Operation Control and Performance Analysis of an Ocean Thermal Energy Conversion System Based on the Organic Rankine Cycle

Abstract

The development and utilization of marine renewable energy is an important measure for achieving energy conservation, emissions reduction and carbon neutrality. Ocean thermal energy is the most stable energy among all the types of marine renewable energy. This paper built a simulation model of an ocean thermal energy conversion system based on actual device specifications by Aspen and MATLAB and put forward a corresponding control strategy. The opening control signal of the control valve at the turbine inlet was the condenser inlet pressure in this paper, and the frequency control of the working fluid pump depended on the evaporating pressure and flow rate of the working fluid. This paper analyzed the key operating parameter changes of the system under different working conditions. According to the analysis results, the turbogenerator in this system was able to generate 50 kW power for about 8 months per year. The highest net output power of the Organic Rankine Cycle was 47.3 kW; the highest cycle thermal efficiency was 3.2%.

1. Introduction

Energy conservation and emissions reduction are important measures for alleviating the energy and environmental crisis. Marine renewable energy is a clean form of energy with zero emissions. In practical applications, marine renewable energy power stations can provide reliable power for remote islands and deep-sea farming bases. A 5 MW power station can meet the electricity demands of a small, developing island state [1]. Due to the small temperature differences (only 0.4 °C [2]) in the surface seawater between day and night, ocean thermal energy is the most stable of all the types of marine renewable energy. In addition to power generation, ocean thermoelectric power stations can also be used for freshwater preparation, deep sea aquaculture and the refrigeration and extraction of deep-sea minerals, etc. [1]. Therefore, ocean thermal energy is considered to be an energy source with development potential.

So far, the research on ocean thermal energy conversion (OTEC) technology has mainly focused on different OTEC cycles [3,4], high-efficiency compact heat exchangers [5,6], turboexpanders [7,8], working fluids [9], economic analyses [10,11] and off-design performance research [12].

In terms of the different OTEC cycles, the thermal efficiency of the Guohai cycle is currently the highest, at about 5.1%, and the lowest is the Rankine cycle, at only 3.1% [13]. Other cycles include the Karina cycle [14,15] and the Uehara cycle [16,17,18], whose efficiencies are between those of the Guohai cycle and the Rankine cycle. In addition, some scholars [19,20,21] have used solar energy to increase the surface seawater temperature of OTEC power stations, thereby improving the circulation efficiency of the OTEC system. Some scholars [22,23] have also used geothermal energy as a high-temperature warm source (not surface seawater) and deep seawater to establish circulation systems. While improving the cycle efficiency, this power station can also obtain deep seawater.

Compared with all kinds of high-efficiency circulation systems, the Organic Rankine Cycle (ORC) is the only OTEC cycle that has been implemented in demonstration projects due to its simple structure and high reliability. In 1881, the French scientist Arsonval first proved the feasibility of ocean thermal energy conversion technology. His student Georges then built the first OTEC factory in 1930. In the application of OTEC technology, the technologies of the United States and Japan are relatively advanced. The first floating closed-power station was the mini-OTEC, established by the United States in Hawaii in 1979 [24]. This power station can generate 53 kW gross power and 18 kW net power. Japan built an ocean thermal power station with a gross power of 120 kW and a net power of 31.5 kW in Naura in 1982 [24].

In 2013, Japan built a 50 kW OTEC power station based on the ORC structure in Okinawa using R134a as a working fluid. The surface seawater temperature was 27 °C, and the deep seawater temperature was only 8.8 °C [25]. In 2014, the United States built a 100-kW demonstration power station in Hawaii and this power station was successfully connected to the grid in August 2015 [26]. In 2013, the French built an experimental prototype of an OTEC power station on Reunion Island. This prototype has entered the testing stage and can generate 15 kW equivalent power [27].

This paper built a simulation model based on actual device specifications by Aspen and MATLAB and simulated the operational performance of the equipment under the full conditions of ocean thermal energy. The target was to obtain the maximum output power of the turbine. This paper linked the control of the thermophysical parameters of the working fluid with the controllable parameters of the actual components (the frequency of pumping and the opening of the control valve).

2. Methods

2.1. Simulation Model

This paper established a 50-kW power generation system based on the Organic Rankine Cycle system. R134a was used as the circulating working fluid for this system.

Figure 1 is the flow chart of an ocean thermal energy conversion system based on the Organic Rankine Cycle. The four major components of the organic Rankine cycle are the evaporator, condenser, turbine and working fluid pump. The key characteristic parameters of the four main components are listed in

Table 1. The key characteristic parameters of the OTEC system.

Component	Type	Parameter	Value
Evaporator	Flooded	Working fluid location	Shell side
		Heat exchange area	301 m2
		Tube Type	Wieland 1575 fpm
		Tube Material	Al-Brass
Condenser	Shell and Tube	Working fluid location	Shell side
		Heat exchange area	301 m2
		Tube type	Wieland 1575 fpm
		Tube Material	Al-Brass
Pump	Canned Motor	Rated flow rate	24.2 m3/h
		Rated head	31.8 m
Turbine	Centripetal	Rated speed	12,500 rpm
		Rated power	50 kW

. In addition, in engineering practice, pipes and pipe fittings are also an important component that cannot be ignored.

Table 2. Detailed information for the pipe system.

Tube Location	Nominal Diameter	Pipe Rise	Pipe Length	Miscellaneous L/D
At turbine inlet	DN150	2 m	5.111 m	160
At condenser inlet	DN200	−0.564 m	6.075 m	140
At pump inlet	DN125	−1.9 m	2.47 m	95
At evaporator inlet	DN100	0	6.5 m	135

lists the key characteristic parameters of the pipe system.

The control valve in the turbine inlet was used to control the pressure at the condenser inlet; we called this the pressure control valve. The control valve in the evaporator inlet was used to control the liquid level height in the shell side of the flooded evaporator; we called this the liquid level control valve.

Figure 2 is the simulation model. The valve marked SHUTOFF in Figure 2 was a pneumatic butterfly valve used for quick shut-off for when the turbine required an emergency shutdown.

In order to improve the efficiency of the circulation system, the energy conversion efficiency of the turboexpander is often required to be relatively high. Centripetal turboexpanders are commonly used in ocean thermal energy conversion systems, and the isentropic efficiency can often reach about 85% or even higher [7]. We wrote the centripetal turbine function script in MATLAB and embedded it in Aspen Plus. The basic method was to use the User2 module to link the Excel template with Aspen Plus, and then, Excel could call the MATLAB program [28]. For the MATLAB program written for the centripetal turbine, we solved the mass conservation equations for the nozzle, impeller and diffuser separately through the fsolve function of MATLAB. The corresponding equations are listed in Appendix A, which are cited from ref. [29]. In addition, the thermophysical parameters of working fluid were queried by calling NIST REFPROP in the MATLAB program [30].

2.2. Control Strategies and Components

Considering that the rectifier inverter system had overpower protection settings in the actual equipment, the maximum output power was limited to 50 kW in this study. When the system was able to generate 50 kW output power, under high surface seawater temperature conditions, control of the system required a constant power (50 kW) output from the turbogenerator. When the system was unable to generate 50 kW of power, under low surface seawater temperature conditions, control of the system required the maximum output power of the turbogenerator. The control strategy of the system consisted mainly of two aspects:

On the one hand, the opening control signal of the pressure control valve at the turbine inlet was the condenser inlet pressure in this paper. The reasons for this control strategy were as follows:

• There was no pipe fitting for adjustments in the pipe between the turbine outlet and the condenser inlet. The pipe structure and length were fixed. When the state parameters of the working fluid at one end of the pipeline and the flow parameters in the pipeline were determined, the state parameters of the working fluid at the other end are were determined. This is equivalent to indirectly controlling the turbine outlet pressure when the pressure control valve controls the condenser inlet pressure.
• The adjustment of the pressure control valve also affected the working fluid state parameters at the turbine inlet. This meant that the pressure control valve actively affected the state parameters of the three positions (turbine inlet and outlet and condenser inlet) at the same time.
• When the structure of a condenser was fixed, the heat exchange capacity of the condenser had an upper limit. If the condensing temperature was too low, meaning that the difference was small between the condensing temperature and the deep seawater temperature, the required deep seawater flow rate was too large when the heat exchange area was fixed. If the flow rate of the deep seawater was too large, the requirements for the deep seawater pump and deep seawater pipeline would be high, including structural size parameters, performance parameters and construction costs.

On the one hand, the frequency control of the working fluid pump is determined by the evaporating pressure and the flow rate of the working fluid. When the working fluid pump operates at a variable frequency, the ratio of the power consumption is equal to the cube of the ratio of the frequency. This method can also achieve the purpose of energy saving and improving the net output power.

For system control, the characteristics of the control valve and the variable frequency pump are particularly important. Figure 3 shows the characteristic curve of the ball valve and globe valve.

Table 3. Detailed information for the control valve.

Nominal Diameter	Type	${\mathit{K}}_{\mathit{V}100}$	Installation Location
DN150	Ball	940	At the turbine inlet
DN80	Globe	100	At the evaporator inlet

shows detailed information on the control valve.

$K_V$ is the flow coefficient of the control valve, which is an index for measuring the flow capacity of the control valve. The $K_{V100}$ is the rated $K_V$ at a valve opening of 100%. A large flow coefficient value indicates that the flow capacity of the valve is large, and that the pressure loss of fluid flowing through the valve is small. The rated $K_V$ is the flow coefficient at 100% opening of the control valve. The valve has different flow coefficients at different openings. The relationship between the flow coefficient and the opening is the valve characteristic curve that is obtained by the manufacturer’s experimental test and provided to the user, as shown in Figure 3.

A ball valve was used as the pressure control valve in the turbine inlet here due to its higher-rated $K_V$. This high $K_V$ value of the valve indicates a lower resistance.

The rated $K_V$ of the butterfly valve was 1150. A globe valve was used as the liquid level control valve in the evaporator inlet. The liquid level control valve is used to control the liquid level height in a flooded evaporator. In this paper, the opening of the liquid level control valve was set to 80% in all working conditions. The liquid level control valve was only used for local fine-tuning of the evaporator liquid level when needed—for example, when the evaporating temperature and condensing temperature were artificially changed and the components’ operating parameters changed drastically. When the ORC runs stably under a certain working condition, the opening of liquid level control valve is considered to remain unchanged.

Figure 4 shows the characteristic curves of the working fluid pump including the head, efficiency and net positive suction head required (NPSHr) characteristic curves. The characteristic curve of the pump was experimentally measured by the pump manufacturer Hermetic and provided to the user. The data that could be actually measured in the experiment included the power, volume flow rate, pressure of the working fluid at the inlet and outlet of the pump and the temperature of the working fluid. The density of working fluid was obtained by querying the thermophysical property database based on temperature and pressure. Then, according to the following formula, we were able to get the head and efficiency characteristic curve of the working fluid pump at different volume flow rates, as shown in Figure 4. According to the measured characteristic curve, we can know that head decreased with increases in volume flow rate, but the shaft power increased. Thus, there would be a peak in the efficiency calculated from the measured data. In engineering, we determine the peak point of efficiency as the best operating conditions point and we preferably make the pump work in the high-efficiency zone of the pump’s operation—that is, at more than 92% of its highest possible efficiency. When the volume flow rate reached 27 m³/h, the pump efficiency reached its maximum value (59.76%). The volume flow rate range of the high-efficiency zone was 18.35–37.85 m³/h and the mass flow rate was about 6.5–13.3 kg/s.

$$H=\frac{1000\ast \mathsf{\Delta }P}{\rho g}$$

(1)

$$N_{eff}=\frac{\rho gHQ}{3600\ast 1000}=\frac{Q\mathsf{\Delta }P}{3600}$$

(2)

$$\eta =\frac{N_{eff}}{N_{shaft}}=\frac{Q\mathsf{\Delta }P}{3600\ast N_{shaft}}$$

(3)

where, $\mathsf{\Delta }P$ is the pressure difference, kPa; $\rho$ is the density, kg/m³; $g$ = 9.8 m/s²; $Q$ is the volume flow rate, m³/h; $N_{eff}$ is the effective power, kW; $N_{shaft}$ is the shaft power, kW; and NPSHr is an inherent characteristic of the pump, which represents the anti-cavitation performance of the pump. This means that the working fluid pump has good anti-cavitation impact performance when the value of NPSHr is small.

There is another parameter involved, the available net positive suction head (NPSHa), in the system analysis and calculations. The NPSHa is calculated from the liquid properties and the installation position of the working fluid pump compared to the condenser. In order to prevent the working fluid pump from being impacted by cavitation, it is necessary that NPSHa > NPSHr.

The value of the NPSHa can be increased by installing the pump below the condenser or increasing the subcooling degree of the working fluid at the condenser outlet. However, this will increase the heat exchange area and the cost of condenser when increasing the subcooling degree at the condenser outlet. So, we installed the pump 1.9 m below the condenser to reduce the need for subcooling of the working fluid at the outlet of the condenser.

2.3. Simulation Condition Settings

This paper mainly assumed that the difference between the surface seawater temperature and the evaporating temperature was 4 °C, and that the difference between the deep seawater temperature and the condensing temperature was also 4 °C. When the surface seawater temperature was 25 °C, 26 °C, 27 °C, 28 °C, 29 °C and 30 °C, the evaporating temperature corresponded to 21 °C, 22 °C, 23 °C, 24 °C, 25 °C and 26 °C.

The saturation pressure at 8 °C of R134a was 387.61 kPa. The pressure loss on the shell side of condenser was about 3–5 kPa. Therefore, we set the condenser inlet pressure as 391 kPa in this paper by controlling the opening of the pressure control valve in the turbine inlet.

The evaporator used in this paper was a flooded evaporator and the working fluid was a saturated vapor phase at the evaporator outlet.

3. Results

Figure 5 shows the changes in the system output power and the mass flow rate of the working fluid with evaporating temperature. The turbine output power remained constant at 50 kW when the evaporating temperature was higher than 22.8 °C. The specific enthalpy difference of the working fluid increased as the evaporating temperature increased when the condensing temperature remained unchanged. The output power of the turbine is the product of specific enthalpy difference and mass flow rate of working fluid. So, the mass flow rate of working fluid decreased with increases in the evaporating temperature when the evaporating temperature was higher than 22.8 °C. When the evaporating temperature was lower than 22.8 °C, the turbine output power and working fluid flow rate decreased with decreases in the evaporating temperature. The specific enthalpy of the working fluid flowing from the evaporator outlet to the turbine inlet remained unchanged and the pressure decreased. The superheat degree of the working fluid increased as the pressure decreased. From Figure 6, we know that the opening of the control valve at the turbine inlet was relatively large when the evaporating temperature was lower than 22.7 °C, leading to the pressure drop from the evaporator outlet to the turbine inlet being relatively small. So, the superheat degree of the working fluid at the turbine inlet was relatively small. When the evaporating temperature was lower than 22.8 °C and the flow rate of the working fluid was higher than the value shown in Figure 5, the working fluid would liquefy in the turbine. This would cause the turbine to be damaged by a liquid hammer. In order to protect the turbine, we could only reduce the turbine output power and the flow rate of the working fluid when the evaporating temperature was lower than 22.8 °C. So, there was an inflection point in the working fluid flow rate at 22.8 °C.

Figure 6 shows the changes in the turbine speed and the opening of the pressure control valve in the turbine inlet with the evaporating temperature. Combining Figure 5 and Figure 6, we can see that when the evaporating temperature was higher than 22.8 °C, the flow rate of the working fluid changed little, and the opening of the pressure control valve in the turbine inlet changed greatly. This means that the stability of the turbine output power was mainly stabilized by the pressure control valve at the turbine inlet in this stage. When the evaporating temperature was lower than 22.8 °C, the output power of the turbine mainly depended on by the flow rate of the working fluid. Changes in the opening of the pressure control valve in the turbine inlet were relatively small.

In the ORC, the evaporating temperature and condensing temperature are artificially set parameters, and the working fluid flow rate is obtained according to the demands of turbine output power. The states of the working fluid are the saturated vapor state at the evaporator outlet and the saturated liquid state at the condenser outlet; that is, the pressure difference between the inlet and the outlet of the working fluid pump is known. At this time, the operating point of the working fluid pump and the frequency corresponding to this point can be determined based on the working fluid pump characteristic curve according to the flow rate and the pressure difference. Thus, the state parameters of the working fluid are known at each point of the entire ORC. That is, the heat duty that the working fluid needs to exchange with the seawater in heat exchanger is also known. The surface seawater and deep seawater flow rate are calculated by Aspen according to the energy balance.

From Figure 7, we can see that the temperature change of the surface seawater and deep seawater in the heat exchanger was basically stable under the various working conditions. When the evaporating temperature was higher than 22.8 °C, the heat duty increased slightly and the flow rate of the surface seawater decreased significantly. When the evaporating temperature was lower than 22.8 °C, the heat duty and flow rate of the surface seawater and deep seawater both increased with increases in the output power of the turbine.

In this study, the evaporating pressure was controlled by the variable frequency operation of the pump. At the same time, the frequency operation can also reduce the power consumption of the pump and improve the net output power of the system. Figure 8a shows the power consumption and operating frequency of the working fluid pump under various operating conditions. After simulation analysis, the pressure at the pump inlet was between 412.67 kPa and 412.98 kPa. The evaporating pressure increased as the evaporating temperature increased. Therefore, the pressure difference between the inlet and outlet of the working fluid pump also increased with increases in the evaporating temperature. The required head provided by the working fluid pump was increased. The head was proportional to the square of the frequency in the variable frequency operation of the pump. Therefore, the operating frequency of the working fluid pump also increased as the evaporating temperature increased. During variable frequency operation, the power of the pump is proportional to the cube of the frequency. So, the power of pump also increased when the operating frequency increased. According to Figure 8b, the installation height of 1.9 m was enough to meet the requirement of NPSHa > NPSHr.

Figure 9 shows the output power and thermal efficiency of the circulation system under various working conditions. When the evaporating temperature was not lower than 22.8 °C, the turbine constantly output 50 kW of power. However, the power consumption of the working fluid pump continued to increase (in Figure 8) with increases in the evaporating temperature at this stage. Therefore, the net output power and thermal efficiency of the circulation system decreased with increases in the evaporating temperature at the 50 kW constant power output stage. According to the analysis results, the net output power and thermal efficiency of the circulation system both increased with increases in the evaporating temperature when the evaporating temperature was lower than 22.8 °C. The highest net output power was 47.3 kW and the highest cycle thermal efficiency was 3.2% when the evaporating temperature was 22.8 °C.

Figure 10 shows the surface seawater temperature data in the South China Sea from 2012 to 2016 [31,32,33,34,35]. We can see that the OTEC system was able to generate 50 kW for about 8 months per year.

4. Conclusions

This paper built a simulation model of a 50 kW output power ocean thermal energy conversion system based on the Organic Rankine Cycle by Aspen Plus and MATLAB, and put forward a corresponding control strategy based on the limitations of the actual equipment, such as the overpower protection settings of the rectifier inverter system. After the simulation analysis, the following conclusions were obtained:

(1) When the evaporating temperature was not lower than 22.8 °C (the surface seawater temperature was not lower than 26.8 °C), the ORC system was able to output 50 kW of power stably. The maximum net power was 47.3 kW when the evaporating temperature was 22.8 °C; the maximum circulation thermal efficiency was 3.2% at this time. The OTEC system was able to generate 50 kW for about 8 months per year.

(2) The rated $K_V$ value ($K_{V100}$) of the pressure control valve at the turbine inlet was 940 in this system. However, the maximum opening reached 95% when the evaporating temperature was 22.7 °C. The opening of the valve decreased with increases in the evaporating temperature when the evaporating temperature was above 22.8 °C, to ensure the maximum constant output power of the turbine and the stability of the pressure at the turbine outlet.

(3) In regular design, the turbine inlet control valve is used to control the turbine speed. In actual operations, the valve meets the operational requirements when the turbine speed is stabilized in the range of 105% of the rated speed. Furthermore, if the turbine outlet pressure is too low, the temperature difference between the condensing temperature and the deep seawater temperature will be small, which results in the required condenser heat exchange area being larger than the actual area; this is not conducive to the safe and stable operation of the condenser. According to the analysis results, the control strategy of controlling the pressure in the condenser inlet had a great effect on stabilizing the rotational speed of the turbine in the constant power output stage. Therefore, we think that the pressure in the condenser inlet is more suitable as the control parameter of the control valve in the turbine inlet than turbine speed. This control method can not only stabilize the speed to a certain extent, but can also ensure the effective operation of the condenser.