Power distribution network reliability calculation method based on collective multi-label classifier and energy entropy

Reliable power supply from the grid is vital to life and work, production activities, and national security. At present, the simulation calculation method of distribution network reliability needs a lot of time. In view of this shortcoming, this paper proposes a multi-label classifier model using the importance sampling method, which can shorten the calculation time by reasonably extracting samples. At the same time, the multi-label classifier can evaluate the failure probability of the electric power distribution network at the bus level. Finally, we use the IEEE RTS model to test the proposed method, and the effectiveness of the proposed method is verified.


Introduction
The distribution network is a momentous part of the electric power system, and it is also a momentous part of the direct power supply to users.In order to ensure that users can obtain a continuous and stable power supply, it is necessary for the distribution network to be in a good working state at all times.Therefore, reliability evaluation of the distribution network is essential [1].So as to achieve the dual-carbon goal, our energy and power will follow the innovative development trend of "clean, comprehensive, intelligent and decentralized" [2].With the high proportion of distributed generation connected to the grid, it is necessary to break down the failure probability of the new type of distribution system.Researchers [3][4][5] have carried out breaking down the failure probability of electric distribution networks containing distributed generation, and other scholars [6][7] further considered the influence of formation conditions of isolated islands and micro-grids on the failure probability of electric distribution network in the case of electric distributed power supply access.However, these simulation algorithms need to consume a lot of computing resources and require a long time to solve.Therefore, this paper proposes an electric distribution network failure probability calculation method stemming from a multi-label classifier.This artificial intelligence method can carry out bus-level evaluation methods so as to overcome the previous shortcomings [8].This more extensive method shall facilitate the application of artificial intelligence algorithms in distribution network failure probability assessment.

The collective multi-label classifier model
The input multi-label samples are (x, y), where d dimension vector , d represents the number of lines of buses, xi represents the difference between the input power and the required power on the i bus, binary label vector It is assumed that Hp(x, y)   ,    ,   on behalf of the energy entropy of (x, y) and C is a constant, considering its distribution p(ꞏ,ꞏ).The maximum entropy theorem assumes that the current optimal model distribution is one that maximizes Hp(x, y) given a set of constraints K:   max ( , ) subject to: ( , ) ( ) Generally, this constraint is described as a constraint on the expectation of a function on (x, y), that is   ( , ) is the expectation on p(ꞏ,ꞏ), and Fk is described as the expectation of the training set.
Combined with the constraint condition of p(ꞏ,ꞏ), that is, Ep [1] = 1, the standard Lagrange multiplier method is used to solve Equation (1) of the equality condition maximum optimization problem.Therefore, the optimal solution belongs to the Gibbs distribution: where , parameters in  could be obtained by taking the maximum value of logarithmic probability: ( , ) log ( ) where D is the data set containing (x, y).Equation ( 3) is a function whose local minimum is equal to the global minimum of  , so its maximum can be solved by optimization.In general, most numerical methods require the gradient of ( ) For sample x to be predicted, the calculated label is: (5)

EE-IS method
This method uses load loss probability (LOLP) to analyze the fault rate of the distribution network.
The distribution system with the GN substation is considered.It is assumed that the system has j similar units that are independent of each other, and each unit has n loci.u is the vector containing the original fault probability of all transformer banks in this environment.Under this condition, the analysis problem of calculating load loss probability can be expressed as: in the equation, i X is the i th sample, M is the number of samples, and H is the verification function.If there is a busbar fault in the predicted label, H equals 1; otherwise, H equals 0.
However, it takes a lot of time to calculate the probability of load loss by using this method.Importance sampling (IS) pays more attention to the probability density function by paying more attention to the random variables that have a greater impact on the target value.Thus, the more important value has a greater chance of being selected, so it can quickly reduce the standard deviation of the target value.Importance sampling can significantly reduce the sample size.By introducing vector v, it can be introduced into the calculation of LOLP:

 
; ; i W X u v represents the ratio of the likelihood function and represents the necessary correction due to the change of vector v during sampling.The calculation method is as follows: x is the failure rate of generator set j.In this process, the problem to be solved is to determine the value of v, which makes the calculation time shortest.
Energy Entropy (EE) can be used to determine the value of v in IS: Step 1: The basic data before the iteration as the sample size N (such as 50000) used in each iteration and the multi-label parameter p (for example, between 0.001 and 0.2) are determined.v 0 = u, t = 1, φ = MPL, and t is the number of iterations, φ is the stop criterion of the evaluation function, and MPL is the maximum peak load of the system.
Step 2: A random sample set of X 1 , X 2 …X N is generated.The energy entropy is used to calculate the performance of the target quantity S = [S 1 , S 2 , …, S(X N )].State properties are sorted in increasing order so that S 1 ≤S 2 ≤…≤S(X N ). (9) Step 4: v is updated using the sample from Step 2.
; ; Step 5: If φ =MPL, the conditions are satisfied, and the optimal parameter is found; otherwise, the number of iterations is increased to t = t + 1, and it is returned to Step 2.
Step 6: Using the optimal parameters generated in Step 5, the load loss probability is calculated in Equation (7).
The overall flow chart of the system is shown in Figure 1.

Experiment and analysis
So as to test the operability and effectiveness of the theoretical method in practice, the topology of the distribution system selected in the experiment is IEEE RTS.RTS consists of 24 buses, 38 cable lines, and 32 generator sets.The sum of the rated active power of the generator units actually installed in the RTS system is 3614 MW, and the half-hour average load that consumes the most electricity in the working shift with the largest load in the whole year is 3020 MW.RTS is shown in Figure 2. In this experiment, an RTS with a constant load level was used, and its peak load was 3100 MW.A total of 8000 samples were used to train the CML model, among which 4000 samples were in the fault state, and the rest were in the successful state.In importance sampling, the initial parameter selection of EE optimization is N = 50000, p = 0.04.After sampling, Monte Carlo simulation (MCS) is conducted until the coefficient of variation of all simulation types specified in the standard at the stoptest stage reaches 1%.
The overall performance comparison of the three algorithms is shown in Table 1.In this case, the performance is compared based on the time resources consumed during LOLP and simulation.  1 that the CML could calculate the LOLP index of RTS with a lower error rate, and compared with the standard MCS method, the proposed CML combination method can significantly reduce the calculation time of calculating relevant indicators.
The simulation results of bus-level classification performance are shown in Figure 3.We can get that the CML proposed in this paper is also suitable for the accurate division of RTS bus fault states.

Conclusion
By combining the CML classifier with the method, a reliability calculation method suitable for both the system level and bus level is proposed in this paper.This method first obtains key samples from a large number of samples through importance sampling technology.Then it inputs these into the multi-label classifier to predict the sample label.Finally, the effectiveness of the proposed method is verified by simulation in RTs and comparison with Monte Carlo sampling.

Figure 3 .
Figure 3. Simulation results of busbar classification performanceIn order to verify the effectiveness of the proposed CML method for electric distribution networks with different topologies, tens of thousands of distribution network frame samples with different structures are used to train the model.The test data is input into the CML classifier to get some test set results, as shown in Figure4.The horizontal coordinate system is 100 sample points of the test set, and the vertical axis is the LOLP index.It can be seen from the figure that the predictive label of CML output is similar to the actual situation of the bus, indicating that the model has good performance.

Figure 4 .
Figure 4. Simulation comparison between CML and real value