Off-Design Performances of Subcritical and Supercritical Organic Rankine Cycles in Geothermal Power Systems under an Optimal Control Strategy

The conditions of heat source and heat sink in a geothermal ORC system may frequently vary due to variations in geological conditions, ambient temperature and actual operation. In this study, an off-design performance prediction model for geothermal ORC systems is developed according to special designs of critical components, and an optimal control strategy which regards the turbine guide vane angle, the refrigerant pump rotational speed and the cooling water mass flow rate as control variables is proposed to maximize the net power output. Off-design performances of both subcritical and supercritical ORCs are analyzed. The results indicate that, under the optimal control strategy, the net power output of both ORCs increase with greater geothermal water mass flow rate, higher geothermal water inlet temperature and lower cooling water inlet temperature, which is mainly due to a greater working fluid mass flow rate, higher turbine inlet pressure and lower condensing pressure, respectively. The net power output of supercritical ORC is always greater than that of subcritical ORC within the range of this study, but the difference tends to decrease when supercritical ORC activates the geothermal water reinjection temperature restriction.


Introduction
Due to the rapid growth of the world economy, the global energy consumption continues to increase significantly, which leads to excessive consumption of fossil fuels and serious environmental deterioration.In this instance, the utilization of low-grade thermal energy, including geothermal energy, solar energy, biomass energy and industrial waste heat, is currently drawing great attention.Geothermal energy presents favorable application prospects owing to its abundant storage capacity and convenient utilization.Among all the available technologies, the Organic Rankine Cycle (ORC) has been regarded as an efficient approach to convert low-grade heat into electricity.A great amount of research concentrated on working fluid selection and system design has been conducted to enhance the performance of ORC systems.Chen et al. [1] screened 35 kinds of working fluids for the subcritical and supercritical ORCs and proposed the selection criteria of working fluids.Zhang et al. [2] compared various working fluids for a low temperature ORC system with five different indicators as criteria.Both subcritical and supercritical ORCs were examined, and it turned out that supercritical ORC using R125 had good economics and high geothermal utilization rates.Guo et al. [3] reported that the choice of optimal working fluid was determined by the profiles of the heat source and heat sink, and the introduction of a regenerator did not always enhance the system efficiency.Liu et al. [4] pointed out that supercritical ORC could yield good performances in both thermodynamic and economic aspects, and R134a was the optimal working fluid.different heat sources conditions, sliding pressure operation, constant pressure operation, and an optimal control strategy combining the former two methods were studied, respectively.The results showed that the optimal control strategy was superior to the other two methods.However, the variation of heat sink condition was not considered in their works.Usman et al. [21] compared the part-load operation of air cooled and cooling water tower-based geothermal ORC systems installed at different geographical locations.A sink auxiliary control optimization was performed to provide maximum power output at off-design conditions by changing the fan speed of cooling tower, air cooled condenser and mass flow rate of sink side.Rajabloo et al. [22] investigated the behaviors of low temperature and high temperature ORCs with varying conditions of the heat source and heat sink, respectively.The turbine inlet pressure, the condensing pressure and the mass flow rate of working fluid following were regulated to meet cycle requirements at off-design conditions.They considered the thermal decomposition of the working fluid and found that the properties of decomposed products could significantly affect cycle efficiency.To study the off-design performance of a small scale subcritical ORC, Liu et al. [23] developed a working fluid charge oriented model based on the component models and discovered that the optimal working fluid charge volume would differ depending on the expander's output work.In this study, the solution of off-design model was based on the optimization of pump rotation speed to keep the system output to a stable value.
Most investigations focused on the off-design analysis of ORC were conducted based on the performance curves or simple formulas of critical components which were not specially obtained from ORC systems.Hence, predicting the off-design performance on the basis of specially designed components would be more dependable.In addition, few studies have compared the off-design performances of subcritical and supercritical ORCs with a specific control strategy.In this paper, to analyze and compare off-design performances of subcritical and supercritical geothermal ORCs with a water cooling system, an off-design performance prediction model is developed based on special designs of the critical components.Then a specific optimal control strategy which maximizes the net power output is proposed to regulate the operating parameters of both ORCs with varying geothermal water mass flow rate, geothermal water temperature and cooling water temperature.The control variables of the control strategy are turbine guide vane angle, rotational speed of refrigerant pump and cooling water mass flow rate.The findings can provide references and guidelines for the off-design operation regulation of a geothermal ORC system.

ORC System
In this work, both subcritical and supercritical ORCs are adopted to utilize the geothermal energy.The layout of geothermal ORC system and T-S diagrams are displayed in Figures 1 and 2, respectively.The following processes are included in ORC: 1-2: The high pressure working fluid vapor expands to do work in the turbine.2-5: The exhausted vapor is condensed by cooling water in the condenser.5-6: The subcooled liquid is pumped to a high pressure in the refrigerant pump.6-1: The high pressure liquid is heated into vapor by geothermal water in the evaporator (vapor generator).

Thermodynamic Modeling
The power yielded by turbine, consumed by the refrigerant pump and cooling water pump are respectively expressed as: Then the net power output of ORC is calculated as: Turbine RP WP P P P P (4)

Thermodynamic Parameter Optimization on the Design Condition
The design condition of the geothermal system is given as Table 1.For subcritical ORC, R600a is selected as a preferred working fluid [17,24,25].Superheating is not advantageous for R600a which is a dry working fluid [26,27], so just a small superheating of 5 K is set to satisfy the practical operational constraints.For supercritical ORC, R134a is chosen due to its good performance [4,25].To avoid cavitation in the refrigerant pump, a subcooling of 2 K is adopted in both ORCs.The regenerator cannot always enhance the thermodynamic performance of ORC at the expense of higher cost [25,27].In addition, the regenerator can bring operative problems when geothermal water temperature is low under off-design conditions [13].Therefore, the regenerator is not considered in this work.The geothermal water reinjection temperature should be not less than 70 °C to avoid silica oversaturation.

Thermodynamic Modeling
The power yielded by turbine, consumed by the refrigerant pump and cooling water pump are respectively expressed as: Then the net power output of ORC is calculated as:

Thermodynamic Parameter Optimization on the Design Condition
The design condition of the geothermal system is given as Table 1.For subcritical ORC, R600a is selected as a preferred working fluid [17,24,25].Superheating is not advantageous for R600a which is a dry working fluid [26,27], so just a small superheating of 5 K is set to satisfy the practical operational constraints.For supercritical ORC, R134a is chosen due to its good performance [4,25].To avoid cavitation in the refrigerant pump, a subcooling of 2 K is adopted in both ORCs.The regenerator cannot always enhance the thermodynamic performance of ORC at the expense of higher cost [25,27].In addition, the regenerator can bring operative problems when geothermal water temperature is low under off-design conditions [13].Therefore, the regenerator is not considered in this work.The geothermal water reinjection temperature should be not less than 70 • C to avoid silica oversaturation.To validate the models developed for the simulation of ORCs, the available data with the same operating conditions and working fluids in the literature are utilized.The comparisons of simulation results with those reported in literature are presented in Figure 3.As can be seen, there is a good agreement between the values of parameters calculated in this paper and those published in literature [24,28].
Energies 2017, 10, 1185 5 of 25 To validate the models developed for the simulation of ORCs, the available data with the same operating conditions and working fluids in the literature are utilized.The comparisons of simulation results with those reported in literature are presented in Figure 3.As can be seen, there is a good agreement between the values of parameters calculated in this paper and those published in literature [24,28].To conduct the thermodynamic performance calculation, some other thermodynamic variables need to be determined in addition to the parameters listed in Table 1.For subcritical ORC, the variables are turbine inlet pressure and condensation pressure, while for supercritical ORC, an additional variable, turbine inlet temperature should be considered.These variables are regarded as decision variables to conduct a single-objective optimization based on a genetic algorithm (GA).The net power output is chosen as optimization objective since the maximum value is desirable for a geothermal power system [29,30].In this work, all the programs are written in MATLAB 2011b (The MathWorks, Natick, Massachusetts, USA), and the thermodynamic properties are attained from REFPROP 9.0 (NIST, Gaithersburg, Maryland, USA).Assumptions and constraints adopted are listed as below: (1) The system is supposed in steady state.
(2) The pressure drops in heat exchangers and pipelines are ignored.
(3) The vapor quality of turbine outlet is restricted to not less than 1 to avoid the droplet wear phenomenon.
The optimization results are displayed in Table 2.The specific internal parameters of ORCs can be calculated based on the optimal decision variable values, including the mass flow rates of working fluid and cooling water, inlet and outlet thermodynamic states of each component.Then the critical components can be specially designed.

System Components Modeling and Design
To conduct the off-design performance analysis of ORC system, the performance prediction model and specific design of each important component should be determined.To conduct the thermodynamic performance calculation, some other thermodynamic variables need to be determined in addition to the parameters listed in Table 1.For subcritical ORC, the variables are turbine inlet pressure and condensation pressure, while for supercritical ORC, an additional variable, turbine inlet temperature should be considered.These variables are regarded as decision variables to conduct a single-objective optimization based on a genetic algorithm (GA).The net power output is chosen as optimization objective since the maximum value is desirable for a geothermal power system [29,30].In this work, all the programs are written in MATLAB 2011b (The MathWorks, Natick, Massachusetts, USA), and the thermodynamic properties are attained from REFPROP 9.0 (NIST, Gaithersburg, Maryland, USA).Assumptions and constraints adopted are listed as below: (1) The system is supposed in steady state.
(2) The pressure drops in heat exchangers and pipelines are ignored.
(3) The vapor quality of turbine outlet is restricted to not less than 1 to avoid the droplet wear phenomenon.
The optimization results are displayed in Table 2.The specific internal parameters of ORCs can be calculated based on the optimal decision variable values, including the mass flow rates of working fluid and cooling water, inlet and outlet thermodynamic states of each component.Then the critical components can be specially designed.

System Components Modeling and Design
To conduct the off-design performance analysis of ORC system, the performance prediction model and specific design of each important component should be determined.

Radial Inflow Turbine
Radial inflow turbines are characterized by easy manufacture, compact structures and high efficiency, and they are suitable for low flow rate and high pressure ratio situations.A variable inlet guide vane (VIGV) is a familiar method to adjust the radial turbine performance.The adjustable nozzles can rotate around the rotation centers, leading to the changes in nozzle outlet angle and area.Then the turbine performance can be regulated to adapt variable working conditions without throttling losses [31].Thus, radial turbine with VIGV presents smooth off-design performance, and it is applied in this paper.A schematic of a radial inflow turbine is displayed in Figure 4.

Radial Inflow Turbine
Radial inflow turbines are characterized by easy manufacture, compact structures and high efficiency, and they are suitable for low flow rate and high pressure ratio situations.A variable inlet guide vane (VIGV) is a familiar method to adjust the radial turbine performance.The adjustable nozzles can rotate around the rotation centers, leading to the changes in nozzle outlet angle and area.Then the turbine performance can be regulated to adapt variable working conditions without throttling losses [31].Thus, radial turbine with VIGV presents smooth off-design performance, and it is applied in this paper.A schematic of a radial inflow turbine is displayed in Figure 4.The one-dimensional analysis method based on mass and energy conservation equations is employed to calculate the turbine performance.Compared with the computational fluid dynamics (CFD), this method is more convenient and practical, moreover, the prediction results can match well those of CFD [8,9].In the turbine, the expansion process is preliminarily assumed to be isentropic, then relevant loss models are introduced to modify the flow process, making the prediction more accurate.
In stator vanes, the flow process can be expressed by the following equations: Supersonic flow is common at the stator outlet in ORC, which leads to a critical flow rate.In such case, the stator outlet flow angle will deviate from the installation angle and should be corrected: A small clearance is set between the stator and rotor to avoid collision, and the tangential momentum is supposed to be conserved [32]: The one-dimensional analysis method based on mass and energy conservation equations is employed to calculate the turbine performance.Compared with the computational fluid dynamics (CFD), this method is more convenient and practical, moreover, the prediction results can match well those of CFD [8,9].In the turbine, the expansion process is preliminarily assumed to be isentropic, then relevant loss models are introduced to modify the flow process, making the prediction more accurate.
In stator vanes, the flow process can be expressed by the following equations: Supersonic flow is common at the stator outlet in ORC, which leads to a critical flow rate.In such case, the stator outlet flow angle will deviate from the installation angle and should be corrected: sin A small clearance is set between the stator and rotor to avoid collision, and the tangential momentum is supposed to be conserved [32]: In the rotors, the flow process can be expressed by: Losses models which include stator loss (L stator ), incidence loss (L i ), passage loss (L p ), disc friction loss (L df ), clearance loss (L c ) and exit loss (L e ) are introduced in this work [33,34]: Then the turbine efficiency is given as: Based on the above equations, a turbine submodel is established to calculate the turbine performance on different operating conditions.By inputting geometric dimensions, rotational speed, backpressure and inlet thermodynamic parameters of the turbine, the efficiency and mass flow rate can be predicted through an iteration process.Here the pressures at stator outlet and rotor inlet are previously assumed, then the thermodynamic parameters and mass flow rate of each section of the turbine can be obtained.The iteration continues by adjusting the pressures until the mass flow rate of each section becomes equivalent, then the turbine performance can be acquired.
To verify the validity of the turbine submodel, the prediction result has been compared with the data from Hu et al. [19].As displayed in Table 3, the submodel can predict the turbine performance within an acceptable error range.Subsequently, the turbines of subcritical and supercritical ORCs are specially designed based on the optimal thermodynamic parameters for the design conditions.A radial turbine design program was developed based on the method presented by Hu et al. [19].In this program, the inlet pressure and temperature, mass flow rate and outlet pressure of the turbine listed in Table 2 are taken as input variables, and α 02 , β 02 , β 04 , N, U/C 0 and r 04 /r 03 are selected as decision variables to regulate the geometric dimensions and turbine performance.In addition, structure restrictions are considered to guarantee the rationality of design.The efficiency of designed turbines should be close to 80%, which is the setting value in the thermodynamic parameter optimization on design condition.Satisfactory designs of turbines are obtained by adjusting the decision variables, and the design results are displayed in Table 4.

Heat Exchangers
Plate heat exchanger (PHE) has been increasingly used in various industries owing to its high heat transfer coefficient, simple maintenance, compact structure and less fouling.Queensland Geothermal Energy Centre of Excellence (QGECE) has been considering PHE as a favorite candidate for use in geothermal power systems [35].A welded construction PHE without any gaskets which can work under temperatures beyond 400 • C and pressures up to 100 bar has been proposed for high temperature and pressure conditions [36], which means that welded construction PHEs can be used as vapor generators in supercritical ORCs.
In this study, PHEs are selected as evaporator (vapor generator) and condenser in both subcritical and supercritical ORCs.Chevron-type corrugation plates are adopted and the basic configuration of the PHE is displayed in Figure 5.

Heat Exchangers
Plate heat exchanger (PHE) has been increasingly used in various industries owing to its high heat transfer coefficient, simple maintenance, compact structure and less fouling.Queensland Geothermal Energy Centre of Excellence (QGECE) has been considering PHE as a favorite candidate for use in geothermal power systems [35].A welded construction PHE without any gaskets which can work under temperatures beyond 400 °C and pressures up to 100 bar has been proposed for high temperature and pressure conditions [36], which means that welded construction PHEs can be used as vapor generators in supercritical ORCs.
In this study, PHEs are selected as evaporator (vapor generator) and condenser in both subcritical and supercritical ORCs.Chevron-type corrugation plates are adopted and the basic configuration of the PHE is displayed in Figure 5.The heat transfer process in each heat changer is divided into many small sections, and log mean temperature difference method is employed to calculate the heat transfer rate in each section: The pressure drop in heat exchanger is given by: For single-phase flow in evaporator and condenser, the Nusselt number and friction factor are given by Equations ( 22) and ( 23) [37,38].
A correlation obtained by experimental analysis is employed to calculate the heat transfer of supercritical fluid in vapor generator [35]: For the evaporation process in evaporator, the following correlations are adopted to determine the pressure drop and heat transfer, and θ max equals to 70 • [39].
If Bd < 4 Bo 0.198 Bd 0.235 (27) where: For condensation process in condenser, the Nusselt number and friction factor are respectively expressed as [40]: Energies 2017, 10, 1185 10 of 25 in which P cr denotes critical pressure, and equivalent Reynolds number is given as: where: If the geometric dimensions of a PHE are specified, the required heat transfer area can be calculated by above corresponding correlations, mass flow rates and thermodynamic parameters on both sides of the PHE.Under off-design conditions, the thermodynamic parameters at the ends of PHE and mass flow rates are not all known, and the required heat transfer area can be acquired by assuming the unknown quantities.The assumed quantities should be adjusted until the obtained area is consistent with the actual heat transfer area of PHE [20].
Afterwards the specific designs of evaporator (vapor generator) and condenser are performed in accordance to the optimal thermodynamic parameters on the design condition.All the PHEs are arranged as counterflow single-pass flow [10,19], and the pressure drops are limited to 2%.The design results of PHEs are displayed in Table 5.

Pump
The methodology of the pump adopted in [16,19] is employed in this work.The non-dimensional performance curve of the refrigerant pump is derived from a centrifugal pump in a real power plant, as presented in Figure 6.The nominal rotational speed is assumed as 1500 rpm, and the efficiency comes to the maximum value of 70% at the design flow rate and head.For off-design conditions, the rotational speed can be adjusted, and the off-design performance can be acquired base on the non-dimensional performance curve and affinity laws.The cooling water pump makes cooling water flow circulate between condenser and cooling tower, and the power consumed by it is quite small.For simplicity, the head and efficiency of cooling water pump are taken as constant values displayed in Table 1 for off-design conditions.

Off-Design Performance Optimization
In a geothermal ORC system, the heat source and heat sink conditions may frequently vary due to the variations of geological conditions, ambient temperature and actual operation, then a specific control strategy should be adopted to keep the system operating stably by adjusting the operating parameters.In this work, for the off-design operation, the subcooling is fixed at 2 K for both ORCs, and the superheating is fixed at 5 K for subcritical ORC.A control strategy which maximizes the net power output is employed, and off-design performance analysis is carried out with variable geothermal water mass flow rate (mgw), geothermal water inlet temperature (Tgw) and cooling water inlet temperature (Tcw).
To predict the off-design performance of a specified operation point, the values of mgw, Tgw and Tcw should be given, the rotational speed of refrigerant pump (NRP), turbine guide vane angle (α02) and cooling water mass flow rate (mcw) are regarded as control variables to adjust the system performance.The ORC system in this work is for power generation and supposed to connect to the grid, therefore the rotational speed of turbine remains constant.To conduct the submodel performance prediction, some operation parameters need to be previously assumed.For subcritical ORC, the assumed variables include turbine inlet pressure (P1), condensation pressure (P2).The turbine inlet temperature (T1) can be obtained by the fixed superheating and P1.While for supercritical ORC, one more variable, namely T1 should be assumed.For both subcritical and supercritical ORCs, according to the values of P1, P2, α02 and T1, the working fluid mass flow rate (mwf), thermodynamic state at the outlet, as well as the off-design performance of the turbine can be determined by the turbine submodel.Then the off-design performances of condenser, refrigerant pump and evaporator (vapor generator) can be successively calculated by the corresponding submodels.It is noteworthy that the assumed operation parameters need to be adjusted until the calculated results agree with the actual component properties.In this work, optimizations based on genetic algorithm are respectively performed for subcritical and supercritical ORCs.The net power output is chosen as optimization objective, and the control variables mentioned above are regarded as decision variables.The detailed flow chart of off-design performance optimization is shown in Figure 7.The cooling water pump makes cooling water flow circulate between condenser and cooling tower, and the power consumed by it is quite small.For simplicity, the head and efficiency of cooling water pump are taken as constant values displayed in Table 1 for off-design conditions.

Off-Design Performance Optimization
In a geothermal ORC system, the heat source and heat sink conditions may frequently vary due to the variations of geological conditions, ambient temperature and actual operation, then a specific control strategy should be adopted to keep the system operating stably by adjusting the operating parameters.In this work, for the off-design operation, the subcooling is fixed at 2 K for both ORCs, and the superheating is fixed at 5 K for subcritical ORC.A control strategy which maximizes the net power output is employed, and off-design performance analysis is carried out with variable geothermal water mass flow rate (m gw ), geothermal water inlet temperature (T gw ) and cooling water inlet temperature (T cw ).
To predict the off-design performance of a specified operation point, the values of m gw , T gw and T cw should be given, the rotational speed of refrigerant pump (N RP ), turbine guide vane angle (α 02 ) and cooling water mass flow rate (m cw ) are regarded as control variables to adjust the system performance.The ORC system in this work is for power generation and supposed to connect to the grid, therefore the rotational speed of turbine remains constant.To conduct the submodel performance prediction, some operation parameters need to be previously assumed.For subcritical ORC, the assumed variables include turbine inlet pressure (P 1 ), condensation pressure (P 2 ).The turbine inlet temperature (T 1 ) can be obtained by the fixed superheating and P 1 .While for supercritical ORC, one more variable, namely T 1 should be assumed.For both subcritical and supercritical ORCs, according to the values of P 1 , P 2 , α 02 and T 1 , the working fluid mass flow rate (m wf ), thermodynamic state at the outlet, as well as the off-design performance of the turbine can be determined by the turbine submodel.Then the off-design performances of condenser, refrigerant pump and evaporator (vapor generator) can be successively calculated by the corresponding submodels.It is noteworthy that the assumed operation parameters need to be adjusted until the calculated results agree with the actual component properties.In this work, optimizations based on genetic algorithm are respectively performed for subcritical and supercritical ORCs.The net power output is chosen as optimization objective, and the control variables mentioned above are regarded as decision variables.The detailed flow chart of off-design performance optimization is shown in Figure 7.

Various Geothermal Water Mass Flow Rates
In this section, subcritical and supercritical ORCs with various mgw are optimized, meanwhile Tgw and Tcw are fixed at the designed values.As displayed in Figure 8, the variations of the optimal control variables with mgw are similar for subcritical and supercritical ORCs.As mgw grows, α02 and NRP both gradually increase.The growth of α02 is obvious, while the increase in NRP is slight.In addition, mcw first gradually increases and then becomes stable with mgw for both ORCs, but the overall change is fairly small.
To further look into the off-design performances of ORCs with mgw, the optimal operation parameters are also analyzed.For both ORCs, P1, namely the pressure of heater (evaporator or vapor generator), is roughly constant, and P2 slowly rises with mgw, as shown in Figure 9a,b.For supercritical ORC, T1 nearly remains constant.The mwf of the whole system is equivalent to the turbine mass flow rate.In this paper, supersonic flow always appears in the turbine nozzle due to the high expansion ratio, then the mass flow rate reaches the critical value.Thus, mwf only depends on P1, T1 and α02.

Various Geothermal Water Mass Flow Rates
In this section, subcritical and supercritical ORCs with various m gw are optimized, meanwhile T gw and T cw are fixed at the designed values.As displayed in Figure 8, the variations of the optimal control variables with m gw are similar for subcritical and supercritical ORCs.As m gw grows, α 02 and N RP both gradually increase.The growth of α 02 is obvious, while the increase in N RP is slight.In addition, m cw first gradually increases and then becomes stable with m gw for both ORCs, but the overall change is fairly small.
To further look into the off-design performances of ORCs with m gw , the optimal operation parameters are also analyzed.For both ORCs, P 1 , namely the pressure of heater (evaporator or vapor generator), is roughly constant, and P 2 slowly rises with m gw , as shown in Figure 9a,b.For supercritical ORC, T 1 nearly remains constant.The m wf of the whole system is equivalent to the turbine mass flow rate.In this paper, supersonic flow always appears in the turbine nozzle due to the high expansion ratio, then the mass flow rate reaches the critical value.Thus, m wf only depends on P 1 , T 1 and α 02 .As displayed in Figure 9c, for both ORCs, mwf grows with mgw, which is mainly due to the increase in α02.The enthalpy rise in the evaporator (vapor generator) is stable due to the roughly constant T1 and P1, and mwf increases to absorb more heat from geothermal water.Meanwhile, the heat transfer rate in the condenser also grows, but mcw changes very little.The slow increase in P2 means the condensation temperature increases, then the condenser pinch temperature difference tends to be  As displayed in Figure 9c, for both ORCs, mwf grows with mgw, which is mainly due to the increase in α02.The enthalpy rise in the evaporator (vapor generator) is stable due to the roughly constant T1 and P1, and mwf increases to absorb more heat from geothermal water.Meanwhile, the heat transfer rate in the condenser also grows, but mcw changes very little.The slow increase in P2 means the condensation temperature increases, then the condenser pinch temperature difference tends to be As displayed in Figure 9c, for both ORCs, m wf grows with m gw , which is mainly due to the increase in α 02 .The enthalpy rise in the evaporator (vapor generator) is stable due to the roughly constant T 1 Energies 2017, 10, 1185 14 of 25 and P 1 , and m wf increases to absorb more heat from geothermal water.Meanwhile, the heat transfer rate in the condenser also grows, but m cw changes very little.The slow increase in P 2 means the condensation temperature increases, then the condenser pinch temperature difference tends to be larger, which could satisfy the higher heat transfer rate in the condenser.As to the refrigerant pump, for both ORCs, with the increase in m gw , the pump head is almost constant while the volumetric flow rate gradually grows due to the rising m wf .Thus, a slow increase in N RP simultaneously satisfies the pump head and volumetric flow rate (see Figure 8b).
The lower the geothermal water reinjection temperature (T re ), the more fully the geothermal energy is utilized.However, T re should not be lower than 70 • C to avoid the silica oversaturation.As displayed in Figure 9d, for subcritical ORC, as m gw grows, the utilization of geothermal energy drops, which can be deduced by the growing T re .This may be due to the limited heat transfer area of the evaporator, while for supercritical ORC, when m gw is smaller than the design value, T re comes to the minimum allowed value of 70 • C, and m wf degrades rapidly as m gw falls (see Figure 9c).This can be explained by the fact that if m wf does not decrease fast, the working fluid would absorb more heat from geothermal water, leading to the consequence that T re is lower than 70 • C When m gw is greater than designed value, T re grows rapidly with m gw , which implies the heat amount absorbed by the working fluid becomes relatively small, resulting in a slow increase in m wf .
For both ORCs, as m gw grows, both the turbine power output and the power consumed by refrigerant pump rise owing to the increase in m wf , and the power consumed by cooling water pump changes very little because of the small variation of m cw .Since the increased turbine power output more than compensates for the increase in power consumed by the pumps, the net power output (P net ) rises with m gw , as shown in Figure 10.Although P net of supercritical ORC is always greater than that of subcritical ORC, the difference between them becomes smaller when m gw deviates from the design value, and this is mostly due to the variation of turbine power output.For supercritical ORC, when m gw is smaller than the design value, the m wf degrades rapidly to satisfy the constraint of T re , resulting in a quick decline in turbine power output, while when m gw is greater than the design value, the slow growth of m wf leads to a slow increase in turbine power output.
Energies 2017, 10, 1185 14 of 25 larger, which could satisfy the higher heat transfer rate in the condenser.As to the refrigerant pump, for both ORCs, with the increase in mgw, the pump head is almost constant while the volumetric flow rate gradually grows due to the rising mwf.Thus, a slow increase in NRP simultaneously satisfies the pump head and volumetric flow rate (see Figure 8b).The lower the geothermal water reinjection temperature (Tre), the more fully the geothermal energy is utilized.However, Tre should not be lower than 70 °C to avoid the silica oversaturation.As displayed in Figure 9d, for subcritical ORC, as mgw grows, the utilization of geothermal energy drops, which can be deduced by the growing Tre.This may be due to the limited heat transfer area of the evaporator, while for supercritical ORC, when mgw is smaller than the design value, Tre comes to the minimum allowed value of 70 °C, and mwf degrades rapidly as mgw falls (see Figure 9c).This can be explained by the fact that if mwf does not decrease fast, the working fluid would absorb more heat from geothermal water, leading to the consequence that Tre is lower than 70 °C When mgw is greater than designed value, Tre grows rapidly with mgw, which implies the heat amount absorbed by the working fluid becomes relatively small, resulting in a slow increase in mwf.
For both ORCs, as mgw grows, both the turbine power output and the power consumed by refrigerant pump rise owing to the increase in mwf, and the power consumed by cooling water pump changes very little because of the small variation of mcw.Since the increased turbine power output more than compensates for the increase in power consumed by the pumps, the net power output (Pnet) rises with mgw, as shown in Figure 10.Although Pnet of supercritical ORC is always greater than that of subcritical ORC, the difference between them becomes smaller when mgw deviates from the design value, and this is mostly due to the variation of turbine power output.For supercritical ORC, when mgw is smaller than the design value, the mwf degrades rapidly to satisfy the constraint of Tre, resulting in a quick decline in turbine power output, while when mgw is greater than the design value, the slow growth of mwf leads to a slow increase in turbine power output.

Various Geothermal Water Inlet Temperatures
In this part, subcritical and supercritical ORCs with various Tgw are optimized, meanwhile mgw and Tcw are fixed at the designed values.The variations of optimal control variables are showed in Figure 11.For supercritical ORC, α02 basically remains the same value, while for subcritical ORC, a slightly decline can be observed.It is noteworthy that abnormal small α02 emerges when Tgw reaches the lowest value of 130 °C for both ORCs.Besides, for both ORCs, NRP gradually increases with Tgw, and mcw remains basically stable.

Various Geothermal Water Inlet Temperatures
In this part, subcritical and supercritical ORCs with various T gw are optimized, meanwhile m gw and T cw are fixed at the designed values.The variations of optimal control variables are showed in Figure 11.For supercritical ORC, α 02 basically remains the same value, while for subcritical ORC, a slightly decline can be observed.It is noteworthy that abnormal small α 02 emerges when T gw reaches the lowest value of 130 • C for both ORCs.Besides, for both ORCs, N RP gradually increases with T gw , and m cw remains basically stable.The variations of optimal operation parameters with Tgw are shown in Figure 12.For both ORCs, P1 gradually increases and P2 slightly rises with Tgw, as shown in Figure 12a,b.For supercritical ORC, as Tgw grows, T1 also gradually increases to generate a better temperature match between working fluid and geothermal water.The variations of optimal operation parameters with T gw are shown in Figure 12.For both ORCs, P 1 gradually increases and P 2 slightly rises with T gw , as shown in Figure 12a,b.For supercritical ORC, as T gw grows, T 1 also gradually increases to generate a better temperature match between working fluid and geothermal water.The variations of optimal operation parameters with Tgw are shown in Figure 12.For both ORCs, P1 gradually increases and P2 slightly rises with Tgw, as shown in Figure 12a,b.For supercritical ORC, as Tgw grows, T1 also gradually increases to generate a better temperature match between working fluid and geothermal water.As presented in Figure 12c, for both ORCs, m wf gradually increases with T gw .For supercritical ORC, α 02 is nearly constant, the increase of m wf is mainly determined by higher P 1 and T 1 .For subcritical ORC, although α 02 basically decreases slowly, which means that m wf has a decline trend, higher P 1 and T 1 can make up for this trend, consequently m wf grows.As to the refrigerant pump, for both ORCs, N RP adds with T gw to satisfy the increases in volumetric flow rate and pump head, which are mainly caused by the increasing m wf and difference between P 1 and P 2 , respectively.
As displayed in Figure 12d, for both ORCs, T re generally increases as T gw rises.Likewise, when T gw comes to the minimum value of 130 • C, T re becomes abnormal.For subcritical ORC, when T gw changes from 135 • C to 130 • C, the decline rate of T re slows down significantly, this may be due to the unusual small α 02 (see Figure 11a), which leads to a small m wf , then the restriction on the lowest T re (70 • C) can be satisfied.For supercritical ORC, abnormal high T re emerges when T gw reaches 130 • C.This is because when T gw reaches 130 • C, P 1 tends to be lower than the critical pressure of 4.06 Mpa for R134a (see the dashed line in Figure 12a).However, P 1 must be higher than the critical pressure to meet the supercritical condition, and high P 1 contributes to large m wf , which leads to abnormal small α 02 (see Figure 11a) to balance m wf , eventually the geothermal energy fails to be fully utilized, and abnormal high T re emerges.
For both ORCs, P net gradually increases with T gw , and P net of supercritical ORC is greater than that of subcritical ORC, as displayed in Figure 13.As T gw rises, working fluid per unit mass flow rate can produce more power due to the higher T 1 and P 1 , and m wf also grows, thus turbine power output increases.The power consumed by refrigerant pump also grows owing to the increases of m wf and difference between P 1 and P 2 .The power consumed by cooling water pump changes very little due to the small variation of m cw.Eventually, P net increases since the increased turbine power output can make up for the increase of power consumed by the pumps.As presented in Figure 12c, for both ORCs, mwf gradually increases with Tgw.For supercritical ORC, α02 is nearly constant, the increase of mwf is mainly determined by higher P1 and T1.For subcritical ORC, although α02 basically decreases slowly, which means that mwf has a decline trend, higher P1 and T1 can make up for this trend, consequently mwf grows.As to the refrigerant pump, for both ORCs, NRP adds with Tgw to satisfy the increases in volumetric flow rate and pump head, which are mainly caused by the increasing mwf and difference between P1 and P2, respectively.
As displayed in Figure 12d, for both ORCs, Tre generally increases as Tgw rises.Likewise, when Tgw comes to the minimum value of 130 °C, Tre becomes abnormal.For subcritical ORC, when Tgw changes from 135 °C to 130 °C, the decline rate of Tre slows down significantly, this may be due to the unusual small α02 (see Figure 11a), which leads to a small mwf, then the restriction on the lowest Tre (70 °C) can be satisfied.For supercritical ORC, abnormal high Tre emerges when Tgw reaches 130 °C.This is because when Tgw reaches 130 °C, P1 tends to be lower than the critical pressure of 4.06 Mpa for R134a (see the dashed line in Figure 12a).However, P1 must be higher than the critical pressure to meet the supercritical condition, and high P1 contributes to large mwf, which leads to abnormal small α02 (see Figure 11a) to balance mwf, eventually the geothermal energy fails to be fully utilized, and abnormal high Tre emerges.
For both ORCs, Pnet gradually increases with Tgw, and Pnet of supercritical ORC is greater than that of subcritical ORC, as displayed in Figure 13.As Tgw rises, working fluid per unit mass flow rate can produce more power due to the higher T1 and P1, and mwf also grows, thus turbine power output increases.The power consumed by refrigerant pump also grows owing to the increases of mwf and difference between P1 and P2.The power consumed by cooling water pump changes very little due to the small variation of mcw.Eventually, Pnet increases since the increased turbine power output can make up for the increase of power consumed by the pumps.

Various Cooling Water Inlet Temperatures
In this section, subcritical and supercritical ORCs with various Tcw are optimized, meanwhile mgw and Tgw are fixed at the designed values.As shown in Figure 14a, for both ORCs, α02 first rises and then drops with Tcw, but the maximum α02 corresponds to different Tcw which is 25 °C for supercritical ORC and 15 °C for subcritical ORC.As presented in Figure 14b, NRP is nearly constant for subcritical ORC, while NRP first increases and then decreases with Tcw for supercritical ORC, and the maximum NRP also corresponds to Tcw of 25 °C Nonetheless, the variations of α02 and NRP are overall small for both ORCs.In addition, mcw is approximately steady for both ORCs.

Various Cooling Water Inlet Temperatures
In this section, subcritical and supercritical ORCs with various T cw are optimized, meanwhile m gw and T gw are fixed at the designed values.As shown in Figure 14a, for both ORCs, α 02 first rises and then drops with T cw , but the maximum α 02 corresponds to different T cw which is 25 • C for supercritical ORC and 15 • C for subcritical ORC.As presented in Figure 14b, N RP is nearly constant for subcritical ORC, while N RP first increases and then decreases with T cw for supercritical ORC, and the maximum N RP also corresponds to T cw of 25 • C Nonetheless, the variations of α 02 and N RP are overall small for both ORCs.In addition, m cw is approximately steady for both ORCs.As presented in Figure 15a, as Tcw increases, for supercritical ORC, P1 keeps roughly constant, while for subcritical ORC, P1 slowly rises except the abnormal high P1 which corresponds to Tcw of 10 °C.For both systems, P2 gradually increases, as shown in Figure 15b.As presented in Figure 15a, as T cw increases, for supercritical ORC, P 1 keeps roughly constant, while for subcritical ORC, P 1 slowly rises except the abnormal high P 1 which corresponds to T cw of 10 • C. For both systems, P 2 gradually increases, as shown in Figure 15b.As presented in Figure 15a, as Tcw increases, for supercritical ORC, P1 keeps roughly constant, while for subcritical ORC, P1 slowly rises except the abnormal high P1 which corresponds to Tcw of 10 °C.For both systems, P2 gradually increases, as shown in Figure 15b.Figure 15c illustrates the variation of m wf with T cw .For supercritical ORC, owing to the slight variations of T 1 and P 1 , the variation of m wf is similar with that of α 02 .For subcritical ORC, m wf is almost constant, this is mainly because the variations of P 1 and α 02 are just opposite (see Figures 14a and 15a), and their effects on m wf offset each other.As to the refrigerant pump, for both ORCs, the pump head is roughly constant as T cw increases, N RP mainly varies to satisfied the variation of volumetric flow rate, which is consistent with the change in m wf .Thus, the variation of N RP is just similar with that of m wf for both ORCs.As displayed in Figure 15d, for both ORCs, T re generally decreases as T cw drops.This indicates that ORC with lower T cw tends to utilize geothermal energy more fully, which is mainly determined by the lower P 2 .However, the decline rate of T re is uneven because of the lowest T re restriction of 70 • C. For supercritical ORC, when T cw is lower than 25 • C, T re is close to 70 • C, and the decline rate of T re obviously slows down.In this case, the lowest T re restriction is activated, α 02 reduces as T cw declines (see Figure 14a); meanwhile P 1 and T 1 are roughly constant, resulting in the decrease of m wf , so that T re is not lower than 70 • C. As to subcritical ORC, when T cw is lower than 15 • C, the decline rate of T re slows down, and the lowest T re restriction is activated.Thus, P 1 and α 02 become abnormal when T cw reaches 10 • C (see Figures 14a and 15a).For both ORCs, as T cw drops, the turbine power output grows owing to the decrease in P 2 , the power consumed by refrigerant pump is almost constant due to the small changes of m wf and difference between P 1 and P 2 , and the power consumed by cooling water pump changes very little .Thus, P net grows as T cw drops, as shown in Figure 16.On the whole, P net of subcritical ORC is always smaller than that of supercritical ORC, however, the difference between them presents a decrease trend as T cw drops, which is owing to the reduction in m wf of supercritical ORC. Figure 15c illustrates the variation of mwf with Tcw.For supercritical ORC, owing to the slight variations of T1 and P1, the variation of mwf is similar with that of α02.For subcritical ORC, mwf is almost constant, this is mainly because the variations of P1 and α02 are just opposite (see Figures 14a and 15a), and their effects on mwf offset each other.As to the refrigerant pump, for both ORCs, the pump head is roughly constant as Tcw increases, NRP mainly varies to satisfied the variation of volumetric flow rate, which is consistent with the change in mwf.Thus, the variation of NRP is just similar with that of mwf for both ORCs.As displayed in Figure 15d, for both ORCs, Tre generally decreases as Tcw drops.This indicates that ORC with lower Tcw tends to utilize geothermal energy more fully, which is mainly determined by the lower P2.However, the decline rate of Tre is uneven because of the lowest Tre restriction of 70 °C.For supercritical ORC, when Tcw is lower than 25 °C, Tre is close to 70 °C, and the decline rate of Tre obviously slows down.In this case, the lowest Tre restriction is activated, α02 reduces as Tcw declines (see Figure 14a); meanwhile P1 and T1 are roughly constant, resulting in the decrease of mwf, so that Tre is not lower than 70 °C.As to subcritical ORC, when Tcw is lower than 15 °C, the decline rate of Tre slows down, and the lowest Tre restriction is activated.Thus, P1 and α02 become abnormal when Tcw reaches 10 °C (see Figures 14a and 15a).For both ORCs, as Tcw drops, the turbine power output grows owing to the decrease in P2, the power consumed by refrigerant pump is almost constant due to the small changes of mwf and difference between P1 and P2, and the power consumed by cooling water pump changes very little.Thus, Pnet grows as Tcw drops, as shown in Figure 16.On the whole, Pnet of subcritical ORC is always smaller than that of supercritical ORC, however, the difference between them presents a decrease trend as Tcw drops, which is owing to the reduction in mwf of supercritical ORC.

Various Geothermal Water Inlet Temperatures and Cooling Water Inlet Temperatures
In practical operation of geothermal ORC power system, mgw can be actively regulated to some extent, but Tgw influenced by geological condition and Tcw determined by ambient temperature depend on objective conditions.These two variables are independent of each other and can simultaneously change.Thus, the off-design performances of both ORCs are further discussed with various Tgw and Tcw.
Figure 17a shows that the variations of α02 are quite different for subcritical and supercritical ORC.For subcritical ORC, α02 first basically remains constant then drops with Tgw, while for supercritical ORC, α02 first increases then becomes roughly stable with Tgw.As displayed in Figure 17b, NRP gradually grows with Tgw for both ORCs.As Tcw varies, NRP is roughly constant for subcritical ORC, while for supercritical ORC, when Tcw is lower than 20 °C, NRP has a declining trend as Tcw drops.

Various Geothermal Water Inlet Temperatures and Cooling Water Inlet Temperatures
In practical operation of geothermal ORC power system, m gw can be actively regulated to some extent, but T gw influenced by geological condition and T cw determined by ambient temperature depend on objective conditions.These two variables are independent of each other and can simultaneously change.Thus, the off-design performances of both ORCs are further discussed with various T gw and T cw .
Figure 17a shows that the variations of α 02 are quite different for subcritical and supercritical ORC.For subcritical ORC, α 02 first basically remains constant then drops with T gw , while for supercritical ORC, α 02 first increases then becomes roughly stable with T gw .As displayed in Figure 17b, N RP gradually grows with T gw for both ORCs.As T cw varies, N RP is roughly constant for subcritical ORC, while for supercritical ORC, when T cw is lower than 20  Figure 18a,b illustrate that P1 gradually increases and P2 slowly rises with Tgw, while P1 does not change significantly and P2 gradually increases with Tcw, for both ORCs.As shown in Figure 18c, mwf gradually grows with Tgw for both ORCs.As Tcw varies, mwf is roughly constant for subcritical ORC, while for supercritical ORC, the variations of mwf are similar with that of NRP (see Figure 17b).When Tcw is low, the decline trend of mwf ensures that Tre is not lower than 70 °C.Figure 18a,b illustrate that P 1 gradually increases and P 2 slowly rises with T gw , while P 1 does not change significantly and P 2 gradually increases with T cw , for both ORCs.As shown in Figure 18c, m wf gradually grows with T gw for both ORCs.As T cw varies, m wf is roughly constant for subcritical ORC, while for supercritical ORC, the variations of m wf are similar with that of N RP (see Figure 17b).When T cw is low, the decline trend of m wf ensures that T re is not lower than 70 • C.  Figure 18a,b illustrate that P1 gradually increases and P2 slowly rises with Tgw, while P1 does not change significantly and P2 gradually increases with Tcw, for both ORCs.As shown in Figure 18c, mwf gradually grows with Tgw for both ORCs.As Tcw varies, mwf is roughly constant for subcritical ORC, while for supercritical ORC, the variations of mwf are similar with that of NRP (see Figure 17b).When Tcw is low, the decline trend of mwf ensures that Tre is not lower than 70 °C.Figure 18d illustrates that for both ORCS, lower Tgw and Tcw leads to lower Tre, and supercritical ORC is more likely to activate the constraint of Tre.This is mainly due to the varying temperature of the working fluid during the transition from liquid to vapor in the vapor generator, which leads to a better temperature match between working fluid and geothermal water.Notably, for supercritical Figure 18d illustrates that for both ORCS, lower T gw and T cw leads to lower T re , and supercritical ORC is more likely to activate the constraint of T re .This is mainly due to the varying temperature of the working fluid during the transition from liquid to vapor in the vapor generator, which leads to a better temperature match between working fluid and geothermal water.Notably, for supercritical ORC, when T gw comes to 130 • C, abnormal high T re appears, which may be owing to the supercritical condition restriction.As presented in Figure 19, for both ORCs, higher T gw and lower T cw bring about the increase in P net .The P net of supercritical ORC is always greater than that of subcritical ORC.However, for supercritical ORC, the growth rate of P net slows down with the decrease of T cw (below   C), leading to smaller difference of P net between supercritical and subcritical ORCs.This is mainly owing to the reduction of m wf (see Figure 18c), which is caused by the constraint of T re .
ORC, when Tgw comes to 130 °C, abnormal high Tre appears, which may be owing to the supercritical condition restriction.As presented in Figure 19, for both ORCs, higher Tgw and lower Tcw bring about the increase in Pnet.The Pnet of supercritical ORC is always greater than that of subcritical ORC.However, for supercritical ORC, the growth rate of Pnet slows down with the decrease of Tcw (below 20 °C), leading to smaller difference of Pnet between supercritical and subcritical ORCs.This is mainly owing to the reduction of mwf (see Figure 18c), which is caused by the constraint of Tre.

Conclusions
In this study, the parameter designs of subcritical and supercritical ORCs applied in geothermal power systems were firstly conducted under the design conditions.Then the off-design performance prediction model of ORC was established based on specially designed turbine and heat exchangers.Lastly, a specific optimal control strategy was proposed to maximum the net power output, and the off-design performances of subcritical and supercritical ORCs were comprehensively analyzed and compared under the optimal control strategy.The main conclusions of this work can be summarized as follows: For both ORCs, under the optimal control strategy, greater geothermal water mass flow rate, higher geothermal water inlet temperature, lower cooling water inlet temperature bring about larger net power output.As geothermal water mass flow rate grows, the turbine guide vane angle gradually increases, and the refrigerant pump rotational speed slowly increases; the turbine inlet pressure changes very little, and the condensing pressure slowly rises.Owing to the increase in turbine guide vane angle, the working fluid mass flow rate rises to absorb more heat from geothermal water, leading to the growth in net power output.As the geothermal water inlet temperature increases, the turbine guide vane angle is relatively stable while the refrigerant pump rotational speed grows; the turbine inlet pressure gradually increases, the condensing pressure slowly rises, and the working fluid mass flow rate grows.The rise of net power output is mainly owing to the increases of turbine inlet pressure and working fluid mass flow rate.With cooling water inlet temperature drops, the turbine guide vane angle and the refrigerant pump rotational speed change a little; the turbine inlet pressure and the working fluid mass flow rate are roughly constant, while the condensing pressure significantly declines.The increase in net power output is mainly determined by the reduced condensing pressure.
Generally, under off-design operating conditions, the optimal control strategies of subcritical and supercritical ORCs are roughly approximate, and the variations of net power output of them are similar.The net power output of supercritical ORC is always greater than that of subcritical ORC, and the difference between them tends to drop when the supercritical ORC activates the restriction of geothermal water reinjection temperature.It is worth noting that smaller the geothermal water mass flow rate, the lower geothermal water inlet temperature and lower cooling water inlet temperature are inclined to activate the restriction of reinjection temperature, especially for supercritical ORC, which is due to the better temperature match in the vapor generator.When the

Conclusions
In this study, the parameter designs of subcritical and supercritical ORCs applied in geothermal power systems were firstly conducted under the design conditions.Then the off-design performance prediction model of ORC was established based on specially designed turbine and heat exchangers.Lastly, a specific optimal control strategy was proposed to maximum the net power output, and the off-design performances of subcritical and supercritical ORCs were comprehensively analyzed and compared under the optimal control strategy.The main conclusions of this work can be summarized as follows: For both ORCs, under the optimal control strategy, greater geothermal water mass flow rate, higher geothermal water inlet temperature, lower cooling water inlet temperature bring about larger net power output.As geothermal water mass flow rate grows, the turbine guide vane angle gradually increases, and the refrigerant pump rotational speed slowly increases; the turbine inlet pressure changes very little, and the condensing pressure slowly rises.Owing to the increase in turbine guide vane angle, the working fluid mass flow rate rises to absorb more heat from geothermal water, leading to the growth in net power output.As the geothermal water inlet temperature increases, the turbine guide vane angle is relatively stable while the refrigerant pump rotational speed grows; the turbine inlet pressure gradually increases, the condensing pressure slowly rises, and the working fluid mass flow rate grows.The rise of net power output is mainly owing to the increases of turbine inlet pressure and working fluid mass flow rate.With cooling water inlet temperature drops, the turbine guide vane angle and the refrigerant pump rotational speed change a little; the turbine inlet pressure and the working fluid mass flow rate are roughly constant, while the condensing pressure significantly declines.The increase in net power output is mainly determined by the reduced condensing pressure.
Generally, under off-design operating conditions, the optimal control strategies of subcritical and supercritical ORCs are roughly approximate, and the variations of net power output of them are similar.The net power output of supercritical ORC is always greater than that of subcritical ORC, and the difference between them tends to drop when the supercritical ORC activates the restriction of geothermal water reinjection temperature.It is worth noting that smaller the geothermal water mass flow rate, the lower geothermal water inlet temperature and lower cooling water inlet temperature are inclined to activate the restriction of reinjection temperature, especially for supercritical ORC, which is due to the better temperature match in the vapor generator.When the restriction of reinjection temperature is activated, the turbine guide vane angle tends to decrease, resulting in a reduction in the working fluid mass flow rate to ensure that the reinjection temperature is not less than 70 • C, which further leads to a decreasing tendency of the net power output.
The proposed optimal control strategy can provide references and guidelines for the off-design operation regulation of subcritical and supercritical ORC systems.On the basis of this research, the next steps of our work are to establish a comprehensive dynamic model of ORC systems, study the dynamic characteristics under off-design conditions, and put forward a reasonable control logic and specific controller model.

Figure 1 .
Figure 1.The layout of a geothermal ORC system.

Figure 1 .Figure 2 .
Figure 1.The layout of a geothermal ORC system.

Figure 4 .
Figure 4.The schematic of radial inflow turbine.

Figure 4 .
Figure 4.The schematic of radial inflow turbine.

Figure 5 .
Figure 5. Basic configuration of the PHE.Figure 5. Basic configuration of the PHE.

Figure 5 .
Figure 5. Basic configuration of the PHE.Figure 5. Basic configuration of the PHE.

Figure 6 .
Figure 6.Performance curve of the refrigerant pump.

Figure 6 .
Figure 6.Performance curve of the refrigerant pump.

Figure 7 .
Figure 7.The detailed flow chart of off-design performance optimization.

Figure 7 .
Figure 7.The detailed flow chart of off-design performance optimization.

Figure 8 .
Figure 8. Variations of optimal control variables with geothermal water mass flow rate: (a) Turbine guide vane angle; (b) Refrigerant pump rotational speed.

Figure 9 .
Figure 9. Variations of optimal operation parameters with geothermal water mass flow rate: (a) Turbine inlet pressure; (b) Condensation pressure; (c) Working fluid mass flow rate; (d) Geothermal water reinjection temperature.

Figure 8 .Figure 8 .
Figure 8. Variations of optimal control variables with geothermal water mass flow rate: (a) Turbine guide vane angle; (b) Refrigerant pump rotational speed.

Figure 9 .
Figure 9. Variations of optimal operation parameters with geothermal water mass flow rate: (a) Turbine inlet pressure; (b) Condensation pressure; (c) Working fluid mass flow rate; (d) Geothermal water reinjection temperature.

Figure 9 .
Figure 9. Variations of optimal operation parameters with geothermal water mass flow rate: (a) Turbine inlet pressure; (b) Condensation pressure; (c) Working fluid mass flow rate; (d) Geothermal water reinjection temperature.

Figure 10 .
Figure 10.Variation of optimal net power output with geothermal water mass flow rate.

Figure 10 .
Figure 10.Variation of optimal net power output with geothermal water mass flow rate.

Figure 11 .
Figure 11.Variations of optimal control variables with geothermal water inlet temperature: (a) Turbine guide vane angle; (b) Refrigerant pump rotational speed.

Figure 12 .
Figure 12.Variations of optimal operation parameters with geothermal water inlet temperature: (a) Turbine inlet pressure; (b) Condensation pressure; (c) Working fluid mass flow rate; (d) Geothermal water reinjection temperature.

Figure 11 .
Figure 11.Variations of optimal control variables with geothermal water inlet temperature: (a) Turbine guide vane angle; (b) Refrigerant pump rotational speed.

Figure 11 .
Figure 11.Variations of optimal control variables with geothermal water inlet temperature: (a) Turbine guide vane angle; (b) Refrigerant pump rotational speed.

Figure 12 .
Figure 12.Variations of optimal operation parameters with geothermal water inlet temperature: (a) Turbine inlet pressure; (b) Condensation pressure; (c) Working fluid mass flow rate; (d) Geothermal water reinjection temperature.

Figure 12 .
Figure 12.Variations of optimal operation parameters with geothermal water inlet temperature: (a) Turbine inlet pressure; (b) Condensation pressure; (c) Working fluid mass flow rate; (d) Geothermal water reinjection temperature.

Figure 13 .
Figure 13.Variation of optimal net power output with geothermal water inlet temperature.

Figure 13 .
Figure 13.Variation of optimal net power output with geothermal water inlet temperature.

Figure 14 .
Figure 14.Variations of optimal control variables with cooling water inlet temperature: (a) Turbine guide vane angle; (b) Refrigerant pump rotational speed.

Figure 15 .
Figure 15.Variations of optimal operation parameters with cooling water inlet temperature: (a) Turbine inlet pressure; (b) Condensation pressure; (c) Working fluid mass flow rate; (d) Geothermal water reinjection temperature.

Figure 14 .
Figure 14.Variations of optimal control variables with cooling water inlet temperature: (a) Turbine guide vane angle; (b) Refrigerant pump rotational speed.

Figure 14 .
Figure 14.Variations of optimal control variables with cooling water inlet temperature: (a) Turbine guide vane angle; (b) Refrigerant pump rotational speed.

Figure 15 .
Figure 15.Variations of optimal operation parameters with cooling water inlet temperature: (a) Turbine inlet pressure; (b) Condensation pressure; (c) Working fluid mass flow rate; (d) Geothermal water reinjection temperature.

Figure 15 .
Figure 15.Variations of optimal operation parameters with cooling water inlet temperature: (a) Turbine inlet pressure; (b) Condensation pressure; (c) Working fluid mass flow rate; (d) Geothermal water reinjection temperature.

Figure 16 .
Figure 16.Variation of optimal net power output with cooling water inlet temperature.

Figure 16 .
Figure 16.Variation of optimal net power output with cooling water inlet temperature.

Figure 17 .
Figure 17.Variations of optimal control variables with geothermal water and cooling water inlet temperatures: (a) Turbine guide vane angle; (b) Refrigerant pump rotational speed.

Figure 17 .
Figure 17.Variations of optimal control variables with geothermal water and cooling water inlet temperatures: (a) Turbine guide vane angle; (b) Refrigerant pump rotational speed.

Figure 17 .
Figure 17.Variations of optimal control variables with geothermal water and cooling water inlet temperatures: (a) Turbine guide vane angle; (b) Refrigerant pump rotational speed.

Figure 18 .
Figure 18.Variations of optimal operation parameters with geothermal water and cooling water inlet temperatures: (a) Turbine inlet pressure; (b) Condensation pressure; (c) Working fluid mass flow rate; (d) Geothermal water reinjection temperature.

Figure 18 .
Figure 18.Variations of optimal operation parameters with geothermal water and cooling water inlet temperatures: (a) Turbine inlet pressure; (b) Condensation pressure; (c) Working fluid mass flow rate; (d) Geothermal water reinjection temperature.

Figure 19 .
Figure 19.Variation of optimal net power output with geothermal water and cooling water inlet temperatures.

Figure 19 .
Figure 19.Variation of optimal net power output with geothermal water and cooling water inlet temperatures.

Table 1 .
Design operating conditions of the geothermal ORC system.

Table 1 .
Design operating conditions of the geothermal ORC system.

Table 2 .
Optimization results of ORC systems on the design condition.

Table 2 .
Optimization results of ORC systems on the design condition.

Table 4 .
Radial inflow turbines design results.

Table 4 .
Radial inflow turbines design results.

Table 5 .
Heat exchangers design results.
• C, N RP has a declining trend as T cw drops.