# Understanding Complexity in Charging Infrastructure through the Lens of Social Supply–Demand Systems

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## Abstract

**:**

## 1. Introduction

## 2. General Abstraction of Infrastructures as Systems of Supply and Demand

#### 2.1. Environment

#### 2.2. Resource Access Points

#### 2.3. Users

#### 2.4. Transactions

#### 2.5. Research Methodologies for Charging Infrastructure as Social Supply–Demand System

## 3. Charging Infrastructure as a Complex System

#### 3.1. Feedback Loops

#### 3.2. Learning and Adaptation

#### 3.3. Emergence

#### 3.4. Network Formation and Resilience

#### 3.5. Self-Organisation

#### 3.6. Non-Linearity

#### 3.7. Path Depencency

#### 3.8. Phase Transitions

## 4. Analyzing the Complexity of the EV System

#### 4.1. How Complex Is the EV System?

#### 4.1.1. Ratio 1: Necessity of Sharing Resources

_{1}, in line with node clustering metrics in bipartite graphs [96]. First, we set a timeframe ($\tau $) to $\tau +{\delta}_{t}$, with a transaction set of ${T}_{t,t+{\delta}_{t}}\subset T$. We define $A$ as the set of all pairs of transactions${t}_{x}^{a},{t}_{y}^{b}$from two different users ${u}_{a},{u}_{b}$, where ${\tau}_{{t}_{x}^{a}},{\tau}_{{t}_{y}^{b}}\in {T}_{t,t+{\delta}_{t}}\wedge {u}_{a}\ne {u}_{b}$ at their given location ${l}_{x},{l}_{y}$, based on the location of the resource access point. We consider the set of considered resources${R}_{{l}_{x}}^{{u}_{a}},{R}_{{l}_{y}}^{{u}_{b}}$ of users and observable resources per location ${R}_{{l}_{x}},{R}_{{l}_{y}}.$ We calculate Ratio

_{1}as follows:

_{1}approaches 0 as (i)$\left|{R}_{{l}_{x}}^{{u}_{a}}\cap {R}_{{l}_{y}}^{{u}_{b}}\right|$ is zero, in most cases, since each user has its own CP (Figure 5a). On the other hand, for DC fast charging, all users may potentially select any of the available outlets at arrival, leading to a value close to 1 (Figure 5c). For public charging infrastructure, we see that the set of overlapping $\left|{R}_{{l}_{x}}^{{u}_{a}}\cap {R}_{{l}_{y}}^{{u}_{b}}\right|$is smaller than $|{R}_{{l}_{x}}\cup {R}_{{l}_{y}}|$, which leads to a value significantly lower than 1 and higher than 0. For semi-public charging, we expect values close to DC fast charging, since both ${R}_{{l}_{x}}^{{u}_{a}}~{R}_{{l}_{y}}^{{u}_{b}}$ and ${R}_{{l}_{x}}~{R}_{{l}_{y}}$. We expect that complexity decreases at the limits of this ratio (0,1).

#### 4.1.2. Ratio 2: Probabilities of Queuing

_{2}) specifically focuses on the complexity of behavior in the system, related to the time aspect (e.g., service rate of supply and demand). This ratio builds upon the concept of supply and demand rates, which has been studied in queueing theory [97]. In queueing theory, the ratio between $\frac{\lambda}{\mu}$ determines the probability of a queue’s existence. In this equation, $\lambda $ is the arrival process, assumed to be a Poisson distribution $\lambda $ (defined in our SSDS as ${\lambda}_{j}$), and $\mu $ is the exponentially distributed service time ($\delta \tau $ in our SSDS) [97]. The literature on DC fast charging infrastructure has modeled outlets as a multi-server network queue [98,99]. Yet, for AC public charging, the following aspects make queuing models complex in highly occupied systems [97]: (i) $\mu $ is not a property of the outlet alone, as it is related to parking behavior, rather than transactions size; (ii) EV users have shown to be strongly habitual, causing multi-modal Gaussian arrival patterns, rather per ${u}_{j}$ [3]; and (iii) when EV users arrive at a location, they have individual preferences for ${R}_{{u}_{j}}$, even if they overlap in locality.

_{2}as the duration time of a transaction divided by the mean time between arrivals at ${r}_{\iota}$. To take locality into account, we average over each set of local observable resources ${R}_{{l}_{k}}$, rather than over the whole system at once (e.g., $\frac{\overline{\lambda}}{\overline{\mu}}$).

_{2}is, therefore, calculated as follows:

_{2}and, consequently, limited changes in the complexity for AC public charging.

#### 4.1.3. Ratio 3: Impact of Transactions on Others

_{3}, in line with literature on cascading failures, as follows [103]. In line with the other ratios, we set a timeframe ($\tau $) to $\tau +\delta \tau $ for a transaction subset of ${T}_{t,t+\delta \tau}\subset T$. For $\forall {t}_{p}{}_{{r}_{\iota}}^{{u}_{j}}\in {T}_{t,t+\delta \tau}$, we initiate the set $S{P}_{{t}_{j}}=\left\{\right\}$, which we fill with transactions ${t}_{l}{}_{{r}_{i}}^{{u}_{j}}$affected by the alternative decisions that ${u}_{j}$ may have made for transaction ${t}_{l}$ and initiate $AO=\left\{\right\},$as the set of alternative ${r}_{j}$, which we have taken into consideration during calculation. We iteratively perform the following calculations.

- (1)
- $\forall {t}_{l}{}_{{r}_{\iota}}^{{u}_{j}}$ of ${u}_{j}$we regard as the set of alternatives minus the already considered $r\in OA$, in using ${R}_{{u}_{j}}-OA$;
- (2)
- For all ${r}_{l}\in {R}_{{u}_{j}}-OA$, we add the set of affected transactions at ${r}_{l}$ during the ${t}_{l}$ interval $[{\tau}_{{t}_{l}{}_{{r}_{k}}^{{u}_{j}}},{\tau}_{{t}_{l}{}_{{r}_{k}}^{{u}_{j}}}+\delta {\tau}_{{t}_{l}{}_{{r}_{k}}^{{u}_{j}}}]$ to $S{P}_{{t}_{j}}$;
- (3)
- For $\forall t\prime \in S{P}_{{t}_{j}}$, we return to (1), while adding transactions to the initial $S{P}_{{t}_{j}},$until ${R}_{{u}_{i}}-OA=\varnothing $.

_{3}to be low for DC fast charging. For private home charging, the spread takes, as a maximum, the value of the number of EVs that share the home charging CPs. The Ratio

_{3}value is expected to be between 0 and 1. For semi-public charging, we also expect this value to be between 0 and 1. For the mature public charging infrastructure, we expect this value to be above 1 [104].

#### 4.2. Conclusions on Complex System Ratios

_{1}is normalized over all pairs. We expect ${R}_{{t}_{k}}$ and ${R}_{{u}_{i}}$ to increase as the density of the CPs increases. We also expect $|{R}_{{u}_{a}}\cap {R}_{{u}_{b}}|$ to decrease as more users have nearby subsets of options. We expect $|{R}_{{t}_{x}}\cup {R}_{{t}_{y}}|$ to increase as the set of alternatives grows. As such, we expect a slow decrease of Ratio

_{1}over time and the complexity to slightly decrease. On the other hand, an increase of ${R}_{{u}_{a}}$ and $\left|U\right|$ may lead to an increase of Ratio

_{3}and the spread of effects of alternative decisions. In the end, this may add to the complexity of the behavior in the system. We, therefore, expect that AC charging infrastructure (separate from its public DC counterpart) will remain within the complex regime.

## 5. Analyzing Interactions and Performance of Complex Systems

#### 5.1. Systemic Metrics for Charging Infrastructure

_{3}), is high.

#### 5.2. Modeling Charging Infrastructure as Complex System

#### 5.3. Proposed Model for Analyzing Charging Infrastructure as Complex System

## 6. Discussion and Implications for Policy Makers and Research

#### 6.1. Implications for Policy Makers

#### 6.2. Implications for Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Glossary

Symbol | Example | Description |

$A$ | Set of all pairs of transactions${t}_{x}^{a},{t}_{y}^{b}$ | |

$c\_i$ | $ci$ | Maximum transaction speed at $ri$ |

$\delta {\tau}_{p}$ | $\delta {\tau}_{p}$ | Duration of transactions $p$ |

$E$ | $E\subset {\mathbb{N}}^{2}$, $lk\in E$. | Environment contains a set of locations ${l}_{k}$ |

${\varphi}_{j}$ | Demand rate user j max uptake speed | |

${l}_{\iota}$ | ${l}_{\iota}\in E$ | Location of resource $\iota $ |

${\lambda}_{j}$ | Mean demand rate for user j in frequency time | |

${\mathsf{\Lambda}}_{t}$ | Local average $\lambda $ used in Ratio_{2} | |

Mj | Memory of connections for user j | |

$\mathbb{N}$ | Environment size | |

${o}_{\iota}$ | ${o}_{\iota}$ =$\left\{{o}_{1}..{o}_{\eta}\right\}$ | Set of outlets at ${r}_{\iota}$ |

${q}_{\iota}$ | Quality of resources at access point $\iota $ | |

${\mathsf{\rho}}_{\mathrm{j}}$ | Demand rate user j in terms of quality | |

$R$ | $R=\left\{{r}_{1},\dots ,rn\right\}$ | Set of resource access points |

${R}^{{u}_{j}}$ | Set of user preferred resource access points | |

${R}_{{l}_{k}}^{{u}_{j}}$ | Set of user preferred resource access points at the given location | |

${R}_{lk}$ | Set of local observable resource access points at the location | |

${r}_{\iota}$ | ${r}_{\iota}=\left\{{l}_{\iota},{o}_{\iota},{c}_{\iota},{q}_{\iota}\right\}$ | Resource access point tuple |

$S$ | $S=\left\{E,R,U,T\right\}$ | System |

$S{c}_{j}$ | Maximum resource uptake speed of user $j$ | |

$S{t}_{j}$ | Storage capacity user $j$ | |

$\tau $ | Time | |

$T$ | $T=\left\{{t}_{1},\dots ,tO\right\}$ | Transactions |

${T}^{{u}_{j}}$ | $T\_j=\left\{{t}_{1},\dots ,t\_J\right\}$ | Set of transactions for user $j$ |

${T}_{{r}_{i}}^{{u}_{j}}$ | Set of transactions for user $j$ at resource access point $\iota $ | |

${t}_{p}$ | ${t}_{p}=\left\{{u}_{j},{o}_{\iota},{r}_{\iota},\tau {s}_{p},\delta {\tau}_{p},{V}_{p}\right\}$ | Transaction tuple |

$\tau {s}_{p}$ | Start time of transaction p | |

$U$ | $U=\left\{{u}_{1},\dots ,{u}_{m}\right\}$ | Set of users |

${u}_{j}$ | ${u}_{j}=\left\{{\mathrm{St}}_{\mathrm{j}},{\mathrm{Sc}}_{\mathrm{j}},{\lambda}_{j},{\varphi}_{j},{\mathrm{T}}_{\mathrm{j}},{\mathsf{\rho}}_{\mathrm{j}}\right\}$ | User tuple |

${V}_{p}$ | Transaction size |

## References

- Wolbertus, R.; van den Hoed, R.; Kroesen, M.; Chorus, C. Charging infrastructure roll-out strategies for large scale in-troduction of electric vehicles in urban areas: An agent-based simulation study. Transp. Res. Part A Policy Pract.
**2021**, 148, 262–285. [Google Scholar] - Funke, S.Á.; Gnann, T.; Plötz, P. Addressing the Different Needs for Charging Infrastructure: An Analysis of Some Criteria for Charging Infrastructure Set-up. In E-Mobility in Europe; Filho, W.L., Kotter, R., Eds.; Springer International Publishing: Cham, Switzerland, 2015; pp. 73–90. [Google Scholar]
- Helmus, J.R.; Lees, M.H.; Hoed, R.V.D. A data driven typology of electric vehicle user types and charging sessions. Transp. Res. Part C Emerg. Technol.
**2020**, 115, 102637. [Google Scholar] [CrossRef] - Helmus, J.; Spoelstra, J.; Refa, N.; Lees, M.; Hoed, R.V.D. Assessment of public charging infrastructure push and pull rollout strategies: The case of the Netherlands. Energy Policy
**2018**, 121, 35–47. [Google Scholar] [CrossRef] - Van Den Hoed, R.; Helmus, J.R.; De Vries, R.; Bardok, D. Data analysis on the public charge infrastructure in the city of Amsterdam. In Proceedings of the 2013 World Electric Vehicle Symposium and Exhibition, Barcelona, Spain, 17–20 November 2013; pp. 1–10. [Google Scholar]
- He, F.; Yin, Y.F.; Zhou, J. Deploying public charging stations for electric vehicles on urban road networks. Transp. Res. Part C Emerg. Technol.
**2015**, 60, 227–240. [Google Scholar] [CrossRef] - Nie, Y.; Ghamami, M. A corridor-centric approach to planning electric vehicle charging infrastructure. Transp. Res. Part B Methodol.
**2013**, 57, 172–190. [Google Scholar] [CrossRef] - Sathaye, N.; Kelley, S. An approach for the optimal planning of electric vehicle infrastructure for highway corridors. Transp. Res. Part E Logist. Transp. Rev.
**2013**, 59, 15–33. [Google Scholar] [CrossRef] - Helmus, J.; Van Den Hoed, R. Key Performance Indicators of Charging Infrastructure. In Proceedings of the EVS 2016—29th International Electric Vehicle Symposium, Montreal, QC, Canada, 19–22 June 2016; pp. 1–9. [Google Scholar]
- Van den Hoed, R. E-Mobility: Getting Smarter with Data, 1st ed.; Amsterdam University of Applied Science: Amsterdam, The Netherlands, 2020. [Google Scholar]
- van der Steen, M.; van Schelven, R.M.; Van Deventer, D.P.; Van Twist, P.D.M.; Kotter, M.A. Policy strategies for an emergent technology: Lessons from the analysis of EV-policy in 8 North-European countries. In Proceedings of the EVS28 International Electric Vehicle Symposium and Exhibition, Goyang, Korea, 3–6 May 2015. [Google Scholar]
- Dorigo, M.; Birattari, M.; Stutzle, T. Ant colony optimization. IEEE Comput. Intell. Mag.
**2006**, 1, 28–39. [Google Scholar] [CrossRef] - Andrenacci, N.; Ragona, R.; Valenti, G. A demand-side approach to the optimal deployment of electric vehicle charging stations in metropolitan areas. Appl. Energy
**2016**, 182, 39–46. [Google Scholar] [CrossRef] - Mu, Y.; Wu, J.; Jenkins, N.; Jia, H.; Wang, C. A Spatial–Temporal model for grid impact analysis of plug-in electric vehicles. Appl. Energy
**2014**, 114, 456–465. [Google Scholar] [CrossRef][Green Version] - Bae, S.; Kwasinski, A. Spatial and Temporal Model of Electric Vehicle Charging Demand. IEEE Trans. Smart Grid
**2011**, 3, 394–403. [Google Scholar] [CrossRef] - Hill, G.; Blythe, P.; Suresh, V. How does the use of a continuously updating database allow for the analysis of a user’s changing behaviour in electric vehicles? In Proceedings of the IET Road Transport Information and Control Conference and the ITS United Kingdom Members’ Conference (RTIC 2010), Better Transport through Technology, London, UK, 25–27 May 2010. [Google Scholar]
- Salah, F.; Ilg, J.P.; Flath, C.; Basse, H.; Van Dinther, C. Impact of electric vehicles on distribution substations: A Swiss case study. Appl. Energy
**2015**, 137, 88–96. [Google Scholar] [CrossRef] - De Ridder, F.; D’Hulst, R.; Knapen, L.; Janssens, D. Applying an Activity based Model to Explore the Potential of Electrical Vehicles in the Smart Grid. Procedia Comput. Sci.
**2013**, 19, 847–853. [Google Scholar] [CrossRef][Green Version] - Geels, F.W. From sectoral systems of innovation to socio-technical systems: Insights about dynamics and change from soci-ology and institutional theory. Res. Policy
**2004**, 33, 897–920. [Google Scholar] [CrossRef] - Pathak, J.; Hunt, B.; Girvan, M.; Lu, Z.; Ott, E. Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach. Phys. Rev. Lett.
**2018**, 120, 024102. [Google Scholar] [CrossRef][Green Version] - Ostrom, E. Governing the Commons: The Evolution of Institutions for Collective Action; Cambridge University Press: Cambridge, UK, 1992. [Google Scholar]
- Ladyman, J.; Lambert, J.; Wiesner, K. What is a complex system? Eur. J. Philos. Sci.
**2013**, 3, 33–67. [Google Scholar] [CrossRef] - Apesteguia, J.; Maier-Rigaud, F.P. The Role of Rivalry public goods versus common-pool resources. J. Conflict Resolut.
**2006**, 50, 646–663. [Google Scholar] [CrossRef] - Andersson, D.; Bratsberg, S.; Ringsmuth, A.K.; de Wijn, A.S. Dynamics of collective action to conserve a large com-mon-pool resource. Sci. Rep.
**2021**, 11, 9208. [Google Scholar] [CrossRef] - Gollwitzer, L.; Ockwell, D.; Muok, B.; Ely, A.; Ahlborg, H. Rethinking the sustainability and institutional governance of electricity access and mini-grids: Electricity as a common pool resource. Energy Res. Soc. Sci.
**2018**, 39, 152–161. [Google Scholar] [CrossRef] - Pitt, J.; Diaconescu, A. The Algorithmic Governance of Common-Pool Resources. Available online: https://wiki.p2pfoundation.net/images/AlgGov-ID3.pdf (accessed on 9 January 2022).
- Künneke, R.; Finger, M. The governance of infrastructures as common pool resources in Bloomington. In Elinor Ostrom and the Blomington School of Political Economy; Lexington Books: Minneapolis, MN, USA, 2018. [Google Scholar]
- Dignum, E.; Boterman, W.; Flache, A.; Lees, M.H. Mechanisms for increased school segregation relative to residential segregation: A model-based analysis. Comput. Environ. Urban Syst.
**2022**, 93, 101772. [Google Scholar] [CrossRef] - Bar-Yam, Y. Improving the Effectiveness of Health Care and Public Health: A Multiscale Complex Systems Analysis. Am. J. Public Health
**2006**, 96, 459–466. [Google Scholar] [CrossRef] - Wilsford, D. Path Dependency, or Why History Makes It Difficult but Not Impossible to Reform Health Care Systems in a Big Way. J. Public Policy
**1994**, 14, 251–283. [Google Scholar] [CrossRef] - Ottens, M.; Franssen, M.; Kroes, P.; Van De Poel, I. Modelling infrastructures as socio-technical systems. Int. J. Crit. Infrastruct.
**2006**, 2, 133. [Google Scholar] [CrossRef][Green Version] - Landegren, F. Critical Infrastructures as Socio-Technical Systems Application to Electricity Distribution. Licentiate Thesis, Lund University, Lund, Sweden, 2014. [Google Scholar]
- Kjølle, G.H.; Utne, I.B.; Gjerde, O. Risk analysis of critical infrastructures emphasizing electricity supply and interde-pendencies. Reliab. Eng. Syst. Saf.
**2012**, 105, 80–89. [Google Scholar] [CrossRef] - Sarabi, S.; Davigny, A.; Riffonneau, Y.; Robyns, B. V2G electric vehicle charging scheduling for railway station parking lots based on binary linear programming. In Proceedings of the 2016 IEEE International Energy Conference (ENERGYCON), Leuven, Belgium, 4–8 April 2016; pp. 1–6. [Google Scholar]
- Williams, R.J. Biology, Methodology or Chance? The Degree Distributions of Bipartite Ecological Networks. PLoS ONE
**2011**, 6, e17645. [Google Scholar] [CrossRef][Green Version] - Dobson, I.; Carreras, B.A.; Lynch, V.E.; Newman, D.E. Complex systems analysis of series of blackouts: Cascading failure, critical points, and self-organization. Chaos
**2007**, 17, 26103. [Google Scholar] [CrossRef] - Wolbertus, R.; Gerzon, B. Improving Electric Vehicle Charging Station Efficiency through Pricing. J. Adv. Transp.
**2018**, 2018, 4831951. [Google Scholar] [CrossRef] - Saunders, F.P. The promise of common pool resource theory and the reality of commons projects. Int. J. Commons
**2014**, 8, 636–656. [Google Scholar] [CrossRef] - Helmus, J.R.; Vogel, I.; Van Den Hoed, R. Exploring Patterns of Social Charging Behavior between EV Users. In Proceeding of the 33rd Electric Vehicle Symposium (EVS33), Portland, Oregon, 14–17 June 2020. [Google Scholar]
- Kannampallil, T.G.; Schauer, G.F.; Cohen, T.; Patel, V.L. Considering complexity in healthcare systems. J. Biomed. Informatics
**2011**, 44, 943–947. [Google Scholar] [CrossRef][Green Version] - Scholz, M.; Alves Furtado, B.; Sakowski, P.; Tóvolli, M. Modeling Complex Systems for Public Policies; IPEA: Brasilia, Brazi, 2011; Volume 46. [Google Scholar]
- Straka, M.J.; Caldarelli, G.; Squartini, T.; Saracco, F. From Ecology to Finance (and Back?): Recent Advancements in the Analysis of Bipartite Networks. arXiv
**2017**, arXiv:1710.10143. [Google Scholar] - Paina, L.; Peters, D.H. Understanding pathways for scaling up health services through the lens of complex adaptive systems. Health Policy Plan.
**2011**, 27, 365–373. [Google Scholar] [CrossRef][Green Version] - Bellouquid, A.; De Angelis, E.; Fermo, L. Towards the modeling of vehicular traffic as a complex system: A kinetic theory approach. Math. Model. Methods Appl. Sci.
**2012**, 22, 1140003. [Google Scholar] [CrossRef] - Schneider, M.; Somers, M. Organizations as complex adaptive systems: Implications of Complexity Theory for leadership research. Leadersh. Q.
**2006**, 17, 351–365. [Google Scholar] [CrossRef] - Anderies, J.M.; Katti, M.; Shochat, E. Living in the city: Resource availability, predation, and bird population dynamics in urban areas. J. Theor. Biol.
**2007**, 247, 36–49. [Google Scholar] [CrossRef] [PubMed] - Li, S.; Tong, L.; Xing, J.; Zhou, Y. The Market for Electric Vehicles: Indirect Network Effects and Policy Design. J. Assoc. Environ. Resour. Econ.
**2017**, 4, 89–133. [Google Scholar] [CrossRef] - Maase, S.; Dilrosun, X.; Kooi, M.; Hoed, R.V.D. Performance of Electric Vehicle Charging Infrastructure: Development of an Assessment Platform Based on Charging Data. World Electr. Veh. J.
**2018**, 9, 25. [Google Scholar] [CrossRef][Green Version] - Wolbertus, R.; Hoed, R.V.D.; Maase, S. Benchmarking Charging Infrastructure Utilization. World Electr. Veh. J.
**2016**, 8, 754. [Google Scholar] [CrossRef][Green Version] - Kontou, E.; Liu, C.; Xie, F.; Wu, X.; Lin, Z. Understanding the linkage between electric vehicle charging network coverage and charging opportunity using GPS travel data. Transp. Res. Part C Emerg. Technol.
**2018**, 98, 141. [Google Scholar] [CrossRef] - Lane, B.W. From early adopters to early quitters. Nat. Energy
**2021**, 6, 458–459. [Google Scholar] [CrossRef] - Okunuki, K.; Sekuzu, I. Studies on the oxidase system of escherichia coli with special reference to inhibition of succinic oxidase system. J. Biochem.
**1955**, 42, 397–409. [Google Scholar] [CrossRef] - Poisot, T.; Gravel, D. When is an ecological network complex? Connectance drives degree distribution and emerging network properties. PeerJ
**2014**, 2, e251. [Google Scholar] [CrossRef][Green Version] - Saavedra, S.; Reed-Tsochas, F.; Uzzi, B. A simple model of bipartite cooperation for ecological and organizational net-works. Nature
**2009**, 457, 463–466. [Google Scholar] [CrossRef] - Xydas, E.; Marmaras, C.; Cipcigan, L.M. A multi-agent based scheduling algorithm for adaptive electric vehicles charging. Appl. Energy
**2016**, 177, 354–365. [Google Scholar] [CrossRef][Green Version] - Wolbertus, R.; Kroesen, M.; Hoed, R.V.D.; Chorus, C. Fully charged: An empirical study into the factors that influence connection times at EV-charging stations. Energy Policy
**2018**, 123, 1–7. [Google Scholar] [CrossRef][Green Version] - Guirao, B.; Molina-Sánchez, R.; Ortuño, A.; Gálvez-Pérez, D. Integration of Free Floating Car Sharing Systems in Rail Stations: A Web Based Data Analysis. Futur. Transp.
**2021**, 1, 4. [Google Scholar] [CrossRef] - Helbing, D.; Buzna, L.; Johansson, A.; Werner, T. Self-organized pedestrian crowd dynamics: Experiments, simulations, and design solutions. Transp. Sci.
**2005**, 39, 1–24. [Google Scholar] [CrossRef][Green Version] - Helbing, D.; Yu, W. The outbreak of cooperation among success-driven individuals under noisy conditions. Proc. Natl. Acad. Sci. USA
**2009**, 106, 3680–3685. [Google Scholar] [CrossRef] [PubMed][Green Version] - Bellomo, N.; Soler, J. On the mathematical theory of the dynamics of swarms viewed as complex systems. Math. Model. Methods Appl. Sci.
**2012**, 22, 1140006. [Google Scholar] [CrossRef] - Nagel, K.; Paczuski, M. Emergent traffic jams. Phys. Rev. E
**1995**, 51, 2909–2918. [Google Scholar] [CrossRef][Green Version] - Marschler, C.; Sieber, J.; Berkemer, R.; Kawamoto, A.; Starke, J. Implicit Methods for Equation-Free Analysis: Convergence Results and Analysis of Emergent Waves in Microscopic Traffic Models. SIAM J. Appl. Dyn. Syst.
**2014**, 13, 1202–1238. [Google Scholar] [CrossRef][Green Version] - Lewis, T.G.; Mackin, T.J.; Darken, R. Critical Infrastructure as Complex Emergent Systems. Int. J. Cyber Warf. Terror.
**2011**, 1, 1–12. [Google Scholar] [CrossRef][Green Version] - Rohr, R.P.; Saavedra, S.; Bascompte, J. On the structural stability of mutualistic systems. Science
**2014**, 345, 1253497. [Google Scholar] [CrossRef][Green Version] - Albert, R.; Barabási, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys.
**2002**, 74, 47–97. [Google Scholar] [CrossRef][Green Version] - Saavedra, S.; Stouffer, D.B.; Uzzi, B.; Bascompte, J. Strong contributors to network persistence are the most vulnerable to extinction. Nature
**2011**, 478, 233–235. [Google Scholar] [CrossRef] [PubMed] - Parandehgheibi, M.; Modiano, E. Robustness of Bidirectional Interdependent Networks: Analysis and Design. arXiv
**2016**, arXiv:1605.01262. [Google Scholar] - Koç, Y.; Warnier, M.; Kooij, R.E.; Brazier, F.M.; Warnier, M. A robustness metric for cascading failures by targeted attacks in power networks. In Proceedings of the 2013 10th IEEE International Conference on Networking, Sensing and Control (ICNSC), Paris, France, 10–12 April 2013; pp. 48–53. [Google Scholar] [CrossRef]
- Davis, J.T.; Perra, N.; Zhang, Q.; Moreno, Y.; Vespignani, A. Phase transitions in information spreading on structured populations. Nat. Phys.
**2020**, 16, 590–596. [Google Scholar] [CrossRef] - Fronczak, P.; Fronczak, A.; Hołyst, J.A. Self-organized criticality and coevolution of network structure and dynamics. Phys. Rev. E
**2006**, 73, 046117. [Google Scholar] [CrossRef] [PubMed][Green Version] - Helmus, J.R.; Wachlin, S.; Vermeulen, I.; Lees, M.H. SEVA: A Data driven model of Electric Vehicle Charging Behavior. arXiv
**2019**, arXiv:1904.08748. [Google Scholar] - Shalizi, C.R.; Shalizi, K.L.; Haslinger, R. Quantifying Self-Organization with Optimal Predictors. Phys. Rev. Lett.
**2004**, 93, 118701. [Google Scholar] [CrossRef][Green Version] - Schelling, T.C. Dynamic models of segregation. J. Math. Sociol.
**1971**, 1, 143–186. [Google Scholar] [CrossRef] - Bak, P.; Tang, C.; Wiesenfeld, K. Self-organized criticality: An explanation of the 1/f noise. Phys. Rev. Lett.
**1987**, 59, 381–384. [Google Scholar] [CrossRef] - Carreras, B.; Newman, D.E.; Dobson, I.; Poole, A.B. Evidence for Self-Organized Criticality in a Time Series of Electric Power System Blackouts. IEEE Trans. Circuits Syst. I Regul. Pap.
**2004**, 51, 1733–1740. [Google Scholar] [CrossRef] - McAteer, R.T.J.; Aschwanden, M.J.; Dimitropoulou, M.; Georgoulis, M.K.; Pruessner, G.; Morales, L.; Ireland, J.; Abramenko, V. 25 Years of Self-organized Criticality: Numerical Detection Methods. Space Sci. Rev.
**2015**, 198, 217–266. [Google Scholar] [CrossRef][Green Version] - Bettencourt, L.M.; Lobo, J.; Helbing, D.; Kühnert, C.; West, G.B. Growth, innovation, scaling, and the pace of life in cities. Proc. Natl. Acad. Sci. USA
**2007**, 104, 7301–7306. [Google Scholar] [CrossRef] [PubMed][Green Version] - Bauer, G.S.; Phadke, A.; Greenblatt, J.B.; Rajagopal, D. Electrifying urban ridesourcing fleets at no added cost through efficient use of charging infrastructure. Transp. Res. Part C Emerg. Technol.
**2019**, 105, 385–404. [Google Scholar] [CrossRef] - Klitkou, A.; Bolwig, S.; Hansen, T.; Wessberg, N. The role of lock-in mechanisms in transition processes: The case of energy for road transport. Environ. Innov. Soc. Transit.
**2015**, 16, 22–37. [Google Scholar] [CrossRef][Green Version] - Almaghrebi, A.; Shom, S.; Al Juheshi, F.; James, K.; Alahmad, M. Analysis of User Charging Behavior at Public Charging Stations. In Proceedings of the 2019 IEEE Transportation Electrification Conference and Expo (ITEC), Novi, MI, USA, 19–21 June 2019. [Google Scholar] [CrossRef]
- Har-Shemesh, O.; Quax, R.; Hoekstra, A.G.; Sloot, P.M.A. Information geometric analysis of phase transitions in complex patterns: The case of the Gray-Scott reaction–diffusion model. J. Stat. Mech. Theory Exp.
**2016**, 2016, 43301. [Google Scholar] [CrossRef][Green Version] - Avetisov, V.; Gorsky, A.; Maslov, S.; Nechaev, S.; Valba, O. Phase transitions in social networks inspired by the Schelling model. Phys. Rev. E
**2018**, 98, 032308. [Google Scholar] [CrossRef][Green Version] - Zhang, X.; Wang, K.; Hao, Y.; Fan, J.-L.; Wei, Y.-M. The impact of government policy on preference for NEVs: The evidence from China. Energy Policy
**2013**, 61, 382–393. [Google Scholar] [CrossRef] - Wang, W.; Chen, Y.; Huang, J. Heterogeneous preferences, decision-making capacity, and phase transitions in a complex adaptive system. Proc. Natl. Acad. Sci. USA
**2009**, 106, 8423–8428. [Google Scholar] [CrossRef][Green Version] - Pathak, J.; Lu, Z.; Hunt, B.R.; Girvan, M.; Ott, E. Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data. Chaos Interdiscip. J. Nonlinear Sci.
**2017**, 27, 121102. [Google Scholar] [CrossRef] - Vermeulen, I.; Helmus, J.R.; Lees, M.; Hoed, R.V.D. Simulation of Future Electric Vehicle Charging Behavior—Effects of Transition from PHEV to FEV. World Electr. Veh. J.
**2019**, 10, 42. [Google Scholar] [CrossRef][Green Version] - Franke, T.; Krems, J.F. Understanding charging behaviour of electric vehicle users. Transp. Res. Part F Traffic Psychol. Behav.
**2013**, 21, 75–89. [Google Scholar] [CrossRef] - Conte, M.; Alessandrini, F.; Pasquali, M.; Rossi, E.; Sglavo, V.; Vellucci, F. Experimental behaviour of Li-ion and supercapacitors cells for HEVs under standardized and tailored-life cycle testing. World Electr. Veh. J.
**2015**, 7, 59–70. [Google Scholar] [CrossRef][Green Version] - Botsfordm, C.W.; Edwards, A. An Integrated Global Philosophy of EV Charging. World Electr. Veh. J.
**2016**, 8, 495. [Google Scholar] [CrossRef][Green Version] - Pincus, S.M. Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. USA
**1991**, 88, 2297–2301. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hartmanis, J.; Stearns, R.E. On the Computational Complexity of Algorithms. Trans. Am. Math. Soc.
**1965**, 117, 285–306. [Google Scholar] [CrossRef] - Lindgren, K.; Nordahl, M.G. Complexity measures and cellular automata. Complex Syst.
**1988**, 2, 409–440. [Google Scholar] - Spiegelhalter, D.J.; Best, N.G.; Carlin, B.P.; van der Linde, A. Bayesian measures of model complexity and fit. J. R. Stat. Soc. Ser. B Stat. Methodol.
**2002**, 64, 583–639. [Google Scholar] [CrossRef][Green Version] - Gell-Mann, M. What is complexity?Remarks on simplicity and complexity by the Nobel Prize-winning author ofThe Quark and the Jaguar. Complexity
**1995**, 1, 16–19. [Google Scholar] [CrossRef] - Latapy, M.; Magnien, C.; Del Vecchio, N. Basic notions for the analysis of large two-mode networks. Soc. Netw.
**2008**, 30, 31–48. [Google Scholar] [CrossRef] - Khodamoradi, K.; Krishnamurt, R.; Rafiey, A.; Stamoulis, G. PTAS for Ordered Instances of Resource Allocation Problems with Restrictions on Inclusions. In Proceedings of the IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013), Guwahati, India, 10–14 December 2013; pp. 1–23. [Google Scholar]
- Aveklouris, A.; Nakahira, Y.; Vlasiou, M.; Zwart, B. Electric vehicle charging: A queueing approach. Perform. Eval. Rev.
**2017**, 45, 33–35. [Google Scholar] [CrossRef] - Liang, H.; Sharma, I.; Zhuang, W.; Bhattacharya, K. Plug-in electric vehicle charging demand estimation based on queueing network analysis. In Proceedings of the 2014 IEEE General Meeting Conference & Exposition, National Harbor, MD, USA, 27–31 July 2014. [Google Scholar]
- Said, D.; Cherkaoui, S.; Khoukhi, L. Queuing model for EVs charging at public supply stations. In Proceedings of the 2013 9th International Wireless Communications and Mobile Computing Conference (IWCMC), Sardinia, Italy, 1–5 July 2013; pp. 65–70. [Google Scholar] [CrossRef]
- Borge-Holthoefer, J.; Baños, R.A.; González-Bailón, S.; Moreno, Y. Cascading behaviour in complex socio-technical networks. J. Complex Netw.
**2013**, 1, 3–24. [Google Scholar] [CrossRef][Green Version] - Wu, Z.-X.; Peng, G.; Wang, W.-X.; Chan, S.; Wong, W.M.E. Cascading failure spreading on weighted heterogeneous networks. J. Stat. Mech. Theory Exp.
**2008**, 2008, P05013. [Google Scholar] [CrossRef] - Korkali, M.; Veneman, J.G.; Tivnan, B.F.; Bagrow, J.P.; Hines, P.D.H. Reducing Cascading Failure Risk by Increasing Infrastructure Network Interdependence. Sci. Rep.
**2017**, 7, 44499. [Google Scholar] [CrossRef] [PubMed][Green Version] - Soltan, S.; Mazauric, D.; Zussman, G. Cascading failures in power grids. In Proceedings of the 5th International Conference on Future Energy Systems, Cambridge, UK, 11–13 June 2014; pp. 195–206. [Google Scholar] [CrossRef]
- Glombek, M.; Helmus, J.R.; Lees, M.; Van Den Hoes, R.; Quax, R. Vulnerability of Charging Infrastructure. A Novel Approach for Improving Charging Station Deployment. In Proceedings of the 2018 Transportation Research Arena, Vienna, Austria, 16–19 April 2018. [Google Scholar]
- Morrissey, P.; Weldon, P.; O’Mahony, M. Future standard and fast charging infrastructure planning: An analysis of electric vehicle charging behaviour. Energy Policy
**2016**, 89, 257–270. [Google Scholar] [CrossRef] - Dacid, P. Key Performance Indicators (KPI): Developing, Implementing, and Using Winning KPIs; Wiley: Hoboken, NJ, USA, 2010. [Google Scholar]
- Candiello, A.; Cortesi, A. KPI-Supported PDCA Model for Innovation Policy Management in Local Government. In Proceedings of the International Conference on Electronic Government, Delft, The Netherlands, 28 August–2 September 2011; pp. 320–331. [Google Scholar] [CrossRef][Green Version]
- Hutcherson, R. Organizational Optimization; Author House: Bloomington, IN, USA, 2014. [Google Scholar]
- Quax, R.; Kandhai, D.; Sloot, P.M.A. Information dissipation as an early-warning signal for the Lehman Brothers collapse in financial time series. Sci. Rep.
**2013**, 3, srep01898. [Google Scholar] [CrossRef] [PubMed] - Varshney, L.R. Fundamental Limits of Data Analytics in Sociotechnical Systems. Front. ICT
**2016**, 3, 2. [Google Scholar] [CrossRef][Green Version] - Strategisch plan laadinfrastructuur gemeente Utrecht tot 2030. Available online: https://api1.ibabs.eu/publicdownload.aspx?site=utrecht&id=100507727 (accessed on 9 January 2022).
- Albert, R.; Jeong, H.; Barabási, A.L. Error and attack tolerance of complex networks. Nature
**2000**, 406, 378–382. [Google Scholar] [CrossRef][Green Version] - Irani, S.; Leung, V. Scheduling with Conflicts on Bipartite and Interval Graphs. J. Sched.
**2003**, 6, 287–307. [Google Scholar] [CrossRef] - Manea, M. Models of Bilateral Trade in Networks. In Oxford Handbook of the Economics of Networks; Oxford University Press: New York, NY, USA, 2016; pp. 697–732. [Google Scholar] [CrossRef][Green Version]
- Dueñas, M.; Fagiolo, G. Modeling the International-Trade Network: A gravity approach. J. Econ. Interact. Co-ord.
**2013**, 8, 155–178. [Google Scholar] [CrossRef] - Tarissan, F. Comparing Overlapping Properties of Real Bipartite Networks. In Proceedings of the ISCS 2014: Interdisciplinary Symposium on Complex Systems, Florence, Italy, 15–18 September 2014; pp. 309–317. [Google Scholar] [CrossRef]
- Available online: https://github.com/biometry/bipartite (accessed on 9 January 2022).
- Guillaume, J.-L.; Latapy, M. Bipartite structure of all complex networks. Inf. Process. Lett.
**2004**, 90, 215–221. [Google Scholar] [CrossRef][Green Version] - Qiao, J.; Meng, Y.-Y.; Chen, H.; Huang, H.-Q.; Li, G.-Y. Modeling one-mode projection of bipartite networks by tagging vertex information. Phys. A Stat. Mech. Appl.
**2016**, 457, 270–279. [Google Scholar] [CrossRef][Green Version] - Sayama, H.; Pestov, I.; Schmidt, J.; Bush, B.J.; Wong, C.; Yamanoi, J.; Gross, T. Modeling complex systems with adaptive networks. Comput. Math. Appl.
**2013**, 65, 1645–1664. [Google Scholar] [CrossRef][Green Version] - Langton, C.G. Computation at the edge of chaos: Phase transitions and emergent computation. Phys. D Nonlinear Phenom.
**1990**, 42, 12–37. [Google Scholar] [CrossRef][Green Version] - Bert, F.E.; Rovere, S.L.; Macal, C.M.; North, M.J.; Podestá, G. Lessons from a comprehensive validation of an agent based-model: The experience of the Pampas Model of Argentinean agricultural systems. Ecol. Model.
**2014**, 273, 284–298. [Google Scholar] [CrossRef] - Gilbert, N.; de Marchi, S.; Page, S.E. Agent-Based Models. Annu. Rev. Polit. Sci.
**2014**, 17, 1–20. [Google Scholar] - Bonabeau, E. Agent-based modeling: Methods and techniques for simulating human systems. Proc. Natl. Acad. Sci. USA
**2002**, 99, 7280–7287. [Google Scholar] [CrossRef][Green Version] - Axelrod, R. Advancing the art of simulation in the social sciences—SSP. J. Jpn. Int. Econ.
**2003**, 12, 16–22. [Google Scholar] - Macal, C.M.; North, M.J. Agent-based modeling and simulation. In Proceedings of the 2009 Winter Simulation Conference (WSC), Austin, TX, USA, 13–16 December 2009; pp. 86–98. [Google Scholar]
- Schouten, M.; Verwaart, T.; Heijman, W. Comparing two sensitivity analysis approaches for two scenarios with a spatially explicit rural agent-based model. Environ. Model. Softw.
**2014**, 54, 196–210. [Google Scholar] [CrossRef] - Elliott, E.; Kiel, L.D. A complex systems approach for developing public policy toward terrorism: An agent-based ap-proach. Chaos Solitons Fractals
**2004**, 20, 63–68. [Google Scholar] [CrossRef] - Zhang, H.; Vorobeychik, Y.; Letchford, J.; Lakkaraju, K. Data-driven agent-based modeling, with application to rooftop solar adoption. Auton. Agents Multi-Agent Syst.
**2016**, 30, 1023–1049. [Google Scholar] [CrossRef] - Jensen, T.; Chappin, J.L. Automating agent-based modeling: Data-driven generation and application of innovation diffusion models. Environ. Model. Softw.
**2017**, 92, 261–268. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Illustration of feedback loop, related to policy makers’ charging point deployment strategies.

**Figure 5.**Overview of different configurations for ratio1. (

**a**) Public charging; (

**b**) private charging; (

**c**) DC fast charging.

**Figure 6.**Illustration of arrival and departure patterns for different type of charging infrastructure.

**Figure 7.**The path of the spread of effect for (

**a**) public charging, (

**b**) private charging, and (

**c**) DC fast charging (green dot indicates start of cascade).

System | Supply Side/Resources | Demand Side/Users | Environment | Transactions | |
---|---|---|---|---|---|

Education | School, classes | Students/pupils | Geospatial map | Knowledge transfer | [28] |

Healthcare | Hospitals, care centers | Patients | Geospatial map | Health Care | [29,30] |

Electricity | Electricity generators: central and decentral | Household | Network of High mid and low voltage grid | Energy | [31,32,33] |

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**MDPI and ACS Style**

Helmus, J.; Lees, M.; van den Hoed, R. Understanding Complexity in Charging Infrastructure through the Lens of Social Supply–Demand Systems. *World Electr. Veh. J.* **2022**, *13*, 44.
https://doi.org/10.3390/wevj13030044

**AMA Style**

Helmus J, Lees M, van den Hoed R. Understanding Complexity in Charging Infrastructure through the Lens of Social Supply–Demand Systems. *World Electric Vehicle Journal*. 2022; 13(3):44.
https://doi.org/10.3390/wevj13030044

**Chicago/Turabian Style**

Helmus, Jurjen, Mike Lees, and Robert van den Hoed. 2022. "Understanding Complexity in Charging Infrastructure through the Lens of Social Supply–Demand Systems" *World Electric Vehicle Journal* 13, no. 3: 44.
https://doi.org/10.3390/wevj13030044