Reactive Power Optimization of Distributed PVConnected to Three-Phase Unbalanced Distribution Network

This study presents an approach to optimize reactive power in three-phase unbalanced distribution networks using an enhanced particle swarm optimization algorithm. The study analyzes the characteristics of reactive power optimization and establishes a reactive power optimization model for the distribution network using a multi-objective optimization method. Inequality constraints are utilized to determine the reactive power optimization model constraints for three-phase unbalanced distribution networks. The study applies an improved particle swarm optimization algorithm to solve the reactive power model and achieve optimization. The experimental results demonstrate that the proposed method considerably reduces the unused power of the optimized power network within 0-500ms and achieves a maximum reactive power optimization time of fewer than 8.2s, thereby enhancing the efficiency of reactive power optimization in distribution networks.


INTRODUCTION
High power quality is essential for ensuring a stable power supply, safe operation of power equipment, and sustainable production in industries and agriculture.Reactive power is among the critical factors that can affect power quality [1][2][3] .Wind power grid reactive power optimization research aims to leverage wind turbines in wind farms to adjust reactive power and voltage in the power distribution network.This is accomplished by establishing a reactive power optimization model and utilizing an optimization algorithm to calculate the distribution networks' reactive power optimization.We reduce node voltage and restore each node's voltage to the restricted voltage value range, which can effectively reduce the system's active power loss, thus ensuring power grid voltage stability and minimizing economic losses [4] .
Relevant scholars have made some progress on this issue.NiShuang and others used the reinforcement learning method for distribution network reactive power optimization [5], the multi-scale analysis methods to analyze distribution trend data, calculated according to the distribution network data clustering algorithm for the clustering centre, to solve the parameters of reactive power in urban distribution, a Markov decision function is employed, which enhances robustness.However, this method can be time-consuming for reactive power optimization in urban distribution.To overcome this limitation, Easy Wenkai proposed an approach for optimizing reactive power in distribution networks based on an improved threshold algorithm [6] .This method utilizes a similarity search algorithm for large sample data and an immune algorithm to obtain load data that are most similar to the distribution network.By leveraging expert knowledge, this method achieves reactive power optimization in urban distribution and improves the precision of the distribution network reactive power optimization algorithm.Nevertheless, the effectiveness of the reactive power optimization algorithm needs further improvement.

Characteristics of reactive power optimization
In recent years, with the continuous expansion of the scale and capacity of distributed photovoltaic source grid-connected projects in China, voltage fluctuation of grid-connected sites frequently occurs.This chapter mainly studies the voltage fluctuation of parallel nodes in distributed photovoltaic source grid-connected systems.It analyzes the influence of distributed photovoltaic source integration into the distribution network on reactive voltage from the perspective of voltage off-limit.Specifically, analyze the changes in distribution network voltage caused by changes in photovoltaic source active power output, user load, photovoltaic source access location and other factors in the scenario of a single photovoltaic source grid-connected.In addition, in the scenario of multiple photovoltaic sources, the changes in the active output of photovoltaic power, user load, photovoltaic power supply connection location, and short-term fluctuations of specific loads were analyzed and studied to achieve better optimization results.
The optimization means are also different, but their essence belongs to the optimal power flow problem, which can be summarized as follows: (1) Nonlinearity There are equality constraints in the power flow calculation, and the formulas with equality constraints have obvious nonlinear characteristics.
(2) Discreteness In the process of optimizing problem processing, there are variables similar to transformer tap devices, which have obvious discreteness.
(3) Large-scale There are many branches and various load nodes distributed in the power grid.The lower the voltage level, the more nodes the distribution network contains.
(4) Convergence depends on the initial value The power flow formula is a nonlinear formula with many complex variables, so there may be multiple feasible solutions for this kind of problem.In order to ensure its continuous and differentiable requirements, variables are required to have continuity as far as possible, but in the actual distribution network, a considerable part of variables are separated.

Optimize model construction
In the process of reactive power optimization modelling, targeted modelling is required based on different project requirements, so the optimization objectives involved in the model are also different.In multi-objective optimization, optimizing multiple objectives simultaneously is usually not feasible.Therefore, it is crucial to carefully consider the relative importance of each objective and select the optimal results within a limited region that best aligns with those priorities.
To study the problem of multi-objective optimization, first of all, it is necessary to transform the actual objective to be achieved into a solvable model that can be described by mathematical symbols and language.Generally speaking, the practical problem is transformed into a function to obtain the extreme value.The general mathematical model is composed of n objective functions and m n  constraints, and its mathematical description is shown in Formulas (1) and (2): ( ) 0, 1, 2,..., . .
where x is an n -dimensional control variable; ( ) f x represents the objective function, which may contain single or multiple different objective functions under the same constraints, and N represents the total number of optimization objectives.Among the corresponding constraints, ( ) The optimal value pursued by multiple optimization targets maybe its maximum or minimum value, and often the maximum problem of multiple targets in the target set is not exactly the same, so as to unify the overall trend of the target.Pareto optimal domain is a set of solutions that can make multiple objectives achieve equilibrium optimization.The total objective function can reach the optimal degree that can be satisfied within the limited range.Accordingly, a multi-objective optimization algorithm is generated to solve the Pareto solution of the target.However, from the perspective of practical engineering application, it is necessary to select a solution corresponding to the engineering requirements from multiple Pareto solutions as the actual implementation scheme, which increases the difficulty of selecting the solution.Therefore, in some studies, the multi-objective problem is transformed into a single-objective problem by a weighted sum of objectives, so as to simplify the complexity of the algorithm and program, namely:

Distribution network reactive power optimization model constraints are determined
In the process of optimization to solve, we need corresponding constraints on each variable and the state, for the use of an intelligent optimization algorithm to solve the problems.Usually, the control variables are chosen to make the corresponding control variable a feasible region.The state variables can also be through the punishment function, in the form of constraints that can be converted to add it tothe objective function as part of the optimization goal.It can be expressed in the form shown in Formula (4).
In the Formula, u  and q  are penalty factors for state variables.The value of penalty factors will be related to the convergence of the algorithm, and the selection can be adjusted according to the proportion between them and the objective function.

Solution of reactive power model for three-phase unbalanced distribution network
In the optimization process, the particle will gradually update its position according to its current position, the best position in its iteration process, and the optimal position under the population cognition, and finally approach the optimal solution of the problem.The mathematical description of its basic principle can be expressed as: It is supposed that there are m particles in d dimensional space, and the velocity variable ( , ,..., ) In successive iterative optimization, the particle will update its velocity and position according to the criteria shown in Formula (5).
Formula ( 5) uses the w said to parameters of an unbalanced three-phase power distribution network and distribution network with k said the number of iterations, expressed in 1 c load characteristic parameters of the distribution network, with 2 c said learning factor of the distribution In this study, we employ an improved particle swarm optimization method to solve the reactive power model.Our approach involves modifying the factor using both exponential and sine functions, as described in Formulas ( 6) and (7).( ) 2 sin 2 In Formula (7), t represents the number of iterations; max T represents the maximum number of iterations, 1 w represents inertia weight, 2 w represents static parameter, and m represents adjusting parameters At the beginning of iteration, the optimization strategy not only increased the inertia weight, but also increased the group learning 1 c and reduced the individual learning factor 2 c , effectively improving the proposed method's global optimisation ability.

Experimental Design
To assess the effectiveness of reactive power optimization in three-phase unbalanced distribution networks, we conducted a study on a distribution network system situated in a city with 21 nodes.The topology of the system is depicted in Figure 1.After simplified topology, the number of nodes is 21, the number of loads is 11, the number of branches is 20, and the total capacity of the transmission station is 1850kW.During the simulation, the system reference capacity was set at 100MWA, and the reference voltage was set at 10kV.Among them, there are four groups of capacitor/reactor groups, which are installed in the distribution network.The adjustment range of capacitor banks is 0-0.4mvar, the adjustment step is 0.08mvar, and the maximum stride length of a single adjustment is not more than five times.

Optimization effect
To assess the effectiveness of the proposed reactive power optimization method in distribution networks, we conducted a comparison with the methods outlined in [5] and [6].The impact of the proposed method on reactive power optimization was evaluated in a three-phase unbalanced distribution network, and the results are depicted in Figure 2.  As illustrated in Figures 2-4, there are discrepancies in the optimization outcomes for reactive power using different methods.Upon analyzing the Figure, it is evident that both the method mentioned in [5] and the one in [6] result in a high amount of unnecessary power in the power grid between 0 and 500ms, even after reactive power optimization.However, the optimization used in this paper method led to a significant reduction in the power grid's reactive power, indicating a noteworthy improvement in its performance.

Optimization time
We utilized the techniques described in [5], [6] and this study to evaluate the time efficiency of reactive power optimisation in the proposed distribution network.Subsequently, we computed the time efficiency of reactive power optimization in the distribution network and presented the findings in Table 1 ( ) [ ( ), ( ),..., ( )] 1, 2,3,.. n

i h x
represents the set of equality constraints, which contains n equality constraints, and ( ) j g x represents the set of m inequality constraints for reactive voltage optimization.So when x D 

Figure 1 .
Figure 1.Simplified topology of a 21-node system

Figure 4 .
Figure 4.The optimization results of the method in this paper

Table 1 .
. Optimize time results