are 0.84 MW, or 6.4% of

production.

The voltage rise may be mitigated by importing reactive power. Point A of

Figure corresponds to an export of

P
¼
0
:
132

Q
¼
0
:
044

Equation (2.24) is again applied. The
XQ
term of the numerator is negative due

to the reactive power export being negative, resulting after three iterations in a

lower estimate for the wind farm voltage:

V
g
¼
1
:
0456

This voltage is within the range of 0.95-1.05 specified above. The power

factor at point A is 0.95 leading - see the 'power triangle' of Figure 2.11. The lower

power factor results in a higher line current and hence losses. These are now

0.97 MW or 7.4% of production, compared with 6.4% previously. Such a small loss

of efficiency would be considered a small price to pay for allowing a greater wind

capacity to be connected within the voltage limits.

Further analysis shows that the number of WTGs that can be accommodated in

this example within the 1.05 per unit voltage ceiling is 14 at unity power factor or

22 at 0.95 leading.

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