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, 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.

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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. L17: Active-power capability of fully-loaded transformers, when supplying loads at different values of power factor

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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

[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 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.

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Fig. L18: Compensation 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

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