# Transient stability risk assessment of power systems incorporating wind farms

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## Abstract

Large-scale wind farm integration has brought several aspects of challenges to the transient stability of power systems. This paper focuses on the research of the transient stability of power systems incorporating with wind farms by utilizing risk assessment methods. The detailed model of double fed induction generator has been established. Wind penetration variation and multiple stochastic factors of power systems have been considered. The process of transient stability risk assessment based on the Monte Carlo method has been described and a comprehensive risk indicator has been proposed. An investigation has been conducted into an improved 10-generator 39-bus system with a wind farm incorporated to verify the validity and feasibility of the risk assessment method proposed.

## Keywords

Wind farm integration Transient stability DFIG Risk indicator Wind farm location## 1 Introduction

Nowadays, low carbon emission has been an irresistible trend for the development of the world industry and economy. The exploitation and utilization of renewable sources (wind power especially) have received high-level attentions in many countries [1, 2]. With the enlargement of the scale of wind farms and the capacity of wind turbines, the influence of wind farms on power systems has always been a research focus, in which the challenge to the transient stability is extremely concerned by researchers.

As for the transient stability analysis of power systems, traditional analysis methods are carried out under the assumption that the system component parameters, operational condition, disturbance mode are deterministic. However, deterministic analysis methods make the stability analysis result too conservative and the security margin too large which could not fulfill the requirement of economical efficiency in power grids. Meanwhile, the result of deterministic analysis is binary (stable or unstable), the transient stability risk could not be quantified. In fact, the electric power sectors need to know the risk level so as to take actions to increase the system security. As a consequence, analyzing the system transient stability by utilizing risk assessment has become an indispensable research method [3].

A series of papers have already been published in the field of transient stability risk assessment in conventional power systems. Reference [4] utilized preconceived accident list to define the system transient stability risk indicators upon the concept of time margin. Reference [5] quantized the transient stability risk as an economic indicator to grid company, power plant, and customers, respectively. Reference [6] focused on combining the steady-state risk and the transient-state risk to establish a comprehensive transient stability risk indicator. However, the above papers did not involve the risk assessment of power systems incorporating with wind farms. Reference [7] studied the probabilistic stability of the power system integrated with wind farms. Reference [8] researched the impact on the transient stability brought by the number and penetration of the wind farm on the basis of [7]. Reference [9] aimed at the probability of transient stability in the power system incorporating with double fed induction generator (DIFG) and squirrel cage induction generator (SCIG). The above papers rarely analyzed the impact on system transient stability by wind power from the viewpoint of risk assessment.

Due to the problems mentioned above, this paper focuses on the risk assessment of transient stability in power systems incorporating with wind farms. The detailed model of DFIG has been established, and the risk assessment method for transient stability has been proposed. Based on the above analysis, a simulation has been done based on the Monte Carlo method on an improved 10-generator 39-bus system incorporating with a wind farm.

## 2 DFIG model

DFIG is a type of wind power generator which is very popular. In a DFIG, a slow wind turbine rotor is connected to a rapid generator rotor. The generator stator connects with the grid directly while the generator rotor connects with the grid through a group of back-to-back AC/DC/AC converters. The grid-side converter exchanges the power bi-directionally by a smoothing reactor and transformer to maintain the capacitor voltage on the DC bus. The rotor-side converter regulates the generator rotor speed by controlling the exciting current to realize the decoupling of the active and reactive powers of the DFIG.

The main components include a windmill aerodynamic module, a drive train module, an upper-level control module, a rotor-side converter, a low voltage power logic, and the asynchronous generator electrical and mechanical equations [10]. The windmill aerodynamic module achieves the capture of the wind energy and transfers it into the kinetic energy of the wind turbine. The drive train module could be seen as a connection component between the wind turbine and the asynchronous generator. The upper-level control module achieves the maximum power point tracking and gives the reactive power signal to DFIG. The rotor-side converter transfers the upper-lever signal into an exciting voltage signal through the power and current dual closed-loop control, by which the active and reactive powers of DFIG could be decoupled.

## 3 Risk assessment method for power systems incorporating with wind farms

### 3.1 Probabilistic model

For analyzing the transient stability of a power system incorporating with wind farms, the most significant factors are the fault probabilistic model and the stochastic output power of the wind farms.

As for the probabilistic model of the line fault, References [7, 8, 9] have considered the main uncertainties, such as fault type, fault location, fault clearing time, and reclosing time. They acquired the statistical characteristics of the above uncertainties from the accumulated historical data or through the reasonable assumption [11].

As for the stochastic output power of the wind farms, many papers have considered the output features of the wind farms as the results of wind speed variation in a long-time scale [12]. However, simulations for transient stability of power systems generally take no more than 10 s, which makes the wind speed be regarded as an invariant. Therefore, this paper only considers the stochastic penetration of the wind farms.

- 1)
Fault location

- 2)
Fault clearing time

*N*(1.15, 0.05).

- 3)
Probabilities of successful auto-reclosing

- 4)
Stochastic output power of wind farm

In order to simulate the variation feature of the wind farm, this paper uses the output power probability data of an actual 900 MW wind farm (the same capacity with the original synchronous generator) [16]. The probability distribution of the wind power approximately obeys the normal distribution shown in Fig. 2. The output power of the DFIG changes from 0 MW to 900 MW during each transient simulation, and the mean value of the distribution is 398.6 MW.

### 3.2 Risk indicator of transient stability in a system with wind farms

The risk assessment method synthesizes the probability and the severity of the fault, and the risk indicator is applied to judge the transient stability of the system. As for the indicators of transient stability, different methods have already been proposed. Economic indicator had once been an index to evaluate the severity of the fault in early days. Although economic indicator has the advantages of clear principle and additivity, it could hardly provide a practical decision support to the operating staff because of the uncertainty of the measured power loss. Therefore, severity indicator has been a common index for the risk assessment analysis.

*E*

_{ i }expresses the

*i-th*system fault;

*X*

_{ t }and

*X*

_{t+1}are the operation states before and after the fault, respectively;

*C*is the system state after the fault;

*P*(

*E*

_{ i },

*X*

_{t+1 }|

*X*

_{ t }) is the probability of

*E*

_{ i }with

*X*

_{t+1}under the condition of

*X*

_{ t };

*I*(

*C*|

*E*

_{ i },

*X*

_{t+1}) is the fault effect under the condition of

*E*

_{ i }with

*X*

_{t+1};

*R*(

*C*|

*X*

_{ t }) is the risk indicator.

*E*

_{ i }is generally in the form of discrete times and

*X*

_{ t }is a time section. Therefore, Eq. (1) is generally replaced by a reduced form as

*I*by severity indicator. Two different severity indicators could be defined: power angle indicator and system voltage indicator.

- 1)
Power angle indicator

*Sev*(

*St*)

_{angle}could be defined by Eq. (3). It is the maximum deviation of power angle during the simulation time. If the system could remain the power angle stability,

*Sev*(

*St*)

_{angle}is less than 1, otherwise is equal to 1.

- 2)
System voltage indicator

*Sev*(

*St*)

_{ v }is defined by Eq. (4), that is the maximum ratio of two time values.

*T*

_{lowv}is the time duration when the bus voltage decreases to 0.75 p.u.,

*T*

_{vmax}is the maximum allowable time (generally equals to 1 s). If the system could remain the voltage stability,

*Sev*(

*St*)

_{ v }is less than 1, otherwise is greater than or equal to 1.

*Risk*(

*St*)

_{angle}and the voltage risk

*Risk*(

*St*)

_{ v }. The two different risks are the multiplication values of the probability

*Like*(

*St*) of preconceived accident

*St*with the fault severity indicator

*Sev*(

*St*)

_{angle}or

*Sev*(

*St*)

_{ v }, so that the Eq. (2) could be written as

*Risk*(

*St*)

_{tra}could be defined as the union of

*Risk*(

*St*)

_{angle}and

*Risk*(

*St*)

_{ v }. The definition is shown as follows:

### 3.3 Preconceived system accident list

If all the fault conditions on each line are considered to form the accident list, a large sample size will cause massive computation and the system risk may not be assessed effectively. In fact, the fault occurrence on system line is influenced by different factors, such as the voltage level, network structure and weather situation. In practical analysis, the preconceived accident list could be selected by fault occurrence probability ranking according to the statistical historical data. The ranked top 15 faults in the historical data could be selected as the preconceived accident list to represent the fault occurrence condition [17].

### 3.4 Transient stability risk assessment based on Monte Carlo method

## 4 Simulation study

### 4.1 Simulation system description

*St*, and the third column is the probability of the fault occurrence which is the value of

*Like*(

*St*).

Preconceived accident list

Fault number | Fault line | Fault probability | Fault number | Fault line | Fault probability |
---|---|---|---|---|---|

1 | 17–18 | 0.1297 | 9 | 3–4 | 0.0460 |

2 | 2–3 | 0.1204 | 10 | 26–28 | 0.0348 |

3 | 1–39 | 0.1136 | 11 | 16–19 | 0.0345 |

4 | 8–9 | 0.1015 | 12 | 29–38 | 0.0344 |

5 | 9–39 | 0.0945 | 13 | 6–31 | 0.0303 |

6 | 4–14 | 0.0791 | 14 | 23–26 | 0.0202 |

7 | 19–33 | 0.0740 | 15 | 21–22 | 0.0187 |

8 | 10–13 | 0.0684 | – | – | – |

### 4.2 Risk calculation based on preconceived accident list

*Sev*(

*St*)

_{angle}and

*Sev*(

*St*)

_{ v }. Taking the severity indicators and the corresponding

*Like*(

*St*) (the fault probability shown in Table 1) into Eqs. (5) and (6), the final risk

*Risk*(

*St*)

_{angle}and

*Risk*(

*St*)

_{ v }of the 15 preconceived faults would be calculated. The values of

*Risk*(

*St*)

_{angle},

*Risk*(

*St*)

_{ v }and

*Risk*(

*St*)

_{tra}are shown in Table 2.

Rank of each risk indicator

Rank | Fault line | \( Risk(St)_{angle} \) | Fault line | \( Risk(St)_{v} \) | Fault line | \( Risk(St)_{tra} \) |
---|---|---|---|---|---|---|

1 | 19–33 | 0.0740 | 1–39 | 0.0408 | 19–33 | 0.0740 |

2 | 17–18 | 0.0646 | 19–33 | 0.0349 | 17–18 | 0.0646 |

3 | 2–03 | 0.0618 | 9–39 | 0.0253 | 2–03 | 0.0618 |

4 | 1–39 | 0.0559 | 8–9 | 0.0248 | 1–39 | 0.0559 |

5 | 8–9 | 0.0460 | 29–38 | 0.0245 | 8–9 | 0.0460 |

6 | 9–39 | 0.0430 | 17–18 | 0.0215 | 9–39 | 0.0430 |

7 | 4–14 | 0.0375 | 2–3 | 0.0198 | 4–14 | 0.0375 |

8 | 10–13 | 0.0353 | 4–14 | 0.0133 | 10–13 | 0.0353 |

9 | 16–19 | 0.0345 | 10–31 | 0.0129 | 16–19 | 0.0345 |

10 | 29–38 | 0.0344 | 26–28 | 0.0090 | 29–38 | 0.0344 |

11 | 6–31 | 0.0303 | 16–19 | 0.0082 | 6–31 | 0.0303 |

12 | 26–28 | 0.0261 | 3–4 | 0.0079 | 26–28 | 0.0261 |

13 | 3–04 | 0.0217 | 6–31 | 0.0072 | 3–04 | 0.0217 |

14 | 23–26 | 0.0202 | 21–22 | 0.0042 | 23–26 | 0.0202 |

15 | 21–22 | 0.0120 | 23–26 | 0.0040 | 21–22 | 0.0120 |

It could be seen from Table 2 that for the modified 10-generator 39-bus system, the power angle stability is much more serious than the voltage stability since the system has an abundant reactive power support. More attention should be paid to the power angle stability when designing controllers to enhance the system transient stability.

### 4.3 Transient stability risk assessment of the system with and without wind farm

It can be seen from the two figures that when the fault is located near the wind farm (line 9–39), the active output power is significantly reduced. Meanwhile, large amount of reactive power is absorbed by the wind farm, which will cause the voltage deteriorated. All these factors will cause the transient stability risk increased when the fault is located near the wind farm.

## 5 Conclusion

The influence of large-scale wind farm integration on system transient stability has become a big issue which is urgently to be concerned. Deterministic analysis method generally neglects the uncertainties in real system. On the basis of this, this paper focuses on the risk assessment of transient stability in power systems incorporating with wind farms. The detailed model of DFIG has been established, the uncertainties of line fault and wind farm output power have been considered, and a system comprehensive risk indicator has been proposed. The transient stability risk assessment of a 10-generator 39-bus system incorporating with a wind farm has been investigated based on the Monte Carlo method. The results show that the risk of the line near the grid-connected point of the wind farm will increase and the risk of the line far from the point will slightly decrease.

## Notes

### Acknowledgments

This work is supported by State Grid Corporation of China, Major Projects on Planning and Operation Control of Large Scale Grid (SGCC-MPLG026-2012), and National HI-Tech R&D Program of China (2011AA05A112).

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