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In recent years, the need to develop environmentally sustainable solutions to cover the increasing global demand for energy has resulted in a significant growth of renewable sources and distributed generation [1]. In this context, the research interest in innovative and efficient micro power systems (in the range of a few to tens of kWel) for on-site concentrated solar power (CSP) and micro-stationary and automotive waste heat recovery (WHR) applications has gained momentum [2], [3], [4]. Among the solutions for converting low grade heat into electrical power, the organic Rankine cycle (ORC) technology is considered as one of the most promising candidates [5], [6]. It stands out in terms of cost-effectiveness, reliability and ease of maintenance [7]. For standard power capacities, say from hundreds of kWel to a few MWel, ORC power systems are a mature and commercially viable solution, e.g. for converting thermal energy from geothermal reservoirs [8][9], biomass combustion [10] and recently CSP [11][12] into electricity. On the other hand, the application of the ORC technology to micro CSP or WHR is still at a research stage [13][14], [15]. In the waste heat recovery field, several studies have been recently published investigating the potential of the ORC technology to transform waste energy from low temperature industrial processes or from commercial combustion engine into useful electricity or mechanical power, adopting multi-objective optimization methods [16][17][18][19] sometimes coupled to economic considerations [20]. For such applications the non-constant nature of the energy source requires the ORC power unit to be flexible. The adoption of dynamic models based on the first and second principles is a key enabler to the application of small ORC systems for transient energy sources, as it allows accounting for the dynamics from the early design stages [21][22]. Dynamic modelling can be adopted to evaluate and optimize the response time of a system under transient boundary conditions, to develop and test control strategies and to support the tuning of the controller. An ORC unit is a complex system that can be mathematically represented by a set of coupled differential algebraic equations (DAE). Solving a DAE system requires a robust solver and is subject to different numerical problems and challenges [23], [24], [25]. The object-oriented programming language Modelica, introduced in 1997 [26], opens new possibilities for modelling of physical processes. It has recently been adopted for dynamic modelling of ORC power systems. Quoilin et al. [27] developed a dynamic model of a small-scale ORC unit equipped with a volumetric expander, to analyse and compare different control strategies based on the regulation of the pump and expander rotational speed. Casella et al. [28] presented the validation of a dynamic, object-oriented model against transient measurements of a 150 kWel commercial WHR ORC turbo-generator. The measurements were obtained while the plant was operating in closed loop, the shape of the response was therefore affected by the controller action. A model based control strategy for ORC systems in automotive WHR is described in Ref. [29]. The control strategy is based on a reduced model of the evaporator and tested using an ORC dynamic model developed in Modelica as a reference. Rettig et al. [30] implemented a dynamic model of a low-capacity ORC system for stationary WHR in the Modelica language. The model is compared against experimental data and it is proposed as a starting point towards the implementation of a virtual test bed software for design, analysis and virtual prototyping of ORC WHR systems. In the literature, other works underline the advantages of adopting dynamic modelling for the development, the tuning and the comparison of different control strategies for WHR ORC systems [31][32]. Recently in a very similar field, Qiao et al. [33] presented the validation of a Modelica model describing a flash tank vapor injection heat pump system. The model was able to replicate the major heat transfer and flow characteristic dynamics when compared against step change, start-up and shut down transients. Most of the works available in literature on ORC dynamic models focus on the application rather than the model validation, although modelling errors and inaccuracies can significantly impact the conclusions of a research based on simulations [23]. The present contribution focuses on the steady-state and dynamic validation of some of the models included within the ThermoCycle library, an open-source Modelica library for the modelling of small thermo-hydraulic system [34]. The validation is performed against an experimental dataset of a stationary sub-critical 11 kWel ORC test rig equipped with a single screw expander. One of the main assets of the experimental data presented in this work is its suitability for the validation of dynamic models: contrary to similar works in the same field, all measurements were performed in open-loop, which avoids the interferences of controller in the measured dynamic response. The shape of the transient responses is entirely determined by the intrinsic dynamics of each component, which could have been corrupted, e.g. by the slow response of a proportional-integral-derivative (PID) controller in the loop. The structure of the paper is as follows: Section 2 presents the ORC unit. In Section 3 the modelling approach of the ThermoCycle library and the models adopted to simulate the ORC system are described. Section 4 details the experimental campaign. In Section 5 the steady-state and dynamic validation of the Modelica model is presented. Section 6 discusses critical aspects when modelling small thermal power units. Finally, in light of the obtained results, the main conclusions are listed in Section 7.



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