A complex network approach for the estimation of the energy demand of electric mobility

ABSTRACT We study how renewable energy impacts regional infrastructures considering the full deployment of electric mobility at that scale. We use the Sardinia Island in Italy as a

paradigmatic case study of a semi-closed system both by energy and mobility point of view. Human mobility patterns are estimated by means of census data listing the mobility dynamics of

about 700,000 vehicles, the energy demand is estimated by modeling the charging behavior of electric vehicle owners. Here we show that current renewable energy production of Sardinia is able

to sustain the commuter mobility even in the theoretical case of a full switch from internal combustion vehicles to electric ones. Centrality measures from network theory on the

reconstructed network of commuter trips allows to identify the most important areas (hubs) involved in regional mobility. The analysis of the expected energy flows reveals long-range effects

on infrastructures outside metropolitan areas and points out that the most relevant unbalances are caused by spatial segregation between production and consumption areas. Finally, results

suggest the adoption of planning actions supporting the installation of renewable energy plants in areas mostly involved by the commuting mobility, avoiding spatial segregation between

consumption and generation areas. SIMILAR CONTENT BEING VIEWED BY OTHERS UNCOVERING STRUCTURAL DIVERSITY IN COMMUTING NETWORKS: GLOBAL AND LOCAL ENTROPY Article Open access 31 January 2022

URBAN SEGREGATION ON MULTILAYERED TRANSPORT NETWORKS: A RANDOM WALK APPROACH Article Open access 10 April 2024 INTERMUNICIPAL TRAVEL NETWORKS OF MEXICO DURING THE COVID-19 PANDEMIC Article

Open access 26 May 2023 INTRODUCTION The expected electrification of mobility is viewed as a great step in the progressive increase of its sustainability. According to the International

Energy Agency, achieving the goal of maximum 2 degrees increase in global temperature established by the Paris Agreement would mean that approximately 19% of the GHG reduction should be

attained through the mitigation of transport emissions. In addition, as urbanization will increase in the next years, electric mobility especially in large urban areas like megacities will

play a fundamental role1. In fact, in 2011 the world’s gasoline share for mobility in 27 megacities was about 9%, and this share is expected to increase further2,3. Consequently, an increase

of GHG emissions and air pollution, as well as a growing dependency on fuel import is expected. Use of alternative, environmentally friendly fuels and power trains are therefore a key

strategy for heading towards sustainable transport systems, and, together with Electric Vehicles (EV), renewable energy sources are considered a further winning strategy to reduce the GHG

emissions from cities. As the number of EV is expected to increase, given the potential high number of vehicles involved, a reliable planning and control of the charging infrastructure will

be fundamental for its successful integration in the power system. In particular, a correct sizing of the needed resources, in term of electricity, charging stations, communication and

management infrastructures must be based on the local mobility needs and on both the distribution infrastructures and electricity market constraints4. In fact, electricity infrastructures,

for decades based on a hierarchical, fossil based model of production and distribution needs to be replaced out by a new, flexible model of generation and distribution whose solid grounds

are based on renewable energy sources, integration, and decentralization. In addition, thanks to an increasing level of digitalization of infrastructures, the integration between distributed

generation and electric mobility is of great benefit. If well planned, it can simultaneously contribute to emission reduction and to grid resilience due to the ability of electric vehicles

to act as distributed storage for stabilizing the power fluctuations on distributed electricity systems5,6,7. With regards to electric mobility initiatives, the existing literature8,9,10

primarily focuses on the evaluation of the impact of electrical mobility infrastructure on a metropolitan scale. This does not take into account the long range impacts on both the mobility

infrastructure and the grid. In fact, high penetration of EV in densely populated areas could impact on the surrounding electricity transmission system, leading to systemic effects which are

difficult to identify by limiting the analysis to the sole city boundaries. In the present paper a multi-layered approach based on complex networks theory11,12,13 is presented. We study the

co-existence of two different network infrastructural layers, energy and mobility, to estimate the impact of electric mobility on a regional scale, with the aim to quantify both short range

and long range effects. The proposed methodology allowed to perform a scale analysis which takes into account a multi-layered infrastructure scheme of the problem. The proposed approach

exploits census data regarding commuting to estimate the origin-destination matrix for the EV trips. Commuting is particularly important for EV mobility, because it it composed by short and

medium range trips, which combines well with the limited ranges of EVs. Moreover, the proposed methodology relies on the map of solar and wind generation plants to identify the

municipalities that are able to produce the low carbon electricity to support the mobility of EV on regional scale. Using these two different datasets, it is possible to estimate the energy

need of charging services both on cities and on freeways, as well as the investigating of the possible integration with the local grid and renewable generation plants. The proposed planning

of electric mobility is performed on different scales, according to the availability of data (including census, the mobility network and the installed generation plants). It is arranged in

three steps: * 1. Data collection and geo-referencing by means of Geographic Information Systems (GIS). * 2. Definition of the complex system able to describe the expected interaction

between mobility and power grids. The proposed approach also includes the estimation of the expected traffic flows starting from census commuting data, integrated by the energy description

of EVs. * 3. Identification of the interactions between the layers of the system to quantify the impact of the energy needs of mobility on the power grid of the territory, in terms of the

associated energy flows. The methodology has been applied on one of the major islands of Italy, the region of Sardinia, considering a scenario of full deployment of electric vehicles to

cover the need of commuting mobility on regional scale. Results show that the current RES production in Sardinia is able to cover the full deployment of electric mobility for commuting.

Moreover, the network analysis of the regional commuting patterns shows that a limited number of municipalities behave as hubs of the regional traffic. Also, in the majority of cases the

energy needs are negative in such areas, i.e. they need further power to sustain the recharge infrastructure. Finally, the optimization analysis of energy flows reveals both long range

effects and spatial segregation phenomena affecting in the energy transmission system. RESULTS The first step of the proposed method is to identify the municipalities more involved in the

commuting mobility: the origin-destination matrix is estimated by building a directed weighted network starting from the census data (see further details in the methods section). In the

proposed representation the municipalities are the nodes of the network, links model the trips and weights correspond to the number of vehicles crossing the municipality borders (both

incoming and outcoming flows is considered). From Table 1 and Fig. 1 it is possible to notice that a limited amount of municipalities concentrate a large share of trips, suggesting to use

centrality measures to identify the most important areas. Figure 2 shows the results of the analysis computed with two methods (darker areas correspond to higher values): panel (a) shows the

betweenness centrality, while panel (b) the eigenvector centrality. These measures offer two slightly different readings: the eigenvector centrality identifies the southern municipalities

as the most central ones, while the municipalities highlighted by the betweenness centrality are distributed on the region, reflecting the distribution of the principal urban areas in

Sardinia. Such difference is mainly due to the large concentration of high strength municipalities (i.e. those showing the higher number of connections and high strength nodes) located in

the southern part of Sardinia, where the main city Cagliari is also located. Such distribution of high degree nodes has a relevant impact on the eigenvector centrality, and is also reflected

in the high energy flows, as we will show later in this section. On the other side, the same effect does not stand for betweenness centrality, that also put in better evidence the

municipalities located in the central and northern areas, leading to a more accurate identification of the central nodes. However, both measures are useful and highlight the role of the main

municipalities located in Sardinia: Cagliari, Nuoro, Oristano and Sassari. On the other hand, the role of Olbia, another important city, is put in evidence only with the betweenness

centrality measures. It is also worth noting that the reconstructed origin destination matrix confirms Macomer (a smaller town with respect to the other mentioned) to play an important role

as a hub for the transport network in Sardinia (see Fig. 1). From the census data it is shown that the above mentioned municipalities concentrate the flow of about 455000 vehicles, as showed

in Table 1 reporting the number of incoming and out-coming vehicles for the first 35 municipalities, chosen by setting a threshold _B_ > 0.005 on the nodes centrality. Furthermore, this

subset (9% of the total municipalities) concentrate the 64% of the trips, corresponding to a energy consumption of the 83% of the total (730 MWh). Moreover, the eigenvector centrality

highlights the central role of south Sardinia in commuting, due to the high number of connections with the capital city, Cagliari. Once identified the key municipalities involved in the

commuting flows, a second layer is considered, introducing the energy balance between the distributed electricity production and the estimated consumption associated to the charging

processes of EVs. The maps are showed in Fig. 3. Particularly, panel (a) shows for each municipality the Renewable Energy Sources (RESs) production, being the main form of distributed

generation in all Sardinian municipalities, while panel (b) shows the electricity demand associated to EV commuting mobility. The energy needs are computed considering three different

charging behaviors (further details in the methods section) and refer to a full EV deployment scenario, accounting for about 700.000 vehicles belonging to the type specified in Table 2. By

comparing Fig. 3a and b it is possible to notice how in some cases the electricity demand matches the corresponding area, while in the majority of cases the energy needs are not matched and

lead to an energy imbalance. In particular, the electricity balances between RES production and EV demands of the larger municipalities are numerically reported in Table 1. It is worth

noting by the analysis of the maps reported in Figs 2 and 3 that the most central municipalities (dark blue ones in 2a), have enough average local and distributed daily energy generation to

support (from yellow to green in Fig. 3c) their EV fleet. On the other hand the same Fig. 3c highlights how the relevant unbalances are generated in the municipalities surrounding the main

cities, revealing that the most unbalanced regions are found around Cagliari, the capital city of Sardinia, and Sassari. As a further step, the impact of the mobility infrastructure on the

power grid is quantified, by computing the daily energy flows associated to the energy unbalances. This has been achieved by solving the flow equation presented in methods section, with the

aim to ensure local power balance in each node minimizing the transmission costs over the power network. Figure 4 shows the energy flows caused by the unbalances. The flows range from 0 to

7800 kWh and green municipalities indicate the ones contributing more to the energy production, while red municipalities are those showing unbalances up to 20 MWh (see Fig. 3c). As a result,

it is possible to notice how the mobility needs of the two biggest cities of the territory can cause high energy flows in the regional grid. Especially the southern zone, highly connected

with the capital city of Cagliari, shows significant energy transactions which extend up to 100 km from the traffic attractor. This effect is also suggested by the eigenvector centrality

analysis in the Fig. 2b. DISCUSSION The proposed method aims to assess the impact on regional scale of electric mobility fueled by low carbon sources. It is organized in the following steps:

* 1. Reconstruction of the origin-destination matrix by means of census data. * 2. Use of complex networks to identify the most important areas interested by the recharge infrastructures. *

3. Modeling the behavior of commuters. * 4. Optimization of flows in order to minimize the energy transmission costs According to the presented results, the proposed method suggests that an

accurate spatial balance between production and consumption areas is needed in order to avoid relevant energy flows that negatively impact on the transmission network. Furthermore, the

results can be used to identify the position of charging stations and RES production areas at regional level. The analysis of the flows clearly shows how the highly populated areas (here,

Cagliari and Sassari, see Fig. 2a) impact the regional power grid even in regions far from their respective areas, suggesting systemic effects on the multilayer system. Since these long

range effects can be detrimental for the power grid operation, this clearly shows how a multilayer analysis on a large scale is necessary to fully understand the impact of electrical

mobilities in big cities. According to the general balance between distributed generation and electric mobility consumption, it is important noting that the actual production of the whole

region is able to sustain the full deployment of EV for commuting with a limited stress on the distribution system. The expected electrification of mobility is viewed as a great step in the

progressive increase of its sustainability. Moreover, the use of parked Electric Vehicles (EVs) implementing the Vehicle to Grid technology as distributed storage systems is viewed as a way

to limit the impact of the intermittent power output typical of Renewable Energy Sources (RES). This will lead to a gradual integration between mobility and smart grids, also leading to the

implementation of Virtual Power Plants in areas where charging stations are concentrated (e.g., parking spaces in connection with public transport stops). Future research will take into

account the temporal patterns of the incoming and outcoming vehicles, considering their impact of the charging and discharging process on the main grid. Furthermore, the direct interaction

of energy and mobility will be studied by using the theoretical results obtained in the field of multiplex networks, with the aim to consider the integration of the RES in the grid and to

include in the energy flows the possibility to use vehicle to grid strategies to further reduce the impact on the network. METHODS The calculation of energy impact on a regional scale is

based on the public available data regarding mobility and RES production, and relies on the knowledge of two key quantities: the mobility network, represented by its adjacency matrix A, and

the distributed energy production \({P}_{m}^{\ast }\) of each municipality _m_. A detailed description of the procedures used for the determination of these quantities is given in the data

subsection. Starting from these two quantities, the daily consumption of charging of EV batteries is calculated, starting from the commuting network. The approach consists in associating an

energy weight _W_ _ij_ to the commuting links, as described in 1. Here, _d_ _ij_ and _N_ _ij_ are the driving distance and the number of trips between municipality _i_ and _j_, respectively.

\(FC=0.123\,\tfrac{kWh}{Km}\) is the energy consumption of each vehicle, estimated from a fleet composed by 80% of Nissan Leaf, 15% of VW E-Golf, and 5% of Tesla Model S. Their

characteristics are given by the constructor and shown in Table 2. The network allows self-loops, and in this case the distance _d_ _ii_ is calculated as the size of the town/city.

$${W}_{ij}={d}_{ij}\cdot FC\cdot {N}_{ij}$$ (1) The calculation of the energy consumption \({C}_{m}^{\ast }\) of each municipality _m_ is performed by assuming the existence of a diffused

charging infrastructure which allow the users to charge their vehicles both at home and at the workplace. Therefore, it has been assumed that the drivers can fall in one of three different

categories: home charger, work charger and regular charger. Home chargers charge only at home, work chargers charge only at workplace, and regular chargers charge half at home and half at

workplace. In the model, each category is represented in the population by the values _f_ _WC_ _f_ _CC_ and _f_ _HC_ , respectively. In this paper,

\({f}_{WC}={f}_{CC}={f}_{HC}=\tfrac{1}{3}\). In this way, the energy need _C_ _i_ of each node _i_ can be calculated as eq. 2. $${C}_{i}=\sum

_{j}\,({f}_{HC}+\tfrac{1}{2}{f}_{CC}){W}_{ij}+\sum _{j}\,({f}_{WC}+\tfrac{1}{2}{f}_{CC}){W}_{ji}+{W}_{ii}$$ (2) The power balance _B_ _m_ of each municipality _m_ is then calculated as 3.

$${B}_{m}^{\ast }=\sum _{t}\,{P}_{mt}^{\ast }-{C}_{m}^{\ast }$$ (3) The power flow optimization is based on the assumption that each municipality has a potential _V_ _i_ , that will define

the incoming and outcoming flows with the neighbors. The values of _V_ _i_ will be obtained by solving the system of equations shown in eq. 4, where _E_ _ij_  = _K_ _ij_  · (_V_ _i_  − _V_

_j_ ). $${B}_{i}-\sum _{j}\,{E}_{ij}=\mathrm{0,}$$ (4) The system of equations in 4 can be easily solved in matrix form, by $${\bf{B}}-{\bf{K}}\cdot {\bf{V}}=0,$$ where B is the vector of

balances _B_ _i_ , K is the matrix of couplings of the system, and V is the vector of _V_ _i_ . K is given by the entries _K_ _ij_ , representing the couplings between node _i_ and _j_ of

the network. It has been obtained by the following eq. 5, where D is a diagonal _L_ × _L_ matrix representing the lines couplings. In this case, the matrix D is choosen as the identity

matrix, representing equal coupling among the nodes. For this reason, the elements _V_ _i_ are obtained from the equation 6. $$K={A}^{T}DA$$ (5) $${\bf{V}}={{\bf{K}}}^{-1}\cdot {\bf{B}}$$

(6) Since, in general, the available resources are higher than the power needs, it is necessary to define a univoque way to allocate the resources. This is done by obtaining the solution

that minimizes the quality function in eq. 7, where B is a vector containing all the balances _B_ _i_ of the municipalities. $$f({\bf{B}})=\sum _{i,j}\,{({V}_{i}-{V}_{j})}^{2}$$ (7) The

solution should be calculated under the constraint given in eq. 8, which represents the balance equation of the system, where \({B}_{i}={P}_{i}-{C}_{i}^{\ast }\), being _P_ _i_ the power

output of municipality _i_. Also, the values _B_ _i_ should respect the inequalities \(-\,{C}_{I}^{\ast }\le {B}_{i}\le {P}_{i}^{\ast }-{C}_{I}^{\ast }\). Given the defined quantities and

constraints, the function _f_(B) has been minimized by means of the Sequential Least SQuares Programming (SLSQP) minimization procedure14. The solution of the minimization problem returns

the vector B _min_ . From this vector, it is easy to obtain the system flows _E_ _ij_ , and the power provided by each municipality \({P}_{i}={B}_{I}-{C}_{i}^{\ast }\). $$\sum

_{i}\,{B}_{i}=0.$$ (8) DATA AND CASE STUDY The proposed methodology has been applied on the Sardinian region, in Italy. The commuting dataset has been obtained from the Italian Census data,

available at the ISTAT website http://www.istat.it/en/. The dataset contains the commuting origin/destination matrix of the territory, for an average workday. The dataset distinguish between

trips performed by car, bus, train, bikes, bicycles, and other means of transportation. Also, in the car category, the dataset distinguishes between car drivers and car passengers, allowing

to identify the number of vehicles moving from each municipality to another one. Also, the dataset contains the expected trips per different hours of the day, which have been here

aggregated for the whole day. The dataset can be represented by means of a directed weighted graph described by its adjacency matrix _A_. The entries _a_ _ij_ of the adjacency matrix are

given by the number of trips occurring from municipality _i_ to municipality _j_. The total number of trips provided by the dataset is 720200. The power produced by RES in each municipality

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Atlaeolico (http://atlanteeolico.rse-web.it/). The information provided for each plant includes the municipality in which it is installed, the nominal capacity and the year of installation.

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RES technology _t_. This quantity is calculated by using eq. 9, where \({P}_{m,t}^{inst}\) is the aggregated installed capacity, and \({k}_{m,t}^{fact}\) are the capacity factors of wind and

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http://volkswagen.com/en.html; https://www.tesla.com/ (Accessed: 11-11-2017). Download references ACKNOWLEDGEMENTS The authors M.M., A.F. and A.D. gratefully acknowledge the Sardinia

Regional Government for the financial support of this research activity developed under the project “Attività di ricerca e sperimentazione nel settore delle smart grid e mobilità elettrica”

within the following frameworks: Art. 15 Legge 241/90. A.F. is also supported by the EU projects OpenMaker (grant num. 687941) and SoBigData (grant num. 654024). G.C. acknowledges the above

projects and the EU project DOLFINS (grant num. 640772). AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * University of Cagliari, Cagliari, Italy Mario Mureddu & Alfonso Damiano * IMT

School for Advanced Studies Lucca, Piazza San Francesco 19, 55100, Lucca, Italy Angelo Facchini & Guido Caldarelli * CRN Institute for Complex Systems, via dei Taurini 19, 00185, Rome,

Italy Angelo Facchini, Antonio Scala & Guido Caldarelli * London Institute for Mathematical Sciences, 35a South Street Mayfair, W1K 2XF, London, UK Guido Caldarelli * Linkalab, Complex

Systems Computational Laboratory, Viale Elmas, 142 09122, Cagliari, Italy Guido Caldarelli Authors * Mario Mureddu View author publications You can also search for this author inPubMed 

Google Scholar * Angelo Facchini View author publications You can also search for this author inPubMed Google Scholar * Antonio Scala View author publications You can also search for this

author inPubMed Google Scholar * Guido Caldarelli View author publications You can also search for this author inPubMed Google Scholar * Alfonso Damiano View author publications You can also

search for this author inPubMed Google Scholar CONTRIBUTIONS A.F., M.M. wrote the paper, M.M. performed computation. A.D. supervised the research activities and reviewed the paper. All the

authors designed the research. CORRESPONDING AUTHOR Correspondence to Angelo Facchini. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare that they have no competing interests.

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Scala, A. _et al._ A Complex Network Approach for the Estimation of the Energy Demand of Electric Mobility. _Sci Rep_ 8, 268 (2018). https://doi.org/10.1038/s41598-017-17838-5 Download

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