Reactive power optimization of distribution network with photovoltaic power based on sparrow search algorithm

With the construction of new power systems centered around new energy, distributed photovoltaic power generation has been rapidly popularized. Photovoltaic power generation with volatility and randomness is connected to the distribution network, causing voltage fluctuations in the distribution network to exceed allowable values and an increase in system losses. The objective of this article is to establish a mathematical model for optimizing the distribution of reactive power using distributed photovoltaic power generation, to minimize system losses and voltage fluctuations. Using an improved sparrow search algorithm to solve the model and taking the IEEE30 node system as an example for simulation analysis, the feasibility of the model and algorithm is verified through case analysis.


Introduction
In recent years, we are in a critical stage of transition towards clean and low-carbon electricity.The high penetration of distributed photovoltaic power generation will have both advantages and disadvantages: the advantage is that photovoltaic power generation scheduling is flexible, which helps to stabilize the power grid to a certain extent.The downside is that photovoltaic power generation has volatility and uncertainty, which can cause node voltage fluctuations to exceed limits and increase system network losses [1] .The main ways for photovoltaic power generation to participate in voltage regulation include reactive power compensation and active power reduction [2] .The energy storage system has a fast energy response speed and can achieve fast charging and discharging, which plays an effective role in suppressing voltage fluctuations and improving the absorption capacity of photovoltaic output [3] .
This article focuses on the problem of increased network losses and voltage fluctuations caused by the integration of photovoltaic power generation into traditional low-voltage distribution networks.A parallel reactive power compensation device is used to compensate for reactive power while improving active power, and a reactive power optimization model including photovoltaic power stations is established.We simulate the IEEE30 system as a case study to verify the feasibility of the model and algorithm.

Modeling of photovoltaic
In Equation ( 2), P λ is the mean value, and P ρ is the standard deviation.The load model approximately follows a normal distribution.

Mathematical modeling of energy storage systems
The energy storage system has a fast energy response speed and can achieve fast charging and discharging, which plays an effective role in suppressing voltage fluctuations and improving the absorption capacity of photovoltaic output [4] . ( In Equation ( 3), 1 char dis FF * ′ , indicating that the battery charging and discharging cannot be carried out simultaneously.

Objective function
We establish a multi-objective function with the minimum system network loss and voltage deviation, and the model expression is: In Equation ( 4), loss P is the compensated system network loss; represent the voltage of nodes, the rated voltage of nodes, the maximum and minimum allowable voltage values, and the phase angle of nodes.

Inequality constraints
We consider the node voltage, transformer tap, reactive power compensation device capacity, the active and reactive power of photovoltaic power generation, as well as the state of charge and charge-discharge constraints of the energy storage system.In summary, the inequality constraints are as follows: In Equation ( 6), the constraint inequalities in the formula are the maximum and minimum values of each variable, respectively.

Implementation of improved sparrow search algorithm in reactive power optimization of distribution networks
The model of the sparrow search algorithm (SSA) is discoverer follower vigilance in response to the problem of easily falling into local extremes and premature convergence in the later stage of SSA iteration, adopting a Sparrow Search Algorithm Combining Sine-Cosine-Cauchy Variations (SCSSA) [5]   .During initialization, a refracted population is generated, and the discoverer's position update introduces sine and cosine, followed by the position update introducing Cauchy variation.The formula is as follows: In Equation (7), ⊗ indicates multiplication.

Example analysis
We use MATLAB to perform reactive power optimization calculations on IEEE30 node examples to verify the optimization effects of SSA and SCSSA algorithms.The IEEE30 node model has a reference value of 100MVA for the system, and [0.95~1.05](pu).This article connects photovoltaic power supply and SVG at nodes 2, 5, and 21.The output of the photovoltaic power station is 10 MW, the upper limit of SVG compensation is 5 MW, and it is switched on and off in 10 levels.Nodes 4, 6, 9, and 28 are equipped with 4 transformers, with a ratio adjustment range of [0.9~1.1].Nodes 10 and 24 are connected to two parallel capacitor compensators, with a compensation limit of 5 Mvar, and are switched in 10 stages; Node 17 is connected to energy storage with a rated capacity of 3000 kWh.The population size is 50, and the number of iterations is 100.

Conclusion
From Table 1, after optimizing the SSA and SCSSA algorithms, the network loss of each node significantly decreases.From Figure 1, before optimization, the lowest hourly voltage value of the system is generally low, and there is a risk of voltage exceeding the limit.After using SSA and SCSSA algorithms for optimization, the overall voltage level of the system has been greatly improved, and they are all within the voltage limit range.From Figure 2, the energy storage device plays an effective role in suppressing voltage fluctuations and improving the absorption capacity of photovoltaic output.
The optimization results show that the method adopted in this article can effectively reduce losses, improve the power quality of system operation, and effectively suppress photovoltaic fluctuations, thus proving the feasibility of the model and algorithm.

Figure 1 .
Figure 1.24-hour SSA and SCSSA network loss and voltage comparison chart.

Figure 2 .
Figure 2. Equivalent diagram of photovoltaic output and energy storage output, optimized photovoltaic fluctuation suppression diagram, voltage diagram of photovoltaic grid connection point.

Table 1 .
Total active power loss value within 24 hours before and after optimization.