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 [8]. Using the risk theory, the frequency deviation, voltage deviation, power angle stability margin and fault removal time margin are quantified to evaluate the transient voltage stability [9]. Based on the Bayesian network and risk theory, measure the severity of N-K fault in power system [10]. Based on the complex network theory and risk theory, the electrical betweenness is introduced into the severity index of the failure consequence to assess the risk in power system [11].

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 [12]:

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 [13].

Based on the optimal power flow algorithm in [14], using the generator busactive power P_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.

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 Figure 2. The low voltage reactor capacity of bus 6 is 100 Mvar. Therefore, when the voltage of bus

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 Table 1.

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.

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 Table 2.

It can be seen from Table 2 that the tenth line is an extremely important line, because that provided the N-2 fault associated with the tenth line, the amount of optimal load shedding at least is 116 MVA. Compared with Table 1, we can see that when the N-2 fault occurs, the chance of load shedding is obviously increased, and the amount of optimal load shedding is also significantly increased, so the occurrence of N-2 fault should be avoided.

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 Table 3.

From Table 3, it can be seen that the first 10 critical lines of IEEE24-RTS contain two 230 kV lines, the whole five 138/230kV transformer power transmission lines and two 138 kV lines. The two lines with the highest risk index are consistent with the optimal load shedding order of N-1 security check. Line 10 is the highest degree of risk in the system, and does not meet the N-1 security check, and it should be redesigned.

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 Table 3 shows the double circuit lines in the same tower are more prone to N-2 fault, while the comprehensive risk indexes of which are low and the reliability of which is high.

The bar graph of IEEE24-RTS risk index is shown in Figure 3.