Research on the assessment of the capacity of urban distribution networks to accept electric vehicles based on the improved TOPSIS method

This study proposes a TOPSIS-based method for assessing the ability of distribution networks to accept electric vehicles. This method establishes an assessment index system in terms of the rationality, safety, and economy of the distribution network operation, and assesses the capacity of the distribution network in all aspects. Firstly, a fuzzy theory-based model of users’ charging psychology under the inﬂuence of time-of-use electricity price was constructed, and the spatio-temporal distribution of EV charging loads in the target area was predicted using travel chain theory and Monte Carlo methods. Secondly, considering the rationality, safety and economy of the distribution network operation, a comprehensive evaluation index system for acceptability has been constructed. Then, a comprehensive weighting method for evaluation indexes based on AHP and entropy weight method is proposed, and the improved TOPSIS is used to evaluate the acceptance capacity of the distribution network when EV charging loads are connected in different ways. Finally, a typical IEEE33 distribution network is used to simulate the time and space distribution of the charging load, and taking the charging load access schemes proposed in this paper to verify the effectiveness of the evaluation method.


INTRODUCTION
With the growing energy and environmental problems, electric vehicles, which have the advantages of being efficient and clean, are being promoted by governments around the world. Global EV ownership exceeds 10 million for the first time in 2020. Among them, the growth trend of new energy EV ownership in China is more obvious, with 4.92 million new energy vehicles nationwide by the end of 2020, accounting for 1.75% of the total number of vehicles, an increase of 1.11 million vehicles or 29.18% over 2019. With further requirements for the construction of new energy vehicles and charging facilities in the 14th Five-Year Plan, EV access is expected to exceed 20 million by the end of the 14th Five-Year Plan. According to the National Development and Reform Commission's Energy studied by scholars, and common methods commonly rely on mathematical statistical models to analyse the temporal and spatial characteristics of EV user trips and take into account factors such as the traffic road network to predict the spatial and temporal distribution of EV charging loads. In [2,3], the trip chain theory and Monte Carlo method were used to build the EV charging load prediction model. LI et al. [4] considered the constraints of the transportation network to predict the urban EV charging load. LI et al. [5] predicted the charging load based on the parking generation rate and the traffic flow of the road network. All of these studies have not considered the impact of time-of-use electricity price on EV users' charging decisions in their modelling, and the changes in users' psychology when they generate charging demand need further analysis.
The access of large-scale EVs will bring major challenges to the security, stability, and economic operation of the distribution network, and will cause problems such as line overload, increased network loss, transformer overload, harmonic pollution, and three-phase imbalance [6]. Scholars have conducted research on the ability of the distribution network to accept EVs, mainly considering reliability, economy, security, coordination, efficiency, and quality [7].
There are three categories of evaluation methods. The first category is the quantitative evaluation method, which directly obtains the maximum number of EVs that can be charged simultaneously in the distribution network through power flow calculation. Liao [8] obtained the maximum number of EVs in the distribution network based on the maximum network loss and maximum node voltage deviation. Liu et al [9] analysed the node voltage deviation based on probabilistic power flow, and analysed the number of EVs that the distribution network can accept. The second category is the evaluation of individual operating index such as the operating economy or reliability of the distribution network. Xu et al. [10] evaluated the reliability of large-scale EVs connected to the distribution network. Yang [11] evaluated the economic impact of the intelligent charging system of EVs on the distribution network from the perspective of charging costs and benefits. Although this kind of method can quantitatively evaluate the individual operation index of the distribution network, its evaluation index is relatively single and lacks a comprehensive evaluation of the distribution network.
The third evaluation method is to use multiple indexes to comprehensively evaluate the ability of the distribution network to accept EVs. According to the construction and operation requirements of the distribution network, the comprehensive evaluation method can combine the planning of future EV charging stations or the optimal scheduling of charging loads, and incorporate the technical rationality, safety and economic indexes into the comprehensive assessment framework and the comprehensive evaluation method of the distribution network's ability to accept EVs, combining the essential characteristics of the indexes and the spatial and temporal distribution characteristics of EV charging loads to make the assessment framework more comprehensive and objective, so as to reflect more scientifically the comprehensive state of the distribution network after accessing large-scale EVs, and provide strong technical support and guarantee for the overall improvement of the safe, stable and economic operation of the urban distribution network.
This method first builds a comprehensive evaluation index system that can reflect the construction and development of the distribution network, and then uses the evaluation calculation method for analysis and research. At present, studies mostly use the Analytic Hierarchy Process (AHP) method to evaluate the capacity of the distribution network to accept EVs [12,13]. However, this method is highly subjective and may lead to a lack of objectivity in the evaluation results. The TOPSIS has been widely used in the evaluation of smart grids and integrated energy systems, it has high applicability, and the accuracy of the evaluation results is not affected by the number of research objects' index or the number of evaluation objects. Zhou et al. [14] used the TOPSIS to evaluate the smart grid. Ju [15] used a comprehensive evaluation method based on TOPSIS to evaluate the economic benefits of the integrated energy system. However, few studies have used TOPSIS to evaluate the ability of EVs to be accepted in the distribution network. Although this method has low requirements on the original data and strong adaptability, the traditional method cannot objectively and effectively reflect the difference between the evaluation scheme and the optimal ideal solution, which may lead to deviations in the evaluation results, need to use other methods to improve so as to achieve comprehensive evaluation.
Therefore, this paper proposes an evaluation method of the urban distribution network's acceptance of EVs based on the improved TOPSIS method. Firstly, the impact of time-of-use price on users' charging demand is considered, a user charging decision model is constructed based on fuzzy theory, and the spatio-temporal distribution of charging loads is simulated using travel chains and Monte Carlo method. Secondly, considering the rationality, safety and economy of the distribution network operation, an assessment index system is established to comprehensively assess the acceptance capacity of the distribution network. Then, using the entropy method to modify the AHP method, this comprehensive assignment method is used to assign weights to each assessment index, and on this basis, an assessment method combining the TOPSIS method and the grey correlation degree is constructed. Finally, the IEEE33 standard distribution network model is used to simulate and analyse the acceptance capacity of EVs when they are connected to the distribution network in different ways.
The major contributions of this paper are summarized as follows: (i) The charging decision of EV users determines the spatial and temporal distribution of the charging load. In this paper, the charging decision process of electric private vehicles is modelled in detail, and users are classified into random type users and demand type users according to their charging demand urgency, and fuzzy theory is introduced to simulate the charging decision of users under the timeof-use electricity price.

FIGURE 1
The flow chart of urban distribution network's capacity assessment of EV charging load (ii) This paper proposes a comprehensive assessment method for the capacity of distribution networks to accept electric vehicles based on an improved TOPSIS method for the first time. Firstly, a framework for evaluating the ability of the distribution network to accept EVs is constructed, and a comprehensive evaluation index system is proposed that integrates the destination layer, the criterion layer and the index layer, in which the rationality, safety and economy of the distribution network operation are taken into account. Secondly, the entropy weighting method is used to improve the AHP method, and grey correlation analysis and TOPSIS are combined, which makes the weighting of each assessment index more objective and the assessment method more scientific. The proposed method is of good theoretical guidance and practical value. Figure 1 illustrates the flowchart for the assessment of the capacity of the urban distribution network to accept the charging load of EVs. Firstly, multiple sources of data such as typical distribution networks, EV parameters, charging station charging equipment configurations and types of functional areas are analysed. Then, the spatial and temporal distribution of EV charging load in the target region is simulated based on trip chain theory and Monte Carlo method to obtain the charging demand of each region under the current EV ownership. Finally, based on the access location and number of EV charging loads in a typical distribution network, a variety of EV charging load access solutions are set up, and the optimal access solution is evaluated using the distribution network acceptance capacity assessment method based on the TOPSIS, and the safety and economic impact of EV charging load access on the distribution network under this solution is then analysed.

Trip chain theory
The trip chain theory is to connect different trip purposes in a specific temporal order to form a trip chain for EVs, which contains information on different types of trip characteristics and can better describe the user's travel process while reflecting the coherence between different trips [16].This paper takes electric private cars as the object of study and uses trip chain theory to investigate their spatio-temporal travel trajectories and travel characteristics. G TC is the set of spatio-temporal characteristic quantities of EVs trips, which can be described as follows: where i is the number of trips taken by the user on that day; s i and d i are the start and end points of the user's ith trip, respectively. The starting and ending points in the proposed trip chains in this paper mainly include residential, work, commercial, recreational and other areas [17], denoted by H, W, C, R and O respectively. Assuming that the user's first trip starts in a residential area, t 0 is the moment of the first trip; t d

Electric vehicle power consumption
This paper simplifies the EV power consumption, ignoring the actual driving process of the user driving habits and the influence of external factors on the vehicle battery power consumption, that the battery power consumption and vehicle mileage is a linear relationship, the vehicle driving process of its battery power consumption and the battery power when reaching the destination can be can be expressed as follows: where e 0 is the electricity consumption per unit mile of the EV, in kWh/km, ΔE s i →d i is the total power consumption of the vehicle from s i tod i , in kWh; B ev is the vehicle battery capacity, in kWh.

EV user charging decision model
EV users are classified into demand-based and random users based on the amount of battery power SOC remaining at their current location. The remaining SOC of the former is not sufficient for the next leg of the journey and should be recharged in time. The latter has a relatively adequate SOC, allowing charging schedules to be arranged according to the cost of charging at the current moment. The specific division principles are: where SOC d i and SOC d i+1 are the battery power of the vehicle at the current position d i and at the end of the next trip d i+1 , respectively. s d is the estimated distance travelled. Assume that the battery margin is 20% and if SOC d i+1 ≤ 20%, then the user is a demand-based user and set his charging decision factor r to 1. If SOC d i+1 > 20%, then the user is a random user and r is unknown under the current judgement condition. The choice of charging mode and charging power P d i at d i for a demand-based user with a rigid charging requirement can be expressed as follows: where t sc are the slow-charging and fastcharging power of the charging station at d i , respectively, in kW When the parking time is longer than the slow charging time, users tend to choose the slow charging to minimise damage to the battery; conversely, users choose the fast charging method to meet the rigid charging demand. For random-type users with free charging demand, in this paper, referring to the fuzzy inference-based charging decision method for randomtype demand users proposed by Zhang [18], we take the timeof-use electricity price and parking time adequacy as the inputs of the fuzzy algorithm and obtain the charging probability of random-type users by fuzzy calculation.

Charging load calculation
The Monte Carlo method is used to simulate all EVs in the target area. The basic idea of Monte Carlo (MC) simulation is that by building a probabilistic statistical model of a random Evaluation framework for the acceptability of EVs by distribution network process, obtaining a probability density function, generating a large number of random numbers that obey a probability distribution, extracting values from them, simulating the random process and repeating the above process over and over again, calculating the approximation of the problem to be solved from the experimental data obtained from the simulation, the accuracy of the approximate solution is expressed in terms of the standard error of the estimate. The Monte Carlo stochastic simulation method, based on probabilistic statistics, has been the modelling tool of more researchers due to its suitability for analysing the stochastic charging behaviour of a large number of EVs, and has achieved a wealth of research results [19,20]. The charging time and the charging load are counted separately for different demand-based users and random users to obtain the total spatial and temporal distribution of charging demand. The charging load calculation flow chart is shown in Figure A1 in the Appendices.

INDEX SYSTEM FOR ASSESSING THE ABILITY OF DISTRIBUTION NETWORK TO ACCEPT EVS
Currently, in the field of distribution network capacity assessment, there is a lack of a more objective, reasonable and comprehensive assessment method. This paper proposes a comprehensive assessment method based on the improved TOPSIS method, which is necessary for a comprehensive and objective analysis of the capacity of distribution networks to accommodate EVs.
Based on the modelling of EV charging load and the evaluation of traditional distribution network operation, this paper considers the impact of EV access on the distribution network and establishes an index system in terms of rationality, safety and economy to assess the acceptance capacity of the distribution network in all aspects. In order to reflect the objectivity and rationality of the method, a combination of AHP and entropy weighting method is used to assign weights to a variety of indicators under different EV charging load access schemes. Finally, TOPSIS is used to assess the capacity of the distribution network when charging loads are connected in different ways. The acceptability assessment framework is shown in Figure 3.
The assessment process has been applied in a number of research areas such as smart grids and active distribution grids [14,21], all of which have achieved more objective and com-prehensive assessment results, with good theoretical guidance and practical value, and the method has strong stability as well as good generalisability. Electric vehicle charging load is a new type of electrical load. The proposed comprehensive assessment framework can effectively assess the capacity of the distribution network to accept EVs, and studies have used this assessment process to effectively analyse the capacity of the distribution network to accept EVs when planning charging stations [22].
On the basis of the traditional distribution network capacity assessment, six assessment indexes were selected based on the three criteria of rationality, safety and economy respectively [10], as shown in Figure 4.
Voltage deviation non-out of limit rateT 1 : The ratio of the number of nodes whose voltage does not cross the limit after the distribution network is connected to the EV charging load to the total number of nodes. This index is used to assess whether the voltage excursions at each node meet the relevant technical standards after the electric vehicle charging load has been connected. Here, 0.9-1.1 is considered as the effective level range for node voltages.
where N v and N are the number of nodes in the distribution network that meet the voltage offset criteria and the total number of nodes in the system, respectively.
(2) Node reactive power non-compliance rateT 2 : The ratio of the number of nodes whose power factor cannot meet the required standard for reactive power configuration to the total number of nodes after the distribution network is connected to the EV charging load. This index is used to assess whether the reactive power at each node is up to standard after the EV charging load has been connected. Here, the standard range of nodal power factors is set to 0.85-1.
where N andN q are the total number of nodes and the number of nodes in the distribution network that meet the reactive power criteria, respectively.
(3) Network security operational indexS 1 : The ratio of the number of lines with current values which exceed the safe load capacity to the total number of lines after FIGURE 4 Evaluation index system of distribution network acceptability the distribution network has been connected to the EV charging load. This index is used to assess whether a single circuit in the network meets the criteria for safe operation after the charging load has been connected.
where L and L out are the total number of lines and the number of lines in the distribution network that exceed the safe operating interval of the maximum current in the network, respectively.
(4) Load rateS 2 : The ratio of the average load of a distribution transformer or line to the maximum load over a short period of time after the distribution network has been connected to the EV charging load. This index is used to assess the impact on the safe operation of the distribution network for a short period of time after the charging load has been connected.
where P av and P max are the short term average load and the maximum load value generated in the distribution network respectively.
(5) Network loss valueE 1 : The sum of the active losses of each line after the distribution network is connected to the EV charging load. These indexes used to assess the impact of the access of charging loads on the operational economy of the distribution network.
where P i and Q i are the active and reactive power of linei, respectively. R i is the resistance of line i and the connected equipment. U i is the voltage of the linei. (6) Additional reactive power consumption feeE 2 : The additional cost of reactive power compensation to ensure that the power factor is at a relatively reasonable value after the distribution network is connected to the electric vehicle charging load. This index is used to assess the additional investment required for reactive power compensation at each node in the distribution network due to insufficient power factor. (13) where is the investment necessary to compensate for the unit capacity of reactive power compensation. Q need is the reactive power compensation capacity required after the electric vehicle charging load is connected, set to 0.01 million/kVar in this paper.

TOPSIS (Technique for order preference by similarity to an ideal solution)
The basic idea of TOPSIS is to standardise the indexes in the original multi-attribute decision matrix, select the best index value to form a positive ideal solution and the worst index value to form a negative ideal solution according to the order of the indicators, and then measure the closeness to the ideal value by the closeness of each scheme to the positive and negative ideal solutions, and rank the schemes according to the closeness [23].
Although the TOPSIS method is less commonly used in comprehensive assessments of distribution networks, the method has a high degree of applicability and the accuracy of the assessment results is not affected by the number of indicators studied or by the number of objects assessed. It has a wide range of applications and can work well in large-scale evaluations of large and complex systems, as well as helping to perform horizontal analysis and longitudinal comparisons between multiple evaluation objects [4]. Indicates that the former is slightly more important than the latter 5 Indicates that the former is more important than the latter 7 Indicates that compared with the first two factors, the former is extremely important than the latter 9 Indicates that the former is absolutely more important than the latter Indicates the importance of the latter to the former in comparison to the former

Comprehensive weighting method
On the basis of the system of indicators for assessing the acceptance capacity of the distribution network in Section 4, the weights assigned to each index are determined. The AHP is widely used to determine the weights, but as it is a subjective method, it relies too much on the experience and opinions of experts in determining the time relationship of each indicator, and has the disadvantage of being subjective and arbitrary. In order to make up for this shortcoming, we use the entropy method for objective weighting, and eventually the subjective and objective weights are comprehensively weighted, and this method is currently a more scientific and general assignment method.

AHP for subjective empowerment
AHP is a subjective empowerment method that can combine qualitative concepts with quantitative data. Through the system of indicators that has been established, the degree of influence of each index on the previous layer of indicators is compared to form a judgement matrix for that layer, followed by a descending layer to carry out the same process of judgement on the degree of influence, up to the bottom layer. Calculating the weight of each index by taking the maximum eigenvalue of the judgement matrix and its corresponding eigenvector. Finally, the consistency test of the judgment matrix is carried out. Here, a judgement matrix is created by means of the scaling criteria shown in Table 1 [24].
Referring to the scaling method in Table 1, we first judge the three criteria of the criterion layer to obtain the judgment matrix of the criterion layer, which can be expressed as follows. Finally, the consistency test is carried out on the judgment matrix: the test coefficient CR of the judgment matrix is calculated, as shown in Equation (15). If the test coefficient is less than 0.1, it means that the judgment matrix has passed the consistency test; otherwise it needs to be adjusted.
where n represents the dimension of the judgment matrix, and RI is the average random consistency index, whose value is different according to different matrix rank, as shown in Table 2.
Taking the judgment matrix A as an example, its test coefficient CR = 0.0176 < 0.1, indicates that matrix A passes the consistency test.
Finally, max is standardised to obtain the weights of technical rationality, safety and operational economy at the criterion level.

5.2.2
The entropy method for objective empowerment The entropy method is an objective weighting method which defines the value and weight of data based on its original dispersion. Information is a measure of the degree of order in a system, while entropy is a measure of the degree of disorder in a system. The lower the information entropy of each indicator, the greater the amount of information it contains, and the greater its value in the assessment process, and should be assigned a higher weight value. Conversely, the higher the entropy value of the indicator, the less information it contains and the lower its weighting. The basic idea of the method is as follows.
(1) Firstly, a multi-attribute decision matrix is constructed using the values of the indicators under the different scenarios as elements. Given that the multi-attribute decision problem has m schemes to be evaluated and n evaluation indicators under each scheme; the multi-attribute decision matrix X is constructed from the ith index value x i j under the j th scheme.
Since the indicators have different scales and orders of magnitude, it is necessary to carry out the appropriate form of indexes standardisation for the different index attributes. The proposed indicators are divided into cost-based indicators (node reactive power non-compliance rate, network security operational index, network loss value, additional reactive power consumption fee), beneficial indicators (voltage deviation non-out of limit rate) and intermediate indicators (load factor), which are standardised according to the following steps: , a i j > q 2 (20) where a max, j and a min, j are the maximum and minimum values of the j th index; a i j represents the j th index in scheme i; b i j is the standardized form of the j th index in scheme i; q 1 and q 2 are the boundary values of the zone in which the intermediate type index is located. Secondly, the characteristic weight p i j and entropy e j of each index are calculated as follows: The standardised index values are therefore normalised by adding 1 in order to avoid losing value due to excessive entropy of the indicator. On this basis, the index weights j are calculated.

Comprehensive weight calculation
By multiplying the subjective and objective weights of the indicators under the index layer and combining them through normalisation, the calculation steps can be expressed as follows:

The evaluation process
This paper firstly standardises the matrix of indicators for the assessment scheme. For the measure of closeness to the ideal, in addition to the Euclidean distance, a grey correlation, which describes the closeness of the relationship between the evaluation objects, a group utility value, which measures the overall closeness of each solution to the ideal solution, and an individual deviation value, which describes the degree of deviation from the worst indexing each solution, are used for a comprehensive assessment, and the solutions are prioritised in terms of their acceptability according to the comprehensive assessment criteria.
The specific assessment process is as follows: (1) Construction of a weighted normalisation matrix The decision matrix X is standardised according to Equations (18)- (20) and the above combined index weights are multiplied with the standardised decision matrix to obtain the weighted standardisation matrix Y.
(2) Determining positive and negative ideal solutions The positive and negative ideal solutions Y + and Y − are determined from the weighted normalisation matrix, where the positive and negative ideal references are selected as follows.
Calculate the closeness between the assessed solution and the positive and negative ideal solutions The Euclidean distance, grey correlation, group utility and individual deviation values were calculated separately to measure the closeness of each solution to the positive and negative ideal solution, and the solutions were ranked in order of closeness priority.
Euclidean distance: used to calculate the distance between different schemes and the ideal solution.
Grey correlation: used to calculate the degree of correlation between the different schemes and the ideal solution.
Grey correlation coefficient: Grey correlation: Group utility values: used to calculate the closeness of different schemes to the positive ideal solution.
Individual deviation values: used to calculate the degree of deviation of the worst index from the ideal index under each scheme.
Identify comprehensive assessment indicators At the level of distance and similarity, the Euclidean distance and grey correlation can be combined.
The positive and negative Euclidean distances and grey correlations are firstly combined to obtain the positive ideal distances R + i and negative ideal distancesR − i according to the user's judgment preferences, as shown in Equations (32), (33).
where and are the preference coefficients of the user when making the assessment.
In the positive ideal distance R + i ,when the Euclidean distance from the negative ideal solution is greater and the correlation with the positive ideal solution is higher, i.e. the larger R + i is, the more similar the scheme to be evaluated is to the ideal solution. Conversely, the larger the negative ideal distance R − i indicates that the closer the scheme to be evaluated is to the negative ideal solution, the worse the acceptance capacity of the distribution network under this scheme. The positive and negative ideal distances are combined to obtain the relative distances of the different solutions to the ideal solution, which are calculated as shown as follows: From the perspective of closeness and individual deviation, the compromise coefficient Q i can be obtained by combining the group utility value and the individual deviation value, and measuring the acceptance capacity through the Q i [25], which can be expressed as follows.
The compromise coefficient reflects the degree of deviation between the worst individual index and the ideal index while reflecting the closeness of the scheme to the ideal scheme. The smaller the compromise coefficient, which indicates that this scheme is as close as possible to the ideal scheme.
The evaluation process of the TOPSIS-based distribution network capacity assessment method for accepting EV charging loads is shown in Figure 5. (1) Distribution network information This paper uses the IEEE 33 nodes distribution network system for simulation (the topology is shown in Figure 6). Set the base power of the distribution network to 10 MVA, the base voltage at the head of the network to 12.66 kV, and the total network load to 3715 + j2300 kVA.
(2) EV information It is assumed that all EVs in the study are of the same type, the battery capacity is 30 kWh and the power consumption per unit mileage is 0.21 kWh/km. Two charging stations with two charging modes are set up in each region, the fast charging power is 30 kW and the slow charging power is 4 kW, and the number of EVs is 5000.
(3) Scheme setting for EV charging load connection to the distribution network This paper sets up four evaluation schemes according to the number of EV accesses and the different access modes as follows.

Analysis of results
(1) Charging load distribution in each region In the charging load prediction, this paper uses the Monte Carlo method to simulate 5000 private cars, and the charging load prediction results for each functional area are the average value after 1000 simulations.
Based on the EV charging load prediction model described in Section 3 of this paper, we obtain the charging load distribution within each functional type of area (H, W Table A1. From Figure 7 and Table A1, it can be seen that in terms of time distribution, EV users generally prefer to charge in residential and work areas where they have plenty of residence time, and the total electricity demand in the two areas accounts for 91.68% of the total demand. There are significant differences in the temporal distribution of charging demand in the different functional types of areas, the charging load peak occurring at 04:00 PM in residential areas. The peak load in the work area is at 10:00 AM, the peak load in the commercial and leisure areas is between 12:00 PM and 02:00 PM and the total regional charging load peaks at 12:00 PM. The distribution of charging loads by region under simple and complex chains is shown in Figure A2 and Figure A3 in the Appendices. (2) Node voltage levels for electric vehicle charging loads under different access schemes The voltage levels at the nodes of the distribution network when the EV charging load is connected to the distribution network with different access schemes are shown in Figure 8, which shows that among the four schemes, the voltage passing rate is higher when the EV charging load is connected to the distribution network with Schemes 2 and 4, which is 100% and 90.9%, respectively.
(3) Evaluation results of the 4 schemes Considering that the current EV charging areas are scattered and the current EV charging load is not significant enough for the overall distribution network, the example analysis in this  paper will evaluate full node, partial node and single node access schemes for EVs of different scales and select the IEEE33 node distribution network to perform the flow calculation. Based on the technical rationality, safety as well as operational economy, we calculate the degree of closeness between the various indexes and the ideal solution in the different schemes and rank the schemes according to the evaluation results. Based on the four schemes established in this paper, the initial values of the assessment indexes under the four schemes were calculated according to the constructed system of acceptance capacity assessment indexes, as shown in Table 3.
The initial data in the table 3 were transposed to form the original index matrix X and standardised, the results of which are shown in Table 4.
The resulting objective and combined weight values are shown in Table 5. The weighted normalisation matrix is obtained by matrix normalisation and weighting, and the positive and negative ideal solutions under each scheme are: Y + = (1, 1, 1, 1, 1, 1) Y − = (0, 0, 0, 0, 0, 0) Based on the above research content, the weighted Euclidean distance, grey correlation, group utility value and individual deviation value between different indicators and positive and negative ideal solutions under each scheme were calculated according to the above formulae, and the closeness between each index and ideal solution of different schemes was measured through different perspectives, and the calculation results are shown in Table 6.
From the above six metrics, the Euclidean distance is used to measure the distance of each solution from the ideal solution. The smaller D + i is, the closer the Euclidean distance from the positive ideal solution; and the larger D − i is, the farther the Euclidean distance from the negative ideal solution, the better the acceptance capacity of the distribution network. The grey correlation can be applied to measure the degree of similarity between different schemes and the ideal solution. The larger G + i is, the more similar the scheme is to the ideal solution; and the smaller G − i is, the less similar the scheme is to the negative ideal solution and the better the scheme is accepted. Group utility value is used to quantify the overall closeness of the different schemes to the positive ideal scheme, the smallerS i , the closer the scheme is to the ideal solution and the better the acceptance at this moment. Individual deviation value is used to measure the deviation of individual indicators from the optimal index in a scheme. The smaller theB i , the smaller the degree of deviation between the worst and ideal indicators under different schemes, and the higher the acceptance capacity of the distribution network at this moment. From the calculation results in Table 6 and the ranking results in Appendices Table A2, it can be seen that the Euclidean distance, grey correlation, group utility values and individual deviation values under Scheme 4 have a higher degree of closeness to the positive and negative ideal solutions, indicating that the distribution network has a better acceptance capacity when the EV charging load is connected to the distribution network in the form of Scheme 4.
Calculating the relative distances to the positive and negative ideal solutions under different schemes, and calculating the compromise coefficients considering both the degree of closeness and the individual deviations, the results are shown in Table 7. The results of the ranking of the two comprehensive assessment indexes under the four schemes are shown in AppendicesTable A2.
From Table 7 and Table A3, it can be seen that the results of the above two comprehensive indicators show that the capacity of the distribution network is optimal in the case of Scheme 4, both at the relative distance level and in terms of the closeness of the deviation values considered. Combined with Table 3, it can be seen that under this scheme, the reasonableness of the distribution network access to the EV charging load is high, and the corresponding evaluation indexes of voltage deviation nonout of limit rate and node reactive power non-compliance rate are 0.909 and 0.181 respectively. The security of the distribution network is also relatively good, its single circuit security operating state and short time load factor are 0 and 0.147 kW respectively. The economy of distribution network operation is also relatively good.

CONCLUSION
For the impact of EV access on the distribution network, an improved TOPSIS-based index system is proposed to evaluate the ability of the distribution network to accept EVs in terms of rationality, safety and economy, respectively, which is drawn from the evaluation of traditional distribution networks. Combined with a typical IEEE33 node distribution network, we consider the electric vehicle charging load to be connected in different schemes and to assess the acceptance capacity of the distribution network. When the EV charging load is connected to the distribution network, the closer the various evaluation indicators are to the ideal point, the better the closeness, the better the acceptance capacity under this scheme.
The specific conclusions are as follows: 1. The method proposed in this paper can be applied to the overall assessment of the capacity of a typical distribution network in a city or district to accept EV charging loads that the results obtained are of reference significance for the planning of charging stations and the capacity increase of distribution networks. 2. The results of the analysis show that under the current EV penetration rate, when the EV charging load is proportionally connected to the head node of the corresponding power distribution network in each functional area in the form of charging stations, the distribution network has the best acceptance capacity, and its security, reasonableness and economy are the best overall performance. Therefore, in the planning of charging stations, it is possible to consider to build shared charging stations at the head node of the distribution network of each functional area. 3. The typical distribution network in this paper is a simplified distribution network without transformers and the proposed assessment method does not take into account the load factor of the transformer. As the penetration of EVs increases further in the future, distribution network transformers will be at risk of overloading. Therefore, in the future, the load rate of the transformer will need to be taken into account when comprehensively assessing the capacity of the distribution network to accommodate EVs.