Review on the Evaluation and Improvement Measures of the Carrying Capacity of Distributed Power Supply and Electric Vehicles Connected to the Grid

<jats:p>With the increasing number of distributed power sources such as photovoltaic power and wind power and electric vehicles connected to the grid, the structure and operation state of the traditional distribution network have undergone great changes. Therefore, through the establishment of a distributed power grid-connected evaluation system, it has become an important research topic to evaluate the access of distributed power and the carrying capacity of electric vehicles in the distribution network of new power systems. Firstly, the situation of distributed power supply and electric vehicles and the impact of grid connection are introduced. Secondly, the traditional distribution network carrying capacity evaluation method is studied and introduced. Then, the distribution network carrying capacity evaluation considering uncertainty is reviewed and investigated. Finally, in view of the lack of existing research, further research is needed, aiming to provide a reference for the realization of distributed power supply and grid-connected EV carrying capacity evaluation and a scientific basis for the future operation planning of distributed power supply and EV integration into the distribution network.</jats:p>

section_content: With the deterioration of the environment and the gradual depletion of traditional fossil energy such as oil, coal, and natural gas, countries all over the world are increasingly developing clean and convenient renewable energy and using it in the power grid [1]. Since the "two-carbon strategy" was proposed, the construction of a clean, low-carbon, safe, and efficient energy system, the implementation of renewable energy alternative actions, and the construction of a new power system with new energy as the main body have become important works in the deployment of a future energy field in China. The Chinese government has issued the "13th Five-Year Plan for the Development of Renewable Energy", the "Notice on Submitting the county (city, district) Roof distributed photovoltaic development pilot Program", the "Notice on submitting the county (city, district) roof distributed photovoltaic Development pilot Program", and other policies to vigorously support the comprehensive utilization of renewable energy according to local conditions. Driven by national policies and technologies to promote the low-carbon transformation of energy, the grid connection of distributed energy has developed quickly. 

Electric vehicles (EVs), as a new type of energy vehicle with low noise, high energy efficiency, and no emissions, have become potential forces for the development of new energy [2]. As a special form of distributed energy storage, electric vehicles have attracted The load-carrying capacity of distributed power supply and grid-connected electric vehicles usually refers to ensuring that the operating conditions of the system are met and that the safe and stable operation of the system is ensured. The maximum capacity of DG and EVs that can be accepted by the energy system is an important basis for measuring and evaluating the access scale of DG and EVs in the system [4]. Literature [5] also refers to the carrying capacity of a distributed power supply as the absorption capacity. However, the emphasis of the two is completely different. The absorption capacity is usually considered from the perspective of power balance regulation, while the carrying capacity is the maximum capacity allowed to access the distribution network under the constraint conditions of the safe and stable operation of the distribution network. 

The large-scale integration of DG and EVs into the distribution network not only improves the flexibility and reliability of the distribution network but also brings about disadvantages. Therefore, it is necessary to carry out the scientific and reasonable deployment of DG and EVs to maximize the benefits without affecting the quality and safety of the power supply. Both the PV and wind power output in distributed power supply and the charging and discharging process of electric vehicles are random and uncertain. Therefore, when evaluating the carrying capacity of the two, the evaluation index, evaluation The load-carrying capacity of distributed power supply and grid-connected electric vehicles usually refers to ensuring that the operating conditions of the system are met and that the safe and stable operation of the system is ensured. The maximum capacity of DG and EVs that can be accepted by the energy system is an important basis for measuring and evaluating the access scale of DG and EVs in the system [4]. Literature [5] also refers to the carrying capacity of a distributed power supply as the absorption capacity. However, the emphasis of the two is completely different. The absorption capacity is usually considered from the perspective of power balance regulation, while the carrying capacity is the maximum capacity allowed to access the distribution network under the constraint conditions of the safe and stable operation of the distribution network. 

The large-scale integration of DG and EVs into the distribution network not only improves the flexibility and reliability of the distribution network but also brings about disadvantages. Therefore, it is necessary to carry out the scientific and reasonable deployment of DG and EVs to maximize the benefits without affecting the quality and safety of the power supply. Both the PV and wind power output in distributed power supply and the charging and discharging process of electric vehicles are random and uncertain. Therefore, when evaluating the carrying capacity of the two, the evaluation index, evaluation method, and improvement measures have many similarities and can be compared. Therefore, the carrying capacity evaluation methods of DG and EVs are jointly summarized and sorted. Firstly, the analysis starts from an overview of the grid connection of the distributed power supply and electric vehicles. Secondly, the evaluation index and the evaluation method of Energies 2024, 17, 4407 3 of 25 the carrying capacity of the distribution network are summarized, and then the uncertain carrying capacity analysis and evaluation are carried out according to the randomness and uncertainty of DG and EVs. Finally, the improvement in the carrying capacity of electric vehicles is described.
section_name: Introduction

section_content: Distributed power supply and electric vehicle grid connection are key to the transformation of modern energy systems. Together, they constitute a flexible, efficient, and sustainable power network that not only improves the overall efficiency and flexibility of the power system but also promotes the consumption of renewable energy. However, this process also faces various challenges. This section will give an overview of the grid connection of DG and EVs through the current research status and the impact of grid connection.
section_name: Overview of Distributed Power Supply and Electric Vehicle Grid Connection

section_content: Distributed generation (DG) refers to small (generally less than 50 MW in capacity) devices installed at or near the user side that can produce or store electrical energy that can supply power directly to the user or run in parallel with the grid. According to their differences in power generation methods, they can be divided into wind power, photovoltaic power generation, small hydroelectric power generation, and fuel cells [6]. 

With the acceleration of the construction of new power systems, emphasizing the formation of a clean, power-centered energy supply and consumption system, and efficiently integrating distributed power into the power system, according to the State Grid Corporation of China's forecast, in 2020 and 2030, China's installed capacity of distributed power could reach 187 million kilowatts and 500 million kilowatts. They accounted for 9. 1% and 17. 3% of the total installed capacity of national energy production in the same period, respectively. Figure 2 shows the forecast of the China Electric Union for the future generation of each power source in China. The advantages of distributed power supply, such as green environmental protection, energy saving, high efficiency, and economic flexibility, provide a good foundation for its development, and the energy utilization problem in the general environment provides an excellent opportunity for its development [7]. 

method, and improvement measures have many similarities and can be compared. Therefore, the carrying capacity evaluation methods of DG and EVs are jointly summarized and sorted. Firstly, the analysis starts from an overview of the grid connection of the distributed power supply and electric vehicles. Secondly, the evaluation index and the evaluation method of the carrying capacity of the distribution network are summarized, and then the uncertain carrying capacity analysis and evaluation are carried out according to the randomness and uncertainty of DG and EVs. Finally, the improvement in the carrying capacity of electric vehicles is described.
section_name: Research on the Development Status of Distributed Power Supply and Electric Vehicles

section_content: Distributed generation (DG) refers to small (generally less than 50 MW in capacity) devices installed at or near the user side that can produce or store electrical energy that can supply power directly to the user or run in parallel with the grid. According to their differences in power generation methods, they can be divided into wind power, photovoltaic power generation, small hydroelectric power generation, and fuel cells [6]. 

With the acceleration of the construction of new power systems, emphasizing the formation of a clean, power-centered energy supply and consumption system, and efficiently integrating distributed power into the power system, according to the State Grid Corporation of China s forecast, in 2020 and 2030, China s installed capacity of distributed power could reach 187 million kilowatts and 500 million kilowatts. They accounted for 9. 1% and 17. 3% of the total installed capacity of national energy production in the same period, respectively. Figure 2 shows the forecast of the China Electric Union for the future generation of each power source in China. The advantages of distributed power supply, such as green environmental protection, energy saving, high efficiency, and economic flexibility, provide a good foundation for its development, and the energy utilization problem in the general environment provides an excellent opportunity for its development [7]. In addition, some governments have set stringent vehicle emission standards, forcing automakers to switch to cleaner technologies. Since September 2020, China has put forward higher requirements for green sustainable low-carbon development and ecological environment construction [8]. These include the following: Accelerate the introduction Energies 2024, 17, 4407 4 of 25 of large-scale EVs into the market; it is expected that by 2030, EVs will occupy an absolute dominant position in the market [9], and strive to realize the strategy of replacing traditional fuel vehicles with EVs as soon as possible. According to the statistics of the Ministry of Public Security on 10 January 2024 reported by Xinhua News Agency, by the end of 2023, the number of motor vehicles totaled 435 million, of which 336 million were traditional vehicles, 20. 41 million were new energy vehicles, and 15. 52 million were pure EVs. Figure 3 shows the increase in the output of new energy vehicles in China over the past 13 years. 

In addition, some governments have set stringent vehicle emission standards, forcing automakers to switch to cleaner technologies. Since September 2020, China has put forward higher requirements for green sustainable low-carbon development and ecological environment construction [8]. These include the following: Accelerate the introduction of large-scale EVs into the market; it is expected that by 2030, EVs will occupy an absolute dominant position in the market [9], and strive to realize the strategy of replacing traditional fuel vehicles with EVs as soon as possible. According to the statistics of the Ministry of Public Security on 10 January 2024 reported by Xinhua News Agency, by the end of 2023, the number of motor vehicles totaled 435 million, of which 336 million were traditional vehicles, 20. 41 million were new energy vehicles, and 15. 52 million were pure EVs. Figure 3 shows the increase in the output of new energy vehicles in China over the past 13 years.
section_name: Research on the Development Status of Distributed Power Supply and Electric Vehicles

section_content: After the distributed power supply is connected to the grid, it can not only reduce the transmission power of the transmission line in the distribution network but also transmit reactive power to make the node voltage more stable [6]. The grid connection of distributed power increases the short-circuit capacity of the grid connection point, reduces the probability of system failure, and makes the distribution network more intelligent. The same optimal control of the distributed power supply and power quality device not only changes the power quality of the distribution network but also reduces the cost of the comprehensive power quality management of distribution network equipment. However, the grid connection of distributed power also brings problems to the distribution network that cannot be ignored. The traditional distribution network usually presents a one-way radial power supply mode, and then multiple distributed power sources are connected to the grid, causing voltage sag and other problems, which changes the power flow distribution. At the same time, the distributed power supply contains a large number of nonlinear power electronic switching devices, resulting in an increase in harmonic content in the distribution network, which can seriously lead to the occurrence of harmonic resonance, which is not conducive to the safe operation of the distribution network [10]. Figure 4 shows the simulation of the fast Fourier transform analysis of the harmonic after the grid-connected distributed power supply [11]. Due to the randomness and uncertainty of the grid connection of the distributed power supply, the uncoordinated operation of the distributed power supply and the load result in a great change in the line power flow, resulting in voltage flicker and fluctuation.
section_name: The Influence of Distributed Power Supply and Electric Vehicles on Distribution Network

section_content: After the distributed power supply is connected to the grid, it can not only reduce the transmission power of the transmission line in the distribution network but also transmit reactive power to make the node voltage more stable [6]. The grid connection of distributed power increases the short-circuit capacity of the grid connection point, reduces the probability of system failure, and makes the distribution network more intelligent. The same optimal control of the distributed power supply and power quality device not only changes the power quality of the distribution network but also reduces the cost of the comprehensive power quality management of distribution network equipment. However, the grid connection of distributed power also brings problems to the distribution network that cannot be ignored. The traditional distribution network usually presents a one-way radial power supply mode, and then multiple distributed power sources are connected to the grid, causing voltage sag and other problems, which changes the power flow distribution. At the same time, the distributed power supply contains a large number of nonlinear power electronic switching devices, resulting in an increase in harmonic content in the distribution network, which can seriously lead to the occurrence of harmonic resonance, which is not conducive to the safe operation of the distribution network [10]. Figure 4 shows the simulation of the fast Fourier transform analysis of the harmonic after the grid-connected distributed power supply [11]. Due to the randomness and uncertainty of the grid connection of the distributed power supply, the uncoordinated operation of the distributed power supply and the load result in a great change in the line power flow, resulting in voltage flicker and fluctuation. 

After large-scale electric vehicles are connected to the grid, due to the good flexibility and adjustability of the electric vehicle load, it is expected that in 2030, the energy storage capacity provided by China's electric vehicle load will reach 23 times that of the total installed energy storage capacity in 2018 [13]. According to the advantages of the flexible load of electric vehicles, the auxiliary functions of peaking and valley filling and peaking of distribution network can be realized through orderly and reasonable charging and discharging methods. Meanwhile, electric vehicles can use Vehicle to Grid (V2G) technology to realize electric vehicles as a backup energy storage system. When the grid load is too high, electric vehicles can feed to the grid to realize a friendly interaction of the vehicle network [14]. While reducing the negative impact of electric vehicles on the power grid, the balance of the power system can be adjusted to avoid the unnecessary construction of the power grid. However, as shown in Figure 5, in some cases, the charging of a large number of electric vehicles will lead to a disorderly charging peak, resulting in local overload, which will have a certain impact on system security and stability [15] and will also damage transformers, reduce the economic reliability of the distribution network, and exacerbate the instability of the distribution network [16]. At the same time, when charging electric vehicles, because some electric vehicle charging piles are single-phase AC charging facilities, this may lead to phase load imbalance, resulting in three-phase voltage imbalance in the distribution network. After large-scale electric vehicles are connected to the grid, due to the good flexibility and adjustability of the electric vehicle load, it is expected that in 2030, the energy storage capacity provided by China s electric vehicle load will reach 23 times that of the total installed energy storage capacity in 2018 [13]. According to the advantages of the flexible load of electric vehicles, the auxiliary functions of peaking and valley filling and peaking of distribution network can be realized through orderly and reasonable charging and discharging methods. Meanwhile, electric vehicles can use Vehicle to Grid (V2G) technology to realize electric vehicles as a backup energy storage system. When the grid load is too high, electric vehicles can feed to the grid to realize a friendly interaction of the vehicle network [14]. While reducing the negative impact of electric vehicles on the power grid, the balance of the power system can be adjusted to avoid the unnecessary construction of the power grid. However, as shown in Figure 5, in some cases, the charging of a large number of electric vehicles will lead to a disorderly charging peak, resulting in local overload, which will have a certain impact on system security and stability [15] and will also damage transformers, reduce the economic reliability of the distribution network, and exacerbate the instability of the distribution network [16]. At the same time, when charging electric vehicles, because some electric vehicle charging piles are single-phase AC charging facilities, this may lead to phase load imbalance, resulting in three-phase voltage imbalance in the distribution network. After large-scale electric vehicles are connected to the grid, due to the good flexibility and adjustability of the electric vehicle load, it is expected that in 2030, the energy storage capacity provided by China s electric vehicle load will reach 23 times that of the total installed energy storage capacity in 2018 [13]. According to the advantages of the flexible load of electric vehicles, the auxiliary functions of peaking and valley filling and peaking of distribution network can be realized through orderly and reasonable charging and discharging methods. Meanwhile, electric vehicles can use Vehicle to Grid (V2G) technology to realize electric vehicles as a backup energy storage system. When the grid load is too high, electric vehicles can feed to the grid to realize a friendly interaction of the vehicle network [14]. While reducing the negative impact of electric vehicles on the power grid, the balance of the power system can be adjusted to avoid the unnecessary construction of the power grid. However, as shown in Figure 5, in some cases, the charging of a large number of electric vehicles will lead to a disorderly charging peak, resulting in local overload, which will have a certain impact on system security and stability [15] and will also damage transformers, reduce the economic reliability of the distribution network, and exacerbate the instability of the distribution network [16]. At the same time, when charging electric vehicles, because some electric vehicle charging piles are single-phase AC charging facilities, this may lead to phase load imbalance, resulting in three-phase voltage imbalance in the distribution network.
section_name: The Influence of Distributed Power Supply and Electric Vehicles on Distribution Network

section_content: In the early or relatively simple power grid environment, the amount of grid connection of distributed power supplies and electric vehicles is relatively small, and their impact is relatively limited. Therefore, for scenarios that do not require high assessment accuracy, traditional carrying capacity assessment methods with a relatively simple calculation can be selected to quickly obtain assessment results. As a multi-attribute feature, the carrying capacity cannot be accurately evaluated and measured by a single or certain index, so it Energies 2024, 17, 4407 6 of 25 needs to be comprehensively considered scientifically and reasonably. Different evaluation methods and the selection of evaluation indicators have different influences on the final evaluation results of the distribution network carrying capacity. Therefore, this paper focuses on the key evaluation indicators and evaluation methods in the evaluation process of the distribution network carrying capacity and analyzes the scope of application and advantages and disadvantages of different evaluation methods.
section_name: Traditional Carrying Capacity Assessment Methods

section_content: Power quality, security, high quality, reliability, and economy are all important influencing factors affecting the grid integration of EVs and DGs. The widespread integration of DGs and EVs into the distribution network can alter the power supply and load characteristics of the network, which will have different degrees of impact on the operation indexes of the distribution network. At present, in evaluating the load-bearing capacity of the distribution network for DGs and EVs, it is usually considered from two aspects: on the one hand, the serviceability indicators, which are mainly used to measure the degree of satisfaction of the power system's services to customers. The serviceability index not only reflects the economy of the power system operation but also directly relates to the users' power reliability and security. On the other hand, it is also evaluated by professional indicators; these indicators are mainly considered from the four aspects of power quality, transfer capacity, adaptability, and power supply reliability. Power quality indicators mainly include voltage deviation, voltage fluctuation, harmonics, and three-phase imbalance; transfer capacity mainly includes line maximum load rate, line N-1 maximum load rate, and load dedicated supply ratio; adaptability indicators include new energy consumption rate, the maximum allowable rate of the climb of net load, etc. ; and the main indicators of power supply reliability are ASAI, SAIDI, CAIFI, and so on. 

Figure 6 lists all the evaluation indicators used in the existing literature to assess carrying capacity. Although there are many relevant evaluation indicators, most bearing capacity evaluation methods generally use four commonly used indicators, such as voltage deviation, voltage fluctuation, voltage harmonics, and three-phase unbalance; the remaining service indicators and professional indicators need to be selected by comprehensive analysis in other specific scenarios combined with the actual situation so as to improve the accuracy of the carrying capacity evaluation [17].
section_name: Indicators for Assessing Traditional Carrying Capacity

section_content: Since DG and EVs have the greatest impact on voltage when they are integrated into the distribution network, most of the literature takes voltage deviation as the main evaluation index when evaluating the carrying capacity of the distribution network [18] [19] [20]. After the DG is integrated into the distribution network, it increases the voltage of all nodes of the power grid and changes the power flow distribution of the distribution network. In severe cases, the power flow may be reversed. If the DG is connected to the distribution network without constraints, voltage deviation may occur. When EVs are connected to the grid, the node load of the distribution network is increased, which increases the power supply burden of the grid. If an EV is connected to the distribution network without constraints, the node voltage may exceed the lower limit, which affects the power supply quality of the distribution network. Usually, the deviation degree between the actual voltage value and the rated voltage value of the monitoring point is used to express the value of the voltage deviation, and the formula can be expressed as follows:

where U re is the actual voltage value and U N is the rated voltage (V) of the power grid [21]. 

According to the limit of voltage deviation mentioned in the national standard GB/T 12325-2008 [22], distribution networks with different voltage levels have different requirements for node voltage deviation, as shown in Table 1 [23].
section_name: Voltage Deviation

section_content: Since DG and EVs have the greatest impact on voltage when they are integrated in the distribution network, most of the literature takes voltage deviation as the main eval ation index when evaluating the carrying capacity of the distribution network [18-2 After the DG is integrated into the distribution network, it increases the voltage of nodes of the power grid and changes the power flow distribution of the distribution ne work. In severe cases, the power flow may be reversed. If the DG is connected to the d tribution network without constraints, voltage deviation may occur. When EVs are co nected to the grid, the node load of the distribution network is increased, which increas the power supply burden of the grid. If an EV is connected to the distribution netwo without constraints, the node voltage may exceed the lower limit, which affects the pow supply quality of the distribution network. Usually, the deviation degree between the a tual voltage value and the rated voltage value of the monitoring point is used to expre the value of the voltage deviation, and the formula can be expressed as follows:

where Ure is the actual voltage value and UN is the rated voltage (V) of the power grid [2 According to the limit of voltage deviation mentioned in the national standard GB 12325-2008, distribution networks with different voltage levels have different requir ments for node voltage deviation, as shown in Table 1 [22]. The three LLphase supply voltage deviation is ±7% of the nominal voltage U ≤ 220 V (Single-phase)

The single-phase supply voltage deviation is +7%, -10% of the nominal voltage
section_name: Voltage Deviation

section_content: When DG or an EV is integrated into the distribution network, the power output and load consumption change, and the voltage of each node of the distribution network changes, resulting in voltage fluctuation. The voltage fluctuation limit is related to the voltage fluctuation frequency and voltage level. According to the limit of voltage fluctuation mentioned in the national standard GB/T 12326-2008, for the distribution network of 35 kV and below, the corresponding relationship between the voltage fluctuation limit and the voltage fluctuation frequency is shown in Table 2 [24]. However, compared with the voltage deviation, the voltage fluctuation changes faster, and the voltage fluctuation range is smaller, usually in the range of 0. 9-11 p. u. Within the range, the ratio of the difference between the maximum and minimum values of the two adjacent voltages in the same fundamental voltage period and the rated voltage is used to represent the voltage fluctuation d in the literature [23]. 

U MIN represents the minimum value (V) of the root mean square of the node voltage; U N indicates the rated voltage (V) of the power grid; f N represents the fundamental frequency value of the adjusted amplitude wave (times/s); and r stands for frequency of change.
section_name: Voltage Fluctuation

section_content: DG power generation and grid-connected EVs involve AC/DC power conversion, which requires a large number of power electronic equipment, including inverters; gridconnected EVs also involve rectifiers and other power electronic equipment, such as nonlinear electronic equipment. Nonlinear electronic equipment integrated into the distribution network can lead to harmonic pollution and other issues, such as increasing network losses and impacting power supply quality, detrimental to the normal operation of the power system [25]. Therefore, in the carrying capacity evaluation of the distribution network, many studies include harmonics in the evaluation index [26] [27] [28] [29]. 

There are many indicators used to evaluate the degree of harmonic influence in the distribution network, mainly voltage type indicators and current type indicators. As current type indicators amplify the degree of harmonic influence and exaggerate the evaluation results, the total harmonic distortion rate of voltage is more inclined to be used to evaluate the harmonic situation. The formula is as follows:

where U 1 represents the square mean root value (V) of the voltage fundamental wave component, U h is the square mean root value (V) of the h harmonic component of the voltage, and M is the number of the highest harmonic. The national standard sets clear limits for voltage harmonics, and the voltage distortion rates of different harmonics are clearly explained according to GB/T 14549-1993 [30], as shown in Table 3. In the case of the normal operation of the power system, the three-phase voltages on the line have equal amplitudes, frequencies, and a phase angle difference of 120 degrees, which is called the three-phase voltage balance state [27]. However, in the actual operation of connecting DG and EVs to the grid, the random and unbalanced output of DG makes the three-phase power supply unbalanced. When an EV is charged at a slow speed, if no protection measures are taken, the problem of unbalanced three-phase load in the distribution network may occur, increasing the loss of lines and transformers and affecting power quality. 

According to the provisions of the national standard GB/T 12343-2008 [31] on the three-phase imbalance, the negative sequence voltage imbalance does not exceed 2% during normal operation of the power grid, and the short-term voltage imbalance shall not exceed 4%. In literature [29], the ratio of the measured three-phase voltage unbalance degree with a high probability of 95% to the standard limit is set as the three-phase unbalance degree. In literature [32], the algorithm in IEEE std 1159 was used for calculation, and the formula is as follows:

where U ab, U bc, and U ca are the line voltages (V).
section_name: Voltage Harmonic

section_content: Bearing capacity evaluation is a very complex nonlinear, mixed integer, multi-objective optimization problem, and it is difficult to find the corresponding Pareto optimal solution set [33]. The different application conditions and evaluation costs of different bearing capacity evaluation methods directly lead to differences in the accuracy and scientific rationality of the final evaluation results, so the appropriate evaluation method is particularly important for the bearing capacity evaluation. This section classifies and summarizes the existing carrying capacity evaluation methods, analyzing the pros and cons of different types of capacity evaluation methods and their suitable conditions, and divides the current traditional carrying capacity evaluation methods into four main types.
section_name: Traditional Carrying Capacity Evaluation Method

section_content: It mainly refers to the calculation of the carrying capacity of the distribution network through the derivation of mathematical formulas. When solving the grid-connected DG carrying capacity assessment problem, the available mathematical optimization algorithms include a quadratic programming method, linear programming, simple gradient method, etc., but the classical mathematical method often has problems, such as poor flexibility and a large calculation amount, which usually requires some prior conditions, but these conditions are difficult to fully meet in the actual grid-connected DG. Literature [18] uses network loss and new energy cost as objective functions and solves the DG model through a quadratic programming method. The results demonstrate that the proposed method can effectively enhance the economic operation of the distribution network. When assessing the EV carrying capacity of the distribution network, the carrying capacity is determined by establishing the power balance equation. In literature [34], the transformer capacity of the distribution network is considered as a constraint, and the carrying capacity for electric vehicles is calculated by deriving the mathematical formula, but the safety and economic constraints of the distribution network are not considered in this literature. Therefore, the evaluation results obtained are idealistic. Since classical mathematical methods often assume that the system response is linear, there may be deviations in dealing with complex EV charging behavior or the nonlinear output of distributed power supplies, resulting in reduced efficiency.
section_name: Classical Mathematical Method

section_content: When using the sensitivity evaluation method to evaluate the carrying capacity, we can identify the variables that have a greater impact on the system so that measures can be taken to increase the robustness of this part, which is conducive to improving the reliability of the system in the face of uncertainties and emergencies. The carrying capacity of the distribution network is evaluated by quantifying the response degree of the output of the distribution network model to the change in input parameters. Literature [35] takes reducing network loss and improving voltage distribution as objective functions and determines the ideal grid-connected DG installation position by calculating the sensitivity coefficient of each node's voltage stability index. Through comparison and verification by experiments, the proposed method can better carry out DG planning location. Literature [36] puts forward the concept of the reliability sensitivity index. Based on the sensitivity of different power expectations to EV scale access, an evaluation index is proposed from the perspective of reliability, and the proportion of EVs whose reliability decreases due to mass increases in EVs is taken as the carrying capacity of the distribution network. The bearing capacity can be obtained when the reliability is optimal. In literature [37], the sensitivity analysis method was used to achieve the accurate assessment of the new energy carrying capacity under the constraints of single index and multi-index, and two fractional calculation methods of forward and backward inference were adopted.
section_name: Sensitivity Based Evaluation Method

section_content: In the simulation circuit model of the distribution network, by adjusting the proportion of DG and EVs connected to the grid, when the evaluation index reaches the critical condition, the connected capacity is the carrying capacity of the distribution network. In literature [34], EV permeability is gradually increased under the peak load of the distribution network, and the variation degree of 380 V bus voltage offset, branch blockage, and total harmonic distortion rate is observed to obtain the EV carrying capacity of the distribution network in the park. Literature [38] uses DigSilent PowerFactory simulation software to build a power system simulation model containing DG and selects voltage and frequency as constraints to calculate the maximum carrying capacity of DG under the condition of the safe and stable operation of a distribution network. Literature [39] builds a distribution network simulation model based on the simulation software OpenDSS. By integrating DG into the network at different capacities and locations, by gradually increasing the capacity of DG, the system's maximum bearing capacity for DG can be determined under the constraints of voltage deviation and voltage harmonics. Through detailed simulation, it is not only possible to find low-loss power transmission paths but also to effectively manage the charging mode of electric vehicles to reduce unnecessary power losses and improve the overall system efficiency. The principle of the simulation calculation method is simple and easy to operate, but it is only applicable to the bearing capacity assessment of a certain actual distribution network and is not universal. Therefore, different simulation models need to be built for different distribution networks, and the application scenarios are relatively limited.
section_name: Simulation Calculation Method

section_content: When using the comprehensive evaluation method to evaluate the carrying capacity, the multi-dimensional optimization can maximize the system efficiency under different operating conditions by considering multiple factors, such as service index and professional index. At the same time, through the subjective and objective weighting method, the evaluation results are not only combined with the subjective experience of experts but also verified based on objective data, which reduces the evaluation error caused by individual factors and improves the overall reliability. An evaluation system is constructed by selecting suitable comprehensive evaluation indicators, and the data from various permeability levels and indicators in the network are comprehensively evaluated. Then, the carrying capacity of the distribution network is analyzed. Literature [40] uses the analysis method of interval gray clustering combined with evidence fusion theory to effectively solve the problem of data classification near the boundary line of the evaluation object and can evaluate the carrying capacity of the distribution network under different permeabilities. Based on the carrying capacity of new energy, literature [41] constructs an evaluation index system for the adaptability of new energy grid-connected schemes from various aspects, uses the analytic hierarchy process (AHP) and entropy weight method to assign index values, and finally realizes the adaptability analysis of new energy grid-connected schemes. Based on fuzzy mathematical theory, the analytic hierarchy process (AHP), and entropy weight method, literature [42] comprehensively scores the carrying capacity of the distribution network under different permeabilities. The evaluation indexes are subjective to a certain extent, and the weights of each index are also different for different distribution networks with different requirements, resulting in the deviation of the calculation results. This method is suitable for the comparative analysis of various different schemes, and the most suitable scheme is selected according to the evaluation score.
section_name: Comprehensive Evaluation Method

section_content: In view of the classical mathematical method, sensitivity evaluation method, simulation analysis method and comprehensive evaluation method, the characteristics, points and shortcomings of their respective are introduced in detail, so as to facilitate users to choose as shown in Table 4. 

Table 4. The advantages and disadvantages of different methods and their applicable scope.
section_name: The Advantages and Disadvantages of Different Methods and Their Applicable Scope

section_content: Classical mathematical method [43] The method relies on mathematical formulas for derivation and allows quantitative analysis of various parameters of the distribution network. 

1. Strong mathematical logic, reliable analysis results. 

2. Suitable for dealing with large amounts of data and complex mathematical calculations. 

The calculation of this method ignores the factors of nonlinearity and stochasticity of the distribution network, leading to errors in the assessment results. 

Sensitivity based evaluation method [44] The method is used as a systems analysis technique to analyze the sensitivity of model outputs to changes in input parameters. 

The method quickly identifies key parameters that have a large impact on the carrying capacity of the distribution network, which helps to understand the behavior of the distribution network system and facilitates optimization and retrofitting. 

The results of the sensitivity analysis are affected by the model assumptions and parameter selection, and the sensitivity analysis calculations may be large when complex systems are encountered. 

Simulation calculation method [18] By building a simulation model of the distribution network, various conditions of actual operation and fault conditions are simulated, and then the maximum carrying capacity is calculated. 

1. The method can take into account the randomness and nonlinear factors of the distribution network. 

2. The simulation results obtained by this method are intuitive and easy to understand and analyze. 

The accuracy of the simulation results depends on the complexity and accuracy of the model, so when the model is complex, its calculation results deviate from the actual situation. 

comprehensive evaluation method [45] The methodology combines multiple assessment methods while utilizing multiple assessment metrics and weighting assignments to provide a comprehensive and integrated assessment of the distribution network. 

1. It can reflect the carrying capacity of the distribution network in an integrated and comprehensive way, avoiding the limitation of the single assessment index. 

2. The weights of the indicators can be adjusted flexibly, which is highly flexible. 

The selection of the allocation of assessment indicators and weights may be influenced by subjective factors, and the computational complexity is high, requiring a large amount of data and computational resources.
section_name: Assessment Method Definition and Characteristics Advantage Drawback

section_content: With the rapid development of distributed power supply and electric vehicles, their access volume has increased year by year, and their impact on the power grid has become increasingly significant. These impacts are characterized by obvious uncertainties and fluctuations, and multiple uncertainties from inside and outside the system, such as multienergy load forecasting errors, will have a great impact on the accuracy of the carrying capacity assessment of DG and EVs [46]. Whether in terms of computational complexity or model complexity, the traditional deterministic carrying capacity assessment method can no longer meet the current assessment needs for a reasonable assessment of carrying capacity. Therefore, it is necessary to conduct analysis and modeling according to the uncertainty of DG and EVs and then carry out the carrying capacity assessment. This section mainly introduces the uncertainty modeling and evaluation methods of distributed power supply and electric vehicles.
section_name: Carrying Capacity Evaluation Method Based on Uncertainty

section_content: Both DG output and EV charging load have stochasticity and uncertainty, and Figure 7 shows the power prediction time series specification of distributed PV with wind power Energies 2024, 17, 4407 and EVs. The distributed PV output is affected by seasons and weather with intermittency and randomness, and PV power generation is higher in sunny weather, while power generation decreases significantly in cloudy and rainy weather [47]. EV charging load is affected by various factors such as charging facilities, users' habits, and traveling demand, and EV charging load has complex characteristics, such as uncertainty in time and space, etc., and EV driving speeds are lower in congested city center areas. In city centers, EVs travel slower and have longer parking times and may require more frequent charging, whereas in suburban areas or highways with smooth traffic flow, EVs travel faster and have shorter parking times and relatively lower charging needs [48] ; therefore, modeling of the uncertainty that accurately describes DG and EVs is a prerequisite for the assessment of distribution network carrying capacity. 

mainly introduces the uncertainty modeling and evaluation methods of distributed power supply and electric vehicles.
section_name: Uncertainty Modeling of Distributed Power Supply

section_content: Both DG output and EV charging load have stochasticity and uncertainty, and Figure 7 shows the power prediction time series specification of distributed PV with wind power and EVs. The distributed PV output is affected by seasons and weather with intermittency and randomness, and PV power generation is higher in sunny weather, while power generation decreases significantly in cloudy and rainy weather [44]. EV charging load is affected by various factors such as charging facilities, users habits, and traveling demand, and EV charging load has complex characteristics, such as uncertainty in time and space, etc., and EV driving speeds are lower in congested city center areas. In city centers, EVs travel slower and have longer parking times and may require more frequent charging, whereas in suburban areas or highways with smooth traffic flow, EVs travel faster and have shorter parking times and relatively lower charging needs [45] ; therefore, modeling of the uncertainty that accurately describes DG and EVs is a prerequisite for the assessment of distribution network carrying capacity. The main carrying capacity research methods in the literature of DG output modeling include the fuzzy method, probability distribution function method, and typical scenario planning method. For example, in literature [46], according to the fuzzy theory, the triangular fuzzy number is used to describe the load and DG processing, and the uncertain parameters can be converted into a range interval plus an internal "most trusted value". Literature [29] describes the uncertainty of solar sunshine intensity and wind speed by establishing Beta distribution, two-parameter Weibull distribution, and normal distribution probability models. Literature [47] takes system reliability and network loss as optimization objective functions, establishes typical distribution network operation scenarios by analyzing historical meteorological data and load characteristics, and builds a reasonable mathematical model for DG location and capacity determination based on a series of scenario combinations. The main carrying capacity research methods in the literature of DG output modeling include the fuzzy method, probability distribution function method, and typical scenario planning method. For example, in literature [49], according to the fuzzy theory, the triangular fuzzy number is used to describe the load and DG processing, and the uncertain parameters can be converted into a range interval plus an internal "most trusted value". Literature [30] describes the uncertainty of solar sunshine intensity and wind speed by establishing Beta distribution, two-parameter Weibull distribution, and normal distribution probability models. Literature [50] takes system reliability and network loss as optimization objective functions, establishes typical distribution network operation scenarios by analyzing historical meteorological data and load characteristics, and builds a reasonable mathematical model for DG location and capacity determination based on a series of scenario combinations.
section_name: Uncertainty Modeling of Distributed Power Supply

section_content: EV charging load demand is affected by EV performance parameters and driver behavior characteristics, and its uncertainty is affected by both time and space. In terms of EV charging load prediction models, there are mainly three kinds: Monte Carlo simulation method, spatio-temporal model based on travel chain, and charging load vehicle-roadnetwork model.
section_name: Uncertainty Modeling for Electric Vehicles

section_content: The Monte Carlo method is also known as the statistical simulation method. Its core idea is to approximate the numerical solution of complex problems by simulating a large number of random samples. Figure 8 shows the flow diagram of the Monte Carlo method. In literature [51], considering the randomness and temporal fluctuations of the disordered charging power of electric vehicles, a temporal model of the charging power of each EV was simulated based on the Monte Carlo model. Literature [52] analyzed the variation characteristics of EV quantity in different road conditions at different time periods through the trip production of different travel chains and used the Monte Carlo sampling method to simulate EV travel and charging behavior under different temporal and spatial distributions. In literature [53], the power demand model of EV charging load was established, and the Monte Carlo method was used to simulate the EV charging load curve 24 h a day. number of random samples. Figure 8 shows the flow diagram of the Monte Carlo method. 

In literature [48], considering the randomness and temporal fluctuations of the disordered charging power of electric vehicles, a temporal model of the charging power of each EV was simulated based on the Monte Carlo model. Literature [49] analyzed the variation characteristics of EV quantity in different road conditions at different time periods through the trip production of different travel chains and used the Monte Carlo sampling method to simulate EV travel and charging behavior under different temporal and spatial distributions. In literature [50], the power demand model of EV charging load was established, and the Monte Carlo method was used to simulate the EV charging load curve 24 h a day. 

The Monte Carlo simulation method can simulate EV charging load according to a variety of situations. However, this method is based on the premise of having a large number of data samples, which is highly dependent on data. Therefore, when the data samples are insufficient, the accuracy of this method is greatly reduced.
section_name: Monte Carlo Simulation

section_content: The spatio-temporal model based on travel chain is similar to the Monte Carlo method in that both require a large number of sample data for driving. The states of electric vehicles include driving, parking, and charging, so the charging load demand can be simulated according to the different travel characteristics of drivers. Literature [51] uses The Monte Carlo simulation method can simulate EV charging load according to a variety of situations. However, this method is based on the premise of having a large number of data samples, which is highly dependent on data. Therefore, when the data samples are insufficient, the accuracy of this method is greatly reduced.
section_name: Space-Time Model Based on Travel Chain

section_content: The spatio-temporal model based on travel chain is similar to the Monte Carlo method in that both require a large number of sample data for driving. The states of electric vehicles include driving, parking, and charging, so the charging load demand can be simulated according to the different travel characteristics of drivers. Literature [54] uses the travel chain analysis method to analyze issues such as EV driving track distance, generate EV charging load demand samples, and solve the optimal configuration of charging stations based on EV charging demand. Literature [55] established the spatial transfer relationship between different activity-travel chains of drivers in a day, and on this basis, they analyzed and studied the spatial-temporal distribution characteristics and charging characteristics of EVs on different activity-travel chains considering the characteristics of traffic networks and the charging characteristics of electric vehicles. Figure 9 shows the flow chart of travel chain simulation with an electric vehicle driver as an example [56]. Based on a large number of EV trip survey data as samples, literature [57] established a probability distribution model to calculate the spatial-temporal distribution of charging demand by combining the relationship between EV start trip time, driving time, parking time, and the start and end point of EV trip. Different travel chain space-time models can reflect different drivers' travel locations and driving times. Compared with the Monte Carlo simulation method, the spatio-temporal model based on travel chain considers the randomness of charging load in both time and space distribution. 

traffic networks and the charging characteristics of electric vehicles. Figure 9 shows the flow chart of travel chain simulation with an electric vehicle driver as an example [53]. Based on a large number of EV trip survey data as samples, literature [54]
section_name: Space-Time Model Based on Travel Chain

section_content: The vehicle-road-network model of EV charging load is established, which not only considers the influence of vehicle charging time on the characteristics of charging load time distribution but also analyzes and evaluates the influence of different traffic paths and traffic conditions on the spatial distribution of EV charging load. Literature [55] simulates the actual EV driving conditions based on the urban road traffic network model so as to build a spatio-temporal prediction model of EV charging load in the "vehicle-roadnetwork" mode, which can improve the prediction accuracy of the temporal and spatial distribution characteristics of EV charging load in urban areas. Figure 10 shows the unified modeling diagram of the "vehicle-road-network" mode. Literature [56] proposes a prediction model of EV charging load spatial and temporal distribution based on the universal gravity model, which can accurately calculate the spatial and temporal distribution of EV charging load and analyze EV charging load demand under different scenarios in order to solve the problem of the inaccurate prediction of EV charging load spatial and temporal distribution due to the insufficient consideration of vehicle-road-station-network interaction. In order to analyze the impact of unordered EV charging on the power quality of the distribution network, literature [43] built a continuous power flow model based on the "vehicle-road-network" model s structure and the impact of driver behavior on the distribution network to quantitatively evaluate the charging load demand and voltage distribution under bad charging conditions.
section_name: Charging Load Vehicle-Road-Network Model

section_content: The vehicle-road-network model of EV charging load is established, which not only considers the influence of vehicle charging time on the characteristics of charging load time distribution but also analyzes and evaluates the influence of different traffic paths and traffic conditions on the spatial distribution of EV charging load. Literature [58] simulates the actual EV driving conditions based on the urban road traffic network model so as to build a spatio-temporal prediction model of EV charging load in the "vehicle-road-network" mode, which can improve the prediction accuracy of the temporal and spatial distribution characteristics of EV charging load in urban areas. Figure 10 shows the unified modeling diagram of the "vehicle-road-network" mode. Literature [59] proposes a prediction model of EV charging load spatial and temporal distribution based on the universal gravity model, which can accurately calculate the spatial and temporal distribution of EV charging load and analyze EV charging load demand under different scenarios in order to solve the problem of the inaccurate prediction of EV charging load spatial and temporal distribution due to the insufficient consideration of vehicle-road-station-network interaction. In order to analyze the impact of unordered EV charging on the power quality of the distribution network, literature [45] built a continuous power flow model based on the "vehicle-roadnetwork" model's structure and the impact of driver behavior on the distribution network to quantitatively evaluate the charging load demand and voltage distribution under bad charging conditions. Although the uncertainty modeling of DG and EVs in the above distribution network carrying capacity assessment has a certain application value in the DG output and EV charging load prediction, there are still common shortcomings in the data requirements, dynamic processing, computational complexity, generalization ability, and comprehensive consideration of multiple factors which need to be improved and optimized.
section_name: Charging Load Vehicle-Road-Network Model

section_content: This section classifies and summarizes the existing evaluation methods on the bearing capacity of uncertain distribution network, which are mainly divided into three types: mathematical optimization method, intelligent optimization algorithm, and stochastic Although the uncertainty modeling of DG and EVs in the above distribution network carrying capacity assessment has a certain application value in the DG output and EV charging load prediction, there are still common shortcomings in the data requirements, dynamic processing, computational complexity, generalization ability, and comprehensive consideration of multiple factors which need to be improved and optimized.
section_name: Load Capacity Evaluation Method of Distribution Network Based on Uncertainty

section_content: This section classifies and summarizes the existing evaluation methods on the bearing capacity of uncertain distribution network, which are mainly divided into three types: mathematical optimization method, intelligent optimization algorithm, and stochastic analysis method. Each method is analyzed and introduced in turn below.
section_name: Load Capacity Evaluation Method of Distribution Network Based on Uncertainty

section_content: Mathematical optimization method:

The load-carrying capacity evaluation method based on the mathematical optimization method mainly uses linearization to optimize the non-convex model into a convex optimization model and uses commercial solvers such as Cplex, Gurobi, and Copt to solve it. Literature [60] takes the maximum capacity of the distributed power supply connected to the distribution network by the reactive power compensation device as the objective function, establishes the load capacity evaluation model, uses the Gurobi solver to transform the model into a second-order cone programming model through second-order cone relaxation for solving, and obtains the final evaluation results. Literature [17] uses a linearized power flow model of the distribution network to evaluate the distributed power supply carrying capacity of the distribution network based on the robust operation of the static VAR compensator (SVG) and the on-load regulator transformer (OLTC). Literature [61], aiming at obtaining the characteristics of the output uncertainty of distributed power supply, modeled it through probability and affine forms, proposed an uncertain optimal power flow model to evaluate the absorption capacity of the distributed power supply, and carried out an equivalent transformation. However, although the mathematical optimization method can optimize the solution in the feasible domain, because the higher-order term is ignored in the optimization solution, there are errors in the accuracy of the obtained power flow results.
section_name: •

section_content: Based on intelligent optimization method:

Compared with the mathematical optimization method, the intelligent optimization method is a kind of optimization algorithm that simulates the natural or biological evolution process. These algorithms have the characteristics of self-adaptation, self-organization, and self-learning, do not need to linearize the model, and can be solved in the original nonlinear condition of the model. Therefore, more influences of limiting factors of carrying capacity can be considered in the assessment of carrying capacity. Literature [62] establishes an online reinforcement learning framework based on the SARSA algorithm for the wind power photovoltaic (PV) energy management model. Due to the characteristics of wind power PV systems such as uncertainty and complex constraints, the adaptive ability of the SARSA algorithm, which does not rely on mathematical models, makes it well suited for solving such problems, and at the same time, the SARSA algorithm has a high computational efficiency in solving the optimization model, which offers a good solution for realizing the optimization and cost-effective energy management of wind power PV energy systems to achieve optimized and cost-effective energy management. Literature [63] analyzes the correlation between the output and load of distributed power supply, constructs an improved correlation sample matrix, and uses the forward push-back generation power flow calculation formula and simulated annealing algorithm to optimize the solution. Based on the principle of the K-means scene clustering algorithm, literature [64] conducted scene clustering on the annual time series of photovoltaic and load power, analyzed their variation rules, and finally calculated the distributed photovoltaic carrying capacity of the distribution network under different photovoltaic access states by improving the whale optimization algorithm. Literature [65] established a probabilistic power flow model of the distribution network considering photovoltaic correlation. Nataf transform was combined with third-order polynomial normal transform based on the moment method to deal with photovoltaic correlation. A chance-constrained optimization model was constructed, and an enhanced random weight particle swarm algorithm was employed to solve it. However, a drawback of intelligent optimization algorithms is their susceptibility to getting trapped in local optima, so the method needs to be improved.
section_name: •

section_content: Stochastic analysis:

The random analysis method is an analysis method combining random sampling and statistical principle, which has a good effect on dealing with the diversity of gridconnected EVs and DG [66]. Literature [67] uses the random load distribution of typical weather data and simulates the real load fluctuation to study and analyze the maximum PV permeability of the system gathered near the feeder source, near the midpoint of the feeder line, and near the end of the feeder line, randomly distributed and evenly distributed in five photovoltaic grid-connected scenarios. Literature [68] uses several typical daily PV output and distribution network load curves in a year for evaluation and generates a large number of PV grid-connected scenarios with different locations, quantities, and capacities through Monte Carlo simulation, making the evaluation more comprehensive and reasonable. Based on the survey data, literature [69] analyzed the charging behavior and modes of various electric vehicle types. Monte Carlo stochastic simulation was used to generate the starting charging SOC and charging time randomly and to analyze and predict the charging load of electric vehicles, but the evaluation process is time-consuming and requires a large number of calculations such as Monte Carlo simulation, which is computationally expensive.
section_name: •

section_content: For Mathematical optimisation method, Intelligent optimisation method and Stochastic analysis method, their respective features, points and shortcomings are described in detail to facilitate the user's choice as shown in Table 5. 

Table 5. The advantages and disadvantages of different methods and their applicable scope.
section_name: The Advantages and Disadvantages of Different Methods and Their Applicable Scope

section_content: Mathematical optimization method [70] The method describes the scheme of grid planning as a mathematical model and establishes the relevant constraints according to the actual situation and then solves the optimal scheme. This method usually has linear planning, multi-objective planning, and dynamic planning. 

1. Has a good sense of principle. 2. Strongly structured. 

1. Complexity of modeling according to the actual situation. 

2. Difficult to solve the model. 3. Difficult to quantify the boundary conditions. 

Intelligent optimization method [71] The method is a class of optimization algorithms that simulate natural or biological evolutionary processes. These algorithms are adaptive, self-organizing, self-learning, and capable of handling complex nonlinear optimization problems. Stochastic analysis method [72] The method is an analytical approach based on random sampling and statistical principles, where a large amount of sample data are generated by random sampling and then statistically analyzed to estimate the overall characteristics and performance. 

1. Strong adaptability. 2. High precision. 

1. Calculation volume is large. 2. Results have randomness.
section_name: Assessment Method Definition and Characteristics Advantage Drawback

section_content: In the new distribution network system, if DG and EVs are integrated into the distribution network without constraints, it will inevitably cause problems such as power quality, safety, and reliability, which seriously restricts the improvement in the carrying capacity of electric vehicles. To facilitate the integration of a large number of electric vehicles into the distribution network for charging and to enhance the network's capacity for electric vehicles, the charging strategy of electric vehicles can be reasonably optimized, and the charging period of electric vehicles can be transferred to the peak and valley periods of the grid load by means of peak shifting without changing the topology of the urban distribution network. This is to prevent peak-on-peak occurrences resulting from the accumulation of electric vehicles and other loads, so it can accept more electric vehicles connected to the grid; on the other hand, distributed photovoltaic power generation is clean and environmentally friendly, with flexibility and reliability, so power can be used to supply electric vehicles with a photovoltaic power output, not only to ensure that photovoltaic consumption is in place, and to promote electric vehicles connected to the grid's carrying capacity.
section_name: Electric Vehicle Grid-Connected Carrying Capacity Improvement Method

section_content: Electric vehicle charging load has different characteristics from other types of loads, which can control the charging process in an appropriate way to improve the characteristics of electric vehicle charging load. In view of the complex diversity of charging demand, literature [73] adopts a dual-objective optimization strategy and takes reducing load fluctuation difference and charging cost as optimization function objectives to design an orderly charging strategy for electric vehicles, thus achieving an effective improvement in EV charging experience. It is mentioned in literature [74] that the charging plan submitted by the driver the day before can be used as the scheduling basis to carry out design planning, such as the day-before charging schedule and price orientation, so as to rationally allocate the charging time. Of course, it can also achieve peak cutting and valley filling and optimal operation of the system directly through V2G technology. Literature [75] has formulated two stages of objective functions for the charge-discharge model. The first stage is to optimize the maximum daily load; the second stage is to further optimize the load curve on the basis of optimizing the load variance in the first stage, so as to realize the participation of electric vehicles in the regulation of the power system. Literature [76] takes peak cutting and valley filling and minimization of charging cost as optimization objectives, combined with the dynamic response of TOU, and then establishes an ordered charging model and uses a heuristic algorithm to solve it. For large-scale electric vehicles in a region, literature [77] proposed an energy demand-oriented orderly charging control strategy for electric vehicles. The findings indicate that this method effectively distributes electric vehicle loads, and strategically scheduling charging times during peak and off-peak periods can enhance regional power load curve stability. However, the above optimization strategy mainly reflects the advantages of an orderly charging strategy from some charging indicators but does not optimize and improve the charging power of each electric vehicle. 

Literature [78] proposes a new control strategy for an electric vehicle intelligent charging station and analyzes the power flow relationship between each electric vehicle and the distribution network under different working conditions. The experimental results show that the proposed intelligent control strategy can effectively realize the bidirectional intelligent distribution of electric vehicle power and improve the carrying capacity of electric vehicles. Literature [79] uses V2G technology to minimize network loss as the goal, puts forward two scheduling strategies for reactive power and active power regulation, and analyzes cost benefits. However, the above literature is only from the perspective of the power grid, not from the perspective of users, and users' responses to the charging strategy is the prerequisite for the implementation of the optimization strategy. The literature [80] takes the minimum peak valley difference in system load and the maximum battery health (SOH) of electric vehicles, with minimizing the charging and discharging costs of electric vehicles as the objective function, considering the requirements of both supply and demand to optimize the scheduling of electric vehicle charging and discharging. Literature [81] constructs a vehicle network interaction (V2G) model of a single EV that can comprehensively consider the response capabilities of active and reactive power. According to the response characteristics of an EV for different uses, an EV energy efficiency power plant model considering user participation is established. Simulation verifies that the response and energy storage capabilities of the energy efficiency power plant have time distribution characteristics. Literare [82] propes a demand response control strategy for electric vehicles by changing the adjustable capacity boundary, studies the influence of model parameters on the charging load of electric vehicles, and determines that the model and control strategy can achieve demand response functionality for electric vehicles while meeting user charging demands. Most of the above studies use qualitative analysis in the analysis of the orderly charging strategy of electric vehicles and lacks quantitative analysis of the distribution network's capacity for electric vehicles under the orderly charging strategy. Therefore, on the basis of qualitative analysis, some scholars quantitatively calculate the carrying capacity by volge deviation, network loss, line carrying capacity, and other indicators. Literature [83] takes the voltage deviation as an evaluation index and evaluates the node voltage after the power flow calculation of the distribution network and then calculates the carrying capacity of electric vehicles. Literature [84] takes the overload rate of distribution transformers as a constraint index to conduct a quantitative evaluation of the carrying capacity of electric vehicles in residential areas. However, the indicators selected for the above quantitative analysis of the orderly charging strategy are relatively single. Literature [85] analyzed the charging load under different charging modes and the impact of the EV charging load of different scales on the power flow of the distribution network and then evaluated the carrying capacity of EVs under different charging modes by combining node voltage deviation and line carrying capacity, as well as other aspects. Literature [40] takes network loss and voltage offset as the evaluation indexes of the carrying capacity of electric vehicles and obtains the total load of the distribution network by summing up the conventional load and the charging load of electric vehicles and then analyzes the carrying capacity from two aspects: network loss and voltage offset. Literature [86] analyzed the power flow analysis of the distribution network from the perspective of active power loss and node voltage and analyzed the carrying capacity evaluation under three different charging strategies: random disordered charging, time-of-sale price charging, and intelligent charging.
section_name: Optimize EV Charging Strategy to Improve Carrying Capacity

section_content: The use of renewable energy to replace the original distribution network for electric vehicle charging has become a new trend, which can not only ease the burden of the distribution network but also effectively alleviate the pollution problem. The integration of electric vehicles and a distributed photovoltaic power generation system has many advantages: on the one hand, it can increase the carrying capacity of the distribution network for electric vehicle charging load; on the other hand, it can use electric vehicle charging to help solve the intermittency problem of the distributed photovoltaic power generation system and can reduce the cost of energy storage. Therefore, the local use of renewable energy can be fully considered in planning and design [87]. Figure 11 shows the integrated system diagram of distributed power supply and an electric vehicle. 

Energies 2024, 17, x FOR PEER REVIEW 21 of 28
section_name: The Distributed Photovoltaic System Connects to Electric Vehicles to Enhance Capacity

section_content: The use of renewable energy to replace the original distribution network for electric vehicle charging has become a new trend, which can not only ease the burden of the distribution network but also effectively alleviate the pollution problem. The integration of electric vehicles and a distributed photovoltaic power generation system has many advantages: on the one hand, it can increase the carrying capacity of the distribution network for electric vehicle charging load; on the other hand, it can use electric vehicle charging to help solve the intermittency problem of the distributed photovoltaic power generation system and can reduce the cost of energy storage. Therefore, the local use of renewable energy can be fully considered in planning and design [84]. Figure 11 shows the integrated system diagram of distributed power supply and an electric vehicle. Solar photovoltaic charging involves converting the low-voltage DC generated by solar panels into 200 volt AC using photovoltaic inverter technology, enabling direct use for electric vehicle charging. This technology improves the charging efficiency and has the characteristics of safety, reliability, and zero pollution. At present, some research on the combination of electric vehicles and the distributed photovoltaic power generation system has been carried out at home and abroad. 

As mentioned in literature [88], Carbon Day Automotive of the United States introduced a photovoltaic plug-in charging station which can convert solar energy into power generation energy without polluting the environment. Photovoltaic charging stations for electric vehicles complement the volatility of photovoltaic power generation with the randomness of electric vehicle charging, thus reducing the grid's susceptibility to the impact of electric vehicle charging loads [89]. Literature [90] simulated different lighting conditions, conducted a comparative analysis of grid-connected EV charging stations and battery energy storage systems with a distributed photovoltaic power supply, considered the cost of energy transmission and the charging state of the battery, and tested this energy management method. Literature [91] studied the effects of large-scale random electric vehicle charging on the distribution network, established an EV charging model considering renewable energy access, and proposed a multi-objective dynamic charging control strategy based on two control objectives: optimization of regional power peak valley difference and stable power fluctuation. 

Aiming at conducting research on the consumption ability of electric vehicles caused by the access of the distributed photovoltaic power generation system, literature [92] proposes a real-time energy management method for electric vehicle charging stations equipped with a renewable energy power generation system and energy storage system. Through the direct load control of electric vehicle charging, the maximum consumption of renewable energy can be achieved. Literature [93] proposes a load balancing strategy for virtual power plants that considers electric vehicle charging demand, enhances renewable energy utilization, and balances power consumption loads. Literature [94] proposes a capacity allocation method that effectively combines EV charging stations and photovoltaic systems that not only improves the influence of EV charging behavior on the distribution network, but also improves the local absorption rate of PV. 

Simultaneously, due to the negative impact of "peak-on-peak" on the total load of the distribution network following electric vehicles connecting for charging, many studies have been conducted to introduce new energy distributed generation technology into the distribution network to alleviate the power supply pressure brought on by the charging load. In view of the situation that a large number of electric vehicles may be connected to the grid and lead to the overload of the distribution network, literature [95] proposes an electric vehicle charging station integrated with mixed renewable energy. Such charging stations generate electricity by renewable energy photovoltaic power, as well as other methods. These charging stations can be connected to the grid or off-grid and are called independent or remote electric vehicle charging stations. Literature [96] proposes a scheduling strategy that can improve the safety and economy of the distribution system by establishing an uncertainty prediction set, and based on the robust optimization idea, in order to improve the rise of the peak value of the load curve caused by electric vehicles connected to the grid, effectively manage electric vehicle charging and discharging, thereby reducing operational costs and peak load values on the distribution network curve. Literature [97] takes electric vehicles and distributed photovoltaic power supplies as research objects and establishes a distribution network scheduling model of a vehicle cluster virtual power plant and highproportion photovoltaic access. This model effectively enhances new energy consumption rates and achieves "peak shaving and valley filling" effects in the distribution network. 

In addition to the two carrying capacity improvement methods mentioned above, strategies from reactive power compensation, energy storage technology, on-load voltage regulator transformer tap adjustment, inverter power factor control, and government R&D subsidies can also potentially improve the carrying capacity of the distribution network. Firstly, from the perspective of reactive power compensation, reactive power compensation devices such as static reactive power compensators can be installed so that when a large Energies 2024, 17, 4407 20 of 25 number of distributed power sources are connected to the grid and cause over-voltage, the voltage level can be reduced by compensating the reactive power, thus improving the carrying capacity of distributed power sources in the distribution network. Secondly, from the perspective of energy storage, energy storage technology as a flexible resource to participate in regulating the power supply and demand balance of the distribution network can reduce the power penetration rate of distributed power grid-connected peak hours so as to ensure that distributed power grid-connected constraints do not overstep the limit, but at present, the overall cost of the energy storage equipment is high, and the actual operation of the problem of economy needs to be considered. Then, from the aspect of on-load transformer tap adjustment, by flexibly adjusting the position of the on-load transformer tap, the system voltage level can be changed so as to prevent the over-voltage problem arising from the grid connection of the large-volume distributed power supply and then enhance the acceptance capacity of the distributed power supply. Then, from the point of view of inverter power factor control, absorbing reactive power at the peak of its output power is also running at the lagging power factor, thus reducing the overall voltage level and thus improving the carrying capacity of the distributed power supply and grid connection of electric vehicles. It is mentioned in literature [98] that the government can solve the consumers' concern about the inconvenience of charging by subsidizing the construction of charging stations, and also through the research and development of electric vehicle batteries. The government can also improve the carrying capacity of EVs by subsidizing the construction of charging stations to address consumers' concerns about the inconvenience of charging and by incentivizing EV manufacturers to produce EVs that are more adaptable to complex environments through, for example, subsidies for EV battery development.
section_name: The Distributed Photovoltaic System Connects to Electric Vehicles to Enhance Capacity

section_content: This paper firstly introduces the development status quo of distributed power supply and electric vehicles and carries out a detailed introduction to the impacts of distributed power supply and electric vehicle grid connection on a distribution network. Secondly, it carries out an introduction to the previous traditional distribution network carrying capacity assessment methods and introduces in detail the construction of the traditional carrying capacity assessment index system, and the advantages and disadvantages of the various traditional assessment methods, as well as their scope of application, are outlined; then, it carries out an introduction to the uncertainty-based carrying capacity assessment methods for the distribution power supply and electric vehicle grid connection and introduces in detail the uncertainty modeling of the distribution network and the modeling based on uncertainty. Then, for the uncertainty of distributed power sources and electric vehicles on-grid, the introduction of carrying capacity assessment methods based on uncertainty is carried out, and the uncertainty modeling of distributed power sources and electric vehicles and the distribution network carrying capacity assessment methods based on uncertainty modeling are introduced in detail, and finally, the strategies of optimizing the charging strategy of electric vehicles, the access of the distributed photovoltaic power generation system to electric vehicles, and other aspects such as reactive power compensation are elaborated in terms of the strategies of optimizing the charging strategy of electric vehicles on-grid, the access of the distributed photovoltaic power generation system to electric vehicles, and reactive power compensation. Finally, the method of EV grid-connected carrying capacity improvement is described from other strategies such as optimizing EV charging strategy, distributed PV generation system access to EVs, and reactive power compensation. It can provide a scientific basis for the future planning of EV grid connection and has the following outlooks for the future research of carrying capacity assessment:

• At present, the modeling of distributed power supply (DG) and electric vehicles (EVs) is mostly based on simplified mathematical models. In the future, the complexity and diversity of their actual operation should be further considered, such as the output characteristics of different types of DG and the driving mode and charging behavior of EVs, and more refined models should be established. • With the progress of technology, the application of electric vehicle charging and discharging technology is promoted, which helps balance the load of the power grid and realize the flexibility and stability of the power grid. At the same time, vehiclegrid interaction technology can be used to realize the two-way exchange of information flow and energy flow, which helps electric vehicles to better interact with the power grid and participate in the balancing and scheduling of the power grid.
section_name: Conclusions and Prospects

section_content: Financial subsidies, tax incentives, and other policies are proposed to reduce the investment cost of distributed power supply and electric vehicles to promote market competitiveness; at the same time, the construction of market mechanisms is encouraged to promote the reform of the electric power market, improve the electric power market mechanism, guide distributed power supply and electric vehicles to participate in electric power market transactions, and to achieve the optimal distribution and efficient use of resources.
section_name: •

section_content: New technical means should also be explored to improve the carrying capacity of the distribution network, such as optimizing energy storage system configurations and establishing virtual power plants. Energy storage systems can provide a regulatory capacity when DG and EV output fluctuate, while virtual power plants can achieve more efficient supply and demand matching by aggregating and dispersing resources.
section_name: •

section_content: Funding: This research was funded by the Science and Technology Project of China Southern Power Grid, grant number ( 090000KK52222153/SZKJXM20222151 ).

section_name: Data Availability Statement:

section_content: The data that support the findings of this study are available from the corresponding author, upon reasonable request.
section_name: Data Availability Statement:

section_name: Conflicts of Interest:

section_content: Authors Qing Wang and Huaying Zhang were employed by the company Shenzhen Power Supply Bureau Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The authors declare that this study received funding from Qing Wang. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article or the decision to submit it for publication.
section_name: Conflicts of Interest: