# Automatic Generation Control of Nuclear Heating Reactor Power Plants

^{*}

## Abstract

**:**

## 1. Introduction

_{e}, and have already been seen as an important trend in the nuclear energy industry [7,8,9,10]. SMRs with integral primary circuits and light-water as primary coolant are called integral pressurized water reactors (iPWRs). The IRIS, NuScale, and mPower designed by the USA and the SMART designed by Korea are all typical iPWR designs with advanced features such as natural circulation, self-pressurization, hydraulic control rod, and passive decay heat removal, which prevents the reactors from hazards such as core-melting, radiological release, and LOCA (Loss of Coolant Accident). Moreover, iPWRs can offer simpler, safer, and standardized modular design by being factory built, requiring smaller initial capital investment and having a shorter construction period [7,8]. Due to their improved nuclear safety level, iPWRs are more feasible than large-scale PWRs.

_{th}test reactor *NHR-5), began to be built at the Institute of Nuclear and New Energy Technology (INET) of Tsinghua University in March 1986, and has operated at full power since December 1989 [11,12,13]. Based on NHR-5, the design of a 200 MW

_{th}nuclear heating reactor (NHR-200) was accomplished in the middle of the 1990s; it is used for electricity generation, district heating, and seawater desalination [14,15,16,17]. On the basis of the NHR-200 design, and by improving the pressure of the primary coolant and live steam for higher efficiency, a nuclear heating reactor NHR200-II with a rated thermal power of 200 MW

_{th}was developed by INET very recently [18]. Although the power rating of NHR-200II is relatively low, due to its inherent safety features it can be adopted to balance renewables by adjusting its electric power output, which relies on the automatic generation control (AGC) of the NHR-200II plant.

## 2. General Description of NHR-200II Power Plant

## 3. Plant Control Scheme with AGC Function

## 4. Automatic Genration Control Laws

#### 4.1. State-Space Modeling for Control Design

_{st}and h

_{fw}are the specific enthalpies of live steam and feedwater of UTSG, respectively; G

_{st}and G

_{fw}are the mass flowrates of live steam and feedwater, respectively; Q

_{in}is the heat transferred from the primary to the secondary sides of UTSG; ρ

_{s}and h

_{s}are the average density and specific enthalpy of the UTSG secondary coolant respectively; and constant V

_{s}is the secondary-side volume of UTSG.

_{s}and specific enthalpy h

_{s}satisfies

_{fw}and h

_{fw}are the density and enthalpy of UTSG feedwater, respectively. Moreover, it is assumed that both ρ

_{fw}and h

_{fw}are constant.

_{st}is the live steam pressure. At steady state, steam pressure P

_{st}equals its steady value P

_{st0}, and

_{in0}, G

_{fw0}, G

_{st0}and h

_{st0}are all steady values of process variables Q

_{in}, G

_{fw}, G

_{st}and h

_{st}, respectively.

_{st}= P

_{st}− P

_{st0}, ΔQ

_{in}= Q

_{in}− Q

_{in 0}, ΔG

_{fw}= G

_{fw}− G

_{fw0}and ΔG

_{st}= G

_{st}− G

_{st0}.

_{in}can be further expressed as

_{thr}is the rated thermal power, Δp

_{r}is the setpoint variation of normalized thermal power, and d

_{th}is the mismatch between ΔQ

_{in}and its expected value given by P

_{thr}Δp

_{r}. Substitute Equation (6) into Equation (5) and we get

**x**,

**d**is the disturbance to be attenuated.

_{m}is the input mechanical power from the turbine, T

_{e}the electromagnetic torque.

_{q}are the self-conductance and transient voltage of the local generator, respectively; δ

_{k}is the phase anlge of the kth (k = 1,

^{…},n − 1) remote generator relative to the local generator; and w

_{k}, E’

_{q,k}, G

_{k}, and B

_{k}are the rotation rate, transient voltage, conductance, and susceptibility of the kth remote generator, respectively.

_{m}, and T

_{e}as δ

_{0}, ω

_{0}, P

_{m0}, and T

_{e0}, respectively, and it can be seen from Equation (18) that ω

_{0}= 1 and P

_{m0}= T

_{e0}. Based on defining Δδ = δ − δ

_{0}, Δω =ω − ω

_{0}, ΔP

_{m}= P

_{m}− P

_{m0}, and ΔT

_{e}= T

_{e}− T

_{e0}, it can then be derived that

_{m}can be decomposed as

_{st0}is the steam flowrate at full power, d

_{m}is the mismatch between the other two terms, Equation (20) can be rewritten as

_{st}should be designed to stabilize frequency error Δω.

#### 4.2. Theorectical Control Problem Formulation

**Problem**

**1.**

_{1}and x

_{2}can be obtained through measurement. Futher, suppose that the differentiation of disturbance d

_{d}is a bounded positive constant. How can we design the control input u so that the closed-loop system is globally bounded and stable?

#### 4.3. Active Disturbance Rejection Control Law

**Theorem**

**1.**

_{d}being bounded. Then, active disturbance rejection control (ADRC)

_{i}> 0 (i = 1, 2) is the feedback gains, and $\hat{d}$ is the estimation of d given by disturbance observer (DO)

_{i}> 0 (i = 1, 2) is the observer gains, positive constant ε∈(0, 1), and

_{i}= k

_{i}or α

_{i}= κ

_{i}(i = 1, 2) is Hurwitz, i.e., the roots of equation G(s) = 0 have negative real parts.

**Proof**

**of**

**Theorem 1.**

_{2}and e

_{d}satisfy the dynamical equation

**A**

_{o}is Hurwitz, which further leads to the fact that for an arbitrarily given diagonal positive-definite matrix

**Q**

_{o}= diag([q

_{o1},q

_{o2}]) (q

_{oi}> 0, i = 1, 2), there must be a symmetric positive-definite matrix

**P**

_{o}so that

_{o}along the trajectory of system (40),

_{max}(∙) gives the maximal eigenvalue of a matrix,

**z**converges asymptotically to a bounded set around the origin, which means that DO (33) provides a globally bounded estimation for total disturbance d. The constant ε is smaller and scalars q

_{oi}(i = 1, 2) are larger; the bounded set is tighter, where larger q

_{oi}(i = 1, 2) are guaranteed by more negative real parts for the roots of equation s

^{2}+ κ

_{1}s + κ

_{2}= 0.

**A**

_{c}is Hurwitz, which means that for an arbitrarily given diagonal matrix

**Q**

_{c}= diag([q

_{c1},q

_{c2}]) (q

_{ci}> 0, i = 1, 2), there exists a symmetric positive-definite matrix

**P**

_{c}so that

_{o}is defined by Equation (45). Then, by differentiating function V given by Equation (54) along the closed-loop trajectory, and by considering inequality (46), it can be seen that

**Remark**

**1.**

_{2}can be directly measured, it can be seen that ADRC (32) can be rewritten as

**Remark**

**2.**

## 5. Simulation Results with Dissuction

#### 5.1. Simulation Program

^{−4}. The control laws in this simulation for regulating the neutron flux, reactor core outlet temperature, and UTSG water level are those presented in [20,21].

#### 5.2. Simulation Results

_{e}. The dynamical responses of the plant process variables such as the neutron flux, core outlet temperature, IC hot leg temperature, live steam pressure, UTSG water level and feedwater temperature, thermal power, electric power, normalized grid frequency, and phase angle are shown in Figure 6.

_{e}lower at 3000 s, and ramps up to its original level at 6000 s, where the ramping rate is 5 MW

_{e}/min. The plant dynamical responses of physical, thermal‒hydraulic, and electric parameters during load ramping are shown in Figure 7, Figure 8 and Figure 9.

#### 5.3. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**Simulation program and the corresponding three-machines/nine-nodes power system: (

**a**) whole plant, (

**b**) simulation unit of NSSS, (

**c**) simulation unit of secondary system, (

**d**) power system.

**Figure 6.**Responses of key process variables in the case of load stepping, n

_{r}: neutron flux, T

_{cout}: core outlet temperature, T

_{hl}: IC hot leg temperature, P

_{st}: live steam pressure, L

_{sg}: UTSG water-level, T

_{fw}: feedwater temperature, P

_{th}: thermal power, P

_{e}: electric power, ω: normalized frequency, and δ: phase angle.

**Figure 7.**Responses of PC and IC process variables in the case of load maneuvering, n

_{r}: neutron flux, T

_{cout}: core outlet temperature, T

_{hl}: IC hot leg temperature.

**Figure 8.**Responses of UTSG process variables in the case of load maneuvering, P

_{st}: live steam pressure, L

_{sg}: UTSG water-level, T

_{fw}: feedwater temperature.

**Figure 9.**Responses of electric variables in the case of load maneuvering, P

_{th}: thermal power, P

_{e}: electric power, ω: normalized frequency, and δ: phase angle.

Parameter | Unit | NHR-200 | NHR-200II |
---|---|---|---|

Thermal Power | MW_{th} | 200 | 200 |

Coolant/Moderator | Light Water | Light Water | |

Circulation Type | Natural Circulation | Natual Circulation | |

Primary Circuit Pressure | MPa | 2.5 | 8 |

Core Inlet/Outlet Temperature | °C | 145/210 | 232/280 |

Intermediate Circuit Pressure | MPa | 3.0 | 8.8 |

IC Cold/Hot Leg Temperature | °C | 95/145 | 203/248 |

Live Steam Pressure | Mpa | 0.25 | 1.6 |

Live Steam Temperature | °C | 127.4 | 201.4 |

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## Share and Cite

**MDPI and ACS Style**

Dong, Z.; Liu, M.; Jiang, D.; Huang, X.; Zhang, Y.; Zhang, Z.
Automatic Generation Control of Nuclear Heating Reactor Power Plants. *Energies* **2018**, *11*, 2782.
https://doi.org/10.3390/en11102782

**AMA Style**

Dong Z, Liu M, Jiang D, Huang X, Zhang Y, Zhang Z.
Automatic Generation Control of Nuclear Heating Reactor Power Plants. *Energies*. 2018; 11(10):2782.
https://doi.org/10.3390/en11102782

**Chicago/Turabian Style**

Dong, Zhe, Miao Liu, Di Jiang, Xiaojin Huang, Yajun Zhang, and Zuoyi Zhang.
2018. "Automatic Generation Control of Nuclear Heating Reactor Power Plants" *Energies* 11, no. 10: 2782.
https://doi.org/10.3390/en11102782