How does ROI differ from IRR in HOMER?

Before I calculate IRR, ROI, NPV, or payback, I calculate the difference in cash flows between the current system and the base case system.  That gives me a single cash flow sequence.  Say the base case is a diesel-only system that costs nothing up front, but costs $100k/yr to operate, and say the current system is a wind-diesel system that costs $250k up front and then $45k/yr to operate.  So compared to the base case, the wind-diesel system has an investment cost of $250k and an annual income of $55k/yr.  Say we use a project lifetime of 10 years.

The IRR is the discount rate that makes the present value of an investment zero.  For this example, the IRR would be 17.68% because -250k + PV(17.68%, 10, 55k) = 0.

The ROI seems less well-defined than the IRR.  I chose to use the following definition:

ROI = (TotalNominalGain / ProjectLifetime) / InvestmentCost

For this example the total nominal gain over the 10 years is $550k.  So the ROI is (550k / 10yr) / 250k = 22%.