# Compensation to increase the available active power output

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 The installation of a capacitor bank can avoid the need to change a transformer in the event of a load increase

Steps similar to those taken to reduce the declared maximum kVA, i.e. improvement of the load power factor as discussed in Method based on reduction of declared maximum apparent power (kVA) , will maximise the available transformer capacity, i.e. to supply more active power.

Cases can arise where the replacement of a transformer by a larger unit, to overcome a load growth, may be avoided by this means. Figure L17 shows directly the power (kW) capability of fully-loaded transformers at different load power factors, from which the increase of active-power output can be obtained as the value of power factor increases.

tan φ cos φ Nominal rating of transformers (in kVA)
100 160 250 315 400 500 630 800 1000 1250 1600 2000
0.00 1 100 160 250 315 400 500 630 800 1000 1250 1600 2000
0.20 0.98 98 157 245 309 392 490 617 784 980 1225 1568 1960
0.29 0.96 96 154 240 302 384 480 605 768 960 1200 1536 1920
0.36 0.94 94 150 235 296 376 470 592 752 940 1175 1504 1880
0.43 0.92 92 147 230 290 368 460 580 736 920 1150 1472 1840
0.48 0.90 90 144 225 284 360 450 567 720 900 1125 1440 1800
0.54 0.88 88 141 220 277 352 440 554 704 880 1100 1480 1760
0.59 0.86 86 138 215 271 344 430 541 688 860 1075 1376 1720
0.65 0.84 84 134 210 265 336 420 529 672 840 1050 1344 1680
0.70 0.82 82 131 205 258 328 410 517 656 820 1025 1312 1640
0.75 0.80 80 128 200 252 320 400 504 640 800 1000 1280 1600
0.80 0.78 78 125 195 246 312 390 491 624 780 975 1248 1560
0.86 0.76 76 122 190 239 304 380 479 608 760 950 1216 1520
0.91 0.74 74 118 185 233 296 370 466 592 740 925 1184 1480
0.96 0.72 72 115 180 227 288 360 454 576 720 900 1152 1440
1.02 0.70 70 112 175 220 280 350 441 560 700 875 1120 1400

Fig. L17Active-power capability of fully-loaded transformers, when supplying loads at different values of power factor

Example:

(see Fig. L18 )

An installation is supplied from a 630 kVA transformer loaded at 450 kW (P1) with a mean power factor of 0.8 lagging. The apparent power

$S1=\frac{450}{0.8}=562\, kVA$

The corresponding reactive power

$Q1=\sqrt{S1^2-P1^2}=337\, kvar$

The anticipated load increase P2 = 100 kW at a power factor of 0.7 lagging.

The apparent power

$S2=\frac{100}{0.7}=143\, kVA$

The corresponding reactive power

$Q2=\sqrt{S2^2-P2^2}=102\, kvar$

What is the minimum value of capacitive kvar to be installed, in order to avoid a change of transformer?

Total power now to be supplied:

P = P1 + P2 = 550 kW

The maximum reactive power capability of the 630 kVA transformer when delivering 550 kW is:

$Qm=\sqrt{S^2-P^2}$

$Qm=\sqrt{630^2-550^2}=307\, kvar$

Total reactive power required by the installation before compensation:

Q1 + Q2 = 337 + 102 = 439 kvar

So that the minimum size of capacitor bank to install:

Qkvar = 439 - 307 = 132 kvar

It should be noted that this calculation has not taken account of load peaks and their duration.

The best possible improvement, i.e. correction which attains a power factor of 1 would permit a power reserve for the transformer of 630 - 550 = 80 kW.

The capacitor bank would then have to be rated at 439 kvar.

Fig. L18Compensation Q allows the installation-load extension S2 to be added, without the need to replace the existing transformer, the output of which is limited to S