Flexible DC distribution network fault location method based on beetle swarm optimization algorithm

To improve the fault location ability of the DC distribution network and ensure its power supply reliability, a fault location method based on the beetle swarm optimization algorithm is proposed. Firstly, the fault characteristics of the DC side after short-circuit fault are analyzed, and the mathematical model for fault location is established; then, the problem of fault location is transformed into the problem of parameter identification by discretization; finally, to verify the effectiveness of the method, a flexible DC distribution network model is built in MATLAB. The simulation results show that the proposed fault location method is accurate, not affected by the transition resistance, and has good robustness.


Introduction
Nowadays, new energy like solar energy and wind energy are widely connected to the distribution system in the form of distributed power supply, which encourages the development of new power systems with new energy as their primary component, but also poses new challenges to the traditional distribution network.A flexible DC distribution network can cope with load diversity, which is the future development direction of the power distribution system [1,2] .The DC distribution system's cablebased line is typically quite difficult to diagnose.Following the occurrence of the fault, an accurate location of the fault must be determined [3] .Many studies on the techniques for DC distribution network fault location have been undertaken by domestic and international academics [4,5] .The fault location is unaffected by the traveling wave approach, which offers good placement accuracy, but it has strict requirements on the number and location setting of observation points [6,7] .Non-traveling wave method mainly uses the line electrical volume for fault location.For example, range-ranging protection is proposed in the literature [8], which improves the limitation of the R-L model used in the DC distribution network.It has good rapidity, but the sensitivity of protection is weak, and the influence of transition resistance is not considered.In literature [9], intelligent algorithms are used to accurately locate the fault location of the DC distribution network, and a parameter identification model based on a genetic algorithm is established.However, the calculating procedure is challenging, and the algorithm's convergence has to be further enhanced.In order to solve the problem of accurate fault location of the DC distribution network, this paper establishes the mathematical model of the DC system when a fault occurs, builds the fitness function under different fault conditions, uses the beetle swarm optimization algorithm (BSO) algorithm to locate faults, builds a model of the DC distribution network using the MATLAB/Simulink simulation environment, and validates the efficacy of the suggested approach.

Mathematical model of distribution network line fault
The DC system has small damping and extremely fast fault development speed, and in a short period of time, the fault current climbs quickly to its maximum value.To avoid the line and converter suffering from a huge current impact, it is necessary to isolate the fault when the voltage is zero, so the model in this paper is based on the capacitor discharge stage [10] .

Inter-electrode short circuit fault
The following equivalent circuits can be obtained by analyzing the two poles of the fault separately [11] .
We eliminate the influence of transition resistance: (2)

Single-pole grounding fault mathematical model
Assuming that the positive pole fails, according to the previous analysis, the capacitor discharge stage can be equivalent to the following figure [12] : 3 Using Kirchhoff's law, for the system i ( i = 1, 2 ), we can obtain: We eliminate the influence of transition resistance.

Acquisition of micro-components
Both Equations ( 2) and ( 4) have second-order micro-components, which cannot be directly obtained in practice.In this paper, the differential method is used to obtain voltage micro-components, and the sampling interval is 25 s  .The formula for calculating the first and second-order differential with voltage is as follows: where t represents time, V dc (t), V dc (t-1), and V dc (t-2) represent the voltage values of three consecutive adjacent sampling times, respectively, and t  is the sampling interval.

Principle of fault location
The unknowns in Equations ( 2) and ( 4) are related to the distance of the fault point, and the fault point can be found by calculating its value.We discretize them and combine Equation (5) to get Equations ( 6) and ( 7)：

Search principle of Beetle Swarm Optimization
The BSO algorithm [13] has been widely used in the field of parameter identification, with good convergence and global optimization ability.The mathematical model for simulating the optimization of beetle is as follows: 1 (1 ) where k represents iterative algebra, S represents space, X js and V js represent the position and current movement speed of the beetle,  is the normal number, and is the incremental function.
The updated formula for beetle speed is as follows: where c 1 and c 2 are normal numbers, r 1 and r 2 are functions with values between [0,1],  is inertia weight, and P j and P g are the extreme values of individual and population of beetle.The expression of  is as follows: where sign() represents a symbolic function, X r and X l respectively represent the positions of the left and right antennae, and  indicates the indicated step length.The position of the antennae of the beetle is determined by Equation ( 11): The update of the position of the beetle depends on the value of the fitness function.The mathematical expressions under different fault conditions have been derived in the previous article.The fitness function is constructed according to Equations ( 6) and ( 7) as follows: To sum up, the flow chart of BSO algorithm positioning is as follows:  Table 1 shows the parameter values in the model.By altering the impedance at the left and right ends of the fault point relative to the length of the line, the impedance value of the line can be altered.The value of the transition resistance can be set freely.The simulation time is set at 0.4s, and the working time of the circuit breaker is set at 0.2 s.

Comparison of fault location results
The location error rate is calculated with Equation ( 13 where s represents the error rate, and X c and X r represent the calculated position and actual position respectively.

Fault voltage direct location results
Theoretically, the fault location can be completed by using the four sets of voltage values after the fault.
Taking the single-pole grounding fault as an example, the fault voltage value is substituted into Equation (7).It is not difficult to see that by only using the fault voltage to locate the fault, the results obtained are unstable, and the error is large, which is concentrated between 0.8% and 3.3%, and even there are positioning errors, which are mainly caused by individual information errors.

BSO algorithm fault location results
Similarly, we set the single-pole grounding fault, obtain 50 sets of fault voltage values, substitute them into the parameter identification program, and calculate the error rate.Table 3 shows the calculation results:  3 shows that using the BSO algorithm, the positioning error rate is within 0.4%.Compared with direct calculation, the error is significantly reduced.In the process of location, multiple sets of fault voltage values are used to eliminate the impact of individual information distortion.In the case of some data measurement errors, the fault location can also be found more accurately, with a strong ability to eliminate the error.

Compare the effectiveness of different fault location methods
In the problem of fault location in traditional distribution networks, the genetic algorithm(GA) and the beetle antennae search algorithm(BAS) [14] have been applied in practice.To verify the quick, precise, and reliable parameter identification approach provided in this paper, the GA algorithm, the BAS algorithm, and the BSO algorithm are respectively used to analyze, and the same group of fault voltage information is processed.Here, a single-pole grounding fault is taken, and the transition resistance is set at 10  .The convergence is shown in the figure below.Compared with the genetic algorithm and the BAS algorithm, the BSO algorithm has a stronger optimization ability.It not only has a large scope of optimization, and is not easy to fall into local convergence, and the number of iterations is also the least, which improves the optimization speed.This is mainly because the GA algorithm needs to carry out operator crossover and mutation, and the calculation process is relatively complex, which greatly affects the identification speed.For the BAS algorithm, although its iterative process is simple, because only a single beetle is used, not only the search speed is slow, but also the local convergence is easy to occur.The BSO algorithm combines the advantages of the particle swarm optimization algorithm and the BAS algorithm, and the iterative process is simple and global.4 shows the location results of the three fault location methods.The location accuracy of the GA algorithm is the worst, and the location error is between 0.7% and 1.3%.The positioning error of the BAS algorithm is concentrated between 0.3% and 0.8%.Compared with the former two algorithms, the positioning accuracy of the BSO algorithm has been greatly improved, reducing the positioning error range from 0.02% to 0.3%.To sum up, the BSO algorithm not only offers exceptional benefits in terms of convergence speed and searchability but also has considerably higher accuracy during the parameter identification process.

Conclusion
This paper proposes a fault location approach for circular DC distribution networks based on the BSO algorithm.The mathematical model for fault location is proposed, which transforms the fault location problem into a parameter identification problem.The fault characteristics of DC inter-pole short circuits and single-pole ground faults are investigated separately.The post-fault voltage value is used to find the fault point and draw conclusions through comparison.The method for locating faults suggested in this study offers the following benefits: 1) It does not rely on fault type and eliminates the effect of transition resistance.
2) The issue of individual information distortion impacting location accuracy is resolved by using several sets of voltage values, and the issue of fault localization is changed into the issue of parameter identification.
3) The BSO algorithm has both the global nature of the PSO algorithm and the good convergence of the BAS algorithm, which can well achieve fast and accurate positioning.

Figure 3 .
Figure 3. Flow chart of BSO algorithm

Figure 4 .
Figure 4. Simulation topology of six-terminal flexible DC distribution

Figure 5 .
Figure 5. Convergence comparison of three algorithms

Table 1 .
Parameter setting of the simulation model

Table 2 .
Fault Voltage Direct Location Results

Table 3 .
Location results of the BSO algorithm

Table 4 .
Location results of three intelligent algorithms