The study of dynamic process of ORC variable conditions based on control characteristics analysis

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1 Available online at ScienceDirect Energy Procedia 00 (2017) IV International Seminar on ORC Power Systems, ORC September 2017, Milano, Italy The study of dynamic process of ORC variable conditions based on control characteristics analysis Yunli Jin, Naiping Gao*, Tong Zhu School of Mechanical engineering, Tongji University, Shanghai , China Abstract The effect of the characteristics of the ORC components including equipment and parameters on system performance has been explored deeply in previous studies. The fluctuation of heat source and load demand in practical application, leads to the change of ORC operation environment. Operation condition variation of ORC system responding to this change should be done, which is realized by certain control strategy. The way that control strategies impose influence on ORC system has not been investigated. The purpose of this paper is to study the impact of control strategy on ORC performance. The control characteristic analysis is introduced which means the dynamic characteristic of ORC system under certain control strategy. Four different control strategies based on different regulated variables, control variables, control algorithm and operation mode are proposed and compared. The dynamic process model is built and simulated. The results show that the selection of regulated variables, control variables and control algorithm directly influences the dynamic behavior of variable conditions, but not the final steady state. The operation mode selection of fixed or slide pressure has the effect on both ORC dynamic process and final steady state The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems. Keywords: ORC, control characteristic, control strategy; 1. Introduction For improving the energy efficiency and reducing pollutant emission, low grade thermal energy utilization has drawn more attention. ORC has great advantages in low temperature heat recovery and has been successfully applied to recycle heat from industrial production, geothermal energy, solar energy, and biomass energy. [1-3] * Corresponding author. Tel.: address: gaonaiping@tongji.edu.cn The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems.

2 2 Yunli Jin et al. / Energy Procedia 00 (2017) Nomenclature B bias of pressure set-point (Pa) Subscripts G transfer function of PI controller c condenser K1-9 gain of transfer function ev evaporator m mass flow rate (kg/s) ex expander n speed (r/min) in inlet PT pressure transmitter mtp mass flow to pressure s Laplace Operator out outlet T1-7 time constant of transfer function (s) p working fluid pump TT temperature transmitter psp pressure set-point W transfer function ptm pressure to mass flow Z valve opening (%) v control valve of expander inlet Greeks Acronyms Δ variation ORC Organic Rankine Cycle PI proportion and integral controller Considerable studies have been done on ORC systems in recent years. Experiments and model analyses conducted by Jung et al. [4-6] all show that zeotropic mixtures with certain molar ratio could achieve higher thermal efficiency and lower exergy loss than pure fluids. For adapting to application environments and gaining higher performance, the ORC system architecture has been further developed. Yang et al. [7-9] designed a dual loop ORC system to recover waste heat originated from diesel engine and geothermal power. Yamada et al. [10-11] studied a small pumpless ORC system by experiments and got better performance. However, there are limited studies focusing on the control strategy of ORC system and its influence on performance. Quoilin et al. [12] developed a dynamic model of small-scale ORC to compare three different control strategies and the model predictive control strategy based on the steady-state optimized evaporating temperature under various conditions showed the best results. With the off-design performance analysis, Hu et al. [13] took variable inlet guide vanes and evaporating pressure as control variables to compare the difference of fixed pressure operation, sliding pressure operation and the optimal control strategy maximizing the net power. Usman et al. [14] experimentally investigated a sliding pressure control strategy to meet the varying load demand by changing evaporation pressure using PI controller with feed-forward and lead-lag compensator. How the control strategy affects the dynamic process of variable conditions has been left little touched in the previous research. The intervention of control results in that the performance of ORC system not only depends on the component, but also is restricted by the control strategy adopted. The control characteristics of ORC system defined by this paper means the dynamic characteristics shown under certain control strategy. So, the control characteristics involve control strategy including regulated variables such as evaporator outlet temperature, control variables such as working fluid pump speed control, control algorithm and operation mode such as fixed pressure or slide pressure operation. The introduction of control characteristic can contribute to understanding the effect of control strategy on system dynamic process, so as to get the optional system configuration, parameters, and control scheme. In this paper, the control characteristic analysis is used to study the mass flow through condenser change under variable conditions. The control characteristics of ORC system is expressed with the transfer functions which structure and parameters can be modified by experiments later. The transfer functions are used to describe the dynamic characteristics of linear system, also can be used to nonlinear system by approximate linearization method. Through model simulation based on linear relations, the variation trend of the mass flow through condenser is given. 2. Dynamic response model based on control characteristics Responding to heat supply varying, the dynamic characteristics of ORC system from the control perspective are affected by two aspects: the inherent control characteristics of system components and the control characteristics

3 Yunli Jin et al. / Energy Procedia 00 (2017) imposed by control strategy adopted. The former consists of the dynamic response characteristics of individual equipment which could be analyzed and expressed with the transfer function. The structure and coefficient of transfer function are based on the equipment characteristic analysis and can be modified by experiments, which not influence the whole analysis process and results. The control strategy defined by this paper involves control mode and operation pressure. The former involves the selection of regulated variables, control variables and control algorithm, and the latter means the operation mode of fixed pressure or slide pressure. The fixed pressure control means keeping the operation pressure constant by controller adjustment under variable conditions. The slide pressure control includes two ways: One way is the operation pressure changes freely with the working condition variation without control action. Another way is the operation pressure changes in accordance with the setting curve by controller adjustment Control mode of ORC system (a) p - (b) T - PT d K dt Valve TT d K dt Valve 1 TT T 1 p PT Recovery Heat - Expander 2 Recovery Heat - Expander 2 Evaporator d K dt Cooling Water Evaporator d K dt Cooling Water 4 ORC n Working Fluid Pump 3 ORC Condenser 4 ORC n Working Fluid Pump 3 ORC Condenser Fig. 1. (a) Control mode A; (b) Control mode B. Fig. 1 shows two different control modes of ORC system. In the control mode A of Fig. 1, the evaporator outlet temperature is regulated by changing working fluid pump speed and the expander inlet pressure is regulated by changing valve opening. Setting the control valve before the expander leads to throttle loss. However, the use of valve makes it easier and faster to control the pressure before expander and the mass flow through the expander which changes the expander power output. And this paper just proposes a control scheme for study to illustrate the method. Contrary to A, in the control mode B, the evaporator outlet temperature is regulated by changing valve opening and the expander inlet pressure is regulated by changing working fluid pump speed. Regulating pump speed and valve opening all adopt PI controller Dynamic response characteristic of ORC components The transfer functions can be obtained from the linear ordinary differential equation of system, the curve fitting of experimental data of component parameters, and the definite physical characteristics. The centrifugal pump is taken as the working fluid pump and obey proportional law. The mass flow change passing through pump is proportional to the pump speed variation, so the transfer function between them is given as: W p (s) = m p(s) n p (s) = K 1 (1) Where s is the Laplace Operator, m p represents the mass flow passing through the working fluid pump, n p is the pump speed, and K 1 means the gain of proportional component. The plate-fin heat exchanger is chosen as the evaporator. The mass flow variation, caused by pump speed change, spreads from pump outlet to expander inlet valve passing evaporator. Based on previous studies [15-16], the transient response of evaporator outlet mass flow to inlet can be approximately expressed with first order inertial characteristic.

4 4 Yunli Jin et al. / Energy Procedia 00 (2017) Then pressure before expander inlet valve gradually changes by the integral of mass flow difference of valve inlet and outlet. The dynamic response of pressure before expander inlet valve to pump mass flow change can be expressed as: W ev (s) = p v,in(s) = 1 K 2 m p (s) 1T 1 s s (2) Where p v,in is the pressure before expander inlet valve, T 1 is the time constant of first order inertial element, and K 2 means the gain of integral element. The valve with linear flow characteristics is selected as the control valve of expander inlet. Then the mass flow change through the valve is proportional to valve opening variation, and transfer function between them is given as: W v (s) = m v(s) Z v (s) = K 3 (3) Where m v is the mass flow through valve, Z v is the valve opening, and K 3 is the gain of proportional component. While the opening of expander inlet valve remains unchanged, the disturbance of valve inlet pressure leads to that the mass flow through valve gradually changes and finally is stabilized at a constant value with a delay. The transfer function of mass flow responding to the valve entrance pressure change can be expressed as: W v,ptm (s) = m v(s) p v,in (s) = K 4 1T 2 s e τ 1s (4) Where K 4 and T 2 are the gain and time constant of first order inertial element respectively, and τ 1 is the delay time of pure delay element. For constant pump mass flow, the decrease of valve mass flow leads to that the valve inlet pressure rises proportionally a certain magnitude at once and then gradually increases with inertial delay and integral accumulation. The dynamic response characteristic of valve inlet pressure to mass flow change can be given as: W v,mtp (s) = p v,in(s) = K m v (s) 5 1 K 6 1T 3 s s (5) Where K 5 means the gain of proportional part, T 3 is the time constant of first order inertial element, and K 6 is the gain of integral element. The transfer function in Eqs. (5) is not the inverse of Eqs. (4). The change of m v is originated from the differential pressure between valve inlet and outlet caused by valve inlet pressure disturbance in Eqs. (4). The change of p v,in (s) is originated from the integral accumulation of mass flow difference between pump outlet and valve outlet caused by valve mass flow change in Eqs. (5). So p v,in (s) also depends on the difference duration time. The scroll expander is chosen in the study. The expander storage makes condenser inlet mass flow delay the mass flow variation through expander inlet valve, so the transfer function between them is given as: W ex (s) = m c,in(s) m v (s) = 1 1T 4 s (6) Where T 4 represents the time constant of first order inertial element Transfer function of controller The entrance pressure of expander inlet valve is controlled by regulating valve opening in mode A, using PI controller. The transfer function of PI controller is given as: G v (s) = K 7 1 T 5 s (7) Where K 7 is the gain of proportional part, and T 5 is the integration time of integral part. The valve inlet pressure is controlled by regulating working fluid pump speed in mode B, using PI controller. The transfer function of PI controller is given as: G p (s) = K 8 1 T 6 s (8)

5 Yunli Jin et al. / Energy Procedia 00 (2017) Where K 8 is the gain of proportional part, and T 6 is the integration time of integral part. 3. Result and discussion Four control strategies of ORC system are proposed and compared, combining the control mode in fig.1 with fixed or slide pressure operation. Under certain control strategy, the dynamic response model of mass flow through condenser is built with transfer function based on the control characteristics of the components. The model simulation based on linear relations is conducted by MATLAB and the trend of mass flow over time is given Control mode A with slide pressure and fixed pressure operation In this section, the control mode A in Fig.1 is studied. Deriving from Eqs. (1)-(7), the dynamic response model of mass flow through condenser to working fluid pump speed change is given as: n p (s) m p (s) 1 K 1 1 T 1 s s W p (s) W ev (s) K 2 p v,in (s) K 4 1 T 2 s e τ 1s W v,ptm (s) Z v (s) K 7 1 K T 5 s 3 G v (s) W v (s) m v (s) 1 1 T 4 s W ex (s) m c,in (s) K 1 m c,out (s) 1 K 6 K 5 1 T 3 s s W p (s) W v,mtp (s) Fig. 2. Dynamic response model with control mode A (Including fixed and slide pressure operation). In the first control strategy, control mode A with slide pressure operation is adopted. When heat source fluctuates, the evaporator outlet temperature is controlled by regulating working pump speed. In the slide pressure operation mode, the pressure changes freely with the working condition variation without expander inlet valve control. The valve opening is fixed, so the transfer function in dashed box is zero in Fig.2. Based on Fig.2, the transfer function between pump speed change and condenser inlet mass flow is given as: W p,cin (s) = m c,in(s) n p (s) W v,ptm (s) = W p (s)w ev (s) W 1 W v,ptm (s)w v,mtp (s) ex(s) (9) The mass flow variation of condenser inlet with time can be obtained by inverse Laplace transform of eq. (9): W v,ptm (s) Δm c,in (t) = L 1 [n p (s)w p (s)w ev (s) W 1 W v,ptm (s)w v,mtp (s) ex(s)] (10) And the function of mass flow variation of condenser outlet is expressed as: Δm c,out (t) = L 1 [n p (s)w p (s)] (11) In the second control strategy, control mode A with fixed pressure operation is adopted. The expander entrance pressure is controlled by regulating expander inlet valve. By the inverse Laplace transform of the transfer function between working pump speed change and condenser inlet mass flow, the functional relation between them is obtained: W v,ptm (s)g v (s)w v (s) Δm c,in (t) = L 1 [n p (s)w p (s)w ev (s) W 1 [W v,ptm (s)g v (s)w v (s)]w v,mtp (s) ex(s)] (12)

6 6 Yunli Jin et al. / Energy Procedia 00 (2017) The dynamic response model of control mode A is simulated by MATLAB and the results are shown in Fig. 3. In the simulation, the forcing variable is the working fluid pump speed. The unit step change of working fluid pump speed follows heat source variation. Fig. 3. Mass flow change over time with mode A: (a) slide pressure operation; (b) fixed pressure operation. Fig. 3(a) shows the trends of condenser mass flow with time in slide pressure operation. In the figure, t1 is the time when the unit step disturbance of working pump speed occurs, t2 is the time when the condenser inlet mass equals to the outlet for the first time after disturbance, and t3 is the time when the system reaches the final stable state. The condenser outlet mass flow at once follows the unit step change of working fluid pump speed at time t1 which amplitude is Δm c,out. However, the inlet mass flow, after a brief delay, slowly decreases to respond to the change. At time t2, the inlet mass flow decreases to equal to the outlet. The response trends of condenser mass flow with time under fixed pressure operation are shown in Fig. 3(b). The step drop of condenser outlet mass flow with pump speed occurs at time t1 which results in the pressure before expander inlet valve decrease. The pressure is controlled by regulating valve with PI controller, which makes condenser inlet mass flow change responding to pump speed variation become more quickly. The inlet mass flow decreases to equal the outlet at time t2 which time the pressure also decreases to the lowest value. And then the condenser inlet mass flow continues to decrease below the outlet value which leads to the pressure turning to going up from time t2. When the inlet mass flow reaches the outlet value again, the dynamic process of variable conditions is over and new stable state is reached. The pressure return to the initial value in fixed pressure operation mode. So, the control strategy has effect on the mass flow change trend of condition variation dynamic process. The change rate of condenser inlet mass flow is faster than the control strategy of slide pressure operation Control mode B with fixed pressure and slide pressure operation While the operation condition varies because of recovery heat change, the control mode B in Fig.1 regulates the expander inlet valve to control the evaporator outlet temperature. Deriving from Eqs. (1)-(6), and (8), the dynamic response model of condenser mass flow to valve opening change is expressed as: Z v (s) K 3 W v (s) K 9 1 T 7 s W psp,b (s) 1 K 6 K 5 1 T 3 s s W v,mtp (s) K 4 1 T 2 s e τ 1s W v,ptm (s) m v (s) m c,in (s) Fig. 4. Dynamic response model with control mode B (Including fixed and slide pressure operation). 1 1 T 4 s W ex (s) n p (s) K 8 1 K 1 T 6 s G p (s) W p (s) 1 K 2 1 T 1 s s W ev (s) m c,out (s)

7 Yunli Jin et al. / Energy Procedia 00 (2017) The control mode B with fixed pressure operation is discussed in the first strategy. The slide pressure set-point bias W psp,b (s) is set to be zero for fixed pressure operation in Fig.4. By performing the inverse Laplace transform of transfer function between the control valve opening change and condenser outlet mass flow, the functional relation between them is given as: W v (s)w v,mtp (s)g p (s)w p (s) Δm c,out (t) = L 1 [Z v (s) ] (13) 1 W v,ptm (s)w v,mtp (s) G p (s)w p (s)w ev (s) The dynamic variation of condenser inlet mass flow also can be obtained from transfer function between condenser inlet mass flow and valve opening change: W v (s)w v,mtp (s)w v,ptm (s) Δm c,in (t) = L 1 [Z v (s) (W v (s) ) W 1 W v,ptm (s)w v,mtp (s) G p (s)w p (s)w ev (s) ex(s)] (14) The second control strategy is slide pressure operation with control mode B. In the slide pressure operation mode, the operation pressure changes in accordance with the set-point curve by controlling working fluid pump speed. The pressure set-point bias in Fig.4 is supposed to be proportional to the mass flow change with inertial delay. Then the transfer function is given as: W psp,b (s) = B psp(s) m v (s) = K 9 1T 7 s (15) Where B psp is the bias of the slide pressure set-point, and K 9 and T 7 are the gain and time constant of first order inertial element respectively. Based on Fig.4, the transfer function of mass flow of condenser outlet and inlet to valve opening change can be expressed as: W v,cout (s) = W v (s)w v,mtp (s)g p (s)w p (s)w v (s)w psp,b (s)g p (s)w p (s) 1 W v,ptm (s)w v,mtp (s) G p (s)w p (s)w ev (s) W psp,b (s)g p (s)w p (s)w ev (s)w v,ptm (s) (16) W v (s)w v,mtp (s)w v (s)w psp,b (s)g p (s)w p (s)w ev (s) W v,cin (s) = (W v (s) W 1 W v,ptm (s)w v,mtp (s) G p (s)w p (s)w ev (s) W psp,b (s)g p (s)w p (s)w ev (s)w v,ptm (s) v,ptm(s)) W ex (s) The simulation of dynamic response model in control mode B is conducted by MATLAB and the results are shown in Fig. 5. In the simulation, the forcing variable is the expander inlet valve opening. The unit step change of expander inlet valve opening follows heat source variation. (17) Fig. 5. Mass flow change over time with mode B: (a) fixed pressure operation; (b) slide pressure operation. The mass flow trends under fixed pressure operation are shown in Fig.5(a). At time t1, the mass flow through valve immediately drops proportionally following the step change of expander inlet valve opening caused by recovery heat variation. The decrease of mass flow spreads to the condenser inlet passing expander with first order inertial delay, and gives rise to the increase of valve inlet pressure. The working fluid pump lowers speed by PI controller to maintain the pressure, with which the condenser outlet mass flow reduces later. The mass flow of condenser outlet decreases to reach the inlet value at time t2. So, the pump PI controller adopting different control parameters affects the trends of mass flow of dynamic process.

8 8 Yunli Jin et al. / Energy Procedia 00 (2017) In slide pressure operation, the pressure set-point is assumed to actively reduce with mass flow decreasing, which makes the regulating action of pump speed controller stronger. Thus, comparing to fixed pressure operation in Fig.5(a), the mass flow of condenser outlet decreases more quickly and touches lower value of Fig.5(b). So, in addition to the PI controller parameters, the mass flow change trends are affected by slide press set-point. 4. Conclusions In this paper, the control characteristic analysis method is introduced to study the dynamic change process of mass flow through condenser under variable conditions. Four different control strategies are compared. The dynamic response model of mass flow through condenser based on control characteristics is built under variable conditions. The simulation is conducted and the results are analyzed. The main conclusions drawn are summarized as the follows: Adopting different control mode including regulated variables, control variables, control algorithm and parameters, influences the variation trends of mass flow of dynamic process. But control mode has no effect on final stable state. The selection of fixed pressure or slide pressure operation affects the final steady state value and dynamic variation trend of parameters. As described in Fig.3 and Fig.5, the variation trends of mass flow can be controlled by changing control mode or operation pressure. So, the parameters change of variable conditions can be limited by control strategy. Acknowledgements The research was funded by the National Basic Research Program of China (973 Program) (2014CB249201). References [1] Ziviani D, Beyene A, Venturini M. Advances and challenges in ORC systems modeling for low grade thermal energy recovery. Appl Energy 2014; 121: [2] Lecompte S, Huisseune H, Broek MVD. Review of organic Rankine cycle (ORC) architectures for waste heat recovery. Renewable and sustainable energy reviews 2015; 47: [3] Tchanche BF, Lambrinos G, Frangoudakis A, et al. Low-grade heat conversion into power using organic Rankine cycles - a review of various applications. Renew Sustain Energy Rev 2011; 15(8): [4] Jung H, Taylor L, Krumdieck S. An experimental and modelling study of a 1kW organic Rankine cycle unit with mixture working fluid. Energy 2015; 81: [5] Shu G, Gao YY, et al. Study of mixtures based on hydrocarbons used in ORC for engine waste heat recovery. Energy 2014; 74: [6] Yue C, Han D, Pu WH, et al. Thermal matching performance of a geothermal ORC system using zeotropic working fluids. Renewable Energy 2015; 80: [7] Yang FB, Dong XR, Zhang HG, et al. Performance analysis of waste heat recovery with a dual loop organic Rankine cycle system for diesel engine under various operating conditions. Energy Conversion and Management 2014; 80: [8] Zhang HG, Wang EH, Fan BY. A performance analysis of a novel system of a dual loop bottoming organic Rankine cycle (ORC) with a lightduty diesel engine. Appl Energy 2013; 102: [9] Guzovic Z, Raskovic P, Blataric Z. The comparison of a basic and a dual-pressure ORC (Organic Rankine Cycle): Geothermal Power Plant Velika Ciglena case study. Energy 2014; 76: [10] Yamada N, Watanabe M, Hoshi A. Experiment on pumpless Rankine-type cycle with scroll expander. Energy 2013; 49: [11] Gao P, Wang LW, Wang RZ, et al. Experimental investigation on a small pumpless ORC system driven by the low temperature heat source. Energy 2015; 91: [12] Quoilin S, Aumann R, Grill A, et al. Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles. Appl Energy 2011; 88: [13] Hu DS, Zheng Y, Wu Y, et al. Off-design performance comparison of an organic Rankine cycle under different control strategies. Appl Energy 2015; 156: [14] Usman M, Imran M, Lee DH, et al. Experimental investigation of off-grid organic Rankine cycle control system adapting sliding pressure strategy under proportional integral with feed-forward and compensator. Applied Thermal Engineering 2017; 110: [15] Abdelghani-Idrissi M A, Bagui F, Estel L. Analytical and experimental response time to flow rate step along a counter flow double pipe heat exchanger. Heat and Mass Transfer 2001; 44: [16] Hartnett J P, Minkowycz W J. Dynamic simulation of a countercurrent heat exchanger modelling-start-up and frequency response. Heat and Mass Transfer 1994; 21: