CN111934320A - Active power distribution network rapid reconstruction method based on linear power flow equation and improved firework algorithm - Google Patents

Abstract

A fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm, including: combining the typical characteristics of distribution network, quantitative analysis of simplified conditions applicable to distribution network; Based on the simplified conditions of the distribution network, the nonlinear high-dimensional power flow equations are linearized, and a set of linear power flow equations are obtained. Improvement; establish the comprehensive objective function of the distribution network, and construct the active distribution network reconfiguration model; combine the linear power flow equation and the improved fireworks algorithm to solve the active distribution network reconfiguration model. The invention proposes a fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm. Compared with the traditional active distribution network reconfiguration model, the method has higher computational efficiency and versatility.

Description

Rapid Reconfiguration of Active Distribution Network Based on Linear Power Equation and Improved Fireworks Algorithm method

technical field

The invention relates to the technical field of active distribution network reconfiguration, in particular to a fast reconfiguration method of an active distribution network based on a linear power flow equation and an improved fireworks algorithm.

Background technique

In recent years, with the increasingly serious problems such as energy shortage and environmental pollution, distributed generation, as an emerging energy utilization method, has received more and more attention. Compared with the large power grid with centralized power supply, its unique environmental protection, economy and high energy conversion rate have become an important measure for energy structure adjustment, which will be an important direction for the future development of the power distribution system. The access of distributed generation (DG) to the distribution network will have an impact on the reliability of power supply of the distribution network, so the influence of DG needs to be considered when reconfiguring the distribution network.

At present, some achievements have been made in the reconstruction of distribution network with DG. The power flow calculation methods used in the commonly used distribution network reconfiguration models mainly include the forward-backward substitution method, the improved Newton method, and the loop impedance method. However, the power flow equations of these methods are nonlinear and involve an iterative process, so the calculation efficiency is not high, and it is difficult to meet the needs of rapid reconfiguration of the distribution network.

In order to improve the efficiency of the power flow calculation method, many literatures have carried out related research. At present, the typical processing method is to use the loop analysis method as the theory of power flow calculation according to the structure of the tree network of the power distribution system, and use the typical power flow calculation method of the power distribution network. Characteristic, the loop voltage equation is linearized to simplify it into a linear algebraic equation system, and finally the voltage distribution result can be obtained by substituting a formula. Or perform polynomial fitting on the trigonometric function term in the basic power flow equation, and then use the operating characteristics of the system to decouple the voltage amplitude and phase angle to obtain a fully linear power flow equation. However, the above methods are not suitable for the distribution network with PV nodes, and it is difficult to directly apply to the active distribution network reconfiguration model. In addition, distribution network reconfiguration often requires intelligent algorithms to solve. However, the traditional intelligent algorithm has the problems of slow convergence speed and low efficiency. Fireworks algorithm is a new type of swarm intelligence optimization algorithm proposed in 2010. It has good convergence and robustness in solving high-complexity problems, and has attracted the attention of many scholars. However, the fireworks algorithm is currently less used in the field of distribution network reconstruction.

In view of this, it is of great significance to study a fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm.

SUMMARY OF THE INVENTION

The existing active distribution network reconfiguration model has the problems of low computational efficiency and low generality. The invention provides a fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm, and compared with the traditional active distribution network reconfiguration method, the method has higher calculation efficiency and versatility.

The technical scheme adopted in the present invention is:

A fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm,

Step 1: Combine the typical characteristics of the active distribution network, quantitatively analyze the simplified conditions applicable to the active distribution network;

Step 2: On the basis of considering the distributed power supply model and the ZIP load model, according to the simplified conditions of the active distribution network, the power flow equation is expanded by Taylor series and the voltage amplitude and phase angle are decoupled to obtain a set of linear power flow equations;

Step 3: In order to improve the convergence speed of the fireworks algorithm, the fireworks algorithm is improved according to the characteristics of active distribution network reconstruction;

Step 4: Establish the comprehensive objective function of the active distribution network, and construct the active distribution network reconstruction model;

Step 5: Combine the linear power flow equation and the improved fireworks algorithm to solve the active distribution network reconfiguration model.

The present invention is a rapid reconstruction method of active distribution network based on linear power flow equation and improved fireworks algorithm, and the technical effects are as follows:

1), the linear power flow equation of the present invention is a pure numerical operation, the model is simple, the calculation amount is small, the calculation speed is fast, and there is no convergence problem,

2) The linear power flow of the present invention not only overcomes the defect that most linear power flow methods cannot handle PV-type DG, but also has higher calculation accuracy.

3) The present invention improves the firework algorithm, accelerates the convergence speed of the algorithm, and improves the stability of the algorithm.

4) The present invention proposes a fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm. It can not only improve the network loss, voltage offset and load balance of the distribution system, but also meet the needs of rapid reconfiguration of the distribution network with DG.

Description of drawings

Figure 1 is a schematic diagram of the IEEE33 node system structure.

Figure 2 is the voltage amplitude distribution diagram of each node of the system

Figure 3 shows the voltage offset diagram before and after the reconfiguration of the distribution network.

Figure 4 shows the algorithm stability analysis and the time-consuming diagram of reconstructing the model.

Detailed ways

A fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm,

Step 1: Combine the typical characteristics of the active distribution network, quantitatively analyze the simplified conditions applicable to the active distribution network;

Step 2: On the basis of considering the distributed power supply model and the ZIP load model, according to the simplified conditions of the active distribution network, the power flow equation is expanded by Taylor series and the voltage amplitude and phase angle are decoupled to obtain a set of linear power flow equations;

Step 3: In order to improve the convergence speed of the fireworks algorithm, the fireworks algorithm is improved according to the characteristics of active distribution network reconstruction;

Step 4: Establish the comprehensive objective function of the active distribution network, and construct the active distribution network reconstruction model;

Step 5: Combine the linear power flow equation and the improved fireworks algorithm to solve the active distribution network reconfiguration model.

Below in conjunction with accompanying drawing, preferred embodiment is described in detail:

1. The simplified conditions applicable to the distribution network are as follows:

Firstly, the typical characteristics of the distribution network are summarized, including: (1) the node voltage amplitude is close to 1.0p.u.; (2) the phase angle at both ends of the line is very small, so that the voltage phase angle of all nodes in the distribution network is in phase with the voltage of the balance node. The angle difference is not big; ③ the ratio of resistance and reactance is large, close to or greater than 1.

According to the typical characteristics of the distribution network, the simplified conditions of the distribution network can be deduced, as shown in formula (1):

Among them, i, j represent the node number; δ _i , δ _j are the phase angles of nodes i, j respectively; δ _ij is the phase angle difference between nodes i and j, V _j is the voltage amplitude of node j; sinδ _ij represents The sine function of _δij .

2. According to the different ways of grid-connected distributed power supply, the distributed power supply model can be divided into the following three categories:

(1) PQ type DG:

The output power direction of PQ type DG is opposite to the direction of load power flow, and its power flow calculation is shown in formula (2):

In the formula, P and Q are the active power and reactive power of the load, respectively; P _G , Q _G are the active power and reactive power given by DG, respectively;

(2) PV type DG:

The active power and voltage of PV-type DG are known quantities, and the power flow calculation model is shown in formula (3):

In the formula, P is the active power of the load; P _G and Q _G are the active power and reactive power given by DG respectively; V is the voltage amplitude of the node; V _G is the node voltage of DG; Q _Gmax and Q _Gmin are respectively are the upper and lower limits of reactive power of DG.

(3) PI type DG:

The active power and current of this type of DG are constant values, and the power flow calculation model is shown in equation (4):

In the formula, P and Q are the active power and reactive power of the load respectively; P _G is the active power given by the DG; I _G is the constant current output by the DG; V is the voltage amplitude of the node; V-related functions.

3. Considering that the size of the load changes with the voltage, the ZIP load model of the node can be established, as shown in formula (5):

Among them, P(V) and Q(V) represent the active power and reactive power of the node load, respectively. V, V _N are the actual voltage and rated voltage of the node, respectively; P _N , Q _N are the active power and reactive power under the rated voltage, respectively. C _Z , C _I , C _P represent the proportional coefficients of node active constant impedance, constant current and constant power load respectively; C' _Z , C' _I , C' _P represent node reactive constant impedance, constant current and constant power load respectively The proportional coefficient of ; the constraints satisfied by each parameter are C _Z +C _I +C _P =1, C' _Z +C' _I +C' _P =1.

4. The expression of the power flow equation is shown in formula (6):

Among them, i, j represent the number of the node; P _Li , Q _Li are the active power and reactive power of the node i load, respectively; P _Gi , Q _Gi are the active power and reactive power of the DG; V _i , V _j are the nodes, respectively The voltage magnitudes of i and node j. G _ij and B _ij are the real and imaginary parts of the admittance matrix, respectively. δ _ij is the voltage phase angle difference between node i and node j. sinδ _ij and cosδ _ij are the sine function and cosine function of δ _ij , respectively.

5. According to the typical characteristics of the distribution network, the method of linearization is shown in formula (7):

Among them, y(V) is the function related to the voltage amplitude; k represents the order; y ^k represents the k power of y; ΔV is the voltage drop; V is the voltage amplitude of the node.

In order to ensure the safe and reliable operation of power equipment, the voltage drop ΔV of each node of the power distribution system is actually very small. When the voltage amplitude V approaches 1 p.u., Taylor series expansion can be performed on the nonlinear terms related to the voltage amplitude V.

6. The expression of the linear power flow equation is shown in formula (8):

Among them, h ₁ =2, h ₂ =1; S, W, _R are the set of balance nodes, _{PQ nodes} , and PV nodes in the distribution network, respectively; Constant power coefficients of node active power and PQ node reactive power; P _IS , P _IW , and Q _IW are the constant current coefficients of balance node active power, PQ node active power, and PQ node reactive power, respectively; V _S , δ _S are respectively are the voltage amplitude and phase angle of the balance node; V _W and δ _W are the voltage amplitude and phase angle of the PQ node respectively; VR and δ _R are the voltage amplitude and phase angle of the PV node respectively; diag ₍ P _PR ), diag( P _PW ) and diag(Q _PW ) are respectively the constant power load coefficient diagonal matrix of PV node active power, the constant power load coefficient diagonal matrix of PQ node active power, and the constant power load coefficient diagonal matrix of PV node reactive power. ; G _RS and B _RS are the real and imaginary parts of the mutual admittance matrix of the PV node and the balanced node, respectively; G _WS and B _WS are the real and imaginary parts of the mutual admittance matrix of the PQ node and the balanced node, respectively; G _WR and B _WR are the real and imaginary parts of the mutual admittance matrix of the PQ node and the PV node, respectively; G _RR and B _RR are the real and imaginary parts of the PV node self-admittance matrix; B _RW and G _RW are the PQ The real and imaginary parts of the mutual admittance matrix between the node and the PV node; G _WW and B _WW are the real and imaginary parts of the self-admittance matrix of the PQ node, respectively.

7. The firework algorithm can be used to solve the distribution network reconstruction model. The principle of the firework algorithm is as follows:

In the firework algorithm, the position of each firework _xi represents a feasible solution, and the explosion radius A _i and the number of sparks S _i of each firework _xi are shown in equations (9) and (10):

In the formula: A _i is the explosion radius of the fireworks x _i ; S _i is the number of sparks; M and A represent the constants for adjusting the total number of explosion sparks and the explosion radius, respectively; y _max and y _min are the maximum and minimum fitness of the fireworks, respectively ; i represents the number of fireworks; N represents the total number of fireworks; f( _xi ) is the fitness value of _xi . ε is a minimum value.

In the fireworks algorithm, the smaller the explosion radius of the fireworks, the more explosion sparks, which means the better the fitness function.

The solution of the reconfiguration model by the fireworks algorithm should combine the characteristics of the distribution network reconfiguration model. That is, each dimension of a feasible solution must be a continuous integer. The convergence speed of the fireworks algorithm in this paper refers to the number of iterations to reach the global optimal solution.

8. According to the characteristics of the distribution network, the fireworks algorithm is improved as follows:

Because the switch combination of distribution network reconstruction must be an integer, and the explosion radius of fireworks should not be too small. Therefore, the minimum explosion radius adjustment mechanism is adopted, as shown in equation (11):

In the formula, A _i,k is the explosion radius of the k-th dimension of the fireworks x _i ; A _min,k is the minimum explosion radius of the k-th dimension; [A _i,k ] means rounding A _i,k .

In order to balance the global search ability and local search ability of the fireworks algorithm, the present invention adjusts the size of the minimum explosion radius A _min,k of the fireworks as follows, as shown in formula (12):

表示随t变化的指数函数。In the formula, A _min,k (t) represents the k-dimensional minimum explosion radius of the fireworks in the t-th iteration; A _init and A _final are the initial and final values of the explosion radius, respectively; t is the number of iterations, and t _max is the maximum iteration frequency.

represents an exponential function that varies with t.

In order to ensure the timeliness of distribution network reconstruction, the fireworks algorithm should reduce the number of distance and power flow calculations in the selection strategy. Therefore, the present invention adopts an elite selection strategy, as shown in formula (13):

In the formula, p( _xi ) represents the probability of fireworks _xi being selected as the next generation; f( _xi ) represents the fitness value of fireworks _xi ; f _max and f _min represent the maximum and minimum fitness values of fireworks _xi respectively. value.

It can be known from equation (13) that if the fitness value corresponding to the spark reaches the minimum, then the spark will be selected to the next generation with a probability of 100%.

9. The comprehensive objective function established by the present invention is shown in formula (14):

为支路i最大允许传输容量。min为最小值符号。where f _loss (x), f _sv (x), f _lb (x), and f represent the network loss function, voltage offset function, load balancing function and comprehensive objective function of the distribution network, respectively; β ₁ , β ₂ , β ₃ are the random weights of the three objective functions; F _loss , F _sv , and F _lb are the minimum values of each iteration of the three objective functions; i is the number of the node; l is the total number of branches in the power distribution system; C _i is the state variable of the branch switch, 0 means open, 1 means closed; R _i is the resistance of branch _i ; Pi and Qi are the total injected active power and reactive power of node _i , respectively. V _i is the voltage amplitude of node i. n is the number of system nodes; V _i,N is the rated value of the node voltage. Si is the complex power amplitude of branch _i ;

is the maximum allowable transmission capacity of branch i. min is the minimum value symbol.

10. The active distribution network reconfiguration model established by the present invention is as follows:

The objective function of the active distribution network reconfiguration model is shown in equation (15):

In the formula, f _loss (x), f _sv (x), f _lb (x), and f represent the network loss function, voltage offset function, load balancing function and comprehensive objective function of the distribution network, respectively; β ₁ , β ₂ , β ₃ are the random weights of the three objective functions, respectively; F _loss , F _sv , and F _lb are the minimum values of each iteration of the three objective functions, respectively.

The constraint function of the active distribution network reconfiguration model is as follows:

(1) The power flow balance constraint, as shown in equation (16):

Among them, i, j represent the number of the node; P _Li , Q _Li are the active power and reactive power of the node i load, respectively; P _Gi , Q _Gi are the active power and reactive power of the DG; V _i , V _j are the nodes, respectively The voltage magnitudes of i and node j. G _ij and B _ij are the real and imaginary parts of the admittance matrix, respectively. δ _ij is the voltage phase angle difference between node i and node j. sinδ _ij and cosδ _ij are the sine function and cosine function of δ _ij , respectively.

(2) The branch current constraint is shown in equation (17):

I _l ≤I _lmax (17)

In the formula, I _l , I _lmax are the current flowing through branch l and the maximum allowable current, respectively.

(3) The node voltage constraint is shown in equation (18):

V _i ^min ≤V _i ≤V _i ^max (18)

In the formula, V _i is the voltage amplitude of node i; V _i ^min and V _i ^max are the lower limit and upper limit of the voltage amplitude, respectively.

(4) Network topology constraints: After the distribution network is reconfigured, the radial topology must be maintained, and there is no ring network.

Taking the IEEE33 node system as an example, the simplified conditions of the power distribution system and the effectiveness of the present invention are analyzed: the IEEE33 node system is shown in Figure 1, and the reference voltage and reference power of the system are 12.66kV and 10MVA respectively. Assume that the head end is a balanced node, the voltage amplitude is 1.0p.u., and the voltage phase angle is 0. Considering the static characteristics of load voltage, nodes 2-6 and 19-22 represent commercial loads, nodes 7-18 represent municipal living loads, and nodes 23-33 represent industrial loads. Node 27 and node 33 are respectively connected to DG, and the specific parameters are shown in Table 1 and Table 2.

Table 1 Reference value of proportional coefficient of load voltage static characteristics

Table 2 Distributed power access situation

Fig. 2 is the distribution diagram of the voltage amplitude of the IEEE33 node system solved by the NR method and the linear power flow equation. It can be found that the calculation results of the present invention and the Newton-Raphson method are highly consistent, which proves the rationality of the simplified conditions of the present invention.

FIG. 3 is a voltage amplitude shift diagram after the IEEE33 node system is reconfigured in the distribution network according to the present invention. It can be found that after the system is reconstructed in the present invention, the voltage amplitude of the node can be increased to a certain extent.

Figure 4 shows the structure after 50 reconstructions of the IEEE33 node system by three different models. Among them, model A represents the adaptive particle swarm algorithm, model B represents the improved fireworks algorithm, and the power flow calculation method of the two models adopts the NR method. It can be seen from the figure that the stability of the present invention is better than that of model A, and the calculation efficiency is better than that of model A and model B

The NR method and the linear power flow method are used to solve the IEEE69, IEEE141, and IEEE874 node systems respectively. The maximum relative error and running time of the two power flow equations in different test systems are shown in Table 3:

Table 3 Errors and running times of different test systems

It can be found from Table 3 that the maximum relative error of the voltage amplitude in the present invention can always be kept within 0.1% in a large distribution network system, indicating that the proposed linear power flow equation is also applicable to other test systems. At the same time, compared with the NR method, the power flow calculation method of the present invention does not need iteration and has higher computational efficiency. In the IEEE874 node test system, the power flow calculation method of the present invention runs 100 times faster than the NR method.

Table 4 is the data of the present invention after the power distribution network reconstruction of the IEEE33 node test system.

Table 4 Comparison of results before and after network reconstruction

It can be seen from Table 4 that after the present invention optimizes and reconfigures the distribution network, the network loss, voltage offset and load balance degree of the distribution network can be further reduced. When the distribution network is reconfigured, reasonable access to DG can also effectively improve various indicators of the system.

Claims (10)

1. A fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm, characterized in that: Step 1: Combine the typical characteristics of the active distribution network, quantitatively analyze the simplified conditions applicable to the active distribution network; Step 2: On the basis of considering the distributed power supply model and the ZIP load model, according to the simplified conditions of the active distribution network, the power flow equation is expanded by Taylor series and the voltage amplitude and phase angle are decoupled to obtain a set of linear power flow equations; Step 3: In order to improve the convergence speed of the fireworks algorithm, the fireworks algorithm is improved according to the characteristics of active distribution network reconstruction; Step 4: Establish the comprehensive objective function of the active distribution network, and construct the active distribution network reconstruction model; Step 5: Combine the linear power flow equation and the improved fireworks algorithm to solve the active distribution network reconfiguration model. 2. The method for fast reconfiguration of active distribution network based on linear power flow equation and improved fireworks algorithm according to claim 1, characterized in that: in the step 1, the typical features of the active distribution network include: ①: The node voltage amplitude approaches 1.0p.u.; ②: The phase angle at both ends of the line is very small, so that the voltage phase angle of all nodes in the distribution network is not much different from the voltage phase angle of the balance node; ③: The ratio of resistance to reactance is large, close to or greater than 1. 3. The fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm according to claim 1, is characterized in that: in described step 1, the simplified condition of active distribution network is as shown in formula (1) :

Among them, i, j represent the node number; δ _i , δ _j are the phase angles of nodes i, j respectively; δ _ij is the phase angle difference between nodes i and j, V _j is the voltage amplitude of node j; sinδ _ij represents The sine function of _δij . 4. the fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm according to claim 1, is characterized in that: in described step 2, the following three types of distributed power model: (1) PQ type DG: The output power direction of PQ type DG is opposite to the direction of load power flow, and its power flow calculation is shown in formula (2):

In the formula, P and Q are the active power and reactive power of the load, respectively; P _G , Q _G are the active power and reactive power given by DG, respectively; (2) PV type DG: The active power and voltage of PV-type DG are known quantities, and the power flow calculation model is shown in formula (3):

In the formula, P is the active power of the load; P _G and Q _G are the active power and reactive power given by DG respectively; V is the voltage amplitude of the node; V _G is the node voltage of DG; Q _Gmax and Q _Gmin are respectively are the upper and lower limits of reactive power of DG; (3) PI type DG: The active power and current of this type of DG are constant values, and the power flow calculation model is shown in equation (4):

In the formula, P and Q are the active power and reactive power of the load respectively; P _G is the active power given by the DG; I _G is the constant current output by the DG; V is the voltage amplitude of the node; V-related functions. 5. the fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm according to claim 1, is characterized in that: in described step 2, ZIP load model is as shown in formula (5):

Among them, P(V), Q(V) represent the active power and reactive power of the node load, respectively; V, V _N are the actual voltage and rated voltage of the node, respectively; P _N , Q _N represent the active power under the rated voltage and the non-reactive power, respectively power; C _Z , C _I , C _P represent the proportional coefficient of node active constant impedance, constant current, and constant power load respectively; C' _Z , C' _I , C' _P represent node reactive constant impedance, constant current, The proportional coefficient of the constant power load; the constraints satisfied by each parameter are C _Z +C _I +C _P =1, C' _Z +C' _I +C' _P =1. 6. the fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm according to claim 1, is characterized in that: in described step 2, power flow equation is as shown in formula (6):

Among them, i, j represent the number of the node; P _Li , Q _Li are the active power and reactive power of the node i load, respectively; P _Gi , Q _Gi are the active power and reactive power of the DG; V _i , V _j are the nodes, respectively The voltage amplitudes of i and node j; G _ij and B _ij are the real and imaginary parts of the admittance matrix, respectively; δ _ij is the voltage phase angle difference between node i and node j; sinδ _ij and cosδ _ij are δ The sine and cosine functions of _ij ; The method of linearization is shown in formula (7):

Among them, y(V) is the function related to the voltage amplitude; k is the order; y ^k is the k-th power of y; △V is the voltage drop; V is the voltage amplitude of the node; In order to ensure the safe and reliable operation of power equipment, the voltage drop △V of each node of the power distribution system is actually very small; when the voltage amplitude V approaches 1p.u. series expansion; The linear power flow equation is shown in Equation (8):

Among them, h ₁ =2, h ₂ =1; S, W, _R are the set of balance nodes, _{PQ nodes} , and PV nodes in the distribution network, respectively; Constant power coefficients of node active power and PQ node reactive power; P _IS , P _IW , and Q _IW are the constant current coefficients of balance node active power, PQ node active power, and PQ node reactive power, respectively; V _S , δ _S are respectively are the voltage amplitude and phase angle of the balance node; V _W and δ _W are the voltage amplitude and phase angle of the PQ node respectively; VR and δ _R are the voltage amplitude and phase angle of the PV node respectively; diag ₍ P _PR ), diag( P _PW ) and diag(Q _PW ) are respectively the constant power load coefficient diagonal matrix of PV node active power, the constant power load coefficient diagonal matrix of PQ node active power, and the constant power load coefficient diagonal matrix of PV node reactive power. ; G _RS and B _RS are the real and imaginary parts of the mutual admittance matrix of the PV node and the balanced node, respectively; G _WS and B _WS are the real and imaginary parts of the mutual admittance matrix of the PQ node and the balanced node, respectively; G _WR and B _WR are the real and imaginary parts of the mutual admittance matrix of the PQ node and the PV node, respectively; G _RR and B _RR are the real and imaginary parts of the PV node self-admittance matrix; B _RW and G _RW are the PQ The real and imaginary parts of the mutual admittance matrix between the node and the PV node; G _WW and B _WW are the real and imaginary parts of the self-admittance matrix of the PQ node, respectively. 7. the fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm according to claim 1, is characterized in that: in described step 3, the principle of fireworks algorithm is as follows: In the firework algorithm, the position of each firework _xi represents a feasible solution, and the explosion radius A _i and the number of sparks S _i of each firework _xi are shown in equations (9) and (10):

In the formula: A _i is the explosion radius of the fireworks x _i ; S _i is the number of sparks; M and A represent the constants for adjusting the total number of explosion sparks and the explosion radius respectively; y _max and y _min are the maximum and minimum fitness of the fireworks, respectively ; i represents the number of fireworks; N represents the total number of fireworks; f( _xi ) is the fitness value of _xi ; ε is a minimum value; The characteristic of active distribution network reconfiguration means that each dimension of the feasible solution must be a continuous integer; The convergence speed of the fireworks algorithm refers to the number of iterations to reach the global optimal solution; The fireworks algorithm is improved as follows: Since the switch combination for distribution network reconstruction must be an integer, and the explosion radius of fireworks is not required to be too small; therefore, the minimum explosion radius adjustment mechanism is adopted, as shown in formula (11):

In the formula, A _i,k is the explosion radius of the k-th dimension of the fireworks x _i ; A _min,k is the minimum explosion radius of the k-th dimension; [A _i,k ] represents the rounding of A _i,k ; In order to balance the global search ability and local search ability of the fireworks algorithm, the minimum explosion radius A _min,k of the fireworks is adjusted as follows, as shown in formula (12):

In the formula, A _min,k (t) represents the k-dimensional minimum explosion radius of the fireworks in the t-th iteration; A _init and A _final are the initial and final values of the explosion radius, respectively; t is the number of iterations, and t _max is the maximum iteration frequency;

represents an exponential function that varies with t; In order to ensure the timeliness of distribution network reconstruction, the fireworks algorithm should reduce the number of distance and power flow calculations in the selection strategy; therefore, the elite selection strategy is adopted, as shown in equation (13):

In the formula, p( _xi ) represents the probability of fireworks _xi being selected as the next generation; f( _xi ) represents the fitness value of fireworks _xi ; f _max and f _min represent the maximum and minimum fitness values of fireworks _xi respectively. value. 8. The fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm according to claim 1, characterized in that: in the step 4, the comprehensive objective function of the distribution network is shown in formula (14) :

where f _loss (x), f _sv (x), f _lb (x), and f represent the network loss function, voltage offset function, load balancing function and comprehensive objective function of the distribution network, respectively; β ₁ , β ₂ , β ₃ are the random weights of the three objective functions; F _loss , F _sv , and F _lb are the minimum values of each iteration of the three objective functions; i is the number of the node; l is the total number of branches in the power distribution system; C _i is the state variable of the branch switch, 0 means open, 1 means closed; R _i is the resistance of branch i; Pi and Q _i are the total injected active power and reactive power of node _i respectively; V _i is the node The voltage amplitude of i; n is the number of system nodes; V _i,N is the rated value of the node voltage; S _i is the complex power amplitude of the branch i; S _i ^max is the maximum allowable transmission capacity of the branch i; min is the minimum value symbol. 9. The fast reconfiguration method of active distribution network based on linear power flow equation and improved fireworks algorithm according to claim 1, is characterized in that: in described step 4, active distribution network reconfiguration model is as follows: The comprehensive objective function of the active distribution network reconfiguration model is established, as shown in equation (15):

In the formula, f _loss (x), f _sv (x), f _lb (x), and f represent the network loss function, voltage offset function, load balancing function and comprehensive objective function of the distribution network, respectively; β ₁ , β ₂ , β ₃ are the random weights of the three objective functions, respectively; F _loss , F _sv , and F _lb are the minimum values of each iteration of the three objective functions, respectively. 10. The method for fast reconfiguration of active distribution network based on linear power flow equation and improved fireworks algorithm according to claim 9, characterized in that: in the step 4, the constraint function of the active distribution network reconfiguration model is to establish corresponding power flow balance constraints, branch current constraints, node voltage constraints and network topology constraints; The constraint function of the active distribution network reconfiguration model is as follows: (1) The power flow balance constraint, as shown in equation (16):

Among them, i, j represent the number of the node; P _Li , Q _Li are the active power and reactive power of the node i load, respectively; P _Gi , Q _Gi are the active power and reactive power of the DG; V _i , V _j are the nodes, respectively The voltage amplitudes of i and node j; G _ij and B _ij are the real and imaginary parts of the admittance matrix, respectively; δ _ij is the voltage phase angle difference between node i and node j; sinδ _ij and cosδ _ij are δ The sine and cosine functions of _ij ; (2) The branch current constraint is shown in equation (17): I _l ≤I _lmax (17) In the formula, I _l and I _lmax are the current flowing through branch l and the maximum allowable current, respectively; (3) The node voltage constraint is shown in equation (18): V _i ^min ≤V _i ≤V _i ^max (18) In the formula, V _i is the voltage amplitude of node i; V _i ^min and V _i ^max are the lower limit and upper limit of the voltage amplitude, respectively; (4) Network topology constraints: After the distribution network is reconfigured, the radial topology must be maintained, and there is no ring network.

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