When we increase the Interest Rate, the Total NPC will decreased while the COE is increased. So the question is that why Total NPC is decreased?

The total net present cost is the total present value of all cash flows.  The present value of a future cash flow decreases with increasing interest rate.  That’s why the total NPC decreases with increasing interest rate.

The cost of energy is the total annualized cost divided by the total load served.  The total annualized cost is almost independent of the interest rate.  The only interest-rate-sensitive part of the total annualized cost is the salvage value, and it usually makes only a small contribution.  So the COE usually does not change, or not very much, with changing interest rate.

HOMER’s online help system gives equations for both the total NPC and the COE.