University of Calgary PRISM: University of Calgary's Digital Repository Graduate Studies The Vault: Electronic Theses and Dissertations 2016 Dynamic Model and Adaptive Control of a Transcritical Organic Rankine Cycle Samiuddin, Jilan Samiuddin, J. (2016). Dynamic Model and Adaptive Control of a Transcritical Organic Rankine Cycle (Unpublished master's thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/25758 http://hdl.handle.net/11023/3343 master thesis University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. Downloaded from PRISM: https://prism.ucalgary.ca UNIVERSITY OF CALGARY Dynamic Model and Adaptive Control of a Transcritical Organic Rankine Cycle by Jilan Samiuddin A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE GRADUATE PROGRAM IN ELECTRICAL ENGINEERING CALGARY, ALBERTA SEPTEMBER, 2016 c Jilan Samiuddin 2016 , Abstract The Transcritical Organic Rankine Cycle (TORC) is a non-linear time-varying heat recovery system for small-scale power generation. It is similar to a boiler-turbine system but uses organic fluid as the primary heat carrier instead of H2O and works in both subcritical and supercritical regions. The heat source can be either renewable energy or industrial waste-heat. In order for the TORC to work efficiently, it is essential the control system tracks the set points as closely as possible while remaining robust to disturbances; the control system design treats the heat source as a time-varying disturbance. To achieve this goal, this thesis presents a design of an adaptive Cere- bellar Model Articulation Controller (CMAC) which uses a single-input-single-output strategy by pairing the controlled variables (CVs) to the manipulated variables (MVs) using Relative Gain Ar- ray (RGA) analysis of the system. The CMAC improves performance and robustness compared to a traditional PI control. ii Acknowledgements First and above all, I praise and thank The Almighty Allah for blessing me with the opportunity and granting me the capability to advance in my journey of life successfully. Several people need to be acknowledged for their help and encouragement throughout my journey preparing for this thesis, and I sincerely apologize for any negligence while I will try my best to give them their dues. I would like to express my sincere gratitude to my supervisor Dr. Chris J.B. Macnab for his pa- tience, support, advice and guidance from the very beginning of this research. Above all and most needed, he provided an excellent and a friendly environment to work in which was an essential for me for my success. I am also very thankful to my co-supervisor Dr. Jeff Pieper for providing constant support and feedback throughout the research. At the same time, I am thankful to my colleagues, Babak Badkoubeh, Mahsa Sadeghassadi and Rachael L’Orsa, for providing a friendly and pleasant working atmosphere in the office during the last two years period. Many thanks to Genalta Power Inc. for financing this thesis and providing support to their best of capabilities. I wish to express my gratitude towards my family who has been a constant source of support and care, mainly my mother, without whom it would have been very difficult to pursue such higher education. Overwhelming love from my family has always been a source of inspiration for me in my journey to the completion of my thesis. Last but not the least, I am grateful to my friends, mainly Abiola Adebayo, Ismail Kamal and Munif Sakib, for making my stay in Canada for the last two years away from home a fantastic experience. iii Table of Contents Abstract . ii Acknowledgements . iii Table of Contents . iv List of Figures . vii List of Tables . ix List of Symbols, Abbreviations and Nomenclature . x 1 Introduction 1 1.1 Background . 1 1.2 Applications . 2 1.3 System description . 3 1.4 Modelling of ORC systems . 5 1.5 Working fluid selection and performance analysis . 9 1.6 Control design for ORC . 16 1.7 Cerebellar Model Articulation Controller (CMAC) . 17 1.8 Thesis contribution . 20 1.9 Summary . 20 2 Modelling 22 2.1 Modelling . 22 2.2 Thermodynamic properties and CoolProp . 23 2.3 Structure of the heat exchangers . 24 iv 2.4 Some important terminology for ORC modelling . 26 2.4.1 Average Void Fraction (g) .......................... 26 2.4.2 Heat Transfer Coefficient (a) ........................ 28 2.4.2.1 Single-phase flow for the inner tube . 28 2.4.2.2 Two-phase flow for the inner tube . 29 2.4.2.3 Single-phase flow for the outer tube . 29 2.4.2.4 Heat-transfer coefficient of air in the condenser . 30 2.5 Slow dynamics components . 31 2.5.1 Condenser . 31 2.5.1.1 Superheated region . 34 2.5.1.2 Two-phase region . 36 2.5.1.3 Sub-cooled region . 38 2.5.2 Evaporator . 43 2.5.3 Recuperator . 48 2.6 Fast dynamics components . 52 2.6.1 Pump . 52 2.6.2 Expander . 54 2.6.3 Valve . 55 2.7 Model validation . 56 2.8 Summary . 59 3 Control development 60 3.1 Control Strategy for determining set-points . 60 3.2 Relative Gain Array (RGA) analysis . 65 3.3 Proportional, Integral, Derivative (PID) control . 67 3.3.1 IMC technique for first-order process . 68 3.4 Cerebellar Model Articulation Controller (CMAC) . 71 3.4.1 CMAC structure and methodology . 71 v 3.4.2 CMAC adaptive control . 76 3.4.3 Stability Proof . 77 3.5 Summary . 80 4 Results 81 4.1 Disturbance rejection . 81 4.2 Set-point tracking . 86 4.3 Step-disturbance rejection . 90 4.4 Summary . 93 5 Conclusion 95 5.1 Conclusion . 95 5.2 Future work . 96 vi List of Figures 1.1 Typical ORC . 3 1.2 ORC with the addition of a recuperator . 4 1.3 Temperature vs Entropy for SORC and TORC . 5 2.1 Cross-view of a concentric annular tube heat exchanger . 24 2.2 Side-view of concentric annular tube heat exchanger - parallel flow and counter flow and their temperature profiles . 26 2.3 Moving boundary model for condenser . 32 2.4 Control volume for each region . 33 2.5 Design inputs and outputs for the condenser . 42 2.6 Schematic of the evaporator . 44 2.7 Design inputs and outputs for the evaporator . 47 2.8 Schematic of the recuperator . 49 2.9 Design inputs and outputs for the recuperator . 52 2.10 Design inputs and outputs for the pump . 54 2.11 Design inputs and outputs for the expander . 55 2.12 Design inputs and output for the valve . 56 2.13 Step change in µ from 0.4 to 0.45 . 57 2.14 Step change in Xpp from 0.4 to 0.45 . 58 2.15 Step change in Nfan from 300rpm to 500rpm ..................... 59 3.1 Changes in Tev,opt with respect to changes in Tsf for a SORC . 62 3.2 W˙ net against changes in Tsf for TORC . 63 vii 3.3 Pev against changes in Tsf for TORC . 63 3.4 Tout,ev against changes in Tsf for TORC . 64 3.5 Tout,c against changes in Tsf for TORC . 64 3.6 Closed-loop PID control . 67 3.7 Closed-loop control response for each pairing . 70 3.8 CMAC structure (Q = 3, m = 3, n = 2) . 71 3.9 CMAC methodology with two input variables . 73 3.10 Mapping for CMAC with two-inputs . 74 3.11 Basis function operating in hypercube for the first layer . 74 4.1 Variation in heat source temperature . 82 4.2 Set-point tracking under the influence of disturbance . 83 4.3 Variation in MVs under the influence of disturbance . 83 4.4 Net power output for disturbance rejection test . 84 4.5 RMS error convergence for disturbance rejection test . 85 4.6 Behavior of weights in CMAC for disturbance rejection . 85 4.7 Change in set-points of the CVs . 87 4.8 Tout,ev channel zoomed . 87 4.9 Variation in MVs for set-point tracking . ..