# Analysis of Transient Interactions between a PWR Nuclear Power Plant and a Faulted Electricity Grid

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model of a PWR Nuclear Power Plant

#### 2.1. Core Neutronics Model

#### 2.1.1. Reactor Point Kinetics

#### 2.1.2. Ex-Core Detectors

#### 2.1.3. Reactivity Feedback

#### 2.2. Thermal-Hydraulics Model

#### 2.2.1. Fuel-Coolant Node

#### 2.2.2. Resistance Temperature Detectors

#### 2.3. Piping and Plenum Model

#### 2.4. Steam Generator Model

#### 2.5. Pressuriser Model

#### 2.6. Turbine-Governor Model

#### 2.6.1. Turbine

#### 2.6.2. Turbine-Governor Valve

#### 2.7. Dynamic Shaft Model

#### 2.8. Turbine-Speed Control Loop

## 3. Transient Stability Enhancement Components

#### 3.1. Automatic Voltage Regulator

#### 3.2. Power System Stabiliser

#### 3.2.1. Generic Power System Stabiliser

#### 3.2.2. Multi-Band Power System Stabiliser

#### 3.3. Flexible AC Transmission System

#### 3.3.1. Static Var Compensator

#### 3.3.2. Static Synchronous Compensator

## 4. Connection, Interaction, and Coordination among Nuclear Power Plant, Grid, and Protection Systems

#### 4.1. Connection

#### 4.2. Interaction

#### 4.3. Coordination

## 5. Simulation Cases, Results, and Discussion

#### 5.1. Case I: Response under Single-Phase Fault

#### 5.2. Case II: Response under Three-Phase Fault

#### 5.2.1. PSS and SVC

#### 5.2.2. PSS and STATCOM

#### 5.3. Case III: Response under Permanent Load Loss

#### 5.3.1. PSS and SVC

#### 5.3.2. PSS and STATCOM

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Protection System | Standard |
---|---|

AC distribution system, Electrical circuit | IEEE Std 242-1986 |

protection, Diesel generator protection | |

Motor protection system | IEEE Std 242-1986, IEEE Std C37.96-1988, |

IEEE Std 666-1991 | |

Power transformer protection | IEEE Std C37.91-1985, IEEE Std 666-1991 |

Feeder circuit to power distribution | IEEE Std 141-1993, IEEE Std 242-1986 |

panel protection | |

Isolation and separation of non-class-1E | IEEE Std 384-1992 |

circuits from class-1E circuits | |

Surge protection of equipments and systems | IEEE Std 141-1993, IEEE Std 242-1986 |

Surge protection of induction motors | IEEE Std C37.96-1988 |

Protection of wire line facilities | IEEE Std 487-1992 |

Circuits with solid-state equipments | IEEE Std 518-1982 |

Surge arresters | IEEE Std C62.2-1987 |

Surge voltage determination | IEEE Std C62.41-1991 |

Surge withstand capability | IEEE Std C62.45-1992 |

Protection for batteries | IEEE Std 946-1992 |

Protection of battery chargers, inverters | IEEE Std 446-1987 |

Ground protection practices | IEEE Std 142-1991, IEEE Std C62.92.3-1993 |

Alarms and indication | IEEE Std 944-1986 |

Electrical penetration | IEEE Std 317-1983 |

Generator 1 and 2 | ||||||

Line-to-Line | Frequency | Stator | Inertia | Pole | Reactances | |

Voltage (kV) | (Hz) | Resistance (pu) | Coefficient (s) | Pairs | (pu) | |

13.8 | 60 | 0.002854 | 3.7 | 32 | $Xd=1.305$, $X{d}^{{}^{\prime}}=0.296$, $X{d}^{{}^{\u2033}}=0.252$, | |

$Xq=0.474$, $X{q}^{{}^{\u2033}}=0.243$, $Xl=0.180$ | ||||||

Excitation System 1 and 2 | ||||||

LPF Time | Regulator | Regulator Time | Damping | Damping Filter | Exciter | Exciter Time |

Constant (s) | Gain | Constant (s) | Filter Gain | Time Constant (s) | Gain | Constant (s) |

0.02 | 200 | 0.001 | 0.001 | 0.1 | 1 | 0 |

Generic PSS | ||||||

Sensor Time | Gain | Wash-out Time | Lead-Lag 1 Time Constant (s) | Lead-Lag 2 Time Constant (s) | ||

Constant (s) | Constant (s) | |||||

0.015 | 2 | 0.7 | ${T}_{num}=0.06$, ${T}_{den}=0.5$ | ${T}_{num}=0$, ${T}_{den}=0$ | ||

Multiband PSS | ||||||

Global | Low | Low Frequency | Intermediate | Intermediate | High | High Frequency |

Gain | Frequency (Hz) | Gain | Frequency (Hz) | Frequency Gain | Frequency (Hz) | Gain |

1.0 | 0.025 | 5 | 0.8 | 25 | 12 | 145 |

SVC | ||||||

Nominal | Frequency | Three-phase Base | Average Time | Droop | Voltage Regulator | |

Voltage (kV) | (Hz) | Power (MVA) | Delay (ms) | (pu/Pbase) | Gain (puB/puV/s) | |

500 | 60 | 200 | 4 | 0.03 | 300 | |

STATCOM | ||||||

Nominal | Frequency | Converter | Converter | DC Link | DC Link | |

Voltage (kV) | (Hz) | Rating (MVA) | Impedance (pu) | Voltage (kV) | Capacitance (F) | |

500 | 60 | 100 | $R=0.0073$, $L=0.22$ | 40 | 350 | |

Maximum Voltage | Droop | ${\mathit{V}}_{\mathit{a}\mathit{c}}$Regulator | ${\mathit{V}}_{\mathit{d}\mathit{c}}$Regulator | Current Regulator | ||

Rate (pu/s) | (pu) | Gains | Gains | Gains | ||

10 | 0.03 | ${K}_{p}=5$, ${K}_{i}=1000$ | ${K}_{p}=0.0001$, ${K}_{i}=0.02$ | ${K}_{p}=0.3$, ${K}_{i}=10$, ${K}_{f}=0.22$ |

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**Figure 1.**Block diagram representation of a pressurised water reactor (PWR)-type nuclear power plant connected to an electric grid.

**Figure 8.**Case I: Variation in network signals during single-phase faults with generic and multiband PSS.

**Figure 9.**Case I: Variation in nuclear power plant variables following single-phase faults with generic and multiband PSS.

**Figure 10.**Case II.1: Variation in network signals during three-phase faults with generic and multiband PSS with a static var compensator (SVC).

**Figure 11.**Case II.1: Variation in nuclear power plant variables following three-phase faults with generic and multiband PSS with SVC.

**Figure 12.**Case II.2: Variation of network signals during three-phase faults with generic and multiband PSS with static synchronous compensator (STATCOM).

**Figure 13.**Case II.2: Variation of nuclear power plant variables during three-phase faults with generic and multiband PSS with STATCOM.

**Figure 14.**Case III.1: Variation in network signals during permanent load loss with generic and multiband PSS with SVC.

**Figure 15.**Case III.1: Variation in nuclear power plant variables during permanent load loss with generic and multiband PSS with SVC.

**Figure 16.**Case III.2: Variation in network signals during permanent load loss with generic and multiband PSS with STATCOM.

**Figure 17.**Case III.2: Variation in nuclear power plant variables during permanent load loss with generic and multiband PSS with STATCOM.

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**MDPI and ACS Style**

Vajpayee, V.; Top, E.; Becerra, V.M.
Analysis of Transient Interactions between a PWR Nuclear Power Plant and a Faulted Electricity Grid. *Energies* **2021**, *14*, 1573.
https://doi.org/10.3390/en14061573

**AMA Style**

Vajpayee V, Top E, Becerra VM.
Analysis of Transient Interactions between a PWR Nuclear Power Plant and a Faulted Electricity Grid. *Energies*. 2021; 14(6):1573.
https://doi.org/10.3390/en14061573

**Chicago/Turabian Style**

Vajpayee, Vineet, Elif Top, and Victor M. Becerra.
2021. "Analysis of Transient Interactions between a PWR Nuclear Power Plant and a Faulted Electricity Grid" *Energies* 14, no. 6: 1573.
https://doi.org/10.3390/en14061573