# Compensation to increase the available active power output

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** L18 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 |

**Example:**

(see **Figure** L19)

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

[math]\displaystyle{ S1=\frac{450}{0.8}=562\, kVA }[/math]

The corresponding reactive power

[math]\displaystyle{ Q1=\sqrt{S1^2-P1^2}=337\, kvar }[/math]

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

The apparent power

[math]\displaystyle{ S2=\frac{100}{0.7}=143\, kVA }[/math]

The corresponding reactive power

[math]\displaystyle{ Q2=\sqrt{S2^2-P2^2}=102\, kvar }[/math]

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:

[math]\displaystyle{ Qm=\sqrt{S^2-P^2} }[/math]

[math]\displaystyle{ Qm=\sqrt{630^2-550^2}=307\, kvar }[/math]

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 into 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.