## Application example

The IEEE New England (10-generator-39-bus) system was employed as benchmark to test the proposed model and method. The single line diagram of the test system is given in Fig. 8. In this system, the classical generator model is applied to the synchronous generator G2. The 4th order generator model with a simplified 3rd order exciter model is applied to the remaining 9 synchronous generators. It should be noticed that there is no any power system stabilizer considered in the test system. All simulations were implemented on the MATLABTM environment.

A wind farm with 200x2MW DFIGs is integrated into the non-generator buses, i.e. busl-bus29. The corresponding parameters of wind turbine and DFIG are given in Table 1.

According to the procedure given in Fig. 6, the frequency distribution of wind speed by applying Monte Carlo method to the Weibull probability distribution of wind speed can be calculated as depicted in Fig. 9. The sample size is set to be 8000 during simulation.

Parameters |
Values |

P |
1.2235 kg/m3 |

R |
45 m |

C |
0.473 |

Vcut-in |
3m/s |

Vcut-off |
25m/s |

Vrated |
10.28m/s |

Rs |
0.00488 |

Xls |
0.09241 |

Xlr |
0.09955 |

Xm |
3.95279 |

Rr |
0.00549 |

H |
3.5 |

Ki |
0.1406 |

Ti |
0.0133 |

K2 |
0.5491 |

T2 |
0.0096 |

800 | ||||||||||

700 | ||||||||||

600 | ||||||||||

n | ||||||||||

e |
500 | |||||||||

tq | ||||||||||

£ |
400 | |||||||||

300 | ||||||||||

200 | ||||||||||

100 | ||||||||||

Fig. 9. Frequency distribution of wind speed Next, in accordance Eq. (1) and the frequency distribution of wind speed as shown in Fig.9, for the wind farm with 200*2MW capacity, the probability distribution of wind farm power output can be finally obtained as shown in Fig. 10. From Fig.10, there exist two concentrations of probability masses in the distribution: one corresponds to the value of zero, in which the wind farm is cut off; the other corresponds to the value of 400MW, in which the rated power output is generated by the wind farm. 3000 2500 fr 2000 S 1000 100 200 300 Wind farm power output (MW) Fig. 10. Probability distribution of wind farm power output Fig. 11 shows the frequency distribution of the real part of eigenvalues when the wind farm is connected to bus20. 3GGG 2SGG 2GGG 1SGG 1GGG Small signal stable region Real part value Fig. 11. Probability distribution of real part of eigenvalues with wind farm integration into bus20 According to the statistical analysis based on Fig. 11, we found that there is a probability of roughly 39.1% (3128 out of 8000 in simulation) that the real part of the eigenvalue will be positive, in which situation the system is small signal unstable. Therefore we can conclude that the stability probability of the test system is 60.9% in current operating condition. Furthermore, there exist two concentrations of probability masses in the distribution: the left one corresponds to the situation that the wind farm is cut off; the right one corresponds to situation that wind turbine generates rated power. Under the same wind speed condition, the wind farm is connected to the bus1-29, respectively. The corresponding results are given in Table 2.
Table 2. Small signal stable probability with different wind farm integration position Table 2. Small signal stable probability with different wind farm integration position Electro-mechanical oscillation mode can be picked out according to the electro-mechanical relative coefficient or the frequency of oscillation, i.e. p>1 or 0.1<f<2.5Hz (Wang et al., 2008). The mean and standard error of the mode properties: frequencies, Electro-mechanical relevant ratio, damping ratio, and the participating factors are given in Table 3. We found that the 9th EM oscillation mode is unstable with a probability of 39.1%, and it is actually the pair of eigenvalue that determines the small signal stability probability of the whole system. In summary, according to the simulation results discussed above, we can conclude that the deterministic small signal stability analysis can be considered as a special case study in the probabilistic small signal stability analysis. Especially, the probabilistic small signal stability based on the Monte Carlo method can evaluate the test power system more objectively and accurately. |

## Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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