88 M. Holl and P.F. Pelz optimization problem. The optimization problem is solved using Monte-Carlo-Simulations. The model quality, the cause and effect relationship of the model as well as dominant input factors are determined by performing a sensitivity analysis as the last step of the method. The last step basically provides the information of how the uncertainty in the model output can be assigned to the respective uncertainty of the model input. The method is presented in this paper on the example of an innovative wind-energy converter called the energy ship concept. The concept involves a wind-powered vessel with a hydrokinetic turbine. The vessel converts the kinetic energy of the wind into kinetic energy of the vessel. The wind is substituted with water for power generation, so that the resulting hydrokinetic turbine can be designed very small in comparison to a regular wind turbine. The electric energy is stored on board of the vessel by means of the electrolytic splitting of sea water into hydrogen and oxygen. The concept was first proposed by Salomon [1] in 1982, followed by Meller [2], Holder [3] and Gizara [4]. More quantitative analysis were performed by Platzer [5–9] and Kim [10–12]. Most recently the first and second author and Platzer [13–15] presented a physically based upper limit for the conversion of wind energy in mechanical energy of the presented concept. Based on this approach, the first and second author introduced a general method for holistic system analysis, the MPSA method [16]. The recent publications have the drawback of treating the energy converter deterministically. This is an assumption which truly does not represent reality sufficient and, thus, in this paper the next evolutionary step of the method is presented by incorporating system analysis under uncertainty to gain a certain degree of robustness in the phase of optimal system design. Consequently, the optimization problem turns over into a stochastic optimization problem. Following this train of thought and the given introduction, the paper is structured in the Sects. 10.2 and 10.3. In Sect. 10.2 the four steps of the method are gradually explained in general and then applied to the energy converter. Highlights and differences in contrast to the previous analysis are outlined as well as the advantages which go hand in hand with the incorporation of the uncertainty consideration. Section 10.3 closes the paper by summarizing the content and emphasizing the gained knowledge. 10.2 Multi-Pole System Analysis 10.2.1 System Synthesis The first step of the MPSA focuses on the question of the shape and topology of the considered system. The definition of a system, according to Buchholz [17] requires a system boundary to delimit the “inner world” to the “outer world” and thus, defines the considered framework. The topology of the system is defined by the number of components within the system boundary and the interconnection through signals. We define these signals as various cross-domain fluxes, e.g. mass flows, energy flows and cash flows that are used for communication in between the components and across the system boundary. Focusing on a single component, the input fluxes are listed in the input vector x and the output fluxes in the output vector y, respectively. The component itself is mathematically described by the matrix Aand represents the effect of the component to each flux and also linkages of fluxes. Thus, the composite of input- and output fluxes and the component can be described as x DAy. If all system components are series-connected, one can easily combine the component descriptions and yields the system description x DQNiD1 Aiy, with the system matrix DQNiD1 Ai. If all components are parallel connected one yields for the system matrix DPNiD1 Ai. As can be seen in Fig. 10.1 the components of the energy converter are, relating to considered energy-, mass- and cash flows, series-connected. Thus, one can achieve the system matrix by multiplying all component matrices. An obvious interaction of the considered fluxes can be seen on the components desalinator, electrolyser and compressor, which require a certain amount of power for functional performance. Also, the periodic cash flow needs at least to be balanced through the periodic revenue, which is gained through the sale of the hydrogen. The matrix notation of the multi-pole model is shown in detail in a recent publication [16] and is here recalled as 0 @ Pavail PmH2O;s PC 1 AD 0 B@ 0 1 CP Gen Ho;H2 Elec C wDes "Elec C wComp 0 0 1 "Des"Elec 0 0 ıTfH2 1 1 CA 0 @ 0 PmH2 PG 1 A ; (10.1) with the mass flows denoted as Pm, efficiency factors denoted as , mass conversion rates as " and mass specific work as w. If one calculates in each specific domain the ratio of output and input quantity, one yields the system efficiency factor …, the mass conversion rate M and the well-known economic indicator return on investment ROI, defined as the ratio of the periodic profit PGand the periodic costs PC
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