Reliability expansion method of urban distribution network based on mixed integer programming and multi-objective optimization

The power supply system in urban area has high complexity, and its expansion is difficult. Therefore, a reliability expansion method of urban distribution network based on mixed integer programming and multi-objective optimization is proposed in this paper. Considering the economic benefits and voltage difference of investment and operation, a general model for optimizing the overall installation of the power grid has been established. Enable particle swarm optimization algorithm to increase the energy storage capacity of the power grid and solve the optimal expansion rate through mixed integer linear programming. Finally, research has shown that this research method can achieve the best scaling effect.


Introduction
As the urbanisation process accelerates and the payload increases, the reliability of urban distribution network in China has been further improved.Due to the continuous expansion of the city scale and the increasing population, it brings more and more load to the urban power distribution system [1][2].The current distribution network structure and equipment capacity cannot meet the needs of rapid development of the city, therefore increasing the reliability of the distribution network is an important way to improve its operational stability and safety.With the deepening of urban construction, the distribution network was thoroughly and thoroughly examined.With the development of urbanization, the population of cities is increasing, and the functions of cities are also increasing, so the demand for energy supply, stability and continuity is also increasing [3][4].
Reference [5] proposes a method for planning the constant capacity of wind power access networks.The expansion of the distribution network is completed taking into account the time characteristics of distribution, the time characteristics of different seasonal loads, and real-time rates.Reference [6] proposes a distribution network expansion design method that considers load price response.This method is a two-level joint optimization model that considers the response of electric vehicle users to compensation prices, establishes a distribution network expansion planning model, optimizes line types and price incentives, and minimizes the annual total investment cost.At a lower level, an optimization model based on the charging and discharging compensation price of electric vehicles has been established to optimize the charging and discharging efficiency of electric vehicles and minimize charging costs.However, due to the huge load on the distribution network, the traditional methods mentioned above cannot meet the application requirements at present.Therefore, this article proposes a reliability expansion method for urban distribution networks based on mixed integer programming and multi-objective optimization.Therefore, this article proposes a reliability expansion method for urban distribution networks based on mixed integer programming and multi-objective optimization.This method combines hybrid programming and multi-objective optimization: hybrid and global linear programming are combined with multiobjective particle swarm optimization algorithms to achieve multi-objective optimization and improve the reliability of urban distribution networks.These innovations include: a. Comprehensive consideration of economic benefit of investment operation and voltage deviation: This method takes economic benefit of investment operation and voltage deviation as optimization objectives, and comprehensively improves the reliability level of urban distribution network from both economic and technical perspectives.
b. Optimization of expansion ratio: Using mixed linear programming with integers to solve the optimal deployment ratio, ensuring that the reliability requirements are met and the expansion cost is reduced as much as possible.
In the future, this method will be applied to the actual planning and operation of urban distribution networks, thereby contributing to the sustainable development of urban power grids.

Distribution network multi-objective optimal configuration model
In the multi-objective optimal allocation, the economic benefit of investment operation and voltage deviation are two important evaluation indexes.
The economic benefit of investment operation refers to the balance between the investment cost and operation cost and the economic benefit obtained in the process of distribution network expansion.This includes factors such as the acquisition cost of the expansion equipment, maintenance and operating costs, as well as the potential income and economic benefits brought by the expansion.Optimizing the cost-effectiveness of investment business can improve cost-effectiveness during the expansion process.Urban distribution network, taking into account the cost of energy reserves and future potential energy-related economic value, it is of great significance to minimize the balance between investment costs and energy supply reserve demand.
Voltage deviation refers to the deviation between the measured voltage and the expected value in a power system.Voltage deviation is one of the most important indices to measure system stability and quality.The normal voltage range ensures the normal operation of the system.However, voltage deviation may cause equipment faults, power consumption increases, and customer dissatisfaction.By optimizing the voltage deviation, the power supply quality and user satisfaction of urban distribution network can be improved.
In the energy storage expansion of urban distribution network, considering expansion investment and operating costs, optimizing economic benefits can ensure the feasibility of expansion schemes and minimize costs.By optimizing voltage deviation, maintaining voltage stability, improve the reliability of the power supply, reduce the risk of power outages and equipment damage to users, effectively managing energy dispatch and reserve demand, reducing energy consumption and environmental impact.

Economic benefits of investment and operation.
In view of the high installation costs of energy storage systems, this Article examines the installation costs of energy storage systems and other electricity generation systems in the distribution network and the cost of purchasing electricity over the network [7].And obtains the economic target, namely the total daily average cost of the distribution network Where, ' f represents the total operating cost of the distribution network, N represents the service life of the energy storage system under normal conditions, () Pt represents the total cost of purchasing electricity from the upper power network, up P represents the total electricity purchased from the upper power network, ( ) G P represents the generation cost of other equipment in the distribution network, and t represents the current operating time of the distribution network.( ) ( ) Where, N represents the number of branch nodes in the distribution network, ( )

Optimization of energy storage capacity expansion in urban distribution network
Connect to the municipal distribution network, the capacity of the energy storage configuration should be clearly and appropriately optimized.In this paper, the sum of the loss sensitivity of the distribution network and the current fluctuations of all branches is added to calculate, and the objective function is constructed to reduce the expansion loss of the distribution network [8][9].Since the constructed objective function is not unique, it is processed by weighted average method, and the calculation formula is as follows: ( ) Where, w represents the network loss generated by the distribution network within 12h, V represents the sum of fluctuations generated by all branches of the distribution network within 12h, N represents the number of branches included in the distribution network, t represents the charge and discharge period, and '  and ''  both represent the weight of multiple objective functions.In order to optimize storage capacity and access conditions to urban distribution networks, it is necessary to analyze the limitations of distribution network operation and the limitations of efficient and responsive energy storage systems [10].
The Multipurpose Particle Swarm Optimization (COAS) algorithm is used to improve energy storage capacity.The detailed program is shown in Figure 1.The implementation process of using multi-objective particle swarm optimization algorithm to optimize the expansion of energy storage capacity in urban distribution networks is mainly divided into three stages:

Reached maximum of iterations？
Step 1: Calculate the standard deviation of the loss sensitivity of the branch network in the distribution network, arrange the calculation results, install energy storage in the branch with the largest standard deviation value, and determine the best installation position for energy storage expansion.
Step 2: Initialize the particle swarm size, and analyze the expansion of each branch of the power system to obtain the total loss and power flow distribution of the distribution network, so as to achieve the calculation of particle swarm fitness; Step 3: When the maximum number of iterations is reached, the algorithm stops and creates Pareto solutions to complete the expansion of the distribution network.

The optimal scaling ratio of reliability is solved based on mixed integer linear programming
The optimal expansion ratio is solved by mixed integer linear programming.The set of computationally feasible solutions is: Among them,  is the reasonable response parameter,  is the fixed variable parameter, and  is the pole parameter.Thus, the feasible solution set is obtained.The data of the set is tested, and the optimal solution is solved, and the optimal proportion is obtained.
Where,  is the constraint domain parameter,  is the other vector dimension, and S is the relaxation constraint parameter, so as to obtain the optimal reliability expansion ratio.

Experimental test
In order to verify whether the proposed method is also reasonable and effective in practical application, IEEE-30-node distribution network (Figure 2) is taken as an example to propose a fixed-capacity planning method for wind-light-storage access distribution network with reference [5] mentioned in the introduction, and a distribution network expansion planning method taking charge load price response into account is proposed in reference [6].Relevant experimental tests were carried out.The DG configuration is shown in Table 1.This test test mainly tests whether the planned expansion method has met the network expansion requirements, and tests the change in signal transmission speed after expansion.In order to make experimental comparison, the traditional literature [5] method and literature [6] method are set as the two comparison methods of the experiment.Set capacity expansion requirements for multiple experimental samples, and obtain capacity expansion results through the operation of different capacity expansion methods, as shown in Table 2.As can be seen from the statistical data obtained in Table 2, after the application of the method [5] and the method [6] to the distribution network expansion, there are certain differences with the ideal target of expansion, and the distribution network capacity reach the ideal value.Especially, the expansion effect is worse when the number of nodes is large.In contrast, when the nodes of the research method are 200/300 and 500, the expansion of the distribution network reaches 80GB, reaching the expansion target.When the number of nodes is 100 or 400, a slight deviation occurs.This is because in the expansion of the distribution network, small deviations are usually difficult to completely avoid, but as long as these deviations do not exceed the prescribed scope, do not affect the normal operation of the equipment and the quality of electricity, it is usually acceptable.In actual operation, corresponding measures can be taken, such as accurate measurement, reasonable parameter setting, etc., to minimize the occurrence of deviation.

Conclusion
The conclusion proposes a reliability expansion method for urban distribution networks based on mixed integer programming and multi-objective optimization.Based on the economic efficiency and bias in the investment process, a multi-objective model is established.The combination of a multiobjective particle cluster optimization algorithm and combined integer linear programming provides optimal degradation rate.Extending and improving the capacity of the distribution network to respond to urban development needs; enhancing the reliability and safety of the power supply system, and expanding the potential and capacity of urban power supply.

2. 1 . 2 .
Voltage deviation index.Because of their own reasons, renewable resources often affect the quality of voltage, current and power flow in urban distribution network when they are used for power generation.Calculate the voltage deviation index '' f as shown in equation (2):

Figure 1
Figure 1 Capacity Integration of Energy Storage Expansion in Distribution Networks.

Figure 2
Figure 2 Distribution network of IEEE-30 nodes.

Table 2
Comparison data of expansion results.