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Based on risk theory, considering the probability of an accident and the severity of the sequence, combining N-1 and N-2 security check, this paper puts forward a new risk index, which uses the amount of optimal load shedding as the severity of an accident consequence to identify the critical lines in power system. Taking IEEE24-RTS as an example, the simulation results verify the correctness and effectiveness of the proposed index.

Many blackouts have taken place in the world these years, such as the large scale blackout in interconnected north America Power Grid on August 14th and the blackout in UCTE Grid on November 4th [

The use of the hidden fault model that the failure of the line will cause at least one of the other lines connected to break to identify the critical lines [

In this paper, based on the path following method and the risk theory, a method for identifying the critical line of power system is proposed. This method is based on the nonlinear optimization model of the optimal load shedding of AC power flow, taking the amount of optimal load shedding as the severity of accident consequence, considering the probability of accident, to identify critical lines in power system. Taking IEEE24-RTS as an example, the simulation results verify the correctness and effectiveness of the proposed index, which has certain guiding significance for the power system planning, design and safe operation.

The risk theory is a comprehensive consideration of the probability of the accident and the severity of its consequences, which is widely used in the power system risk assessment and vulnerability assessment. Based on the risk theory, the risk assessment of voltage collapse is carried out from two aspects: the probability of voltage collapse and the influence of voltage collapse [

The equation of risk theory is:

In the Equation (1), R represents the risk index of the accident; P represents the probability of the accident; S represents the severity of the accident.

The probability of accident is random, because of the random fluctuation of the load level, the random fluctuation of the new energy and the uncertainty of the external factors. It can be seen from the statistics that the probability of the power system accident is basically in accordance with the Poisson distribution [

In the Equation (2), λ_{i} is the rate of accident E_{i}.

The interior point method is the most widely used algorithm for solving optimal power flow model, can be used in linear programming, two programming and nonlinear programming. There are two kinds of algorithms, such as affine scaling method and path following method. The path following method is widely used in power system because of its fast convergence speed, strong robustness and insensitivity to initial value selection [

Based on the optimal power flow algorithm in [_{G}, generator bus reactive power Q_{G}, load bus P_{D} and Q_{D} as control variables, the optimal load shedding model is proposed:

In the equation, P_{Gi}, Q_{Gi} represents the generator active power and reactive power output; P_{Di}, Q_{Di} represents the load active power and reactive power; P_{i}, Q_{i} represents the bus active power and reactive power; P_{Ci}, Q_{Ci} represents the active power and reactive power of load shedding; V_{i} represents the voltage amplitude; S_{ij} represents the apparent power of line i-j; N_{Ld} represents the number of transmission lines.

According to the risk theory and the optimal load shedding model, the flow chart of critical lines identification in power system is shown in

The following are the main steps:

1) Obtain the basic data of the system, including technical data, operating constraints, line fault data, etc.

2) Use the interior point method to calculate the amount of optimal load shedding of N-1 and N-2 security check.

3) Calculate the amount of optimal load shedding of each line according to Equation (4).

In the Equation (4), CC_{i} represents the comprehensive amount of optimal load shedding of line i; j represents the optimal load shedding associated with line i; f represents the amount of optimal load shedding of N-1 and N-2 security

check.

4) Calculate the probability of each line accident according to Equation (2).

5) Based on the risk theory, considering the probability of the accident and the severity of the consequences, calculate the risk index of each line according to Equation (5).

In the Equation (5), R_{i} represents the risk index of line i; P_{i} represents the probability of line i accident.

6) Obtain the critical lines in power system by listing the risk index in descending order.

In this paper, IEEE24-RTS is taken as an example for simulation calculation, which consists of 33 generators, 17 load buses, 38 transmission lines, the total installed capacity of 3000.00 MW and the total load capacity of 2850.00 MW. The Electrical connection diagram of IEEE24-RTS is shown in

6 is low, the priority is to reduce the reactor capacity of bus 6.

Using the deterministic method, disconnect a line in turn to simulate the three-phase permanent fault of the line. Then use the interior point method to calculate the amount of optimal load shedding. The simulation results are shown in

The table shows that the IEEE24-RTS does not conform to the traditional N-1 security check. When the tenth line of the system is disconnected because of the fault, the voltage of bus 6 will decrease, resulting in the relay protection action and the bus load is reduced. Considering the total reactor capacity and 41.4 + j8.53 of the amount of bus 6 load shedding, the amount of optimal load shedding is 116 MVA. When the 27th line of the system are disconnected because of the fault, the voltage of bus 3 and bus 24 will decrease. The amount of optimal load shedding is 45 MVA.

Fault Line No. | Amount of Optimal Load Shedding (100 MVA) |
---|---|

10 (6 - 10) | 1.16 |

27 (15 - 24) | 0.45 |

Using the deterministic method, disconnect two lines in turn to simulate the three-phase permanent fault of the line. Then use the interior point method to calculate the amount of optimal load shedding. The simulation results are shown in

It can be seen from

Combining the amount of optimal load shedding of N-1 and N-2 security check, calculate the comprehensive amount of optimal load shedding according to Equation (4). Considering the probability of the accident, calculate the risk index of each line according to Equation (5). The results are shown in

From

The first 10 critical lines concentrated in the 230 kV lines and 138/230kV transformer power transmission lines, indicate that the higher the line voltage level, the higher the degree of the risk. The transformer power transmission lines are important channels, once the fault occurred to these lines, it will affect the power transmission and stability and the comprehensive risk degree is high. The system includes 4 sets of 230 kV double circuit lines. And

The bar graph of IEEE24-RTS risk index is shown in

Based on risk theory, considering the probability of an accident, this paper puts forward a new risk index, which uses the amount of optimal load shedding of N-1 and N-2 security check as the severity of an accident consequence to identify

Fault Lines No. | Amount of Optimal Load Shedding (100 MVA) | Fault Lines No. | Amount of Optimal Load Shedding (100 MVA) |
---|---|---|---|

19, 23 | 1.98 | 10, 12 - 26 | 1.16 |

10, 27 | 1.44 | 10, 28- 38 | 1.16 |

10, 5 | 1.39 | 6, 27 | 1.14 |

10, 11 | 1.32 | 2, 27 | 1.09 |

10, 1-4 | 1.16 | 11, 13 | 0.99 |

10, 6-9 | 1.16 | 6, 7 | 0.95 |

Line No. | Risk Index (10^{−4}) | Line No. | Risk Index (10^{−4}) |
---|---|---|---|

10 (6 - 10) | 15.165536 | 8 (4 - 9) | 0.2491983 |

27 (15 - 24) | 2.5301777 | 38 (21 - 22) | 0.2337650 |

7 (3 - 24) | 1.6319176 | 20 (12 - 13) | 0.2239413 |

14 (9 - 11) | 1.1796199 | 3 (1 - 5) | 0.2213088 |

15 (9 - 12) | 1.1121911 | 25 (15 - 21) | 0.2129794 |

16 (10 - 11) | 0.7515991 | 26 (15 - 21) | 0.2129794 |

17 (10 - 12) | 0.7276336 | 18 (11 - 13) | 0.2121259 |

2 (1 - 3) | 0.4561541 | 34 (19 - 20) | 0.1973929 |

19 (11 - 14) | 0.4559433 | 35 (19 - 20) | 0.1973929 |

23 (14 - 16) | 0.4421734 | 9 (5 - 10) | 0.1886618 |

11 (7 - 8) | 0.3882275 | 32 (18 - 21) | 0.1818064 |

6 (3 - 9) | 0.3627048 | 33 (18 - 21) | 0.1818064 |

13 (8 - 10) | 0.3481193 | 28 (16 - 17) | 0.1818062 |

4 (2 - 4) | 0.2951963 | 1 (1 - 2) | 0.1810950 |

12 (8 - 9) | 0.2824963 | 36 (20 - 23) | 0.1766107 |

31 (17 - 22) | 0.2805341 | 37 (20 - 23) | 0.1766107 |

21 (12 - 23) | 0.2701406 | 29 (16 - 19) | 0.1766107 |

22 (13 - 23) | 0.2545510 | 24 (15 - 16) | 0.1714140 |

5 (2 - 6) | 0.2518010 | 30 (17 - 18) | 0.1662191 |

the critical lines in power system. Taking IEEE24-RTS as an example, the simulation results verify the correctness and effectiveness of the proposed index

The proposed index has certain guiding significance for the power system planning, design and safe operation, and provides reliable reference for the power system operation and maintenance personnel.

The higher the line voltage level, the higher the degree of the risk. And the transformer power transmission lines are important channels, the comprehensive risk index of which is high. Therefore, the operation and maintenance personnel should pay close attention to the higher voltage level and transformer power transmission lines to ensure the security and stability of power system in the process of electric power production.

Technology Major Project of China Southern Power Grid Co., Ltd. (GZ2014- 2-0049).

Liu, M.S., Zhao, L.J., Huang, L., Zhang, X.W., Deng, C.H. and Long, Z.J. (2017) Identification of Cri- tical Lines in Power System Based on Optimal Load Shedding. Energy and Power Engineering, 9, 261-269. https://doi.org/10.4236/epe.2017.94B031