Heating System for a Group of Condominiums Rory Clune Dept. of Civil & Environmental Engineering, Massachusetts Institute of Technology ESD.71 Application.

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Presentation transcript:

Heating System for a Group of Condominiums Rory Clune Dept. of Civil & Environmental Engineering, Massachusetts Institute of Technology ESD.71 Application Portfolio

1. Introduction 2. Uncertainties 3. Modelling & Design Levers 4. Decision Tree 5. Binomial Lattice 6. Conclusion

1. Introduction -What is the system? -Heating plant – natural gas boiler heats water & pipes it to holiday homes Hot water to homes Cold water returned Gas (fuel) in

2. Uncertainties -Two major uncertainties (a) Price of natural gas – an input cost Source: Energy Information Administration ( ) ν = 0.90% σ = 14.00%

2. Uncertainties (b) Demand for heat Assumption: Demand for heat ~ number of tourists visiting condos ~ number of tourists visiting Ireland (for which data available) Source: Central Statistics Office of Ireland ( ) ν = 3.63% σ = 6.74%

3. Modelling & Design Levers -Excel – Based on thermodynamic/HVAC theory -NPV over 10 years. Monthly resolution -Option to ‘expand medium’, ‘expand big’ or do nothing at year 5

1. Introduction 2. Uncertainties 3. Modelling & Design Levers 4. Decision Tree 5. Binomial Lattice 6. Conclusion

4. Decision Tree Fixed Design Capacity to meet forecast demand level at year 5 (my decision point) Bigger now means less efficient initially – boiler theory Flexible Design Capacity to meet today’s demand only Capability to expand to meet anything up to maximum possible demand Two uncertainties (gas price & demand level) 3 levels over each period – favourable, forecast & unfavourable

4. Decision Tree 2 uncertainties, each with 3 possible outcomes 2 decision nodes (shown in yellow)

5. Binomial Lattice -Analysis over 6 years -Just one uncertainty – natural gas price Monthly σ, ν parameters from regression converted to annual ($ per kWh of gas)

5. Binomial Lattice -Option: close at any time, without penalty. Can be exercised only once Annual undiscounted cash flows (Year 0 includes Capex) Double-checked using standard NPV of annual cash flows method

5. Conclusion -Decision Tree: Flexibility increases E(NPV) & shifts most of VARG to the right Noticeably reduced downside -Binomial Lattice: Flexibility to expand increases E(NPV) Effect on VARG curve not remarkable (short time period) More awkward to apply – assumptions had to be made -number of uncertainties = 1 -path independence Easy to adapt to situation, but laborious

End