Multi objective reactive power and voltage optimization of distribution network based on adaptive genetic annealing algorithm

. In this paper, a multi-objective reactive power optimization model of distribution network is established, which takes the minimum of line loss, reactive compensation capacitor switching loss and node voltage deviation as objective, considering the constraints of node voltage, reactive power of wind turbine, capacitor switching times. The improved adaptive genetic annealing algorithm is used to solve the model. IEEE33 system is taken as an example to verify the effectiveness of the reactive power optimization model. When the shunt capacitor and wind turbine are in the optimal reactive power compensation, the line loss of the distribution network can be minimized.


Introduction
Reactive power optimization of distribution network is usually a multi-objective optimization problem which considers the economy and security of distribution network operation [1] .
At present, many scholars use intelligent optimization algorithm to solve the reactive power optimization problem. Wang [2] proposed a chaos particle swarm optimization algorithm based on golden section to solve the reactive power optimization. Zhao [3] designed an adaptive phased genetic algorithm to solve the reactive power planning problem. Yan [4] designed a two-level optimal reactive power compensation model and solved the model by harmonic search particle swarm optimization algorithm. Liu [5] established a multiobjective optimization model and solved it with NSGA-II algorithm. Hu [6] added the penalty function of investment scale constraint in the objective function and used genetic algorithm to solve the optimal configuration of reactive power compensation. Hu [7] used the genetic algorithm and the two-level dynamic programming to solve the optimal operation scheme of the whole day equipment.
The doubly fed induction generator (DFIG) does not absorb the grid reactive power when it is running [8] . Many scholars established the distribution network reactive power optimization model considering DFIG reactive power compensation [9] . This paper considers the randomness of the active output and load of DFIG. Monte Carlo method is used to sample all day wind speed, and k-means algorithm is used to get wind speed scene division. The reactive power optimization model is established to minimize the line loss, capacitor switching cost and node voltage deviation in the whole day, and the improved adaptive genetic annealing algorithm is used to solve the model. N is the number of distribution system nodes. , and , is the active and reactive power of the node. , is node voltage and is the branch impedance. The goal of objective function is to minimize the total line power loss throughout the day.

• , 2
Here is the unit power loss cost of the k-th period. The goal of objective function is to minimize the equipment loss caused by capacitor switching.
3 is the total switching times of the k-th capacitor in the whole day, and is the cost loss caused by

Constraint condition
The power balance equation of the node is as follows.
and , is the active and reactive output of single wind turbine at node i.
is the number of DFIG incorporated by node i. The reactive power constraints for wind turbine is as follows.

6
The node voltage constraint is as follows.

8
Where is the maximum allowed number of capacitor switching times.

Adaptive genetic annealing algorithm
The following adaptive crossover probability and probability of variation is used [10] . , is the average fitness of population. and is the maximum and minimum fitness of the population. ′ is the maximum fitness of two chromosomes to be crossed.

Case study
IEEE33 node system considering wind turbine access and shunt capacitor is shown in Figure 1. Node 17 and 32 is respectively connected to 300MW and 200MW DFIG. Parallel compensation capacitors are connected at node 12 and 28, with capacity of 3 × 300 kvar and 2 × 300 kvar respectively.  Figure 2 shows the curve of active power loss and node voltage before and after reactive power optimization. When DFIG and capacitor participate in reactive power regulation at the same time, it can effectively reduce the system power loss and improve the nodes voltage, as shown in Figure 3.

Conclusion
In this paper, a multi-objective reactive power optimization model with minimum of line loss, capacitor switching cost and node voltage deviation is established. The improved adaptive genetic annealing algorithm is used to solve the model. A simulation of IEEE33 system node verified the validity of the model.