# Response Based Emergency Control System for Power System Transient Stability

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Instability Detection

#### 2.1. Identification Method of Transient Instability for an Autonomous SMIB System

- (1)
- The phase trajectory is convex if $l\cdot \mathrm{\Delta}\mathrm{\omega}>0$;
- (2)
- The phase trajectory is concave if $l\cdot \mathrm{\Delta}\mathrm{\omega}<0$;
- (3)
- The trajectory is on the inflexion point if $l\cdot \mathrm{\Delta}\mathrm{\omega}=0$.

#### 2.2. Identification Theory of Transient Instability for a Non-Autonomous SMIB System

## 3. Control Method

#### 3.1. The Slope of the State-Plane Trajectory

#### 3.2. Calculation of Control Quantity for SMIB

#### 3.3. Approximation Method to Calculate Control Quantity

#### 3.4. Seeking for FEP

- (1)
- Obtain the prediction curve of the electrical power;
- (2)
- Preset zero to the generator shedding ratio and UPE: ${\mathrm{\lambda}}^{(0)}=0$, ${{\mathrm{\delta}}_{u}}^{(0)}=0$;
- (3)
- Mechanical power decreases at the same ratio:$${{P}_{m}}^{(k)}=(1-{\mathrm{\lambda}}^{(k-1)}){{P}_{m}}^{(k-1)}$$
- (4)
- Search for the power equilibrium point as ${{\mathrm{\delta}}_{b}}^{(n)}$;
- (5)
- Acquire the ${\mathrm{\lambda}}^{(k)}$ according to the ${{\mathrm{\delta}}_{b}}^{(n)}$;
- (6)
- If $\left|{{\mathrm{\delta}}_{b}}^{(n)}-{{\mathrm{\delta}}_{b}}^{(n-1)}\right|\le \mathrm{\epsilon}$, complete the iterator; or return to step 3.

#### 3.5. Control Method for Multi-Machine System

## 4. Simulation Result

#### 4.1. SMIB System

Component | Parameters |
---|---|

The initial state | ${\mathrm{\omega}}_{0}=2\mathrm{\pi}f$, $f=50\text{Hz}$, ${\mathrm{\delta}}_{0}={34.49}^{\circ}$ |

The generator | ${P}_{m}=120\text{MW}$, ${T}_{j}=6\text{s}$, ${\text{x}}_{\text{d}}=1.83\text{p.u.}$, ${\text{x}}_{\text{q}}=1.83\text{p.u.}$, ${{\text{x}}_{\text{d}}}^{\prime}=0.3\text{p.u.}$, ${{\text{x}}_{\text{q}}}^{\prime}=1.83\text{p.u.}$, ${{x}_{q}}^{\u2033}=0.25\text{p.u.}$, ${{x}_{d}}^{\u2033}=0.25\text{p.u.}$ |

The transmission line | ${x}_{1}={x}_{2}=0.486\text{\Omega /km},\text{}{x}_{0}=4{x}_{1}$ |

The Moment of Fault-Clearing | Simulation Results | Detection Results | The Moment of Instability Detected | The Angle of Instability Detected |
---|---|---|---|---|

0.17 s | Stable | Stable | \ | \ |

0.18 s | Stable | Stable | \ | \ |

0.187 s | Stable | Stable | \ | \ |

0.188 s | Unstable | Unstable | 0.56 s | 121.9° |

0.19 s | Unstable | Unstable | 0.46 s | 114.9° |

0.20 s | Unstable | Unstable | 0.37 s | 106.2° |

0.21 s | Unstable | Unstable | 0.34 s | 102.9° |

0.22 s | Unstable | Unstable | 0.33 s | 102.8° |

The Moment of Fault-Clearing | Simulation Results | The Moment of Instability Detected | The Angle of Instability Detected | The Moment of Angle Reach the Threshold of 180° |
---|---|---|---|---|

0.17 s | Stable | Stable | - | - |

0.18 s | Stable | Stable | - | - |

0.187 s | Stable | Stable | - | - |

0.188 s | Unstable | 0.56 s | 121.9° | 1.44 s |

0.19 s | Unstable | 0.46 s | 114.9° | 1.14 s |

0.20 s | Unstable | 0.38 s | 108.5° | 0.86 s |

0.21 s | Unstable | 0.34 s | 102.9° | 0.76 s |

0.22 s | Unstable | 0.34 s | 105.6° | 0.68 s |

Fault-Clearing Time | Distinction Time | Calculated Minimum Control Quantity (%) | Real Minimum Control Quantity (%) |
---|---|---|---|

0.18 s | None (stable) | None (stable) | None (stable) |

0.19 s | 0.46 s | 5.61 | 4.55 |

0.20 s | 0.37 s | 14.1 | 13.5 |

0.21 s | 0.34 s | 22.4 | 20.6 |

0.22 s | 0.33 s | 30.1 | 28.4 |

Fault-Clearing Time | Distinction Time | Calculated Controlled Quantity (%) | Real FEP after Control |
---|---|---|---|

0.18 s | None (stable) | None (stable) | None (stable) |

0.19 s | 0.46 s | 8.91 | 129.1° |

0.20 s | 0.37 s | 18.6 | 126.8° |

0.21 s | 0.34 s | 22.5 | 128.1° |

0.22 s | 0.33 s | 35.6 | 128.8° |

#### 4.2. IEEE 39-Bus System

Fault | A Three-Phase Grounding Fault Occurs on the Line between Bus 4 and Bus 14 | |
---|---|---|

Fault duration | 0.23 s | |

Detection time | 0.41 s | |

Detection angle | 126.5904° | |

Control objective | scheme one | scheme two (145°) |

Control law (MW) | G31 (439) | G31 (521) |

FEP after control | 148.0° | 144.8° |

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Wang, H.; Zhang, B.; Hao, Z.
Response Based Emergency Control System for Power System Transient Stability. *Energies* **2015**, *8*, 13508-13520.
https://doi.org/10.3390/en81212381

**AMA Style**

Wang H, Zhang B, Hao Z.
Response Based Emergency Control System for Power System Transient Stability. *Energies*. 2015; 8(12):13508-13520.
https://doi.org/10.3390/en81212381

**Chicago/Turabian Style**

Wang, Huaiyuan, Baohui Zhang, and Zhiguo Hao.
2015. "Response Based Emergency Control System for Power System Transient Stability" *Energies* 8, no. 12: 13508-13520.
https://doi.org/10.3390/en81212381