DYNAMIC MODELING OF ORGANIC RANKINE CYCLE (ORC) SYSTEM FOR FAULT DIAGNOSIS AND CONTROL SYSTEM DESIGN

Transcription

1 DYNAMIC MODELING OF ORGANIC RANKINE CYCLE (ORC SYSTEM FOR FAULT DIAGNOSIS AND CONTROL SYSTEM DESIGN Sungjin Coi and Susan Krumdieck University of Canterbury, Private Bag 48, Cristcurc 84 New Zealand Keywords: Organic Rankine Cycle, Dynamic Modeling and Control, Moving Boundary Lumped Parameter Metod ABSTRACT Dynamic simulation plays an important role of providing a iger-level of process analysis of te system and supporting system configuration, operation, maintenance, diagnosis and design of te control system. Te purpose of tis researc is to develop a virtual simulation tool for current suite of geotermal power plants. Tis article provides a numerical modeling framework for te dynamic modeling including detailed component models and a generic dynamic feedback control and fault diagnosis model for an organic Rankine cycle (ORC system. A moving boundary metod wit switced system model is used to model time-varying performance of a eat excanger in various flow conditions. A custom library for models of ORC components and system dynamic models as been built in Matlab/Simulink environment. Te developed model is capable of designing a component- and system level control strategy and fault diagnosis system.. BACKGROUND Renewable energy sources are making a major contribution to reduce global carbon emission and will make a great contribution to future global energy supplies and sustainable energy system. Growing price instability and insecurity of non-renewable energy suc as fossil fuels due to its limited reserve stock and restricted geograpical distribution leads investment invigoration and tecnological growt in renewable energy industry. Geotermal energy is a clean and sustainable renewable resource wic as a vast amount of eat energy generated and stored in te eart. Te temperature range of te geotermal fluid ranges from 5 to 5 but it is mostly below 5. Organic Rankine Cycles (ORCs are capable of extracting and converting low entalpy eat sources into electrical power by means of an organic working fluid, suc as ammonia, pentane, exane, R22 etc. Design of an ORC system requires a robust understanding of its termal and ydraulic components, system operating conditions and dynamic beaviors. Some of te key issues tat need to be considered at te design stage are control system syntesis for process regulation and optimization, as well as start-up and sut down strategies. To acieve an integrated approac to te system design, all issues related to steady state and dynamic response of plant operation must be taken into account. Having a compreensive understanding of te system is required not only for early development objectives but also for te purpose of maintaining optimum operating conditions. A traditional steady state analysis is an essential tool for analysis of system operability and controllability and can be useful for capturing te slow dynamics of te system (ours, days, or years. However it is unable to describe sort term transient beaviors in a cycle caused by varying operating conditions and unfavorable dynamics. A system migt occasionally need to be operated in an unusual circumstance suc as sut-down/ start-up or it sometimes experiences a decrease in performance due to te internal or external disturbance suc as cange of resource condition and system/component malfunction at te operating system level. As a plant undergoes suc a transition, it is required to adjust and improve system performance and reconfigure te system and operation strategies. Dynamic simulation is capable of supporting analysis of te impact of te uncertainty on te system performance and detailed pase of design of te system and operation strategies. At te operation level, it would be an essential tool for fine-tuning of te plant and establising a plan in te event of unusual operation suc as sut-down/ start-up and system breakdown. Unlike a static analysis and experimental study, limited researc on dynamic modeling and control of an ORC system are available, especially in geotermal applications. Quoilin (Quoilin, Aumann, Grill, Scuster, Lemort & Splietoff, 2 presented dynamic model of a small scale ORC using volumetric expander and studied a control strategy against a varying eat source. Zang (Zang, Zang, Hou & Fang, 22 studied control strategies for te supereated temperature of an ORC process using generalized predictive control. Casella (Casella, Matijssen, Colonna & Buijtenen, 2 developed a software library of modular reusable dynamic models of ORC components under Modelica environment. Proctor (Proctor, Yu, Young, 25 modeled an ORC system in geotermal application using te process simulator VMGSim and studied a control strategy for te position of valves located at te geotermal wellead. In tis work, a moving boundary lumped parameter approac is adopted to model te dynamic aspects of te eat excanger. A Matlab/Simulink based custom library as been developed as a dynamic simulation tool seeking to establis a model-based control-oriented modeling framework for ORC system. Te final aim of te work is to explore underlying dynamics of ORC system in geotermal application focusing on operation and control strategies. Te fault detection and isolation and fault tolerant control metod on te system will also be addressed. Tis paper outlines te modeling and simulation strategies of ORC system focusing on control and fault diagnosis system design purpose. Te paper will examine in detail te eat excanger model approac and te design of te Proceedings 8t New Zealand Geotermal Worksop 2-25 November 26

2 modeling tools. Simple example problem will be presented as a numerical test. 2. MODELING A numerical framework in Matlab/Simulink platform for te generic dynamic feedback control model as been developed. Te model uses a moving boundary lumped parameter approac to analyze te dynamics of eat excanger. Te modeling as been developed in state space form by linearizing around operating points to facilitate a control system design. Figure sows a scematic diagram of te generic dynamic feedback control model. Te model inputs are steady state design or operation data and empirical parameters of te components. Te control strategy can be best analyzed and designed troug considering a steady state aspects of te system along wit an optimization model. Te fault diagnosis and tolerant control sceme can ten be applied into te control-oriented model. Te model would provide any information necessary to system re-/configuration, control and operation strategy and fault diagnosis results. Te design or realitybased plant model would be effectively implemented under te current modeling framework and is expected to be used for various purposes. 2. Organic Rankine Cycle A fundamental principle of ORCs is same as Rankine cycle except te working fluid is an organic fluid instead of water. Figure 2 sows a scematic diagram of te standard ORC system. Te termodynamic processes are described on temperature-entropy diagram wic is sown in Figure. Te liquid state of working fluid undergoes an increase in pressure by te pump. In evaporator, te temperature of working fluid is increased in a liquid form until it reaces a sligtly supereated state. Te vapor state of working fluid expands troug te turbine, generating electricity in te generator. Finally te vapor from te turbine turns it back into liquid state wile traveling troug te condenser. Figure 2. Basic configuration of Organic Rankine Cycle Figure. Generic dynamic feedback control model Definition Definition ρ density A i,o inner/outer surface p pressure L lengt entalpy P perimeter T temperature V volume m mass flow rate W power α eat transfer coeff. η efficiency γ void fraction _a ambient x vapor fraction _w wall C p specific eat _in inlet A cross-sectional area _out outlet Table Nomenclature In tis section, a modeling metod and design of te modeling tool are presented. A general case of te moving boundary approac for two-pase eat excanger is illustrated wit vapor and liquid conditions at inlet and outlet respectively. Te model offers various modes of te eat excanger based on te fluid condition around te eat excanger. Table sows a list of symbols and meanings used in tis paper. Temperature [K] Entropy [kj/kg K] Figure T-s diagram of Organic Rankine Cycle 2.2 Component Models Te dynamics of ORC system are assumed to be dominated by te dynamics of te eat excanger. Te dynamics of oter components (e.g. expander, pump, valve, etc. are generally an order of magnitude faster tan te eat excangers and are modeled wit static relationsip. Terefore te modeling of te eat excanger is most critical part in modeling te ORC system. Te eat excanger components; evaporator, condenser, preeater and recuperator, can be modelled using moving boundary approaces (MacArtur & Grald, 989, 992. Te moving boundary approac was rigorously studied by Alleyne s group for applications in a dynamic modeling of vapor compression cycle. (Eldredge, Rasmussen & Alleyne, 28, Li & Alleyne, 2, etc.. Te moving boundary eat excanger model captures dynamics of boundary between regions of different fluid state. Te model is designed to facilitate low order control design models by simplifying two-pase flow problems into te type of lumped-parameter systems. 4 Proceedings 8t New Zealand Geotermal Worksop 2-25 November 26

3 Te fluid properties in te two-pase region are estimated and modeled using te mean void fraction assumption. ρ 2 = ρ f ( γ + ρ g (γ, 2 = f ( γ + g (γ (8 Figure 4. Scematic of moving boundary model (vapor condition at inlet, liquid condition at outlet Figure 4 sows scematic of tree region (Supereated, Two-pase, Subcooled moving boundary model of a condenser. Te modeling approac can be applied to develop various modes of te eat excanger suc as evaporator, 2-region and single pase eat excanger, etc. Te transport of mass, momentum and energy for a fluid in te eat excangers can be described by te conservation of te quantities being transported. It is assumed one dimensional fluid flow along a long circular tube and te pressure and viscous dissipation is negligible. Terefore te governing conservation laws for mass, energy of working fluid are respectively given by (ρa + (m = ( t z (ρa Ap (m + = P t z i α i (T w T (2 were te subscript w indicates te eat excanger wall. Te energy equation for te wall is: (C p ρv w T w t = α ia i (T T w + α o A o (T a T w ( Te conservation equations for eac region are obtained by integrating over te supereated (from to L, two-pase (from L to L + L 2 and subcooled region. (from L + L 2 to using Leibniz s rule wic is given by z 2 (t f(z, t dt = d z t dt 2 (t f(z, tdz f(z 2 (t, t d(z (t 2 z (t z (t dt + f(z (t, t d(z (t (4 dt Terefore te mass and energy equations over te supereated region are given by A(ρ ρ g L + AL [ ρ + ρ d g ] p + p 2 p 2 ( ρ p AL in = m in m 2 A(ρ ρ g g L + AL [( ρ + ρ d g p 2 p + 2 d g ρ ] p + AL 2 [ρ + ( ρ ] in = m in in m 2 g + α i A i ( L (T w T (5 (6 were ρ 2 = ρ g, 2 = g. Te average properties in te supereated region are assumed = in + g, T 2 = f T (p, (7 Experimental correlations of void fraction ave been studied and can be founded in a number of references. In tis study, we assume slip ratio correlation and te Zivi s correlation (964 is used to estimate slip ratio S. γ = x x + ( x(ρ g /ρ f S, S = (ρ f/ρ g / (9 Te mean void fraction can ten be calculated by integrating over te inlet and outlet quality of te two-pase region x out x out x γ = γ(xdx = x + ( x(ρ g /ρ f S dx ( x in x in Te mass and te energy balance for te two-pase are: AL 2 [ dρ f ( γ + dρ g (γ ] p + A(ρ g ρ f L + A(ρ g ρ f (γ L 2 = m 2 m 2 ( A(ρ g g ρ f f L + AL 2 [ d(ρ f f ( γ + d(ρ g g (γ ] p + A γ (ρ g g ρ f f L 2 = m 2 g m 2 f + α i2 A i ( L 2 (T w2 T 2 (2 were ρ 2 = ρ f, 2 = f. For te subcooled region, te average properties are assumed = out + f, T 2 = f T (p, ( Integration of te mass and energy equations over te subcooled region gives AL [ d f ] p + 2 ( AL out + A(ρ f ρ (L + L 2 = m 2 m out A(ρ g g ρ L + A(ρ f f ρ L AL [ρ + ( ] out + AL [( d f + (4 d f ρ 2 ] p = m 2 f m out out + α i A i ( L (T L w T T (5 Te energy equation for te eat excanger wall describes tat te rate of eat transfer between te wall and bot te working fluid and secondary fluid must equal te rate of wall energy cange due to temperature cange. Te wall equation for te eac region is: (C p ρv w T w + (C p ρv w ( T w T w2 L L = α i A i (T T w + α o A o (T a T w (6 (C p ρv w T w2 = α i2 A i (T 2 T w2 + α o A o (T a T w2 (7 Proceedings 8t New Zealand Geotermal Worksop 2-25 November 26

4 (C p ρv w T w + (C p ρv w ( T w2 T w L (L + L 2 = α i A i (T T w + α o A o (T a T w (8 Te system of equations can be rearranged into 7 equations wit 7 state variables by eliminating dependent variables and written in te matrix form Q(x, u x = R(x, u circumstance suc as sut-down/ start-up or tere are abrupt canges in te system conditions due to te internal or external disturbances. In suc a case te eat excanger may suffer a loss of supereated and/or subcooled region during te operation and te model would suddenly become unusable because te structure of te region in te model, representing te fluid conditions, does not cange wit time. { x = Q R = F(x, u y = G(x, u (9 were Q = Q Q Q 2 Q 22 Q 2 Q 24 Q Q 2 Q Q 4 Q 4 Q 42 Q 4 Q 44 Q 5 Q 55 Q 66 Q 7 Q 72 [ Q 77 ] x = L L 2 p out T w T w2 [ T w ] R = [ m in( in g + α i A i ( L (T w T m in g m out f + α i2 A i ( L 2 (T w2 T 2 m out( f out + α i A i ( L (T L w T T \ m in m out α i A i (T T w + α o A o (T a T w α i2 A i (T 2 T w2 + α o A o (T a T w2 α i A i (T T w + α o A o (T a T w ] Te elements of te matrix Q can be found in Appendix. Te ODE system can simply be simulated by direct numerical integration. Te model also can be linearized around te operating points x o, u o. Te operating points (initial conditions for simulation can be obtained by considering steady state solutions of te system. Ten te 7 t order linear system can be written using state space representation as follows: were x = Ax + Bu { y = Cx + Du A = [Q xo,u o ] [ R x x o,u o ] C = G x x o,u o (2 B = [Q xo,u o ] [ R u x o,u o ] D = G u x o,u o Te input and output variables can be defined as u = [m in m out in T a,in m a] T y = [L L 2 p out T w T w2 T w T a,out T out m] T Te moving boundary model requires modification in te structure of te zones based on te operating conditions of te eat excanger in te system. Figure 5 sows some of te model variations tat can be derived using te same approac. Eac model as a different matematical formulation to be implemented. Figure 5 Model variations McKinley (McKinley & Alleyne, 28 suggested a switced model approac for eat excangers to cope wit te limitation of te original model. Te current modelling tool as adopted te switced model to facilitate simulation of extreme operating conditions. Te response time of oter components suc as te turbine and pump is muc faster tan tat of eat excanger in te normal operating condition. Tus, a steady state model of te turbine and pump are generally used in a system model. Te turbine model estimates te state of te outflow along wit te generated mecanical power at given isentropic efficiency. Te pressure is decreased along te component keeping mass flow rate constant. Te first law of termodynamics for te turbine is given by W 4 = η G m ( 4 (2 η T,s = 4 4s (22 were is an entalpy, W 4 is work done by te turbine. Te generator efficiency is denoted by η G. Te subscript s refers to te isentropic process. Te liquid pump model estimates te state of te outflow along wit te required mecanical power consumption. W 2 = m ( 2 (2 Te work input to te pump is denoted by W 2. Te isentropic pump efficiency is defined as η p,s = 2s 2 (24 Te primary purpose of te dynamic model is to support operation planning and control strategy design, especially wen te system needs to be operated in an unusual Proceedings 8t New Zealand Geotermal Worksop 2-25 November 26

5 2. Fault Tolerant Control An automated system control ensures te stability of te system and yields a pre-defined performance in te case were all system components operate safely. As te system increases in complexity, te risk of a fault in te system suc as malfunctions in actuators, sensors or oter system components increases, potentially resulting in performance degradation and instability of te system. Figure 6 sows te general type of te faults in te system. 2.4 Software Development In tis work Matlab/Simulink based ORC analysis/ simulation tool, (call ORCAT for convenience, as been developed wit grapic user interface. ORCAT offers two different platforms: ORCAT (Figure 8 for static analysis and ORCAT-DYN for dynamic analysis. Te development objectives of te software is to elp manage te complexity of te system analysis wic includes key components and cycle design, dynamic and control system analysis. Figure 6 Type of faults Fault-tolerant control (FTC elps te system perform in normal operating conditions wen taking into account te occurrence of faults. Most of te researc work in FTC as been driven by te industry wic involves mostly safety critical systems. Wit more empasis from large-scale power plants on reliability, maintainability and survivability, attention to te FTC problem in industrial processes is also growing, but only a few related studies ave been presented. Zang (Zang, Yue, 26 provided a general review on te fault diagnosis and FTC metod for power plants. Te model based fault detection and tolerant control system as been developing wic is applicable to dynamic model of ORC system. Figure 8 Steady State Analysis Tool Te ORCAT-DYN offers te Simulink libraries for system components suc as eat excanger, turbine, pump and etc. Eac of te component blocks as te same interface delivering te fluid properties and oter information so it can be replaceable in te system model. Termodynamic properties are computed using REFPROP integrated into te custom Simulink library. Te developing ORCAT-DYN library is sown in te Figure 9. Figure 7 Model-based Fault Diagnosis Metod Figure 7 sows te structure of model-based fault diagnosis sceme wic is te preceding stage of FTC sceme. Te diagnosis process consists of tree pases: Residual generation, evaluation and decision making. (Noura, Teilliol, Ponsart, Camseddine, 29. Te diagnosis process provides information of magnitude and location of te fault over tese pases. Te FTC sceme ten uses te information to compensate for te fault effect on te system and to reconfigure te control law. Te fundamental teory of fault diagnosis and FTC scemes are extensively explored in several references (Noura, Teilliol, Ponsart, Camseddine, 29 and will not be furter discussed in tis paper. Te detailed modeling approac of fault diagnosis and tolerant control system integrated into te ORCs will be discussed in te future. Figure 9 Modeling Library in Dynamic Simulation Tool Proceedings 8t New Zealand Geotermal Worksop 2-25 November 26

6 Figure Masked Subsystem of Component Te main library is composed of 5 subcategory blocks: eat excanger, expander, pump, miscellaneous tools, and termodynamic properties. Eac block contains subsystems associated wit te subcategory. Any pysical parameters and necessary information can be specified using a masked subsystem as sown in Figure System Model Figure sows ORC system model implemented using te developed model libraries. Te connecting lines represent a flow signal wic as information of flow properties suc as pressure, entalpy, mass flow rate and vapor fraction. To build a proper system model, eac component as to be connected in a structured and logical manner troug considering fundamental features of te cycle Figure 2 Lengts of Subcool (L, Two-pase (L 2, Supereat (L Regions Te pump speed is increased by 5 % at time = 2 [s], wic leads to increase in mass flow rate of te working fluid. Te lengt of te subcooled and two-pase region is ten starting to stretc and te outlet temperature of working fluid is dropped. Te outlet eat transfer coefficient is increased by % at time = 5 [s]. Te amount of eat transferred troug te wall is ten increased wic result in a decrease in te lengt of subcooled and two-pase region and rise in outlet entalpy. Figure Modeling of ORC system using ORCAT-DYN. SIMULATION In tis section, we demonstrate te simulation of a eat excanger model troug a simple example. Te example is representative of evaporator model wit moving boundary approac. Te pysical parameters are adopted from te reference (Jensen, Tummesceit, 22 for te simulation. Te working fluid followed by te liquid pump is assumed entering te evaporator in liquid condition. Te outlet is assumed to be vapor condition. Te cange of te lengt of subcooled (L, two-pase (L 2 and supereat (L region are demonstrated in Figure 2. Figure sows outlet entalpy canges during te simulation 4. CONCLUSIONS Figure 2 Outlet Entalpy A modeling strategy of dynamic system of ORC as been presented. Te moving boundary approac for te eat excanger as been explained wit te case of condenser. A numerical test as been performed using te developed evaporator model wic is derived from te same approac. A modeling and simulation tools ave been developed to support system configuration, operation, diagnosis and design of te control system. Two different numerical frameworks based on steady state and dynamic regime is implemented under Matlab/Simulink environment along wit grapic user interface. Proceedings 8t New Zealand Geotermal Worksop 2-25 November 26

7 APPENDIX Q = Aρ ( g Q = AL [( ρ 2 2 (d g ρ ] Q 2 = A(ρ g ρ f ρ d g ( g + Q 22 = A[(ρ g g ρ f f γ + (ρ f f ρ f ] Q 2 = A [( ρ 2 d(ρ g g ρ Q 24 = AL 2 f ( Q = Aρ ( f Q 2 = Aρ ( f Q = AL [( d g gl + ( d(ρ f f ( γ + γ L 2 + ( 2 (d f ρ ] d f ( f + Q 4 = AL 2 [( ( f + ρ ] Q 4 = A(ρ ρ Q 42 = A[(ρ g ρ f γ + (ρ f ρ ] Q 4 = A [( ρ 2 ρ d g dρ g γ L 2 + ( Q 44 = AL 2 ( Q 5 = (C p ρv w ( T w T w2 L Q 55 = (C p ρv w Q 66 = (C p ρv w Q 7 = (C p ρv w ( T w2 T w L Q 72 = (C p ρv w ( T w2 T w L Q 77 = (C p ρv w L + ( dρ f d f L ] d f fl ] ( γ + ACKNOWLEDGEMENTS Supported by Department of Mecanical Engineering, University of Canterbury. REFERENCES Quoilin, S., Aumann. R., Grill, A., Scuster, A., Lemort, V. and Splietoff, H.: Dynamic modeling and optimal control strategy of waste eat recovery organic rankine cycles. Applied Energy, vol. 88, no. 6, pp (2. Zang, J., Zang, W., Hou, G and Fang F.: Dynamic modeling and multivariable control of organic rankine cycles in waste eat utilizing processes. Computer & Matematics wit Application, vol. 64, no. 5, pp (22. Casella, F., Matijssen, T., Colonna, P. and Buijtenen, J.: Dynamic modeling of organic rankine cycle power systems. Journal of Engineering for Gas Turbines and Power, vol. 5, no. 4, p. 42. (2 Proctor, M.J., Yu, W. and Young, B.R.: Simulation of setpoint feed-forward control of wellead valves in an organic rankine cycle geotermal power plant. Asia- Pacific Journal of Cemical Engineering, vol., no. 4, pp-5-5. (25 McKinley, T.L. and Alleyne, A.G.: An advanced nonlinear switced eat excanger model for vapor compression cycles using te moving boundary metod. International Journal of Refrigeration, vol., no. 7, pp (28. Eldredge, B.D., Rasmussen, B.P. and Alleyne, A.G.: Moving boundary eat excanger wit variable outlet pase. Journal of dynamic systems, measurement, and control, vol., no. 6, p. 6. (28 Li, B. and Alleyne, A.G.: A dynamic model of a vapor compression cycle wit sut-down and start-up operations. International Journal of Refrigeration, vol., no., pp (2 Jensen, J.M and Tummesceit, H.: Moving boundary models for dynamic simulations of two-pase flows. Modelica 22 Proceedings, pp (22. MacArtur, J.W. and Grald, E.W.: Unsteady compressible two-pase flow model for predicting cyclic eat pump performance and a comparison wit experimental data. International Journal of Refrigeration, vol. 2, no., pp (989 Grald, E.W. and MacArtur, J.W.: A moving boundary formulation for modeling time dependent two pase flows. International Journal of Heat and Fluid Flow, vol., no., pp (992. Zang, Z. and Yue, H.: Fault diagnosis and fault-tolerant control in power plants and power systems. Measurement and Control, vol. 9, no. 6, pp (26 Noura, H., Teilliol, J., Ponsart., C. and Camseddine, A.: Fault tolerant control systems: Design and practical applications. Springer Science & Business Medea. (29 Proceedings 8t New Zealand Geotermal Worksop 2-25 November 26