Cogeneration planning under uncertainty. Part II: Decision theory-based assessment of planning alternatives Enrico Carpaneto a , Gianfranco Chicco a,⇑ , Pierluigi Mancarella b , Angela Russo a a Dipartimento di Ingegneria Elettrica, Politecnico di Torino, corso Duca degli Abruzzi 24, I-10129 Torino, Italy b Dept. of Electrical and Electronic Engineering, Imperial College London, Exhibition Road, SW7 2AZ London, UK article info Article history: Received 16 March 2010 Received in revised form 6 August 2010 Accepted 16 August 2010 Available online 29 September 2010 Keywords: Cogeneration planning Decision theory Internal combustion engines Microturbines Uncertainty modeling Weighted regret criterion abstract This paper discusses specific models and analyses to select the best cogeneration planning solution in the presence of uncertainties on a long-term time scale, completing the approach formulated in the compan- ion paper (Part I). The most convenient solutions are identified among a pre-defined set of planning alter- natives according to decision theory-based criteria, upon definition of weighted scenarios and by using the exceeding probabilities of suitable economic indicators as decision variables. Application of the cri- teria to a real energy system with various technological alternatives operated under different control strategies is illustrated and discussed. The results obtained show that using the Net Present Cost indicator it is always possible to apply the decision theory concepts to select the best planning alternative. Other economic indicators like Discounted Payback Period and Internal Rate of Return exhibit possible applica- tion limits for cogeneration planning within the decision theory framework. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction This paper completes the formulation of the general framework introduced in the companion paper [1] by dealing with the details of taking into account large-scale uncertainties in the long-term time frame. In the multi-year time horizon for cogeneration plan- ning, it is difficult to envision the expected trends of evolution of energy loads and, even more, of electricity and gas prices. Hence, proper alternative techniques of assessment of the foreseeable solutions have to be identified and applied. Literature studies have been based on sensitivity analyses of specific indicators (typically economic variables [2]) with respect to electricity and gas price variations. For instance, the simple payback period and the Internal Rate of Return have been used as indicators in [3] to carry out sen- sitivity analyses with respect to the variation of electricity price, fuel price and investment cost, for a Combined Heat and Power (CHP) application. Similarly, a deterministic approach has been used in [4] to find the most convenient technological alternative among a set of pre-defined candidate alternatives through minimi- zation of the annualized total costs. Then, a sensitivity analysis has been performed to address the effects of upgraded performance of the equipment, reduction in the initial capital costs, and reduction in the electricity and gas prices. Sensitivity analyses have also been performed in [5] to test the robustness of the optimal solutions found for cogeneration systems coupled to cooling generation de- vices in the presence of large variations of energy market prices. In general terms, sensitivity analyses are useful to get indica- tions on the effects of pre-defined scenarios of variation of relevant variables. However, they give no information on how to combine the results obtained from different individual scenarios, and on the effects of actual occurrence of a scenario after the plant is in- stalled. In order to get additional insights in this direction, different levels of involvement of the decision-maker can be considered [6]. In particular, the decision-maker can actively participate in the decision process, for instance choosing the scenarios to be ana- lyzed and assigning to each of them a relative weight on the basis of specific expertise or personal preferences. In this way, the char- acteristics of alternative planning solutions available to the deci- sion-maker can be explained by looking at the results obtained in each combined scenario considered. Approaches moving in this direction have been proposed for distributed generation siting and sizing in [7,8]. The nature of the results to be obtained (e.g., deter- ministic or probabilistic) is a further element driving the choice of the type of analysis. For instance, when taking into account uncer- tainty, the results can be conveniently expressed in probabilistic terms, providing the probability distributions of the planning out- comes. In this respect, it is possible to exploit the framework pro- posed in [1]. Instead of evaluating only best or worst cases, the hazard to which the decision-maker is exposed because of uncer- tainty is represented by the probability of occurrence of the out- comes. The relevant aspect is the evaluation of the probability of 0306-2619/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2010.08.019 ⇑ Corresponding author. Tel.: +39 011 090 7141; fax: +39 011 090 7199. E-mail address: gianfranco.chicco@polito.it (G. Chicco). Applied Energy 88 (2011) 1075–1083 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy