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1 Example
The calculation example is an actual network structure diagram in a certain area of Shanghai, with a total of 34 nodes, 31 segment switches and 5 tie switches. Among them, No. 1, No. 2 and No. 3 nodes are power nodes, which respectively originate from the 10 kW outgoing lines of the substations in the other three regions. The reference voltage of the distribution network is 10 kilowatts, and the total load is 9.68+j6.05MVA. The original data is shown in Appendix 3, and the network structure is shown in Figure 1.1:
Figure 1.1 The actual network structure of a certain area in Shanghai
The initial population particle number is 50, the upper limit of the inertia weight coefficient is 1, the lower limit of the inertia weight coefficient is 0.8, the upper limit of the inertia weight coefficient is 1, the lower limit of the inertia weight coefficient is 0.8, the learning factor is basically equal to about 2.0, and the maximum speed is 4.0. The minimum speed is -4.0 and the maximum number of iterations is limited to .
Because the optimization object involved in the example in this paper is in a discrete state, an improved binary particle swarm optimization algorithm for the discrete state needs to be used. Before reconstruction, the disconnected branches in the line are 8-23, 10-11, 13-27, 21-29, 20-26. After reconstruction, the disconnected branches in the line are: 13-14, 19-20, 22-23, 23-24, 10-11. Experimental results: According to this method, the average number of algorithm iterations is 15.3 times, which is very fast. Improving the previous algorithm for iteration, the efficiency is too slow, the speed is too slow, the average number of iterations exceeds 200, and the model solvability rate is low. The data before and after reconstruction are given below, as shown in Table 1.2.
Table 1.2 Example Results before and after reconstruction
| project |
Before refactoring |
after refactoring |
| disconnect branch |
8-23 10-11 13-27 21-29 20-26 |
13-14 19-20 22-23 23-24 10-11 |
| Network loss (kW) |
79.16 |
63.56 |
| Minimum node voltage (pu) |
0.98046 |
0.98363 |
The voltage of each node before and after reconstruction is shown in Table 1.3:
Table 1.3 Voltage comparison of each node before and after reconstruction in a certain area of Shanghai
| Node number |
Node voltage before reconstruction |
Node voltage after reconstruction |
Node number |
Node voltage before reconstruction |
Node voltage after reconstruction |
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 |
1 1 1 0.99822 0.99686 0.99541 0.99453 0.99349 0.99328 0.99324 0.98302 0.98307 0.98311 0.98314 0.98385 0.99080 0.99589 |
1 1 1 0.99837 0.99712 0.99579 0.99498 0.99365 0.99345 0.99342 0.98619 0.98623 0.98627 0.99405 0.99429 0.99631 0.99825 |
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 |
0.99349 0.99148 0.99088 0.98046 0.98070 0.98109 0.98153 0.98216 0.98964 0.99092 0.99202 0.99374 0.99377 0.99393 0.99409 0.99444 0.99541 |
0.99438 0.99347 0.98363 0.98931 0.98919 0.99316 0.99406 0.99411 0.98456 0.98649 0.98836 0.98998 0.99053 0.99117 0.99146 0.99200 0.99403 |
According to the data results in the above table, the node voltages before and after the 34 groups of experiments are plotted, and the two can be compared according to the high and low fluctuation states in the figure.
Figure 1.3 Voltage comparison before and after node reconstruction in a certain area in Shanghai
It can be seen from the data in the figure that after the reconfiguration and optimization of the distribution network, the network loss of the power grid is greatly reduced, and the specific value reaches 20%. The minimum value of the network voltage of the power grid has been increased. Although it is very small, it is also an effective increase. The specific increase is 0.00317pu. The change of the two factors from the reduction of network losses and the increase of the minimum voltage fully shows that the reconfiguration of the distribution network has an obvious effect.
2 Summary
This chapter first introduces the mathematical model of distribution network reconstruction, the source of the basic particle swarm algorithm and its model setting, and then based on this, according to the actual needs, the principle and model design of the particle swarm algorithm under improved conditions are introduced. Certainly.
For the reconstructed mathematical model, this chapter mainly expounds multiple objective functions in the model and multiple constraints of the functions.
For the traditional particle swarm algorithm, the inspiration of the algorithm and the details of the model are discussed one by one, and there is a detailed description of the calculation formula and process of the algorithm. For the improved algorithm and the binary particle swarm algorithm, first of all, a description is given to the machine in terms of the improvement of the algorithm, and the performance of the parameter transformation and calculation speed in the model, especially the real-time adjustment of the inertia weight coefficient, has an impact on the performance of the whole algorithm. contribution to the improvement. After that, the fitness function of the algorithm, the processing of convergence or not, the algorithm parameters, and the modules of the program are described in detail.
本章中，改进的二进制粒子群算法性能更有，效率更高，运用更加方便。