Sizing a Transformer for a Growing Commercial Building
A three-storey office building has a calculated maximum demand of 420 kVA at 0.85 power factor lagging. The existing 500 kVA, 11 kV/400 V distribution transformer serves only this building and runs at 78% loading during peak hours with a top-oil temperature rise of 52 K against a rated 55 K rise. The owner plans to add a 90 kVA (at 0.85 pf) air-conditioning load and a 30 kW resistive water-heating load within 18 months. Ambient design temperature is 40 C, and the utility limits transformer loading to 100% of nameplate. The client asks whether to keep the existing unit, derate it, or replace it, and wants the cheapest compliant option.
1. Compute the post-expansion apparent power demand and determine whether the existing transformer remains compliant.
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Existing demand S1 = 420 kVA at pf 0.85, so P1 = 357 kW, Q1 = 420 x sin(acos 0.85) = 420 x 0.527 = 221 kvar.\n\nNew loads: AC S = 90 kVA at 0.85 pf -> P = 76.5 kW, Q = 90 x 0.527 = 47.4 kvar. Water heating P = 30 kW, Q = 0.\n\nTotals: P = 357 + 76.5 + 30 = 463.5 kW; Q = 221 + 47.4 = 268.4 kvar.\nS = sqrt(463.5^2 + 268.4^2) = sqrt(214,832 + 72,039) = sqrt(286,871) = 535.6 kVA.\n\nLoading = 535.6 / 500 = 107% of nameplate. Exceeds the 100% utility limit, so the existing unit is non-compliant after expansion. Note the result is above 500 kVA even though the arithmetic sum of kVA (420+90+30=540) overstates it because the heating is unity pf.
2. The client proposes adding 120 kvar of switched capacitors instead of replacing the transformer. Evaluate this against the loading limit and the thermal constraint.
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With 120 kvar of capacitors, net Q = 268.4 - 120 = 148.4 kvar.\nS = sqrt(463.5^2 + 148.4^2) = sqrt(214,832 + 22,023) = sqrt(236,855) = 486.7 kVA.\nLoading = 486.7 / 500 = 97.3%, within the 100% limit.\n\nHowever, the unit already runs at 52 K top-oil rise at 78% load against a 55 K rating, and the ambient is 40 C. The permissible rise at 40 C ambient for a 105 C insulation hot-spot class is lower than at the standard 20-30 C reference, so the thermal margin is thin even at 97% load. The capacitors reduce line current and losses but do not remove the real-power thermal load (463.5 kW is unchanged; only reactive current falls). The correct judgement is that capacitors restore apparent-power compliance but the thermal margin should be checked against the manufacturer's temperature-rise data and ambient correction before accepting; a load tap or forced cooling may still be needed. Capacitors also cannot follow the AC load if it is switched off, causing overcompensation at light load, so automatic switching by pf controller is required.
3. Recommend a decision and state the key assumptions.
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Recommendation: install the 120 kvar automatically switched capacitor bank as the lowest-cost compliant option, contingent on confirming with the manufacturer that the unit can carry 97% load at 40 C ambient without exceeding its hot-spot limit. If the thermal check fails, replace with a 630 kVA unit (next standard size above 535.6 kVA) or add forced cooling.\n\nAssumptions: (1) the 90 kVA AC figure is at the same 0.85 pf and is a maximum-demand contribution, not a connected load; (2) diversity between the AC and heating loads is not applied - if they never coincide, the demand is lower and the case for capacitors strengthens; (3) the 100% loading limit is a hard utility constraint, not a guide; (4) no harmonics are present that would require detuned reactors on the capacitor bank. Each assumption should be verified before purchase, because the decision flips if the AC load coincides with heating or if the thermal margin is inadequate.