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Design of CSP Plants with Optimally Operated Thermal Storage obtain a specific value of the storage at the end of the operational period; this can be instrumental in comparing the performance of the optimal control to that of the original control strategy on equal grounds. The above-described optimal control problem can be readily encoded using the Optimica language [33], an extension of Modelica that also allows to specify the control objective and the constraint equations, see also §6.4 and listing 2 in A.3. 6.4 Computational Infrastructure Traditional codes for plant design and optimization are written from scratch in programming lan- guages such as Fortran or C++, which is tedious and error-prone. The approach proposed in this work leverages on modern, high-level modelling languages for the problem formulation, and on software tools that automatically transform this description of the problem into low-level code that can be coupled with state-of-the-art numerical solvers. The model is encoded using the Modelica language [32, 34], which is a high-level, non- proprietary, equation-based language for the modelling of systems described by differential-algebraic equations, while the optimization problem is encoded using the Optimica extension to the Modelica language [35]. The Modelica/Optimica language is supported by different tools, each implementing alternative strategies for the solution of the dynamic optimization problem [36, 37]. The tool described in [36] was used in the work described here. A collocation method was adopted in order to solve the problem [38, 39]: the time-varying variables of the problem are ap- proximated by Lagrange polynomials, that define the values of the variable in the optimization interval tin ≤ t ≤ t f in as a direct function of the values at a finite set of nodal points, which become the unknowns of the problem. In this way, the infinite-dimensional optimal control problem stated in §6.3.2 is transcribed into a large, finite-dimensional nonlinear programming (NLP) problem, which is then solved by an open-source NLP solver [40]. In order to directly compare the results with those obtained by the SAM program, which solves the differential equation by Euler’s method, 0-order polynomials (i.e., piecewise constant functions) were used, with one-hour time intervals. It is worth pointing out that the proposed approach easily allows to use more accurate interpolations, simply by changing the set-up of the problem tran- scription. It is also easy to experiment with alternative solution strategies (e.g., multiple-shooting instead of collocation), as well as with different techniques to reduce the size of the NLP by means of symbolic manipulation, in order get the best performance in terms of convergence robustness and CPU time. In all these cases, the high-level formulation of the problem remains the same, only the choice of the tool and its configuration need to change, thus avoiding problem-specific low-level programming. Last, but not least, the computational framework used to obtain the results presented in this chapter has been entirely built using open-source software and open standards. It is then possible to use it as the foundation of extensions to publicly available tools such as the SAM program, without any issue that might arise from the use of commercial software. 6.5 Results & Discussion The first analysis aims at assessing the performance of the model developed in this work, see §6.2, by comparing its predictions to the yearly simulation results yielded by a reference SAM model (i.e., with all the main settings keeping their default values). The simulation is performed with a control algorithm emulating the SAM control strategy, see §6.3. The results are shown in Fig. 157PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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