Bachelor Informatica
Cascading effects of rerouting
behaviour in electric vehicle
charging networks
Melle Vessies
June 28, 2018
Inf
orma
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Universiteit
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Ams
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Abstract
The Netherlands is one of the world leaders in electric vehicles (EV) and EV charging infrastructure. The roll-out strategies of new charge-points are widely studied in an attempt to smoothen the transition from fossil fuel cars to EV’s. In these studies the cascading effects of rerouting behaviour are often left out. This thesis proposes 3 models to study the effects of rerouting behaviour in EV-charging infrastructure and concludes that increasing the knowledge of users about the occupancy of charge-points will not have a large effect on inconvenience. The applied method does however confirm that influencing rerouting behaviour can greatly reduce users inconvenience because of charge-point failures.
Chapter 1
Introduction
The Netherlands is one of the world leaders in electric vehicles (EV) and EV charging infrastructure [1][2]. The municipality of Amsterdam promotes the use of EV’s in an effort to decrease air pollution and support innovation [3]. One of these efforts is maintaining a sufficient charging infrastructure for EV users by the roll-out of charging stations throughout the city. The IDO-Laad project 1 works with various charging point operators (CPO’s) to collect data
of the many charge-points across the Netherlands. The data is then cleaned and used to develop prediction and simulation models to assist companies and government organizations in tackling the problems that they experience in the transition from fossil fuel to electrical powered vehicles.[4]
As concluded in Spoelstra and Helmus (2015) [5] the roll-out strategy (the placement of new charge-points) for charging infrastructure should consist of both demand driven and strategic deployment. Here demand driven deployment refers to placement of a charge-point after a user requested one and strategic de-ployment refers to placement of a charge-point by a municipality when need for an expansion of the infrastructure is expected. In an effort to improve strategic roll-out strategies research has been done to model user charging behaviour and detect infrastructure vulnerabilities [5] [6] [7] [8] [9].
Cascading effects play major roles in many forms of infrastructure. Exam-ples range from perpetuating delays in scheduling of flights and their crews [10] [11] to massive blackouts in complex power grids [12]. EV charging infrastruc-ture can also be subjected to a form cascading effects after disruptions in the network. When a charge-point becomes unavailable this means users have to charge elsewhere, causing disruptions in the network and forcing other users to reroute. And so, a disruption in availability of a single charge-point may lead to an increased load on the rest of the infrastructure and thereby influence whether or not users can charge at certain locations. Even though surges in power consumption may lead to component failure in charging infrastructure [13], there is a far bigger range of reasons a charge-point can be unavailable to users. Examples are roadblocks (e.g. due to construction) and occupancy by non-charging vehicles, but charge-points can also simply be occupied at full
pacity. This capacity constraint means that even though the rest of the network functions as it’s supposed to, disruptions in availability of a single charge-point may lead to cascading effects across the network.
Figure 1.1: Figure used to illustrate cascading failure in EV charging infrastruc-ture. The figure shows a map with 4 charge point located near a shopping mall (cp1 to cp4). Because of a roadblock cp1 is unavailable.
An example of a situation that causes cascading effects in charging infras-tructure can been seen in Figure 1.1. In the figure an hypothetical situation is given of 4 charging points (cp1, cp2, cp3 and cp4) surrounding an arbitrary point of interest for users (the green rectangle), in this case a shopping mall. Because of the interest of the users in the shopping mall, cp1 and cp2 are generally the busiest charge-points, as they are the closest to the mall. Due to construction, the road where cp1 is located is blocked (indicated by the yellow triangle), thus cp1 is unavailable. With cp 1 being one of the busier charge-points, a lot of users will have to find another charge-point and since cp2 is the closest to the mall, chances are that cp2 is the charge-point they will choose. This means that cp2, which was already a busy charge-point, is now even busier and almost always occupied. Users that originally wanted to charge at cp2 may now find their preferred spot is already taken when they arrive and will have to divert to cp3 or cp4. And so, the failure of cp1 leads to users having to reroute from cp2 as well, a clear example of cascading effects. In this example it can even be that cp3 and cp4 also get over-occupied, creating a chain of users having to reroute that continues over an even greater number of charge-points.
This paper aims to simulate these effects using models that are designed to represent certain rerouting behaviours after a charge-point has become unavail-able. Comparing these models shows how changes in rerouting may also change
the effect unavailability of a charge-point has on the rest of the network. Using this knowledge it may be possible to improve roll-out strategies and measure the effects rerouting behaviour has on the network. Practical measures that influ-ence rerouting behaviour may even be implemented as an alternative for placing extra charge-points. We expect to show how extending user knowledge about occupancy of charge-points affects users inconvenience and what the maximum effect of changing rerouting behaviour on users inconvenience can be.
Chapter 2
Related work
Rerouting behaviour of EV users is inherently hard to measure in real life data. Ways of collecting data such as GPS in EV’s or charging-data collected at charge-points produce data from which rerouting behaviour can not be read directly. In the case of charging-data for example, users are only registered at the charge point where they eventually decide to charge. The steps the user took to arrive at this charge-point are not measured and if the user would decide not to charge because their initially preferred charge point is not available, there is no interaction with the charging network at all. This makes it necessary to find new ways to detect or simulate rerouting behaviour so that it can be analyzed and its effects can be studied. This section describes the work done in this area by briefly introducing work about cascading effects in other infrastructures, then describing work on capturing charging behaviour, followed by discussing EV data based modelling of cascading effects.
2.1
Cascading effects in other infrastructures
Cascading effects in the scheduling of flights and their crews [10] [11] show sim-ilarities with with cascading effects in EV charging infrastructure. When for example a gate becomes unavailable at an airport the flights scheduled to leave from that gate will have to leave elsewhere. This leads to other gates being busier and potentially causing delays for other flights that had to leave at those gates. Even though this situation seems incredibly similar to users having to charge elsewhere after a charge-point has become unavailable, there is a very distinct difference. The choice of an alternative charge-point is dependent on preference of users, while for flights the schedule is controlled by the airline or airport. Therefore solutions found in flight scheduling, that are mainly based on the scheduling of future flights, can not be applied to charging infrastructure. In power grids cascading effects have been identified as one of the main fac-tors causing blackouts [12]. Common causes of node failure, such as natural disasters (e.g. lightning strikes), human error and component failure often lead to the failure of a single node and can be mitigated by increasing the load on the rest of the grid. However, this may lead to various other problems such as overcurrent and undervoltage that can increase the chance of component failure
in other nodes. If this component failure does in fact occur it will once again require the rest of the grid to mitigate the outage and thus increase the chance of another failure. Because of this redistribution mechanism failure of a single node can lead to a chain-reaction of other node failures causing massive black-outs. In power grids, the rest of the network is subjected to actual component failure because of load redistribution, while in charging infrastructure the rest of the network still functions as its supposed to. Common measures of network vulnerability applied to power grids focus on the connectedness of the network as a whole under these effects. However, in charging infrastructure failure of a node does not directly impact connectedness as users have many routes to travel to their desired charge-point, not necessarily passing over other nodes in the network. The only factor limiting connecectedness in charging infrastruc-ture is the willingness of users to travel to other charge-points. This is why it is critical to have models to capture actual rerouting behaviour of users.
2.2
Capturing charging behaviour
Extensive research has been done by Wachlin (2017) [14] to model EV charging behaviour in such a way that it can predict where, when and how long a user will charge its EV. To train this model a large real world data-set was used (over 3 million charge sessions), in contrast with other studies that use small data-sets or data from a controlled environment. One of the conclusions drawn in the study is that the 3 main factors influencing user choice in selecting a charge-point are distance, price and charge-speed. Of these factors, the price can be split in 2 sub-factors, namely price per kW h and parking tariffs. Based on these factors and using the data from the data-set, models are trained to capture the behaviour of individual users. With these models it is possible to predict where, when and how long a user will want to charge its EV. This can be used to test and evaluate different roll-out strategies. The results from the models are however not precise enough to accurately say exactly which charge-point the user will use. The models return an area in which multiple charge-points may lie. This means that even though the models may be used for large scale analy-ses, they can not be used to identify problems between individual charge-points. The study provides interesting insights in what factors make a user decide to use a specific charge point, but due lack of accuracy the models can not be used to analyze rerouting behaviour. As implied by the distance based user prefer-ence in the choosing of a charge-point[14], rerouting behaviour generally takes place within a small set of charge-points in a specific area, making it necessary to know exactly which charge-points are involved. Therefore there is the need for a model that can capture rerouting behaviour precise enough to measure cascading effects on an individual level.
2.3
EV data based cascading failure model
This thesis continues the work of the paper by Glombek et al (2018) [9] that proposes two measures of network vulnerability based on cascading effects in EV charging network. The two new measures can be used to calculate the
vulnerability of charge-points to cascading effects on an individual level. An explanation of the data-set used can be found in Section 3.2 and an example of how the method works in practice can be found in Section 3.3. For the men-tioned paper a subset of the described data-set is used consisting of the sessions of a single month.
To simulate cascading failure the charge network is represented as a complex network where each node represents a charge-point and each edge refers to a connection between reachable charge-points. The capacity of each node refers to the number of sockets of each charge-point and the load of each node can be seen as the number of EV’s currently charging at the charge-point. With this representation unavailability of a charge-point because it is occupied is also considered as the failure of a node. The load of the failing node is redistributed to its alternatives through its edges.
Figure 2.1: Scheme of the cascading failure model as provided by original paper [9]
In the paper a model is proposed that simulates cascading behaviour based on previous charging data by making charge-points unavailable at the start of charge sessions and then redirecting these charge-sessions to relevant alterna-tives. This is a way of simulating a user arriving at a charge point that turns out to be unavailable after which the user searches for an alternative. The alter-natives are selected within a radius of 500m of the original charge-point and the model assumes the user will always pick the closest available alternative unless there is a charge-point that causes no further cascade for other users. After the initial relocation of the charge session, the simulation checks whether or not this means another session has to be relocated, when this is the case it is measured as a cascade, when for any session no alternative is available it is measured as a complete failure. By these measures, Service failure vulnerability and Incon-venience vulnerability are calculated respectively indicating the relative number of complete failures for each charge-point and longest chain of cascades failure of each charge-point has caused. The flow-chart used to visualize the algorithm used for this model is visible in Figure 2.1. Finally, these vulnerabilities are compared to other commonly used vulnerability measures of complex networks
and it is concluded that they, due to the fact that they show little correlation with other measures, are a valuable addition in measuring charging network vulnerability.
This thesis will build on much of the work done in this paper. There are, however, some assumptions made in the proposed model that make it possible to improve how well the model reflects reality and how changes in rerouting affect users inconvenience. Therefore this thesis proposes 3 new models that are further discussed in Section 4.
Chapter 3
Background information
This section serves to further explain the concepts from related work that are adopted in our own methodology. This includes adopted terminology, an expla-nation of the data-set used and also an example of how the model proposed by Glombek et al (2018) [9] (explained in Section 2.3) works in practice.
3.1
Adopted terminology
In this thesis much of the same terminology is used as defined in Glombek et al (2018) [9]. We will apply the same representation of the charging network as a graph with edges representing links between alternatives and the capacity of a node as the number of sockets. Because the same representation is used we adopt the same definition of cascading failure. In the rest of this thesis cascading failure and related terms are defined as below.
• Failure of a charge-point - A charge-point being unavailable for a user at a certain point in time. This includes a charge-point being unavailable because it is occupied by other users.
• Cascading failure - A chain of users having to reroute because a charge-point has failed.
• A cascade - A user having to divert to another charge-point because its preferred charge-point is unavailable.
• Cascading score - The number of cascades caused by relocation of a single charge-session.
• Inconvenience Vulnerability - The maximum cascade score of a charge-point. Or in other words the longest chain of cascades relocation of a charge-session belonging to a specific charge-point causes.
• Complete failure - The failure to relocate a sessions at any of a charge-points alternatives.
• Alternatives of a charge-point - Charge-points that lie within a 500m radius [9] of a specific charge-point.
3.2
The data-set
Figure 3.1: Parameters of used data as explained in Van den Hoed and Helmus (2013) [6]
The data used by the paper consists of a large list of charge-sessions that took place in the city of Amsterdam since 2014. The exact make-up of the data and some of its potential uses are explained in Van den Hoed and Helmus (2013) [6]. The parameters of the data-set are visible in Figure 3.1. Parameters of interest for this thesis are Charge point adress, Start date, Start time, End date and End time. The original data-set consists of over 3 million charge sessions in 4 major cities in the Netherlands. The set is estimated to include about 90% of the charge-sessions conducted in the Netherlands and is considered one of the largest real world EV charging data-sets in the world [14]. The data-set or a subset of the data-set was used by both papers mentioned in related work as well as in much of the other research done by the IDO-laad project [4].
3.3
The original model in practice
A concrete example of the simulation used by Glombek et al (2018) [9] (explained in Section 2.3), an example situation is given in Figure 3.2. The figure shows the charge-sessions of a charge-point and its alternatives at a certain point in time. This representation visualizes how the simulation uses the data-set, which
consists of a list of charge-sessions located at different charge-points. Cp1 is the charge-point of interest and has one session of length n starting at time t that is visible in green. The other charge points (cp2 to cp5) are sorted from shortest to longest distance relative to cp1 and their sessions are given in red. To calculate the cascading score of the session located at cp1, we assume cp1 is unavailable and attempt to relocate the session to one of cp1’s alternatives. To do this we follow the flow-chart as visible in Figure 2.1. Since all charge-points shown lay within the relevant radius, the simulation will look which alternative can accommodate the entire session of cp1. This results in cp5 being chosen and no further cascade being caused. If however, we assume cp5 is unavailable (shown in Figure 3.3), the simulation will look for a charge-point that is free at time t. This will result in 2 charge-points being considered as options: cp2 and cp3. Because cp1 is closer to cp3 (200m) than to cp2 (485m) the simulation will choose cp3 as the best alternative and place the session there. The 2 sessions originally placed at cp3 will now have to be relocated, meaning a cascading failure has occurred. This will be done by recursively using the same algorithm on both sessions.
Figure 3.2: Visualization of charge-session data at time t. Each block represents a charge-session.
Figure 3.3: Visualization of charge-session data at time t. Each block represents a charge-session. In contrast with Figure 3.2 cp5 is occupied at time t.
Chapter 4
Method
The models proposed here are designed to each represent a specific form of rerouting behaviour after a charge-point has failed. The models are then com-pared to show what effect certain changes in rerouting behaviour could have on inconvenience. All simulations are run on a subset of the data-set supplied by the IDO-laad project that was also used in Glombek et al (2018) [9] and Wach-lin (2017) [14]. More information about the data-set can be found in Section 3.2 The data-set used for simulation in this thesis consists of the first week of June 2017 in the city of Amsterdam, containing more than 13000 charge-sessions spread over 1200 charge-points.
For all the models we assume user preference for alternatives is based on the walking distance from the original charge-point. We do this under the assump-tion that the original charge-point is located the closest to the final destinaassump-tion of the user and that the user will try to stay as close to it as possible. Choice of alternatives is limited to a 500m radius from the original charge-point. We do not expect a significant change in vulnerability if this radius is increased [9]. The remainder of this section is split up in to two subsections: one explain-ing general changes to the original model proposed by Glombek et al (2018) [9] and one proposing three new models that each represent a specific form of rerouting behaviour. The new method of specifying a cascade, which described in Section 4.1.1, is applied to all models. The actual occurrence of a cascades does however depend on the metrics defined by the model itself. For comparison of the models cascading scores will be calculated for all sessions in the data-set. The cascading score of each charge-point, or inconvenience vulnerability, is still defined as the maximum cascade length relocation of a session belonging to the charge-point has caused. Both the distribution of cascading scores over all sessions and the inconvenience vulnerability scores will be used to compare the models.
4.1
Modifications to the Original Model
This section proposes general changes to the method described by Glombek et al (2018)[9]. The first change will be to redefine the way cascades are counted
so that individual users inconvenience is better captured. The second change will disregard assumptions made by the original model so that the model bet-ter reflects reality. Both changes are then implemented in three new models described in Section 4.2.
4.1.1
Redefining cascades
The first proposed change to the method used by Glombek et al (2018) [9] is changing the way cascades are counted. The original method counts cascades as the number of charge-sessions that have to be relocated after a charge-point has become unavailable. In practice this means the number of cascades that are counted is equal to the number of users affected by the failure of a charge-point. We propose changing this to counting each time a user would attempt to connect to a charge-point during their rerouting as a cascade. The idea behind this is that it not only captures the number of users affected by a cascade but also the inconvenience that was caused for an individual user. As an example of how cascading scores change with this new method Figure 4.1 shows a situation where a user looks for an alternative after its preferred charge-point (shown in blue) has become unavailable. The old method (shown in purple) would simply redirect the user to the available charge-point (shown in green) and return a cascade score of 1. The new method (shown in yellow), assumes the user will drive past alternatives in order of distance until it has found one that is available. Each time a user passes a charge-point that turns out to be unavailable, this is counted as a cascade. This results in a final cascade score of 6 instead of 1.
Figure 4.1: Figure used to illustrate the new calculation method for cascade scores. The figure shows a schematic representation of a map with seven charge-points and two routes that represent the old and the new calculation methods.
4.1.2
Reducing model assumptions
The second proposed change to the original model is to remove the step “Does the whole charge session fit in any alternative?” from the flow-chart shown in Figure 2.1. This step implies the user has full knowledge of the occupancy of a
charge-point for the entire intended charge time, which is in fact not the case. For this step to make sense, a user would have to be able to “see the future” and know that a charge-point will be free for the entire time the user plans to charge. To make the proposed models better reflect reality, the step will me removed from the distance based model (Section 4.2.1) and extended user knowledge model (Section 4.2.2). In the network load model (Section 4.2.3) a similar step is used, this model is however meant to represent an ideal rerouting scenario and thus the step can be used.
4.2
The proposed models
In this section three new models are proposed that each reflect a specific form of rerouting behaviour. All models are based on the original model described by Glombek et al (2018) [9] but with specific modifications. The changes described in Section 4.1 are applied to all models, the effect of these changes does however depend on the model itself. The first model serves as the base model and implement the changes described in Section 4.1. The second model is an example of how a change in rerouting behaviour can change users inconvenience. The last model shows what the maximum effect of changing rerouting behaviour on inconvenience can be.
4.2.1
Distance based rerouting model
Figure 4.2: Flow-chart of distance based rerouting model
The distance based rerouting model is meant as the simplest possible represen-tation of actual user behaviour in charging-networks. This model combines the changes proposed in Section 4.1.1 and 4.1.2 and will serve as the base model for comparisons made in this paper. As specified in the general methodology, user preference is always based on distance and alternatives are selected within a
500m radius. The model assumes a user will always try to find another charge-point if their original preference turns out to be unavailable. Only when there are no (more) alternatives, a complete failure occurs and the session is disre-garded. In case of a complete failure each cascade it took to conclude that there are no available alternatives is still counted. There is no additional penalty imposed in case of a complete failure.
When the model is applied to the example given in Figure 3.2 that was pre-viously used for the original model, we can see that the simulation will first attempt to place the sessions of cp1 at cp4. Because cp4 is not available the cascade counter will be incremented by one and the simulation will continue to look for an alternative. Since cp3 is the next closest alternative the simulation will check and see that it is available at the starting time of the session. The session of cp1 will be placed at cp3 and the sessions of cp3 that overlap with the session from cp1 will have to be relocated as well. The simulation will thus run the same algorithm on the 2 sessions of cp3 and calculate how many cas-cades relocating them causes. The final score of the relocation of cp1’s session is the sum of it’s own cascade score and the cascades caused by relocating cp3’s sessions.
The main purpose of the model is having a more accurate representation of reality that can be compared to the other models in which various changes are made. The comparison between these models will then allow us to conclude what effect different factors have on network convenience.
4.2.2
Extended user knowledge rerouting model
Figure 4.3: Flow-chart of extended user knowledge rerouting model The extended user knowledge rerouting model extends the distance based model by assuming the user has full knowledge of which charge-points are available at the start of their session. This model simulates a situation where all users have a source of information, a mobile app for example, showing them the occupancy
of charge-points in their area. This knowledge will prevent them from having to drive past alternatives looking for one that is available. When no alternative is available, the user will know this in advance and does not reroute at all. Be-cause no additional penalty is imposed in case of a complete failure there is a possibility of the model returning cascade scores of zero.
When applied to the example in Figure 3.2 the extended user knowledge model will select cp3, cp5 and cp2 in the first step and then pick cp3 as it is the clos-est one. Just like in the distance model the simulation will then relocate the sessions at cp3 to the alternatives of cp3. The cascades these re-locations cause are then added to the final cascade score of the session at cp1.
The purpose of this model is showing what effect an increase in user knowledge about the occupancy of charging-points can have. When the inconvenience of the extended user knowledge model turns out to be much lower than that of the distance based model we can conclude that investing in a system that pro-vides users with better occupancy information may be a valid alternative for extending the charging network itself.
4.2.3
Network load based rerouting model
Figure 4.4: Flow-chart of network load based rerouting model
The network load based model redistributes sessions to alternatives in way that is most favorable to the network itself. It calculates the number of cascades that placement of the sessions at each of the alternatives would cause and redirects the user to the charge-point that causes the fewest cascades. This model as-sumes a situation where it can “see the future” and knows how much cascades redistribution causes at a certain point in time, allowing for system-optimal so-lutions.
system-optimal performance in a charging network actually is, as there is a trade-off between long cascades and complete failures. From the network’s point of view it may in some cases be better to cause a complete failure somewhere rather than to reroute a user to another charge-point and cause a lengthy cascade. To prevent the network-load model from causing a large number of complete fail-ures, complete failures are penalized by a cascading score equal to the number of unavailable alternatives.
When applying the network load model to the example in Figure 3.2 the simula-tion will choose cp5 as the best alternative because it causes no further cascades. If we, for the sake of a better example, assume cp5 is unavailable (show in Fig-ure 3.3), the simulation will calculate the number cascades that relocating the session from cp1 at cp3 or cp2 would cause. Either of the charge-points could have a sessions that causes a long cascade, we will assume relocation of the ses-sions causes a single cascade per session. For cp3 this would mean an additional cascade score of 2, because cp3 has 2 sessions that overlap with the session of cp1. For cp2 this would mean an additional cascade of 1 as cp2 only has one overlapping session. Since choosing cp2 as the alternative for the session of cp1 results in a smaller cascade than choosing cp3, the simulation will choose cp2 and return a cascading score of 2 (1 for the relocation of cp1’s session and 1 for cp2’s session).
The purpose of the network load based model is showing how well the charging-network can perform if users are rerouted in an optimal way. When compared to the distance based model this model will show how much can be gained by rerouting users optimally compared to the current situation. This method will show what the maximum effect of changing rerouting behaviour could be on inconvenience and with that whether or not it is worth investigating. The model might not have a concrete practical implementation because it bases its decisions on future data which is not possible in real life. It can however be possible to train a model from charging data that can predict how many cas-cades rerouting a user to a different charge-point will cause, which would allow a closer approximation of this model. Possible implementations of such a model are discussed in the section about future work.
Chapter 5
Results
Each of the models described in Section 4.2 is expect to show a different distri-bution of cascading scores for all sessions. The distance based model is expected to show the highest cascading scores, followed by the user knowledge model and then the network load based model. These expectations are based on the design choices made in the models. The user knowledge model will always choose the same alternative as the distance based model, only with less cascading steps in between, this is why lower cascading scores are expected. The network load based model is designed specifically to generate the lowest possible cascading scores, this is why here much lower cascading scores than the other 2 models are expected. The sizes of these differences between the models are however completely unknown. The sizes of the differences may tell us whether or not measures to change rerouting behaviour are a valid alternative for increasing the size of the infrastructure to reduce users inconvenience.
Judging by the results shown by Glombek at al (2018) [9] higher inconvenience vulnerability scores are expected to be clustered in Amsterdam’s city center. Intuitively this expectation holds for all models, because charge-points in the city center are generally busier and lay closer together giving them a higher chance of having alternatives that have overlapping sessions and cause cascades. Distributions of cascading scores of the 3 models are given in Figure 5.1, 5.2 and 5.3. A combined plot of all distributions is given in Figure 5.4. Table 5.1 shows the total number of cascades and the maximum cascade length per model. Table 5.2 shows the total number of cascades and the maximum cascade length per model compared to the distance based model.
Figure 5.1: Distribution of cascading score occurrence of the “Simple distance based rerouting model” with logarithmic y-axis
Figure 5.2: Distribution of cascading score occurrence of the “User knowledge based rerouting model” with logarithmic y-axis
Figure 5.3: Distribution of cascading score occurrence of the “Network load based rerouting model” with logarithmic y-axis
Figure 5.1, 5.2 and 5.3 show that the cascading score distributions of all the models are clearly skewed to the left. This indicates that short cascades occur far more frequent than long cascades. The network load model shows a small range of cascading scores, with a maximum of 11 that occurs only once and the cascade score of 1 occurring over a 1000 times. The distance based and user knowledge model each show a wider distribution, with scores between 1 and 167.
Figure 5.4: Distribution of cascading score occurrence of all models with loga-rithmic y-axis
Comparison of the density plots of all models shows that the network load model produces much lower cascading scores than the distance based and user knowledge model. The distance based and user knowledge model appear to show somewhat the same distribution. All models show a clear drop in frequency as cascades get longer.
Figure 5.5: Distribution of cascading score occurrence of all models with loga-rithmic x- and y-axis
Plotting the results on both a logarithmic x- and y-axes shows that the distance based and user knowledge model follow a straight line until the less frequently occurring higher cascade scores are reached. This may imply a mono-mial or powerlaw relation (y = axk) between the length of a cascade and the
frequency of its occurrence. The network load model shows a similar line-like shape but located more to the left because of lower cascade scores.
Total cascade count Max cascade count Distance based 37002 167
User Knowledge 34761 157 Network load 13163 11
Table 5.1: Model statistics table of total and maximum cascade scores
Total relative Max relative Distance based 1 1
User Knowledge 0.9394 0.9401 Network load 0.3557 0.0658
Table 5.2: Model statistics table of total and maximum cascade scores compared to the Distance based model
Table 5.1 shows the total number of cascades and the maximum cascade score of all 3 models. Table 5.2 shows the same statistics relative to the distance based model.
Figure 5.6: Inconvenience vulnerability as calculated by the distance based rerouting model
Figure 5.7: Inconvenience vulnerability as calculated by the extended user knowledge rerouting model
Figure 5.6 and 5.7 show the inconvenience scores of the distance based and user knowledge models. The plots show that higher vulnerabilities do in fact belong to the charge-points located in the city center. Due to the low frequency of very high cascade scores most charge-points are shown in bright green, indi-cating their inconvenience vulnerability lies below 40.
Figure 5.8: Inconvenience vulnerability as calculated by the network load based rerouting model
Figure 5.8 shows the inconvenience scores of the network load model. It confirms that high cascades score are very rare as implied by Figure 5.3. The higher vulnerability scores do appear to lie at the outskirts of the city, in contrast with the expected results. Possible reasons for this are further discussed in Section 5.1
5.1
Discussion of results
The results align with our hypothesis. The distribution of each model is in fact different and the distance based model does have the highest total amount of cascades followed by the user knowledge model and then the network load based model. The difference between distance based model and the user knowledge model does however appear minimal, with a reduction of only 6% that is visible in Table 5.2. This would suggest that increasing the knowledge of occupancy of charge-points can only slightly decrease the amount of cascades caused. The network load based model does show much lower cascading scores, resulting in a distribution that is clearly skewed to the left and a total amount of cascades that is only 36% of the distance based total. Perhaps most remarkable is the difference in the maximum cascade lengths of the network load and distance based models (167 vs 11), implying a 93% reduction. From this we can con-clude that the amount of cascades can greatly be reduced by changing users rerouting behaviour after the failure of a charge-point.
The placement of the charge-points with higher inconvenience scores of the distance based and user knowledge models are in line with the expectations based on the results of Glombek at al (2018) [9]. The network load model does however not confirm this hypothesis. A reason for this may be the penalty im-posed on complete failures in the network load model. Glombek at al (2018) [9] showed that complete failures occur more frequently at the outskirts of the city. If these are penalized by relatively high inconvenience scores it makes sense that we see higher inconvenience scores at the same locations.
Chapter 6
Conclusion
In this thesis we have proposed 2 improvements on a method to simulate cas-cading effects due to rerouting in EV charging networks. These improvements where then used to create a model of user rerouting behaviour that better reflects reality: the distance based rerouting model. From the new model 2 other mod-els where derived that each represented a specific form of rerouting behaviour. The first of these, the extended user knowledge rerouting model, served as an example to show how a change in rerouting behaviour can change the inconve-nience caused by cascading failure. The second of the two, the network load based rerouting model, showed what the maximum effect of changing rerouting behaviour on inconvenience can be.
Comparison of the models showed that increasing user knowledge is not likely to have a major effect on inconvenience. As visible in Table 5.2 the total number of cascades was reduced by only 6%. Considering that the user knowledge model assumed that every user would follow this new rerouting pattern, which is not likely, practical implementations may not even reach this 6% decrease. Therefore we conclude that increasing user knowledge about occupancy of charge-points is not an efficient method for decreasing user inconvenience.
The network load model showed that changing rerouting behaviour can in fact have a major effect on inconvenience. As shown in Table Table 5.1, 5.2 and Figure 5.4 the network load model achieved far lower cascade scores than the other two models. Even though the model represents an unrealistic ideal situ-ation it does show the potential of changing rerouting behaviour. The drop of 64% in the total number of cascades shows that inconvenience can be reduced significantly be changing rerouting behaviour.
Ultimately, this thesis has provided an improved model for real rerouting be-haviour. This model can be compared to other models to see how much changes in rerouting behaviour can influence users inconvenience. The user knowledge model served as an example of how real life measures to change rerouting can change users inconvenience. The network load model has shown that it is worth investigating this type of practical measures because they can potentially have a major effect on user inconvenience.
Chapter 7
Discussion and Future work
As mentioned in the description of the network load model choices had to be made on how to let the model handle complete failure. This decision had to be made to ensure the functionality of the model by avoiding complete failures instead of cascades. The penalty that was imposed is however simply a design choice and not based on previous research. Depending on the desired result and what is considered as a optimal situation, one could impose a higher penalty to avoid more complete failures or use a lower penalty to achieve lower cascade scores. In the distance based and user knowledge model complete failure only plays a minor role because its effects are not studied in this thesis. Work of Spoelstra (2014) [8] may however suggest that the assumption that users will always try to find an alternative charge-point is not valid. Spoelstra states that whether or not a user charges at a charge-point is largely dependent on conve-nience rather than the actual need to charge because of an empty battery. The exact effect this has on cascading behaviour will have to be studied in future work.
Besides the possible improvements to better capture complete failures there is also work that can be done to improve the accuracy of the models by adding additional parameters. As concluded by Wachlin (2017) [14] besides distance, charging speed and price also play major roles in users choice of charge-points. To better reflect real user behaviour these factors can be used to extend the distance based model. Each factor can also be implemented individually so that their separate effects on cascading failure can be studied. The addition of park-ing zone’s that are free for people with permits but cost money for other users may for example gravely impact the way users choose their alternatives and thus result in very different results. Studying these effects may lead to prac-tical implementations for changing rerouting behaviour. Raising parking rates in areas where charge-points are often occupied and reducing parking rates in less busy areas may motivate users to change their charge-point preference and reduce cascading effects.
Users inconvenience as defined in this paper is based on whether users have to reroute from their preferred charge-point at all. The network load model aims to reduce the number of cascades in a way that forces users to choose charge points that are not necessarily the closest to their preferred charge-point. This
means that they may have to walk longer then they initially intended to make sure other users do not have to find another charge-point as well. The distance other users would have to walk may however be shorter than the distance the rerouted user has to walk. Therefore it may be interesting to change the net-work load model in a way that does not try to limit the number of cascades but the distance users have to walk to reach their destination. Assuming total walking distance is a better measure of inconvenience than a cascade itself it may be possible to further reduce user inconvenience.
As previously stated, the network load model does not have a direct practi-cal implementation because it bases its rerouting choices on future data, which is not possible in real life. It may however be possible to train a model based on previous data that can predict how many cascades rerouting of a user to a charge-points will cause. That model can then be used to reroute users and achieve a semi-optimal situation (depending on the accuracy of the predictions). A direct example would be to order alternatives based on their inconvenience vulnerability as previously calculated by the distance based model. By sending users to the alternative with the lowest inconvenience vulnerability, they would in fact be send to the charge-point with the lowest expected cascade length.
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