Transformer Replacement Timing Under Geometric Load Growth
A cooperative's 5 MVA, 13.8/0.4 kV transformer carries a peak demand of 3.6 MVA. Its planning rule limits continuous loading to 85% of nameplate, and the supplier quotes 18 months from purchase order to energization. Peak demand has grown at a stable 7% per year, compounded annually, and no load transfers are planned. The planning engineer must decide when to place the order for the replacement unit so that the new unit is energized before the 85% limit is reached. A separate irrigation project is also under review; if approved, it would add 0.35 MVA of demand immediately at the start of the same year.
1. Using the 7% growth assumption and no irrigation load, determine the time in years until the 85% loading limit is reached.
Read the worked answer
The allowable peak is 0.85 x 5 MVA = 4.25 MVA.
Solve 3.6(1.07)^n = 4.25:
(1.07)^n = 4.25/3.6 = 1.18056
n = ln(1.18056)/ln(1.07) = 0.16598/0.06766 = 2.45 years (about 2 years 5 months).
2. Determine the latest date, in months from today, to issue the purchase order, allowing the full 18-month lead time.
Read the worked answer
The order must be placed 1.5 years before the limit is reached:
n_order = 2.45 - 1.50 = 0.95 year
0.95 x 12 = about 11.4 months from today.
If the order slips past roughly 11 months, the existing unit will exceed the 85% rule before the replacement is energized.
3. If the irrigation load is connected now, recompute the time to the limit and state the procurement decision.
Read the worked answer
New starting demand = 3.6 + 0.35 = 3.95 MVA.
3.95(1.07)^n = 4.25
(1.07)^n = 1.07595
n = ln(1.07595)/ln(1.07) = 0.07319/0.06766 = 1.08 years.
The 18-month lead time (1.5 years) exceeds the 1.08 years available, so the order must be issued immediately; otherwise the transformer will be overloaded before the replacement arrives. The judgment call is that lead time, not just growth rate, drives the decision.