System description

As presented in Fig. 1, in the overall system of the molten salt reactor with a combined cycle for power generation, the liquid fuel salt of the first loop enters the core. The fuel salt undergoes nuclear fission reactions and releases fission energy primarily in the form of heat. The fuel salt acts as a coolant and transports the heat out of the core. The heat is then transferred to the coolant salt of the second loop through a dual molten salt heat exchanger located between the two loops. Typically, the coolant salt in the second loop is FLiNaK molten salt. The first loop is isolated for safety purposes utilizing the second loop. This paper introduces a third loop utilizing nitrate salts to achieve safe load following for nuclear plants, where the heat is stored in a high-temperature molten salt tank[17]. When electricity is needed, the high-temperature molten salt is released from the tank, and the heat is transferred to compressed air through a heat exchanger in the fourth loop. The resulting high-temperature, high-pressure gas drives the turbine to generate electricity, converting the thermal energy into electrical energy. Simultaneously, the heat from the high-temperature exhaust gas produced by the gas turbine is recovered by a waste heat boiler, generating steam that enters a steam turbine generator for power generation. The study systematically analyzes the impact of three-loop molten salt regulation on the back-end power generation unit.

Fig. 1Full-screen View

Process of molten salt reactor combined cycle

Compressor

The compressor module comprises characteristics such as temperature rise, flow rate, power consumption, and other modules, which can effectively reflect the operating dynamic characteristics of the compressor. The characteristic module describes the operating state of the compressor through the characteristic curve. The characteristic curve is drawn by an equivalent flow $g_{\text{c}}$, equivalent rotary speed $n_{\text{s}}$, pressure ratio ${\pi }_{\text{c}}$ and efficiency ${\eta }_{\text{iso},\text{c}}$, which is suitable for different inlet temperatures and pressure. The characteristic curve is represented as a two-dimensional table after obtaining a large amount of experimental data from the performance test of the compressor. The equivalent flow rate and compressor efficiency can be obtained on the characteristic curve by determining the compressor's pressure ratio and equivalent rotary speed. The pressure ratio and equivalent rotary speed of the compressor can be determined as follows[18]: ${\pi }_{\text{c}}=\frac{P_{\text{c},\text{out}}}{P_{\text{c},\text{in}}},$ (1) $n_{\text{s}}=\frac{n_{\text{c}}}{\sqrt{T_{\text{c},\text{in}}}},$ (2) where $P_{\text{c},\text{in}}$ and $P_{\text{c},\text{out}}$ are the compressor inlet pressure and outlet pressure, Pa; $n_{\text{c}}$ is the actual speed of the compressor, rpm; $T_{\text{c},\text{in}}$ is the actual inlet temperature of the compressor, K.

As the physical compressor of this paper has not yet been obtained, a coefficient fitting method can be utilized to obtain the compressor characteristic curve suitable for this paper[19]. The flow rate module of the compressor is defined as follows. $g_{\text{c},\text{in}}=\frac{g_{\text{c}}·P_{\text{c},\text{in}}}{\sqrt{T_{\text{c},\text{in}}}},$ (3) where $g_{\text{c},\text{in}}$ is the actual flow of the compressor, kg/s.

A compressor's temperature rise and power consumption module represent its actual work capacity. The definition of the temperature rise module and power consumption module of a compressor are as follows[20]. $T_{\text{c},\text{out}}=T_{\text{c},\text{in}}+T_{\text{c},\text{in}}·\left|{\pi }_{\text{c}}{}^{\frac{k-1}{k}}-1\right|\cdot \frac{1}{{\eta }_{\text{iso},\text{c}}},$ (4) $N_{\text{c}}=g_{\text{c},\text{in}}\cdot C_{\text{p},\text{air}}{T}_{\text{c},\text{in}}\cdot \left|{\pi }_{\text{c}}{}^{\frac{k-1}{k}}-1\right|\cdot \frac{1}{{\eta }_{\text{iso},\text{c}}},$ (5) where $T_{\text{c},\text{out}}$ is the compressor outlet temperature; K; k is the specific heat capacity ratio, k = 1.4; $C_{\text{p},\text{air}}$ is the specific heat capacity of air at constant pressure, J/kg·K.

Molten salt-air heat exchanger

This study focused on the heat transfer process of a molten salt-air heat exchanger, which involved convective heat transfer on both the molten salt and air sides. In ideal conditions, based on the principle of energy conservation, the heat released by the high-temperature molten salt is equal to the heat absorbed by the air. The static heat transfer equation for the molten salt-air system can be described as follows[21]. $q_{\text{air}}\cdot C_{\text{p},\text{air}}\cdot \left(t_{\text{air},\text{out}}-t_{\text{air},\text{in}}\right)=KS\text{Δ}{T}_{\text{m}},$ (6) $q_{\text{xcl}}\cdot C_{\text{p},\text{xcl}}\cdot \left(t_{\text{xcl},\text{in}}-t_{\text{xcl},\text{out}}\right)=KS\text{Δ}{T}_{\text{m}},$ (7) $\text{Δ}{T}_{\text{m}}=\frac{\left(t_{\text{xcl},\text{in}}-t_{\text{xcl},\text{out}}\right)-\left(t_{\text{air},\text{out}}-t_{\text{air},\text{in}}\right)}{\text{ln}\left(\frac{\left(t_{\text{xcl},\text{in}}-t_{\text{xcl},\text{out}}\right)}{\left(t_{\text{air},\text{out}}-t_{\text{air},\text{in}}\right)}\right)},$ (8) where $q_{\text{air}}$ is the air flow rate, kg/s; $q_{\text{xcl}}$ is the molten salt flow rate, kg/s; $t_{\text{air},\text{in}}$ is the air inlet temperature, K; $t_{\text{air},\text{out}}$ is the air outlet temperature, K; $t_{\text{xcl},\text{in}}$ is the molten salt inlet temperature, K; $t_{\text{xcl},\text{out}}$ is the molten salt outlet temperature, K; $C_{\text{p},\text{xcl}}$ is the specific heat capacity of molten salt at constant pressure, J/kg·K; k is the heat transfer coefficient, W/(m²·K); S is the total heat transfer area, m²; $\text{Δ}{T}_{\text{m}}$ is the effective average temperature difference, K.

It is difficult to determine the heat transfer coefficient under variable conditions, hence, the heat transfer coefficient within the error can only be obtained by analyzing the heat transfer principle. Regarding ignoring thermal radiation, heat conduction and convective heat transfer are the main heat transfer in this process. The heat transfer coefficient can be defined as follows. $\frac{1}{K}=\frac{1}{{\alpha }_{\text{o}}}+\frac{1}{{\alpha }_{\text{i}}}\left(\frac{A_{\text{o}}}{A_{\text{i}}}\right)+r_{\text{o}}+r_{\text{i}}\left(\frac{A_{\text{o}}}{A_{\text{i}}}\right)+\frac{\delta A_{\text{o}}}{{\lambda }_{\text{w}}{A}_{\text{m}}},$ (9) where ${\alpha }_{\text{o}}$ is the convective heat transfer coefficient of the fluid outside the tube, W/(m²·K); ${\alpha }_{\text{i}}$ is the convective heat transfer coefficient of the fluid in the tube, W/(m²·K); $r_{\text{o}}$ and $r_{\text{i}}$ are the fluid fouling resistance outside the tube and inside the tube (m²·K)/W; $A_{\text{o}}$ and $A_{\text{i}}$ are the outer surface and inner surface heat transfer area of the heat exchange tube, m²; $A_{\text{m}}$ is the average heat transfer area inside and outside the heat exchanger tube, m²; $\delta$ is the thickness of the heat exchange tube wall, m; ${\lambda }_{\text{w}}$ is the thermal conductivity of the tube wall material, W/(m²·K).

Turbine

Like the compressor module, the turbine module can be described by its characteristic curve to represent its operating characteristics. The turbine module comprises a characteristic module, a temperature drop module, and a power generation module. In the characteristic module, the characteristic curve of the turbine can also be obtained with the coefficient fitting method. The pressure ratio and flow rate of the turbine are determined as follows[22]. ${\pi }_{\text{t}}=\frac{P_{\text{t},\text{in}}}{P_{\text{t},\text{out}}},$ (10) $g_{\text{t},\text{in}}=\frac{g_{\text{t}}\cdot P_{\text{t},\text{in}}}{\sqrt{T_{\text{t},\text{in}}}},$ (11) where ${\pi }_{\text{t}}$ is the pressure ratio of the turbine; $g_{\text{t}}$ is the equivalent flow rate; ${\eta }_{\text{ios},\text{t}}$ is the turbine efficiency; $P_{\text{t},\text{in}}$ is the turbine inlet pressure, Pa; $P_{\text{t},\text{out}}$ is the turbine outlet pressure, Pa; $T_{\text{t},\text{in}}$ is the turbine inlet temperature, K.

The outlet temperature and turbine work can be expressed as follows[23]. $T_{\text{t},\text{out}}=T_{\text{t},\text{in}}-T_{\text{t},\text{in}}\cdot \left|1-{\pi }_{\text{t}}^{\frac{k-1}{k}}\right|\cdot {\eta }_{\text{iso},\text{t}},$ (12) $N_{\text{t}}=g_{\text{t},\text{in}}·C_{\text{p},\text{air}}{T}_{\text{t},\text{in}}·\left|1-{\pi }_{\text{t}}^{\frac{k-1}{k}}\right|·{\eta }_{\text{iso},\text{t}}$ (13) where $T_{\text{t},\text{out}}$ is the turbine outlet temperature, K; $N_{\text{t}}$ is the turbine output power, W.

Rotor

Any set point of the engine is defined by the amount of power demanded by the grid and the frequency at which the power is to be generated. Thus, the power turbine must rotate constantly at 8000 rpm–50 Hz for direct coupling between the engine and generator or at another speed if a gearbox is present. Considering that the compressor and the turbine are coaxial in the system, assuming the same speed, the differential equation of the rotor module given by reference can be defined as[24] $\frac{\text{d}n}{\text{d}t}=\frac{900}{I·{\pi }^2·n}\left(N_{\text{t}}-N_{\text{c}}\right),$ (14) where I is the moment of inertia of the rotor, kg·m²; n is the rotary speed, rpm.

Waste heat boiler

The construction of the waste heat boiler module is like that of the molten salt air heat exchange module. The heat transfer process of the boiler involves the convective heat transfer on the water and air sides. According to the energy conservation equation, it can be concluded that the heat release of air is equal to the heat absorption of the waterside under ideal conditions, which can be expressed as follows[25]. $q_{\text{air}}\cdot \left(h_{\text{air},\text{in}}-h_{\text{air},\text{out}}\right)=q_{\text{w}}\cdot \left(h_{\text{w},\text{out}}-h_{\text{w},\text{in}}\right),$ (15) where $h_{\text{air},\text{in}}$ and $h_{\text{air},\text{out}}$ are the enthalpy of inlet and outlet air of the waste heat boiler, J/kg; $h_{\text{w},\text{in}}$ and $h_{\text{w},\text{out}}$ are the enthalpy of inlet and outlet water of the waste heat boiler, J/kg; $q_{\text{w}}$ is the water flow, kg/s.

Steam turbine

In the combined cycle, the steam turbine has no regulating stage; only the working stage is set, and the working medium is in a subcritical state during the entire working process. The calculation equations of the flow module and the work module of the steam turbine are defined as follows[26]: $\frac{D}{D_0}=\sqrt{\frac{P_1^2-P_2^2}{P_{10}^2-P_{20}^2}}\sqrt{\frac{T_{10}}{T_1}},$ (16) $P_{\text{e}}=D\left(h_1-h_2\right),$ (17) where D is the main steam flow rate of the steam turbine, kg/s; $P_1$ and $P_2$ are the pressure of the inlet and outlet steam of the steam turbine, Pa; $T_1$ is the temperature of the inlet steam of the steam turbine, K; the subscript 0 represents the known standard working condition parameters; $h_1$ and $h_2$ are the enthalpy values of the steam at the inlet and outlet of the steam turbine.

Control logic

The control module is composed of a rotary speed control system, which guarantees stable and safe operation of the system. If the actual speed does not match the reference speed, the control system will output an appropriate signal to adjust the size of the molten salt flow rate and subsequently regulate the entire system. Figure 2 presents the flowchart of the rotary speed control structure. The definition of rotary speed PID control algorithm is as follows[27]: $e_n=n_{\text{r}}-n_{\text{c}},$ (18) $\text{Δ}{U}_{\text{p}}=K_{\text{p}}\left(e_n-e_{n-1}\right),$ (19) $\text{Δ}{U}_{\text{i}}=K_{\text{i}}{e}_n,$ (20) $\text{Δ}{U}_{\text{d}}={\text{K}}_{\text{d}}\left({\text{e}}_{\text{n}}-2{\text{e}}_{\text{n}-1}+2{\text{e}}_{\text{n}-2}\right),$ (21) $\text{Δ}U=\text{Δ}{U}_{\text{p}}+\text{Δ}{U}_{\text{i}}+\text{Δ}{U}_{\text{d}},$ (22) where $n_{\text{r}}$ is the current cycle speed reference, rpm; $e_n$ is the deviation between the current cycle target speed and the actual speed, rpm; $e_{n-1}$ is the deviation between the target speed and the actual speed in the previous cycle, rpm; $e_{n-2}$ is the deviation between the target speed and the actual speed of the previous two cycles, rpm; $K_{\text{p}}$ is the proportional coefficient; $K_{\text{i}}$ is the coefficient of the integral term; $K_{\text{d}}$ is the differential coefficient; $\text{Δ}{U}_{\text{p}}$ is the proportional feedback; $\text{Δ}{U}_{\text{i}}$ is the integral feedback; $\text{Δ}{U}_{\text{d}}$ is the differential feedback; $\text{Δ}U$ is the amount of feedback.

Fig. 2Full-screen View

Flowchart of rotary speed control structure

Establishment of numerical model

Matlab-Simulink is a modeling platform supporting linear, nonlinear, continuous, and discrete-time systems, which can realize modeling, simulation, and analysis of dynamic systems[28]. Simulink can represent models in the form of block diagrams and can add existing models to a composite or user-developed module to a model. Simulink allows modification of the module parameters, and Matlab analyzes the simulation results scientifically. The molten salt reactor combined cycle system model can be obtained by connecting each module on the Simulink. As presented in Fig. 3, the system comprises the compressor, molten salt tank, heat exchanger, turbine, rotor, waste heat boiler, and steam turbine.

Fig. 3Full-screen View

Model of molten salt reactor combined cycle system

As illustrated in Fig. 4, the output parameters of the compressor can be obtained by compressor inlet temperature $T_{\text{c},\text{in}}$, inlet pressure $P_{\text{c},\text{in}}$, actual speed $n_{\text{c}}$ and outlet pressure $P_{\text{c},\text{out}}$. The output parameters of the compressor are pressure ratio ${\pi }_{\text{c}}$, actual flow $g_{\text{c},\text{in}}$, outlet temperature $T_{\text{c},\text{out}}$, compressor efficiency ${\eta }_{\text{iso},\text{c}}$ and power consumption $N_{\text{c}}$. The molten salt flow rate $g_{\text{xcl}}$, molten salt inlet temperature $t_{\text{xcl},\text{in}}$, molten salt outlet temperature $t_{\text{xcl},\text{out}}$ and compressor output parameters of the molten salt reactor are input into the molten salt air heat exchanger to obtain the flow rate of the turbine $g_{\text{t},\text{in}}$, air temperature $t_{\text{air},\text{out}}$, pressure $P_{\text{t},\text{in}}$ and $P_{\text{t},\text{out}}$ after heat transfer. The high-temperature air parameters are input into the turbine to obtain the turbine outlet exhaust temperature $T_{\text{t},\text{out}}$, turbine flow rate $g_{\text{t},\text{out}}$ and turbine power $N_{\text{t}}$. The enthalpy $h_{\text{w},\text{out}}$ and flow rate of outlet water vapor $g_{\text{w}}$ can be obtained by inputting the turbine outlet exhaust parameters into the waste heat boiler. The parameters of the outlet steam are input into the steam turbine to obtain the power of the steam turbine $N_{\text{s}}$. The $n_{\text{c}}$ can be adjusted to realize the dynamic balance of the system by $N_{\text{c}}$, $N_{\text{t}}$ and $N_{\text{s}}$.

Fig. 4Full-screen View

Process of parameter calculation

Verification of numerical model

The accuracy of the molten salt reactor combined cycle system model established here was ensured by validating the system simulation results. Comparing the performance of the simulated and actual systems is an appropriate method for verifying the simulation’s accuracy. Here, the reliability of the simulated system was validated with the parameters of the S109FA combined cycle[10]. Table 1 presents the basic parameters of the S109FA combined cycle. Table 2 presents a comparison of the design value, calculation value, and simulation value of the S109FA combined cycle.

Table 2 presents the discrepancies between the simulated and the design values, and the calculated values of the S109FA combined cycle. The main reason for the error is the pressure loss caused by the flow of the working medium in the pipeline during the establishment of the numerical model. The dynamic simulation model of the combined cycle system established within a reasonable error has high accuracy and effectiveness.

Influence of high-temperature molten salt tank outlet temperature

This paper presents a simulation of a disturbance in the outlet temperature of a molten salt tank, potentially caused by poor circulation. Figure 5 presents the introduction of various perturbations to the temperature at the outlet of the high-temperature molten salt tank at 200 s after reaching steady-state conditions. At this point, the temperature commenced a simultaneous descent of 5 K and 10 K, with rates of –0.2 K/s and –0.4 K/s, respectively, from its initial value of 973 K. The temperature also exhibited concurrent increments of 5 K and 10 K, with corresponding rates of increase of 0.2 K/s and 0.4 K/s. These variations persisted for 25 s.

Fig. 5Full-screen View

(Color online) Variations in outlet temperature of high-temperature molten salt tank

The decrease in the outlet temperature of the molten salt from the high-temperature molten salt tank results in a reduction in the temperature of the molten salt entering the heat exchanger, thereby reducing the heat transfer between the molten salt and air. As presented in Fig. 6(a), this leads to a decrease in the inlet temperature of the turbine, resulting in a decrease in its rotational speed. As presented in Fig. 6(b), when the control component detects a rotational speed below the reference value, the speed controller outputs a signal to increase the flow rate of the molten salt. However, an increase in the outlet temperature of the molten salt from the high-temperature molten salt tank results in a rise in the temperature of the molten salt entering the heat exchanger, thereby increasing the heat transfer between the molten salt and air. This leads to an increase in the inlet temperature of the turbine, increasing its rotational speed. When the control component detects a rotational speed above the reference value, the speed controller outputs a signal to decrease the flow rate of the molten salt. With the help of the control system, the system ultimately returns to a stable state.

Fig. 6Full-screen View

Variations in rotary speed and molten salt flow rate with changing outlet temperature

Figure 7 presents the power changes of the controlled and uncontrolled systems when the molten salt outlet temperature decreases by 5 K and 10 K, respectively. In Fig. 7(a), the controlled system's output power deviation from its rated value is lower than 1.28% and 2.52%, respectively, under the regulation of the control system. In contrast, the uncontrolled system's output power deviation from its rated value is above 1.80% and 3.62%, respectively. Figure 7(b) demonstrates that the control system compensates for decreased molten salt outlet temperature, ensuring the frequency deviation from its rated value is lower than 0.09%. In contrast, uncontrolled power systems cannot maintain shaft stability owing to a lack of regulation, resulting in frequencies falling below the lower limit of the grid frequency.

Fig. 7Full-screen View

(Color online) Effects of decreasing high-temperature molten salt tank outlet temperature by 5 K and 10 K on net output power and grid frequency variation. (a) Comparison of net output power; (b) Comparison of grid frequency

Figure 8 demonstrates the power changes of the controlled and uncontrolled systems when the molten salt outlet temperature increases by 5 K and 10 K, respectively. In Fig. 8(a), under the control system's regulation, the output power deviation from its rated value is lower than 1.19% and 2.43%, respectively. However, the uncontrolled system's output power deviation from its rated value is higher than 1.79% and 3.55%, respectively. Figure 8(b) indicates that the control system can compensate for the molten salt outlet temperature increase, ensuring that the frequency deviation from its rated value is lower than 0.08%. Conversely, the uncontrolled system's frequency deviation exceeds the grid frequency upper limit.

Fig. 8Full-screen View

(Color online) Effects of increasing high-temperature molten salt tank outlet temperature by 5 K and 10 K on net output power and grid frequency variation. (a) Comparison of net output power; (b) Comparison of grid frequency

Influence of high-temperature molten salt tank outlet flow rate

Here, we simulated the molten salt outlet flow disturbance scenario, which the molten salt level fluctuation inside the tank may cause. Figure 9 presents the introduction of various perturbations to the flow rate at the outlet of the high-temperature molten salt tank at 200 s after reaching steady-state conditions. At this point, the flow rate commenced a simultaneous descent of 5% and 10%, with rates of –1%/s and –2%/s, respectively, from its initial value of 43.69 kg/s. The flow rate also exhibited concurrent increments of 5% and 10%, with corresponding rates of increase of 1%/s and 2%/s. These variations persisted for 5 s.

Fig. 9Full-screen View

(Color online) Variations in outlet flow rate of high-temperature molten salt tank

A reduction in the molten salt flow rate at the outlet of the high-temperature salt tank will decrease the molten salt's flow rate entering the heat exchanger. As illustrated in Fig. 10(a), with a decrease in heat transfer between the molten salt and air, the inlet temperature of the turbine decreases, resulting in a reduction of its rotational speed. As illustrated in Fig. 10(b), the control component monitored the speed, and when it fell below the reference value, the speed controller output a signal to increase the molten salt flow rate. Conversely, when the speed exceeds the reference value, the speed controller outputs a signal to decrease the molten salt flow rate. Through the adjustment of the control system, the turbine eventually returned to a stable state.

Fig. 10Full-screen View

(Color online) Variations in rotary speed and molten salt flow rate with changing outlet flow rate. (a) Rotary speed; (b) Flow rate of molten salt

Figure 11 presents the power changes of the controlled and uncontrolled systems with 5% and 10% reductions in molten salt outlet flow rates. Figure 11(a) illustrates that the controlled system maintained an output power deviation from its rated value of less than 4.06% and 8.2%, respectively, under the adjustment of the control system. In contrast, the uncontrolled system had an output power deviation above 4.82% and 9.80%, respectively. As presented in Fig. 11(b), the control system compensated for the decrease in the molten salt outlet flow rate, resulting in the frequency deviation from its rated value of less than 0.25%. However, the frequency of the uncontrolled system deviated from its rated value and ultimately exceeded the lower limit of the grid frequency.

Fig. 11Full-screen View

(Color online) Effects of decreasing high-temperature molten salt tank outlet flow rate by 5% and 10% on net output power and grid frequency variation. (a) Comparison of net output power; (b) Comparison of grid frequency

Figure 12 presents the power changes of the controlled and uncontrolled systems with 5% and 10% increases in molten salt outlet flow rate. Figure 12(a) illustrates that the controlled system maintained an output power deviation from its rated value of less than 3.82% and 7.56%, respectively, under the adjustment of the control system. In contrast, the uncontrolled system had an output power deviation above 4.68% and 9.20%, respectively. As illustrated in Fig. 12(b), the control system compensated for the increase in the molten salt outlet flow rate, resulting in the frequency deviation from its rated value of less than 0.22%. However, the frequency of the uncontrolled system deviated from its rated value and ultimately exceeded the upper limit of the grid frequency.

Fig. 12Full-screen View

(Color online) Effects of increasing high-temperature molten salt tank outlet flow rate by 5% and 10% on net output power and grid frequency variation. (a) Comparison of net output power; (b) Comparison of grid frequency

The simulation results of the power system indicate that the fluctuation of the high-temperature molten salt tank outlet parameters significantly impacts the system's operating parameters. First, introducing a control system can minimize the impact of different disturbances and maintain its output frequency in line with the grid. Second, under the control system's influence, the output power and frequency change gradually reduced and stabilized at the initial values. In contrast, the uncontrolled system had larger output power and frequency deviations, eventually deviating from the initial values.