A Reduced-Order Model of a Nuclear Power Plant with Thermal Power Dispatch
Abstract
:1. Introduction
2. Modeling and Integration
2.1. Primary Coolant System
2.2. Steam Generator
2.3. Secondary Coolant System
2.3.1. Thermodynamic State Calculation
- At steady state, steam exiting the steam generator is saturated. The same assumption was made earlier with the steam generator model, i.e., and . Considering a standard operating condition, steam pressure is known for a given reactor power level.
- Changing the TPD extraction level will result in fluctuation of steam pressure at the SG outlet. To maintain the main steam at the given pressure setpoint, the feedwater control system regulates the feedwater supply to the steam generator. Therefore, the feedwater flow rate is an unknown variable that should be calculated at the given TPD extraction level.
- Pressure drop of steam across the valves is negligible. The pressure drops across the moisture separator, reheater, FWHs, feedwater lines, and deaerator are negligible.
- The heat addition in the SG, reheater, and FWHs and the heat rejection in the condenser are adiabatic processes. The pressure values at the inlets and outlets of these equipment are equal.
- Assuming the valve positions for turbine extraction and reheater lines are changed together for different TPD extraction levels, the relative flow resistances of the turbine and feedwater lines also remain the same. Thus, the ratios of flows through different lines and the ratios of pressure drops do not change. The pressure of the steam extracted from a turbine is proportional to the turbine inlet pressure.
- The LP and HP pumps are controlled to maintain their pressure output in a constant ratio with .
2.3.2. Absolute Mass Flow
2.3.3. Turbine Power Output
2.3.4. Thermal Power Dispatch
2.4. Coupled Industrial Process
2.5. Model Initialization
2.6. Model Integration and Simulation
3. Results
3.1. Secondary System Validation
3.2. Thermal Power Dispatch System Validation
3.3. Integrated Model Results
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Average neutron flux, per unit (pu) | |
Delayed neutron fraction (0.007) | |
Prompt neutron lifetime (2 × 10−5 s) | |
C | Delayed neutron precursor concentration (pu) |
Decay constant (0.1 s−1) | |
Net core reactivity and external reactivity due to the control rod | |
Fuel and moderator temperature coefficients of reactivity (−2.16 × 10−5, −1.8 × 10−4/°C) | |
Average temperature of SG metal lump and secondary coolant lump in SG region (°C) | |
Reactor rated power and instantaneous thermal power (Wt) | |
Fraction of thermal power in the fuel (0.97) | |
Mass of primary coolant in the core and SG region (kg) | |
Mass of fuel lump and SG metal lump (kg) | |
Mass of primary coolant in hot and cold leg plenums (kg) | |
Mass of saturated liquid and saturated vapor in SG region (kg) | |
Heat transfer coefficients for fuel to primary coolant, primary coolant to SG metal lump, and SG metal lump to secondary coolant, °C) | |
Effective heat transfer area for primary coolant to SG metal lump and SG metal lump to secondary coolant (m2) | |
Effective heat transfer area of fuel to primary coolant (m2) | |
Average temperature of primary coolant in SG region, hot leg and cold leg (°C) | |
Average temperature of fuel, primary coolant node 1 and primary coolant node 2 (°C) | |
Mass flow rates of primary and secondary coolant (kg/s) | |
, | Mass flow rates of primary coolant due to natural circulation for and respectively (kg/s) |
Primary coolant flow rate due to foced circulation (kg/s) | |
Specific heat capacity of fuel lump, primary coolant lump in core region, and primary coolant lump in SG ( °C) | |
Specific heat capacity of SG metal lump, saturated liquid in secondary of SG, and saturated vapor in secondary of SG ( °C) | |
Specific heat capacity of feedwater to the secondary of SG, °C) | |
Internal energy of saturated liquid and vapor in SG secondary (J/kg) | |
Difference of internal energy of saturated liquid and vapor in SG secondary (J/kg) | |
Difference of specific volume of saturated liquid and vapor in SG secondary (J/kg) | |
Specific volume of saturated liquid and vapor in SG secondary (m3/kg) | |
Saturated vapor pressure at the secondary of SG (steam header) (Pa) | |
Turbine efficiency | |
Feedwater inlet temperature (°C) | |
Temperature deviation of fuel rod from initial steady state (°C) | |
Temperature deviations at coolant nodes 1 and 2 from initial steady state (°C) | |
Pressure of fluid at secondary coolant node i (MPa) | |
Temperature of fluid secondary coolant node i (°C) | |
Enthalpy of fluid at secondary coolant node i (J/kg) | |
Steam fraction of fluid at secondary coolant node i | |
Entropy of fluid at secondary coolant node i (J/kg °C) | |
Mass flow rate of fluid at secondary coolant node i (kg/s) | |
Ratio of pressure at node i to steam header pressure | |
Ratio of mass flow rate at node i to main steam flow rate | |
, | Mechanical work produced by high-pressure and low-pressure turbines (W) |
, | Mechanical work consumed by high-pressure and low-pressure pumps (W) |
Total mechanical power output (W) | |
Total heat supplied through thermal power dispatch (J) | |
Residence times of hot and cold leg coolant lumps (s) |
Appendix A. Thermodynamic State Calculations of Secondary Coolant Circuit
Appendix A.1. Main Steam
Appendix A.2. HP Turbine
Appendix A.3. Moisture Separator and Reheater
Appendix A.4. LP Turbines
Appendix A.5. Condenser
Appendix A.6. LP Pump
Appendix A.7. LP FHWs
Appendix A.8. Deaerator
Appendix A.9. HP Pump
Appendix A.10. HP FWHs
Appendix B. Additional Thermal Power Dispatch Figures
Secondary steam flow | |
Steam flow to turbine | |
Steam to thermal delivery loop | |
Saturation temperature of secondary in the SG | |
Feedwater temperature to SG | |
Total power (MWe) | |
HPT power calculated from flow and enthalpy drop (MWe) | |
LPT power calculated form flow and enthalpy drop (MWe) | |
Heat used by industrial process through thermal delivery loop (MWt) |
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Parameter | RO-SMR | RO-PWR |
---|---|---|
(160 MWt) | (2900 MWt) | |
Mass of fuel lump (kg) | 11,252 | 82,000 |
Heat transfer area of fuel to coolant (m2) | 583 | 4415 |
Primary coolant volume (m3) | 1.879 | 160 |
Circulation (kg/s) | Passive up to 586.86 | Active at 14,267 |
Volume of cold loop (m3) | 26.8 | 50.76 |
Volume of hot loop (m3) | 9.7 | 14 |
Volume of primary coolant in the SG (m3) | 3.564 | 30.5 |
Heat transfer area of primary to SG metal lump (m2) | 1123 | 25,272 † |
Heat transfer area of SG metal lump to secondary (m2) | 1214 | 42,615 † |
Secondary steam pressure (MPa) | 2.71 | 6.89 |
Volume of SG (m3) | 13.391 | 70.08 |
Parameter | GPWR (2900 MWt) | RO-PWR (2900 MWt) |
---|---|---|
Secondary pressure (MPa) | 6.89 | 6.89 |
Primary coolant flow (kg/s) | 14,267 | 14,267 |
Cold loop temperature (°C) | 292.3 | 285.88 |
Hot loop temperature (°C) | 326.8 | 322.29 |
Node | Name | T | p | h | s | x | |
---|---|---|---|---|---|---|---|
°C | MPa | kJ/kg | kJ/kg·°C | kg/s | |||
1 | gv | 289 | 7.38 | 2767 | 5.79 | 1.00 | 1652 |
2 | ms_reheater | 289 | 7.38 | 2767 | 5.79 | 1.00 | 176 |
3 | hpt | 289 | 7.38 | 2767 | 5.79 | 1.00 | 1476 |
4 | hpt_stg1 | 253 | 4.17 | 2685 | 5.83 | 0.93 | 157 |
5 | hpt_stg2 | 216 | 2.16 | 2594 | 5.89 | 0.89 | 103 |
6 | hpt_stg3 | 180 | 0.99 | 2492 | 5.96 | 0.86 | 1216 |
7 | deaerator | 180 | 0.99 | 761 | 2.14 | 0.00 | 172 |
8 | reheater | 180 | 0.99 | 2777 | 6.59 | 1.00 | 1044 |
9 | reheater_hpfwh1 | 289 | 7.38 | 1287 | 3.16 | 0.00 | 176 |
10 | lpt | 288 | 0.99 | 3026 | 7.08 | 1.00 | 1044 |
11 | lpt_stg1 | 201 | 0.39 | 2864 | 7.19 | 1.00 | 72 |
12 | lpt_stg2 | 113 | 0.13 | 2700 | 7.32 | 1.00 | 66 |
13 | lpt_stg3 | 70 | 0.03 | 2526 | 7.47 | 0.96 | 54 |
14 | lpt_stg4 | 33 | 0.01 | 2336 | 7.65 | 0.91 | 851 |
15 | cond_mix | 33 | 0.01 | 139 | 0.48 | 0.00 | 1044 |
16 | cpump | 33 | 0.99 | 140 | 0.48 | 0.00 | 1044 |
17 | lpfwh3 | 66 | 0.99 | 277 | 0.90 | 0.00 | 1044 |
18 | lpfwh2 | 103 | 0.99 | 431 | 1.34 | 0.00 | 1044 |
19 | lpfwh1 | 139 | 0.99 | 587 | 1.73 | 0.00 | 1044 |
20 | fwpump_suction | 164 | 0.99 | 695 | 1.99 | 0.00 | 1652 |
21 | fwpump | 165 | 7.38 | 702 | 1.99 | 0.00 | 1652 |
22 | hpfwh2 | 197 | 7.38 | 841 | 2.29 | 0.00 | 1652 |
23 | hpfwh1 | 234 | 7.38 | 1012 | 2.64 | 0.00 | 1652 |
24 | hpfwh1_stm_out | 253 | 4.17 | 1099 | 2.82 | 0.00 | 333 |
25 | hpfwh2_stm2 | 216 | 2.16 | 1099 | 2.84 | 0.09 | 333 |
26 | hpfwh2_stm_out | 216 | 2.16 | 926 | 2.48 | 0.00 | 436 |
27 | deaerator_hpfwh_stm | 180 | 0.99 | 926 | 2.50 | 0.08 | 436 |
28 | lpfwh1_stm_out | 143 | 0.39 | 602 | 1.77 | 0.00 | 72 |
29 | lpfwh2_stm2 | 106 | 0.13 | 602 | 1.79 | 0.07 | 72 |
30 | lpfwh2_stm_out | 106 | 0.13 | 446 | 1.38 | 0.00 | 138 |
31 | lpfwh3_stm2 | 70 | 0.03 | 446 | 1.40 | 0.07 | 138 |
32 | lpfwh3_stm_out | 70 | 0.03 | 292 | 0.95 | 0.00 | 193 |
33 | cond_fw | 33 | 0.01 | 292 | 0.98 | 0.06 | 193 |
34 | hpfwh1_stm2 | 253 | 4.17 | 1287 | 3.18 | 0.11 | 176 |
Node | T | p | h | s | x | |
---|---|---|---|---|---|---|
6 | 0.0% | 0.0% | 0.5% | 0.5% | 0.8% | −10.3% |
12 | 6.3% | 0.0% | 0.4% | 0.4% | 0.0% | 3.5% |
20 | −8.5% | 0.0% | −8.8% | −7.0% | 0.0% | 39.5% |
21 | −8.8% | 0.0% | −9.0% | −7.3% | 0.0% | 2.7% |
22 | −7.2% | 0.0% | −7.5% | −5.9% | 0.0% | 2.7% |
23 | −5.8% | 0.0% | −6.3% | −4.8% | 0.0% | 2.7% |
24 | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 117.5% |
25 | 0.0% | 0.0% | 0.0% | 0.0% | 0.2% | 117.5% |
26 | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 72.0% |
27 | 0.0% | 0.0% | 0.0% | 0.0% | 0.1% | 226.3% |
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Lew, R.; Poudel, B.; Wallace, J.; Westover, T.L. A Reduced-Order Model of a Nuclear Power Plant with Thermal Power Dispatch. Energies 2024, 17, 4298. https://doi.org/10.3390/en17174298
Lew R, Poudel B, Wallace J, Westover TL. A Reduced-Order Model of a Nuclear Power Plant with Thermal Power Dispatch. Energies. 2024; 17(17):4298. https://doi.org/10.3390/en17174298
Chicago/Turabian StyleLew, Roger, Bikash Poudel, Jaron Wallace, and Tyler L. Westover. 2024. "A Reduced-Order Model of a Nuclear Power Plant with Thermal Power Dispatch" Energies 17, no. 17: 4298. https://doi.org/10.3390/en17174298
APA StyleLew, R., Poudel, B., Wallace, J., & Westover, T. L. (2024). A Reduced-Order Model of a Nuclear Power Plant with Thermal Power Dispatch. Energies, 17(17), 4298. https://doi.org/10.3390/en17174298