**6. Case Analysis**

In this paper, the IEEE-33 standard node distribution network is used as an original network for analysis [21]. The distribution network structure is shown in Figure 9.

**6. Case Analysis** 

movements.

( ) *ij* τ

*j*) at time *t*+1

ρ

current cycle, ( ) *ij* Δ

th ant in the path (*i*, *j*).

where

ρ

α

(3) Pheromone Update

location and *j* is the end location. ( ) *ij*

calculated, and then the path is selected.

is in the range of (0, 1). ( ) *ij* Δ

τ

has a value range of (0,5).

η

τ

*k k*

*Q L*

algorithm. *Lk* represents the total cost of the path taken by the *k-*th ant in this cycle.

is the pheromone volatilization coefficient, 1-

τ

*t* =0 at the initial time. ( ) *<sup>k</sup>*

*ij*

τ *t* Δ =

selection path during the movement. The value range of

denotes the role that information accumulated by ants during exercise plays in the selection of ant

importance of characterizing the visibility of the path, that is, the role that the ant plays in the ant

*t* represents the pheromone strength on the path (*i*, *j*) at time *t*. Where *i* is the beginning

According to the expected value of each capacity of each node and the pheromone concentration value on the path, the transition probability of the *n*-th ant at each capacity point on the node is

In order to prevent excessive heuristic pheromone and flooding the heuristic information, the residual pheromone is updated after the ant completes an ergodic operation on all *m* position capacities. According to Equations (27) and (28), adjusting the amount of information on the path (*i*,

( 1) (1 ) ( ) ( ) *ij ij ij*

1 () () *<sup>m</sup> <sup>k</sup> ij ij k*

/ if the kth ant passes the path (i,j) () 0 else

where *Q* represents the pheromone strength, and its value affects the convergence speed of the

 τ *t t* =

ρ

 τ

*t* represents the pheromone increment on the path (*i*, *j*) during the

 *t tt* + = − +Δ ρ τ

τ

*ij* Δτ

βis (0,5).

is the heuristic factor of expectation, which is the

(27)

is the pheromone residual coefficient, and

Δ =Δ (28)

*t* represents the number of pheromones left by the *k-*

(29)

*t* is a heuristic function, which is generally the reciprocal of

β

the sum of the DG installation cost at location *j* and the distributed power source operating cost.

**Figure 9.** IEEE-33 standard node distribution network. **Figure 9.** IEEE-33 standard node distribution network.
