Estimating the Payback Period of In-line Micro Turbines with Analytical Probabilistic Models

This paper presents a new analytical probabilistic model that can characterize the energy recovery and economic payback period of in-line micro turbines in water distribution applications.The analytical probabilistic model incorporates elements of derived probability distribution theory. A probability distribution function for the power produced by the turbine is first derived assuming that the power produced by the turbine is functionally dependent on the flow rate through the turbine. A probability distribution function for the payback period of the turbine is also derived assuming that the payback period is both functionally dependent and inversely proportional to the power produced.The analytical probabilistic model was applied to a water distribution network to evaluate the expected values and standard deviation of payback period. The case study was used to examine the impact of the coefficient of variation of turbine flow, initial capital cost of the turbine, and electricity price on the expected value and standard deviation of payback period for an optimized turbine location. The results suggested that the coefficient of variation of turbine flow had little impact on the expected value and standard deviation of payback period. The initial capital cost and electricity price had a significant impact on the expected value of payback period but only a small impact on the standard deviation of payback period. The results will help municipalities better understand how the uncertainties associated with demand, initial capital costs, and electricity pricing will affect the economic viability of in-line micro-turbine projects in their systems.