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Data‐driven robust planning of electric vehicle charging infrastructure for urban residential car parks

2020; Institution of Engineering and Technology; Volume: 14; Issue: 26 Linguagem: Inglês

10.1049/iet-gtd.2020.0835

1751-8695

Ziming Yan, Tianyang Zhao, Xu Yan, Leong Hai Koh, Jonathan A. Go, Wee Lin Liaw,

Transportation and Mobility Innovations

IET Generation, Transmission & DistributionVolume 14, Issue 26 p. 6545-6554 Research ArticleFree Access Data-driven robust planning of electric vehicle charging infrastructure for urban residential car parks Ziming Yan, Ziming Yan School of Electrical and Electronic Engineering, Nanyang Technological University, SingaporeSearch for more papers by this authorTianyang Zhao, Tianyang Zhao Energy and Electricity Research Center, Jinan University, Guangzhou, ChinaSearch for more papers by this authorYan Xu, Corresponding Author Yan Xu xuyan@ntu.edu.sg School of Electrical and Electronic Engineering, Nanyang Technological University, SingaporeSearch for more papers by this authorLeong Hai Koh, Leong Hai Koh School of Electrical and Electronic Engineering, Nanyang Technological University, SingaporeSearch for more papers by this authorJonathan Go, Jonathan Go Housing & Development Board, SingaporeSearch for more papers by this authorWee Lin Liaw, Wee Lin Liaw Housing & Development Board, SingaporeSearch for more papers by this author Ziming Yan, Ziming Yan School of Electrical and Electronic Engineering, Nanyang Technological University, SingaporeSearch for more papers by this authorTianyang Zhao, Tianyang Zhao Energy and Electricity Research Center, Jinan University, Guangzhou, ChinaSearch for more papers by this authorYan Xu, Corresponding Author Yan Xu xuyan@ntu.edu.sg School of Electrical and Electronic Engineering, Nanyang Technological University, SingaporeSearch for more papers by this authorLeong Hai Koh, Leong Hai Koh School of Electrical and Electronic Engineering, Nanyang Technological University, SingaporeSearch for more papers by this authorJonathan Go, Jonathan Go Housing & Development Board, SingaporeSearch for more papers by this authorWee Lin Liaw, Wee Lin Liaw Housing & Development Board, SingaporeSearch for more papers by this author First published: 17 February 2021 https://doi.org/10.1049/iet-gtd.2020.0835Citations: 2AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The number of electric vehicles (EVs) is expected to grow significantly, which calls for effective planning of charging infrastructures. While the planning of the charging infrastructure relies on an accurate charging demands, the behaviours of EVs charging are not always predictable and can be sensitive to many uncertain future environmental factors. Considering such uncertainties, this study aims to robustly and optimally determine the chargers and main switch board (MSB) capacities without violating queuing time constraints and load flow constraints. The non-parametric estimations of charging demands are derived with data-driven charging behaviour analysis considering diverse social factors, including travelling patterns, queuing, and changes of charging facilities. Then, the impacts of the EV integration are modeled by a stochastic load flow program. The samples of the stochastic load flow stipulate the conditional value-at-risk constraints for the planning of chargers and MSBs, which consider the probabilities and scenarios in a box of ambiguity with bounds. Afterwards, by limiting the frequency and severity of constraints violation, the total investment cost is minimized with a distributionally robust optimisation program. Simulation based on a real-world residential community in Singapore is carried out to testify the effectiveness of the proposed method. 1 Introduction In recent years, lots of nations around the world have launched their financial and technological support for the electric vehicle (EV) penetration. Global EV Outlook by International Energy Agency during 2018 and 2019 have provided details on how the EV industry is growing worldwide [[1], [2]]. For example, Canada targets 30% of new passenger light-duty vehicles in 2030 to be EVs. China targets 150,000 additional public chargers in recent years. India plans a USD 1.4 billion three-year budget to encourage the uptake of EVs from April 2019. California of the US has targeted 5 million EVs on the road by 2030. However, EV charging has an element of randomness that reduces grid predictability and increases network management complexity [[3]]. A large-scale adoption of EVs could introduce a large number of unpredictable load demands [[4]] into the system. In the future, the unpredictability of EV charging load demands could increase the risk of stress on the network and reduce the overall reliability of the low-voltage distribution network if not managed properly. As an important part of future 'smart nation', Singapore has also been promoting EV utilisation, e.g. the e-mobility expects that 54% cars will be EVs by 2050 [[5]], and the SP group has planned 2000 charging points across the whole country [[6]]. In addition, Dyson will be setting up an EV factory in Singapore, and in the future, Singapore will become a worldwide centre for EV production. Moreover, Nissan has recently committed that by 2022, all its new car models arriving here will be either fully battery-powered or hybrids. Therefore, it is expected that the number of EVs will also rapidly grow in the future, and this would significantly affect the existing Singapore power grid. Compared with state-wide planning and siting of charging stations, the planning of the EV charging infrastructure at residential areas could provide more convenience to drivers [[7]]. Therefore, it is necessary to study the impacts of integrating EVs for the Singapore residential community and properly plan the charging infrastructure against the uncertain EV load demands. Recently, the integration of EVs has attracted great research interests. In the literature, many works are focused on the planning of the EV infrastructure and EV integration impact analysis. On the one hand, the works for the EV infrastructure planning are concentrated on the placement of charging stations, optimisation of the distribution system, and capacity expansion of transformers. Zhang et al. [[8]] planned the location of charging facilities considering traffic congestion. Yao et al. [[9]] planned the EV charging systems and integrated power distribution with a multi-objective model, where the annual investment and energy losses are minimised by siting of chargers. Bayram et al. [[10]] proposed the charging station capacity planning based on a different class of customers. However, the randomness of charging behaviour at a charging point cannot be considered with these models. To account for the randomness of charged energy and charging duration, Wang et al. [[11]] proposed a stochastic planning model to minimise investment and operation cost of the distribution system and maximise captured traffic flow. The authors in [[12], [13]] proposed a robust planning for locating and sizing of charging facilities under uncertainties. It is assumed that the EV charging demands can be represented by an ideal probability distribution. However, actual EV charging behaviours are dependent on much more environmental factors such as time, date, and technical advances (e.g. different battery capacity), which cannot be accurately considered by a simple probability distribution model. Other works aim to study the impacts of the EV integration with a path-based charging model or probability-based charging model, including the impacts on voltage [[14]], capacity [[15]], and power quality [[16]] of the distribution network. The uncertain impacts of the EV integration on the distribution network can significantly change the constraints for the planning of the charging infrastructure, which is rarely considered in existing planning methods. There is still a need for a robust infrastructure planning method that more realistically considers the randomness of charging behaviours and the impacts of the EV integration on the distribution network. The robust planning of the charging infrastructure shall satisfy queuing time constraints and power flow constraints under the uncertainties of future EV charging behaviours. To satisfy the constraints of the infrastructure planning, the characterisation of the stochastic EV charging demands is necessary. Currently, various theories and models have been proposed to study the stochastic EV charging demands. The authors in [[13], [17]] assume that the number of charging EVs follow a normal distribution. The authors in [[18], [19]] proposed time-varying EV load modelling methods to quantify the power demand of EVs. Zhu et al. [[20]] indicate queuing is imperative for representing the actual availability of charging capacity and charging demand. However, these models cannot take the randomness of travelling behaviour into account. To consider such randomness, Fotouhi et al. [[21]] proposed a general model for representing EV drivers' behaviour, but it cannot consider future environmental factors such as increasing battery capacities due to the technological advance. The planning of the infrastructure shall consider the future load demands, which is difficult to be achieved with existing models. Qian et al. [[22]] model EV load demand with a stochastically quantified state of charge (SoC) considering four different scenarios. It provides helpful indications on how EV load may reshape the total load profile but planning for a residential community EV charging infrastructure (such as chargers, main switch boards (MSBs), and transformers) cannot be implemented with such a generalised load demand model. For a robust planning of the EV infrastructure at residential communities, the randomness of future drivers' charging behaviours shall be considered, and the constraints due to the uncertain impacts of EVs on distribution networks shall be also addressed. In consequence, this paper aims to more comprehensively and accurately characterise the charging demands based on data-driven methods and provide an optimisation-based support for a robust planning of the charging infrastructure. The contributions of this paper are threefold: • A data-driven EV charging behaviour analysis method considers the travelling pattern, random individual behaviour, queuing, and uncertain future environmental factors. To probabilistically predict the EV charging demands at future residential car parks, a two-step Monte Carlo simulation method is presented to derive the aggregated charging loads and probabilistic charging loads. By modelling total charging demands as the aggregation of random individual demands, multiple environmental factors including queuing, travelling habits, and facilities' advance can be considered with the proposed data-driven method. • The formulation of conditional value-at-risk (CVaR) constraints is based on the EV integration impact analysis with a stochastic load flow. The samples of the stochastic load flow stipulate the CVaR constraints and consider the stochastic scenarios in a box if ambiguity with bounds. Based on the electrical networks model and the obtained probabilistic EV charging demands, the load flows distribution on distribution lines, MSBs, and substations are calculated for each uncertain scenario. • With the EV integration CVaR constraints, a distributionally robust chance-constrained optimisation-based planning method is proposed to determine the optimal sizing, location of EV charging facilities as well as the distribution network expansion plan. The total investment cost for EV fast/slow chargers and MSB capacity is minimised with the distributionally robust optimisation program. The decision variables are EV charger number and additional MSB capacity. The remaining paper is organised as follows. The data-driven EV charging behaviours analysis method to predict probabilistic EV charging demands is presented in Section 2. The distributionally robust chance-constrained optimisation for charging infrastructure planning and the formulation of CVaR constraints based on stochastic load flows are presented in Section 3. A case study is presented in Section 4, followed by the conclusions in Section 5. 2 Data-driven charging behaviour analysis 2.1 Method framework The characterisation of the future charging demands is preliminary for a robust EV infrastructure planning. An overview of the proposed data-driven charging behaviour analysis method is introduced in Fig. 1. The future random social behaviours (i.e. travelling pattern, queuing, preference to choose chargers) and uncertain equipment parameters (such as charging power, batteries capacity, consumed electricity per kilometre) are simultaneously considered with the proposed method. Fig. 1Open in figure viewerPowerPoint Procedure of the data-driven EV charging behaviour analysis method The randomness in social behaviours could significantly change the power demand of EV charging. For example, the habits of drivers to leave/arrive at the car park, weekdays/weekends or the locations of the car parks can dramatically reshape the profile of charging demands. Fortunately, the identify unit (IU) recordings for the driver travelling behaviour can provide effective insights on how does the drivers' behaviours vary with respect to different scenarios. Based on the statistical social behaviours derived from the IU data, this paper develops a data-driven framework to progressively derive the expected future charging load profiles from individual EV charging to probabilistic aggregated charging behaviours. As shown in Fig. 1, the proposed framework consists of individual charging behaviour modelling, aggregated charging behaviour modelling, and two Monte Carlo simulation steps to probabilistically predict the future charging load profile. The individual charging behaviour considers the travelling pattern (based on data analytics) and charging pattern (based on the parameters of charging facilities and SoC), which will be introduced in Section 2.2. Each individual charging will contribute a power demand increase to the total charging power inside a car park, which is modelled as an aggregated charging load inside a car park with the first Monte Carlo simulation. Afterwards, by sampling the aggregated charging loads, the second Monte Carlo simulation derives the probabilistic charging load demand inside a car park considering diverse social factors. 2.2 Individual charging behaviour The probabilistic charging power demands consist of numerous samples of individual charging. The individual charging behaviour modelling aims to formulate the single sample charging profile based on travelling behaviours, availability of chargers, SoC, charging power, and charging duration. To determine the statistical behaviour of individual charging behaviours for all vehicles, the data from the travelling IU data set is utilised. In this paper, the statistical analysis and charging process simulation are incorporated to model the individual EV charging behaviour as illustrated in Algorithm 1 (see Fig. 2). Fig. 2Open in figure viewerPowerPoint Algorithm 1: Individual charging behaviour modelling algorithm In Algorithm 1 (Fig. 2), statistical analysis on the IU data set is firstly employed to determine the arrival time for each EV and its corresponding parking duration, which is step 0. To sample the residential parking behaviours for step 0, this paper utilises 93 million recordings of individual car parking events from 2017 to 2018 provided by the Housing Development Board based on the IU data set. The arrival and departure patterns for modelling the individual drivers are shown in Figs. 3a–d, respectively. The parking duration is dependent on the arrival time as shown in Fig. 4, which is already considered in the modelling of individual charging behaviours. For example, it can be seen that EVs arriving from 19:00 to 20:00 are more likely to stay overnight than EVs arriving from 07:00 to 08:00. Fig. 3Open in figure viewerPowerPoint Individual EV arrival/departure probability for sampling parking behaviour in Algorithm 1 (Fig. 2) based on the IU data set (a) Departure of weekdays, (b) Arrival of weekdays, (c) Departure of weekends, (d) Arrival of weekends Fig. 4Open in figure viewerPowerPoint Histogram of parking duration for two typical arrival time based on the IU data set (a) 07:00 to 08:00, more cars will leave within 8 h, (b) 19:00 to 20:00, more cars tend to stay overnight Secondly, the probability distribution of SoC can be derived based on the distribution of travelling distance. The consumed energy is dependent on the travelling mileage and energy efficiency of EV (kWh electricity consumed per 100 km). The charging time duration is related to charging power and the consumed energy. For each random sample, the battery SoC when the ith EV arrive at car parks at the jth day SoC i , j (i.e. before charging) and total charging duration for the ith EV at the jth day is calculated as follows: SoC i , j = SoC i , j ′ − D i η d C b , ∀ i ∈ I , j ∈ T (1) t i , j = ( 1 − SoC i , j ) C b P EV i η c (2) f d ( D i ) = 1 2 π σ d exp − ( D i − D μ ) a 2 2 σ d 2 (3) where I is the set of EVs, T is the set of simulation days. t i , j is the charging duration of the ith EV at the jth day. D i is the travelling distance for the ith EV at this day, following a normal distribution N ( D μ , σ d ) for the residential areas suggested by Land Transport Authority (LTA) of Singapore [[23], [24]]. η d is the EV energy efficiency in kWh/100 km. SoC i , j is the initial SoC (i.e. before travelling) of the ith EV at the jth day. P EV i is the charging power (by faster charger or slow charger), C b is the battery capacity. η c is the charging efficiency. Then, the program will check the SoC, parking time T p i (sampled from the IU data set), and the availability of chargers when simulating the ith EV sample. The EV will only charge the battery when its SoC is below the threshold and parking time is longer than the threshold. In this paper, the EVs with SoC smaller than θ SoC = 70 % are assumed to need charging. The choice of a fast/slow charger is dependent on the parking time of the ith EV. Only the vehicles staying longer than θ park = 30 min are viewed as the charging vehicles, and θ fast = 120 min. The maximum queuing time t allowed is set to 10 min. It should be noted that the average queuing time is much shorter than the maximum queuing time. If the conditions of the SoC and parking duration are satisfied, the EV will queue (if needed) until there is an available charger. Since the planning is for residential car parks, the EV will not immediately leave the chargers even if its SoC is full. Therefore, the chargers will be occupied as long as the ith EV is parked there. After simulating all the EVs, the queuing time t q for each EV can be calculated. To consider the queuing time constraints, Algorithm 1 (Fig. 2) will iteratively increase the number of chargers until the queuing time constraints are satisfied. The number of fast chargers and slow chargers will be utilised as one of the constraints for a robust infrastructure planning. With the data-driven individual behaviour modelling, the aggregated charging behaviour in a car park can be much more accurately determined compared with presumed probability distributions. Based on the individual behaviour model, the raw samples to feed for the Monte Carlo simulation of aggregated charging power can be generated. 2.3 Probabilistic aggregated behaviour The second and third step of data-driven charging behaviour analysis aim to compute the aggregated EV charging power demand inside one car park. Two Monte Carlo simulations are carried out. The first Monte Carlo simulation is carried out to determine the power demands of adding up all individual EV behaviours as aggregated EVs inside a car park. The second Monte Carlo simulation is carried out to derive the probabilistic EV load profile by analysing the probability distribution of charging loads. In the first Monte Carlo simulation, based on the sum of these individual behaviours and introducing temporal–spatial parameters (environmental variables), the aggregated EV behaviour inside one car park can be determined. If the future scenarios are changed, the probabilistic EV load profile can be derived following the aggregated EV behaviour model and individual charging behaviour given in Algorithm 1 (Fig. 2). For the car park, its EV load is the summation of all EVs that are currently charging inside the car park. In one randomly generated scenario, the aggregation of EV charging demands P c ( t ) in a car park can be calculated by summing up all the individual charging power profiles P EV i ( t ) based on Algorithm 1 (Fig. 2). P c ( t ) = ∑ i = 1 N P EV i ( t ) (4) By generating numerous samples, each simulating a day with 1440 min, the precise aggregated load profiles inside car parks can be calculated. Based on Algorithm 1 (Fig. 2) and the scenarios, a certain number of EVs arriving in the day will determine the total charging load demands. Each car arriving has its own parking duration, charging duration, and random SoC calculated based on the behaviour of users. The chargers are gradually occupied by the arrival EVs as long as the EV needs charging, which will eventually reduce the availability of chargers. The consumed energy will remain in the next day if the car is not charged. During this process, the number of remaining chargers will be counted (for both fast charging and slow charging), and the new arrival EVs will join the queue if the available chargers are not enough as shown in Fig. 5. Fig. 5Open in figure viewerPowerPoint Availability of chargers considering queuing based on the modelling of aggregated charging behaviour After obtaining the samples for the car park aggregated EV power demand for each scenario, the second Monte Carlo simulation is employed to analyse the probabilistic EV charging power demand. All the variations of environmental constraints and parameters can be simply considered by feeding the parameters or probability distribution into the model. The final results could tell the probabilistic distribution of EV charging power demand into the distribution network with respect to time at each car park. 2.4 Charging demands and kernel density estimation Since the underlying probability distribution of charging power demands is unknown, we can estimate a distribution to approximate it by a data-driven approach. For this purpose, kernel distributions can be a non-parametric representation of the probability density function random charging demands. A kernel distribution is defined by a smoothing function and a bandwidth value. For the value of total charging demands P ( t ), its kernel density estimator's formula f ^ h ( P ) is given by f ^ h ( P ) = 1 ∏ j h j ∑ n i = 1 K P − P i h i (5) where K ( . ) denotes a Borel measurable kernel function with dimension 1, satisfying ≥ 0 and ∫ K ( x ) d x = 1, h denotes the smoothing parameter of the kernel function. Similarly, the kernel density estimator for MSBs' load flow S m , k can be also obtained based on the data samples of stochastic load flow (which is to be illustrated in Section 3.3) f ^ H ( S m , k ) = 1 ∏ j H j ∑ n i = 1 K S m , k − S m , k , i H i (6) In this paper, the Gaussian kernels K ( u ) is employed for density estimation K ( u ) = 1 2 π e − u 2 2 (7) To quantify the difference between the true distribution and the nominal distribution, the L 1 distance [[25]] is employed as the distance measure for (5), which can be easily calculated through historical data. For a discrete pdf with finite support, i.e. Ξ : = ξ i , i = 1 , … , m , the L 1 distance-based ambiguity set D ( π , π 0 ) is as follows [[25]]: p − p 0 1 = ∑ i = 1 m p i − p i 0 ≤ d , 1 T p = 1 (8) where p 0 denotes a nominal probability mass; d > 0 denotes a tolerance, which can be determined by the data-driven approach (4). Using Gaussian kernels, with the amount of historical data sufficiently large, the distance between the estimated probability distribution and true distribution for a given confidence level a can be determined as follows: ϵ = M ∏ j h j 1 2 N log ⁡ 2 1 − a (9) where M = sup u K ( u ), a is the confidence level that shows how the estimated probability distribution approximates the true probability distribution within distance tolerances [[25]]. 3 Impact analysis and charging infrastructure planning under an ambiguity set 3.1 Overview The overview of the proposed data-driven optimal charging infrastructure planning method for urban residential car parks is shown in Fig. 6. As shown in Fig. 6, the obtained probabilistic aggregated charging behaviour in Section 2 will be utilised to quantify the distribution of EV loads for EV charging impact analysis. Based on the non-parametric probability distribution of EV loads and base residential loads, the load flows through the MSBs and substations can be calculated. By studying the probability distribution of load flows through MSBs and substations, the minimum power capacity expansion constraints for MSB planning can be obtained. To minimise the total investment cost, satisfy charging demand constraints, and capacity expansion constraints, a distributionally robust chance-constrained program is developed for an optimal planning of the charging infrastructure. Fig. 6Open in figure viewerPowerPoint Overview of the proposed charging infrastructure planning method for urban residential communities The proposed data-driven EV charging infrastructure planning method is based on data and configuration of urban residential communities in Singapore. For an urban residential community with EV charging car parks, a typical single line diagram of the electrical network structure is shown in Fig. 7. A direct graphic, denoted by G : = { V , E } is adopted to depict the power flow on this network. V : = { V 0 ∪ V MSB } is a set of main grid V 0 and MSBs, i.e. V MSB . The end-side users include the residential blocks and car parks, where the chargers for EVs are located in the car parks. The main grid and MSBs are connected by a set of transformers and distribution lines, denoted by E : = { E trans ∪ E line }. The power flow on each transmission line is depicted by the current injection power flow model. Fig. 7Open in figure viewerPowerPoint Single line diagram at the distribution network of the residential car park (MSBs are after transformers) 3.2 Impacts analysis with stochastic load flow When integrating the charging of EVs into the distribution network, it might result in the over current of MSBs, distribution lines, and transformers. These impacts are analysed under the probabilistic aggregated behaviour of EVs and quantified by the power transferred on specific MSBs, lines, and transformers. (In the standard design, two parking lots share one slow charger.) A stochastic power flow is implemented to obtain the power transferred on the infrastructure under nominal power density, as in Algorithm 2 (see Fig. 8). Fig. 8Open in figure viewerPowerPoint Algorithm 2: Stochastic power flow algorithm In Algorithm 2, by generating numerous samples, each simulating a day, we will be able to have precise empirical load profiles. According to the random scenarios ran, a certain number of EVs arriving in the day can be considered. Each car arriving has a random SoC calculated based on the behaviour of users. The type of fast/slow charger usage is determined with the parking duration of users. The probabilistic aggregated charging load obtained with Algorithm 1 (Fig. 2) and (1)–(5) will be fed into the model of stochastic load flow. 3.3 Impacts of ambiguity on power flow As shown in Algorithm 2 (Fig. 8), the stochastic power flow can only obtain the power flow distribution under given density function, i.e. p 0 . Considering this density is uncertain and bounded by (8), a distributionally robust CVaR under L1 norm distance is given under a given infrastructure j, as follows: max p ∈ D CVaR β ω 1 : m , j = max p ∈ D min η η + 1 1 − β E p [ ω 1 : m , j − η ] a + = max p ∈ D min η η + 1 1 − β ∑ i = 1 m p i [ ω i , j − η ] a + (10) where β is a given confidential level. As shown in (10), it is a max–min optimisation problem, which can be reformulated as the following linear programming problem, using Lagrange duality [[25]]: min η , ω i , j + , z i + , z i − , z η + 1 1 − β d z + ∑ i = 1 m p i 0 ( z i + − z i − ) + ν s.t. z i + + z i − ≤ z , ∀ i ω i , j + ≤ z s + − z s − + ν , ∀ i ω i , j − η ≤ ω i , j + , ∀ s ω i , j + , z i + , z i − , z ∈ R + (11) Using (11), the impacts of ambiguity on the given infrastructure can be estimated. 3.4 Infrastructure planning under a data-driven ambiguity set With the EV integration impacts analysis considering random charging be