Reconfiguration of distributed power distribution networks based on improved gravitational search algorithms

In order to solve the problem of weak global search ability and premature convergence of GSA, a hybrid algorithm combining GSA and PSO is proposed. This algorithm can effectively use the advantages of PSO in global search. In addition, the update strategy of the gravitational constant is optimized, which improves the early search ability of the algorithm. Taking the reduction of network loss as the objective function, the improved algorithm is used to reconstruct the distribution network with distributed generation. The simulation results of the IEEE33 system show that this algorithm can efficiently decrease the network loss and enhance the node voltage.


Introduction
With the access of distributed power sources, it brings about a change in the current distribution characteristics and voltage distribution characteristics of the traditional power grid [1].Taking into account the impact of DG's integration into the grid, network losses are to be reduced in order to be able to realise efficient use of the distribution network and to save on operating costs [2].Distribution network reconfiguration is a method to reduce network losses by controlling the opening and closing states of distribution network switches to achieve a change in network topology, and to find the theoretically optimal distribution network structure that best satisfies the constraints of the system [3].
Many scholars have studied the problem of distribution network reconfiguration with DG. [4] takes into account the impact of a high proportion of clean energy access.Wei et al. [5] propose a distribution network reconfiguration considering data uncertainty in the vehicle-to-grid mode.Fu et al. [6] take the network loss and distributed wind and light curtailment as the optimization objectives, and propose a distribution network reconfiguration method that divides the two objectives into two layers of dynamic time periods.Zhang et al. [7] decouple the distribution network reconfiguration problem into two problems: load distribution optimization problem and power supply topology optimization problem.Su et al. [8] solve the distribution network fault problem containing DG and EV with an improved genetic algorithm.
This paper proposes a hybrid algorithm combining GSA and PSO.And improving the updating strategy of the gravitational constant to optimise the algorithmic capability

Objective function
Taking the minimum network loss of the distribution network as the objective function, the formula is (1).

Network topological constraints.
The reconstructed network structure is required to meet the connectivity, radial and free of ring networks and islands.

Gravitational search algorithm
The gravitational search algorithm(GSA) is a heuristic algorithm derived from the law of universal gravitation [9].In the law of universal gravitation, every particle in space is subject to the force of gravity generated by other particles in space The larger the mass, the greater the gravitational force generated by the particles.Therefore, it can be considered that the particles move toward the particles with the largest mass.So the mass represents the fitness of the particle and the position of the particle with the largest mass is the optimal solution to the problem.
It is assumed that there are many particles in space, and the formula for the inertial mass of the particle is (4).
Ft is the force of interaction between particles, and its calculation formula is (5).
where the gravitational constant changes during the iteration process, and the formula is (6).
Solving for the combined force of the particles yields their acceleration, the formula is (7).
() () () The particle will iterate the new velocity and position under the new acceleration, and the formula is (8).

3.2
The improvement strategy of gravitational search algorithm algorithm 3.2.1 PSO-GSA.Particle swarm optimization(PSO) is a simulated biological swarm optimization algorithm.Each particle will change its position by adjusting its own speed according to its own experience and population experience.GSA also uses this method to find the best position, that is, the optimal solution in space.The gravitational constant decreases with the iterative process, so that its global search ability is insufficient.The advantage of the strong global search ability of PSO can make up for its shortcomings in this aspect, and GSA can also alleviate the situation that PSO can easily fall into local optimum.The formula is (9).

Dynamically adjust the update strategy of G.
The gravitational constant has a strong influence on the algorithm, which ultimately affects the position of particles by changing the gravity.The traditional gravitational constant update strategy makes G decline very quickly in the early stage of the iteration, which makes the algorithm weak in the early searchability, and the change in the later stage of the iteration does not significantly affect the efficiency.This paper proposed a dynamical adjustment strategy to update the gravitational constant.In the early stage of the iteration, the gravitational constant decreases gently while maintaining a large value, and a small value can be maintained in the later stage.The formula is (10).

Algorithm procedure
The flowchart of the algorithn is shown in Figure 1.

Example analysis
The IEEE33 node system is used to verify the performance of the algorithm, and the simulation is realized by Matlab.The nodes and branches of this system are shown in Figure 2. In the original network, numbers 1-32 are closed sectional switches and numbers 33-37 are disconnected contact switches.From Table 2, we can see that the network loss of the system in the original network is 202.6471kW, and the minimum node voltage is 0.9133 pu.After the reconfiguration, the network loss of the system is decreased to 139.4731 kW.
Compared with the results of Deng et al.'s work [10], the improved algorithm can efficiently decrease the network loss and enhance the minimum node voltage.Figure 3 shows that the improved algorithm makes up for the shortcomings of the original algorithm.When iterating to 20 times, it basically converges to the optimal solution.In the subsequent, it is not limited to the local optimal solution, and at the same time, it still maintains the global search ability in the later stage of iteration.Figure 4 shows that after reconfiguration, the voltage of each node has been significantly improved, and the voltage level has been improved.

Distribution network reconfiguration with DG
The parameters of the distributed power supply connected to IEEE 33 are shown in Table 3.The Table 4 shows that with the access of DG, the network loss in the original network decreased from 202.6471 kW to 96.3288 kW, and the minimum node voltage also enhanced from 0.9133 pu to 0.9431 pu.Therefore, the access of DG can improve the network loss of the system and enhance the node voltage value to a certain extent.After reconfiguration with the improved algorithm, the network loss is decreased to 69.926 kW and the minimum node voltage is also enhanced to 0.9624 pu compared to the original network with DG. Figure 5 shows that the reconstructed voltage curve has been significantly improved.

Conclusion
This paper proposes a hybrid algorithm combining GSA and PSO.The update of the gravitational constant of the GSA is optimized, which overcomes the defect of the weak global search ability and also makes up for the problem that PSO can easily fall into the optimal solution.In the face of a large number of DG access to the distribution network, the results of the case study show that after the reconstruction of the improved algorithm, not only convergence speed, but also can effectively decrease the network loss and enhance the voltage profile.

Figure 3 .
Figure 3. Algorithm convergence curve.Figure 4. Voltage change curve of node after reconfiguration without DG.

Figure 4 .
Figure 3. Algorithm convergence curve.Figure 4. Voltage change curve of node after reconfiguration without DG.

Figure 5 .
Figure 5. Voltage change curve of node after reconfiguration DG.

Table 1 .
The parameter settings in the hybrid algorithm are given empirically in Table1.Parameter settings for the algorithm.

Table 3 .
Distributed power supply parameters.

Table 4 .
Reconfiguration results with DG.