1 Massachusetts Institute of Technology ESD.71 – Engineering Systems Analysis for Design Application Portfolio Heating System for a Group of Condominiums Rory Clune December 20082 3 4 Executive Summary In the context of a natural gas-fired heating system for a group of condominiums in the West of Ireland, the impact of uncertainty and the value of incorporating flexibility in design are investigated. The heating system is modelled using a combination of real input data and typical performance parameters reflective of such a system. The variability in demand for heat, taken to be directly proportional to the number of tourists visiting the region, and the price of natural gas are the key uncertainties considered. The net present (monetary) values of the system with and without flexibility in design are evaluated using a two-stage decision tree over ten years and a binomial lattice over six years. In both cases, the incorporation of flexibility increases the expected NPV of the system. Other decision-making criteria besides NPV are explored. The results of these analyses are presented and discussed.5 Contents: 1. Introduction and problem outline 2. Recognition of uncertainties 3. Formal system definition 4. Decision analysis 5. Binomial lattice analysis of evolution of a major uncertainty 6. Binomial lattice valuation 7. Conclusion 8. Appendices6 1. Introduction and problem outline A new building technology company, HeatWise Plc, has been awarded the contract to provide heat to a group of fifty condominiums built just outside Killarney in Ireland, an area noted for attracting national and international tourism. The condominiums are to be rented to tourists visiting the area, and will be marketed as a more ‘authentic’ Irish experience than a standard hotel. Given the country’s temperate climate, most buildings in Ireland are heated almost year-round – especially buildings accommodating tourists who are used to warmer climates. Air conditioning is rarely employed in residential settings, and it is only in the height of summer that buildings are not heated at night. The conditions of the contract stipulate that the company will provide a service which has a certain minimum heating capacity, as defined by the developer of the condominiums. HeatWise sells the heat by the kilowatt-hour to the consumer – the developer has little experience of building technology and does not wish to manage such a system. In the case of the heating capacity of HeatWise’s plant being exceeded by the heating demand, the developer has arranged for an outside source to bring in separate storage heaters. In such a scenario, HeatWise would miss out on additional revenues, but the buildings would not go unheated. The developer has indicated that the current group of fifty condominiums represents only the first phase of construction, and that he intends to construct another phase five years after the first. The size of this second phase of condominiums will be determined by his perceptions of the demand for the first phase and by his predictions of future tourism levels. It is, therefore, entirely possible that none of this second phase will be built. It has been agreed that the heating contract for the second phase will initially be offered to HeatWise before being offered to the market. The total amount of condominiums he can build is constrained by planning regulations to eighty. For the sake of simplicity, the second construction phase is considered to add either thirty, ten or zero condominiums to the scheme. The rationale for this is explained in a later section. 1.1 The heating system - What does it include, and what does it exclude? The system in this project is defined as the natural gas boiler plant which HeatWise has selected for installation. The plant will heat water in a gas boiler system, and pipe it through a closed network to the condominiums. The revenues generated are proportional to the heat delivered to each condominium unit, as determined by a fixed cost per kilowatt-hour charged to the consumer. The cost of generating the heat is dependent on the cost of natural gas. What makes this problem interesting is that the efficiency (simply defined as heat output divided by heat input) of a gas boiler declines as the load on the boiler decreases below the design load. This adds an extra degree of complexity to the system, as the relationship between the cost and the amount of heat supplied is nonlinear. 1.2 Principal design levers Two distinct design scenarios are envisaged: (1) The construction of a plant comprising a single large boiler, capable of meeting the heating demand from all possible eighty condominiums at winter design temperatures.7 (2) The construction of a plant building of similar geometric proportions, but with a smaller boiler capable of meeting the heating demand for the first phase of construction only. Should the developer go ahead with subsequent phases, the system can be expanded by installing a second boiler into the network, capable of meeting the demand from 30 additional units. It is assumed that the initially installed piping network to the boiler plant room remains unchanged after initial construction, as the retrofitting of such a network upon plant expansion would be entirely impractical. 1.3 Numerical model Based on the author’s previous experience of building technology projects, a model is constructed in Microsoft Excel. The model determines the heating load of a typical condominium based on monthly average temperatures for the region. This can be converted to a set of requirements for the gas boiler. The model as described so far will, for all practical purposes, act as a ‘black box’ which relates the demand on the system (and, of course, the revenue generated) to the total cost of generating the heat to meet this demand, comprising an initial capital investment plus a stream of annual/monthly variable costs over the system’s design life. Further details of this model are explored at a later stage. The benefit of the system to HeatWise is the financial profit generated by its operation, defined here as the net present value of costs and revenues. It is not intuitively clear at the outset how the compounding factor of variable boiler efficiency will affect the end results. Fig 1.1 Spreadsheet model screenshot8 1.4 Contextual factors that will affect the value of system performance (1) The demand for the