Stochastic Programming for Planning Charging Points for Electric Vehicles “A Case Study Applied to West Flanders, Belgium”

STOCHASTIC PROGRAMMING FOR PLANNING CHARGING POINTS FOR ELECTRIC VEHICLES “A CASE STUDY APPLIED TO WEST FLANDERS, BELGIUM”

Aantal woorden / Word count: 27.340

Sarah Sintobin Stamnummer / student number : 01504605

Promotor / supervisor: Prof. Dr. Dries Goossens Contactpersoon / contact person: Ms. Xiajie Yi

Masterproef voorgedragen tot het bekomen van de graad van: Master’s Dissertation submitted to obtain the degree of:

Master in Business Engineering: Operations Management

Academiejaar / Academic year: 2019-2020

CONFIDENTIALITY AGREEMENT

PERMISSION

I declare that the content of this Master’s Dissertation may be consulted and/or reproduced, provided that the source is referenced.

Signature: Sarah Sintobin

Foreword

Unbelievable, the last five years went so fast. Studying Business Engineering was one big rollercoaster with ups and downs. I hardly knew what to expect, and I could only hope to make it to the end. And now we are here, the end is near.

I am so grateful for all the great opportunities and challenges that my studies have offered me. The biggest challenge was undoubtedly writing a Master’s Dissertation, save the best for the last! This was certainly a mission impossible without a topic that attracted me completely. Therefore, I would like to thank Prof. Dr. Dries Goossens for giving me the opportunity to develop all my acquired operations management skills in a very interesting real-life problem. Also a special thanks to Ms. Xiajie Yi for guiding me through my research.

My whole journey at Ghent University, including this Master’s Dissertation as a real climax, would not have been possible without the help of some people. Therefore, I would like to thank some people who helped me for reaching my goals. First of all my lovely parents who provided me with delicious food and many lucky charms during the exams, and always supported, motivated and believed in me. My brother and sister who stayed strong when they missed me because I was busy studying or writing my Master’s Dissertation instead of entertaining them. And last but not least, my awesome university friends. I will never forget our library meetings, great teamwork, delicious food dates and late nights out.

Preamble

The last five years were unforgettable, although I had imagined the end of my studies a little different. In February I came back from a relaxing ski holiday and I was totally ready to enjoy my last semester to the fullest. But after five weeks my last semester in Ghent suddenly came to an abrupt end. The corona virus had reached Belgium and the government told us all to stay at home. The first moment I was wondering if I would be able to finish my Master’s Dissertation without the library. It was a good environment for me to focus on my work and from time to time I could take a pleasant break with my friends. Once I had survived the first shock and accepted to finish my thesis alone in my room at home, some other practical problems arose that made it a little more difficult for me.

First of all, sometimes it was not possible to consult some sources due to the corona measures. That was really disappointing when an article seemed interesting, but anyway I could always look for an alternative that was available. Secondly, to obtain some data or information I mailed some people and companies, and sometimes it took a bit longer to get an answer. This was sometimes frustrating because I had to wait, but nevertheless I got all the information I needed. Communication in general was a lot more difficult. Instead of planning a meeting with your contact person to ask all of your questions, everything was communicated via mail. This made it much more complex to understand each other and therefore it sometimes took some time to get a clear answer or some feedback. Finally, due to the corona measures it was very difficult to take some time off. The last couple of weeks I was clustered behind my computer and I only went outside to go for a run. These difficult uncertain times are certainly a real test for your mental health.

Beside some practical and mental issues, I was perfectly able to complete my research as expected. It would have been more pleasant without the corona measures, but I survived. The most important thing is that everyone is healthy and I was able to deliver my Master’s Dissertation as I had hoped.

This preamble is drawn up in consultation between the student and the supervisor and is approved by both.

Table of Contents

Table of Contents ...... III

List of Abbreviations ...... V

List of Tables ...... VI

List of Figures ...... VII

1. Introduction ...... 1 1.1. Research question ...... 1 1.2. Relevance of the research ...... 1 1.3. Structure of this Master’s Dissertation ...... 3

2. Electric vehicles and charging ...... 4 2.1. Terminology ...... 4 2.2. Environmental friendly vehicles ...... 4 2.3. Electric driven vehicles ...... 5 2.3.1. Hybrid Electric Vehicle (HEV) ...... 5 2.3.2. Plug-in Hybrid Electric Vehicle (PHEV) ...... 6 2.3.3. Battery Electric Vehicle (BEV)...... 6 2.4. EV Charging ...... 7 2.4.1. Mode 1 charging ...... 7 2.4.2. Mode 2 charging ...... 7 2.4.3. Mode 3 charging ...... 8 2.4.4. Mode 4 charging ...... 8 2.5. Current situation analysis ...... 9 2.5.1. Clean power for transport ...... 9 2.5.2. Current charging point infrastructure in West Flanders ...... 10

3. Literature review ...... 14 3.1. Charging infrastructure planning models in current literature ...... 14 3.1.1. Deterministic approaches ...... 14 3.1.1.1. Estimating the Required Density of EV Charging Stations (ERDEC) model ...... 14 3.1.1.2. Mixed integer linear programming (MILP) ...... 14 3.1.2. Stochastic approaches ...... 16 3.1.2.1. Two-stage stochastic programming ...... 16 3.2. Modeling under uncertainty ...... 19 3.2.1. Robust optimization ...... 20

III

3.2.2. Fuzzy optimization ...... 20 3.2.3. Probabilistic dynamic programming ...... 22 3.2.4. Bayesian methods ...... 24 3.3. Stochastic programming ...... 25 3.3.1. Concept ...... 25 3.3.1.1. Infeasibility ...... 26 3.3.1.2. Stochastic Linear Programming ...... 28 3.3.2. Applications for location problems ...... 32

4. Methodology ...... 34 4.1. Two-stage stochastic programming formulation ...... 34 4.2. Demand ...... 38 4.2.1. EV-to-vehicle ratio ...... 39 4.2.1.1. Normal distribution ...... 39 4.2.1.2. Simulation procedure ...... 42 4.2.2. Inhabitants ...... 43 4.2.3. Workers ...... 44 4.2.4. Tourists...... 45 4.2.5. Percentage that needs a recharge at a public charging point ...... 46 4.3. Capacity ...... 47 4.4. Cost coefficients ...... 50

5. Results and interpretation ...... 53 5.1. Scenario creation ...... 53 5.1.1. EV-to-vehicle ratio ...... 53 5.1.2. Simulation results ...... 55 5.1.2.1. Discrete values for EV-to-vehicle ratio ...... 55 5.1.2.2. Different scenarios ...... 58 5.2. Optimal charging infrastructure West Flanders for 2020 ...... 59 5.3. Evaluation current charging point infrastructure ...... 72

6. Discussion ...... 77 6.1. Conclusions arising from the research ...... 77 6.2. Limitations of the research ...... 79 6.3. Directions for future research ...... 80

References...... VIII

Attachments ...... XII

List of Abbreviations

AC Alternating current AFV Alternative-fuel vehicles BEV(s) Battery electric vehicle(s) BN Bayesian networks CNG Compressed natural gas DC Direct current DV Decision variable(s) EMC Emergency medical center ERDEC Estimating the Required Density of EV Charging EV(s) Electric vehicle(s) GIS Geographic information system GPS Global positioning system HEV(s) Hybrid electric vehicle(s) IC-CPD In-Cable Control- and Protecting Device ICCB In Cable Control Box ICE Internal combustion engine ICEV(s) Internal combustion engine vehicle MILP Mixed integer linear programming PHEV(s) Plug-in hybrid electric vehicle(s) RO Robust optimization SDP Stochastic dynamic programming SLP Stochastic Linear Programming SO Stochastic optimization SOC State of charge TMC(s) Temporary medical centers V2G Vehicle-to-grid

List of Tables

Table 1: Categorization of current public charging points in West Flanders according to type and provided charging speed ...... 13

Table 2: Parameter values of the house selling problem (SDP) ...... 23

Table 3: EV-to-vehicle ratio for the years 2007-2019 in Belgium (Voertuigenpark Statbel, 2019) 40

Table 4: Capacities of every type of charging point according to a certain situation ...... 49

Table 5: The 21 discrete values for the EV-to-vehicle ratio with corresponding probability of occurrence ...... 58

Table 6: Overview of the different model parameters and their values for a first solution ...... 59

Table 7: Optimal solution for the decision variables !", $ with parameters equal to Table 6 ...... 60

Table 8: Overview of the different model parameters and their values as a starting point to decide upon the optimal values for w and s ...... 64

Table 9: Solution results for different values of the shortage cost parameter s ...... 65

Table 10: Solution results for different percentages of cases in which waste is observed ...... 66

Table 11: Overview of the different model parameters and their optimal values ...... 71

Table 12: Optimal solution of the model for the decision variables !", $ and for the parameters equal to Table 11 ...... 71

Table 13: Number of charging points of each type that need to be installed in the municipalities where there are currently too few charging points to serve the demand in 2020 (values !", $) . 76

List of Figures

Figure 1: Map of charging station locations in a few regions in West Flanders (Reprinted from Milieuvriendelijke voertuigen, s.d.-c) ...... 11

Figure 2: More specific information about the chosen charging station in Roeselare (Reprinted from Milieuvriendelijke voertuigen, s.d.-c) ...... 11

Figure 3: Degree of membership of 24°C in a crisp and in a fuzzy set ...... 21

Figure 4: Membership function of temperatures suitable for swimming ...... 21

Figure 5: Upper branch of the decision tree of the house selling problem ...... 23

Figure 6: Bayesian network for the garden problem...... 25

Figure 7: Time plot EV-to-vehicle ratio Belgium 2007 – 2019 ...... 40

Figure 8: Time plot personal vehicle fleet Belgium 2007 - 2019 ...... 44

Figure 9: Transformed EV-to-vehicle ratio variables approached by a linear trendline ...... 53

Figure 10: Transformed EV-to-vehicle ratio variables approached by a linear trendline for only a part of the available data (2012 – 2019)...... 54

Figure 11: Frequency distribution for simulation runs going from 10 to 1 million ...... 56

Figure 12: Frequency distribution for number of bins going from 5 to 25 ...... 57

Figure 13: Solution results for different values of the shortage cost parameter s ...... 66

Figure 14: Sum of the %", & decision variables for each municipality for different percentages of total cases in which waste is observed ...... 69

Figure 15: Total number of charging points and charging point type 2 share for different percentages of total cases in which waste is observed ...... 70

Figure 16: Sum of %", & for every municipality according to the current charging point infrastructure and the future demand scenarios (2020) ...... 73

Figure 17: Cases in which waste observed for the optimal solution when the current charging point infrastructure is taken into account ...... 76

VII

1. Introduction 1.1. Research question

Electric Vehicles (EVs) are not the future anymore, they are the number one sustainable alternative to conventional vehicles nowadays. EVs need electricity, just as Internal Combustion Engine Vehicles (ICEVs), need diesel or gasoline. But EVs lack behind conventional ICEVs regarding charging and range. A problem today is that the EV charging network is less developed than the refuelling network and in comparison to ICEVs who can carry a gasoline canister, there is no portable charging option for EVs. On top of that is the range of an EV much less compared to ICEVs (Rauh, Franke, & Krems, 2014). This raises the need to develop a good charging point infrastructure network to stimulate the adoption of EVs.

This research presents a possible approach to determine the number of charging points required in each unit area of a study area to meet future demand. It is important that the number of charging points is well-balanced, because both too many and too few charging points involve some consequences, referred to as “costs”. Since a good charging infrastructure is one of the main drivers for people to obtain an EV, an appropriate infrastructure network must be deployed before the actual demand is observed. This leads to two-stage stochastic programming, which is a common used method for modeling under uncertainty (see Section 3.3.2). The stochastic element is the future demand for charging points in every unit area, for which different possible scenarios will be created. In a first stage the optimal number of charging points in each unit area is determined. In a second stage a resource response to the shortage or waste that the number of installed charging points entails in every scenario appears. The approach is applied to the study area of West Flanders, where the 64 municipalities serve as unit areas.

This leads to the following research topic:

“Stochastic programming for planning charging points for electric vehicles : A case study applied to West Flanders, Belgium.”

1.2. Relevance of the research

Hot topics such as climate change, ecology and global warming are more than ever present in our personal lives. People are concerned about the growing issues the earth is facing and are ready to take a small part of the responsibility to tackle the rising problems. ‘Youth for climate’1 is probably the greatest

1 Youth for climate is an action group in Belgium that passes through the streets of Brussels to call for better and more effective climate actions.

and most recent proof of the rising awareness that things are getting out of control and the confirmation that something has to change. It is no longer a secret that transport plays a crucial role in the emission of CO2 leading to global warming effects. Therefore, the current transportation system seems unsustainable. Despite the efforts to promote public transportation, the amount of people choosing to commute by personal cars is still massive. A few other initiatives to lower the air pollution are already taken in Belgium. An example are the low emission zones (LEZ), which are zones where vehicles that emit too many harmful substances are no longer allowed (Vlaams Departement Omgeving, s.d.). But this is not enough to solve the growing issues of CO2 emissions. In order to further improve the air quality and reduce the impact of vehicles on the climate, the Flemish Government is striving for a greener vehicle fleet (Team Duurzame Ontwikkeling, s.d.). This could be done by changing the way of fueling cars, leading to EVs which are gaining traction (News European Parliament, 2019). In research done by Joeri Van Mierlo (2018) at the VUB, is investigated that EVs emit 3 to 4 times less carbon dioxide than their diesel counterparts. On top of that is their impact on the environment in a full lifecycle 5 times smaller.

Many studies agree, EVs are better for the environment. But why is the total share of EVs much lower than was expected five years ago? If people are becoming more environmentally conscious, why don’t they buy EVs en masse? A main obstacle for the widespread introduction of EVs is range anxiety (Egbue & Long, 2012; Nilsson, 2011). Egbue & Long (2012) state there is a gap between what people expect regarding range capacity, and the actual distances people daily drive. This is called the range anxiety, which presents the fear of people to run out of electricity before reaching their destination. One of the approaches to limit this range anxiety is to provide as many publicly available charging points as possible (Nilsson, 2011). However, placing too many charging points leads to waste, which is not desirable either. In order to stimulate the growth of the EV share in the total personal vehicle fleet, an appropriate, well- balanced planning approach for public charging points is needed.

Two-stage stochastic programming is a widely used method to solve the charging point location planning problem (see Section 3.1.2.1). Yet this will not just be another research in line. A number of things will be tackled differently than they have been done so far by using two-stage stochastic programming. A lot of existing studies determine the exact location for charging points. For doing so, a lot of specific information about for example driving behavior (origin-destination paths) and potential candidate sites for placing charging points needs to be known. This research will be solely based on the demand for charging points, coming from tourists, inhabitants and workers in each unit area. To the best of my knowledge, this will be the first research using two-stage stochastic programming to determine an optimal density map for charging points where the exact location lies outside the scope of the research.

The approach proposed in this Master’s Dissertation is therefore ideal for planning on a larger scale, when little information about driving and charging behavior is known.

The approach is applied to the study area of West Flanders which could be divided into 64 unit areas, namely municipalities. A few years ago, Belgian grid operators drew up a plan to determine the optimal number of charging points required in each municipality in Flanders. They estimated a pure EV fleet of 60.500 for 2020 in Flanders, which was used as a starting point to determine the total number of charging points needed by 2020 (Vlaams Departement Omgeving, 2015). A model including a number of parameters like for example number of inhabitants, decided upon the optimal number of charging points in each municipality (J. Cockx, personal communication, April 14, 2020). Nevertheless, with 15.338 pure EVs for whole Belgium in 2019, the total number of charging points seems rather overestimated (Voertuigenpark Statbel, 2019). Now the EV market is trending, more data from recent years is available leading to more accurate estimations for the future EV fleet. Therefore, the optimal number of charging points exercise could be reviewed, in order to decide upon future actions.

The proposed approach could be easily applied to other study areas like for example other provinces in Belgium. On top of that, when every year new numbers about the EV vehicle fleet are revealed, the model can be applied every year to keep track on the number of charging points required and the amount already installed.

1.3. Structure of this Master’s Dissertation

The remainder of this Master’s Dissertation is further divided into five main parts. Section 2 gives a general introduction about electric vehicles and charging infrastructure. A current situation analysis of the number of charging points currently present in West Flanders is also presented. A brief literature review about solution methods in current literature but also about possible solution approaches is given in Section 3. Section 4 discusses the followed methodology, which broadly comprises the two-stage stochastic model formulation and how the parameters needed to solve the model are obtained. The methodology is followed with the results in Section 5. The optimal charging point infrastructure for West Flanders for 2020 is presented and the current infrastructure is evaluated and possible actions are recommended. Finally, in Section 6, conclusions, limitations and future research directions are given.

2. Electric vehicles and charging

2.1. Terminology

Different terminology is sometimes used when referring to EV charging. In this Master’s Dissertation some basic terminology is used formatted within EVORA and their “code for public charging” (2015), aimed to achieve some kind of uniformity.

- Charging station or charging pole: physical hardware that contains one or more charging points. Different vehicles could charge on one charging station at the same time if more charging points are present. - Charging point: one identical socket foreseen on a charging station which could be used to connect your charging cable to for charging your EV. One charging point could only be used by one EV at a time. - A public charging point: a charging point that is available for everybody on every day of the week and every hour of the day (24/7). - A semi-public charging point: the availability of a semi-public charging point is somewhat limited, when for example the access is closed at night or only customers are allowed to use the infrastructure. - Charging speed: the power that can be charged expressed in kW (kiloWatt). Sometimes the time it takes to charge is also referred to as charging speed. The time it takes to charge depends not only on your EV, but also on the power of the used charging point. Therefore, both are interrelated : the higher the power, the faster the charging process proceeds. In order to avoid confusion, following terminologies are used : - Normal charging : 11 kW - Accelerated charging : 22 kW - Fast charging : 50 kW

2.2. Environmental friendly vehicles

According to the website ‘Mileuvriendelijke voertuigen’ from the Flemish government (s.d.-a), are environmental friendly vehicles powered by electricity, natural gas or hydrogen. Electric vehicles which are powered by electricity are thus environmental friendly vehicles. Some short-term environmental benefits of environmental friendly vehicles are better air quality, lower CO2 emissions and less noise pollution in comparison to ICEVs.

Thus, not only electric vehicles are meant when talking about environmental friendly vehicles, but also a few other vehicle types falling into this category. These types of vehicles, besides EVs, are very important in the battle for greening the fleet, but are not relevant for this research as they do not rely on electric charging points to renew their fuel. An example of a vehicle using hydrogen as an energy source is a fuel cell car. More precisely, this car uses fuel cells as an energy source which converts the chemical energy of hydrogen directly into electrical energy. Therefore, this vehicle has no emissions, and because it is dependent on hydrogen, it has no need for charging points to recharge. A CNG (compressed natural gas) car is an example of a car that drives on natural gas or CNG.

2.3. Electric driven vehicles

An electric driven vehicle or in short an electric vehicle (EV) is a vehicle that uses an electric motor as propulsion. Electric energy nourishes the electric motor, where the electric energy is converted into mechanical energy. Emadi, Lee, & Rajashekara (2008) and Axsen & Kurani (2013) agree that a general classification of three main classes can be made: Hybrid Electric Vehicles (HEVs), Plug-in Hybrid Electric Vehicles (PHEVs) and Battery Electric Vehicles (BEVs). Their insights are combined to get a better understanding of what these different classes involve, and each class is further specified below.

2.3.1. Hybrid Electric Vehicle (HEV)

Hybrid vehicles combine different ways of propulsion. They have two or more energy and/or power sources, and in this way benefits of different techniques can be achieved. A Hybrid Electric Vehicle (HEV) has an electric motor combined with an internal combustion engine (ICE) or shortly referred to as engine. A further general classification leads to series hybrid and parallel hybrid electric vehicles.

In a series HEV, the electric motor and the engine are placed in series. The engine charges the electric motor (via a generator and a power converter) which results in an onboard system of charging the batteries. The electric motor on his turn is driving the wheels which makes that the engine is not directly connected to the wheels. A parallel HEV in contrary, places the engine and the electric motor in parallel. This results in the possibility to both simultaneously or separately driving the wheels. A detailed description of the functioning of these different types is outside the scope of this research.

The HEVs are an improvement for the environment, but they are still dependent on gas stations. They do not need charging points to recharge their battery, instead the battery can only be charged while driving by reason of the engine. It is the engine that serves for charging the electric motor and the only source for driving the engine is fuel, which could be obtained at a gas station. In other words, the electric motor

is subordinate to the ICE. This makes HEVs relevant for the environment but irrelevant for this research as they do not rely on charging points and are never plugged in.

2.3.2. Plug-in Hybrid Electric Vehicle (PHEV)

An advancement of the HEV and a further improvement for the conventional vehicles in the struggle against global warming is the Plug-in Hybrid Electric Vehicle (PHEV). PHEVs are HEVs but with a larger battery pack that can be charged externally, thus are designed to plug into the electrical grid. Both, the fuel tank and the battery pack rely on external sources to be refilled or recharged. In contrary with the conventional HEVs, is the engine subordinate to the electric motor for PHEVs. This means that a PHEV acts like a pure EV with a fully charged battery (see Section 2.3.3) and only switches to hybrid mode when battery level drops below a certain value, or extra power is demanded. There could be concluded that a combination of pure EVs and HEVs arises with the PHEV, and benefits of both are achieved.

PHEVs are usually every day charged during nighttime, but they still partly count on public charging points. Range anxiety is somewhat solved due to the use of the engine when necessary, but they still rely on public charging points for distances that exceed the battery capacity. For example while parked at the company during office hours, or while shopping at the mall for the afternoon, PHEVs could be plugged into the electrical grid via charging points. However, PHEVs need to be recharged less frequently because they always have kind of a back-up plan (the engine as a second resource). This makes that they rely less on public charging points in comparison to pure EVs. Therefore, they will not be taken into account for determining the number of charging points needed in a municipality.

2.3.3. Battery Electric Vehicle (BEV)

A last category contains the Battery Electric Vehicles (BEVs), also referred to as pure electric vehicles. This type of vehicles solely rely on a strong rechargeable battery pack and does not depend on an internal combustion engine for propulsion anymore. BEVs utilize electricity instead of diesel or gasoline and need to be externally charged, thus are totally dependent on the public charging infrastructure if recharging en route is needed. The biggest part of the demand for electric charging points comes from this group, so the focus of this research lies on BEVs.

For convenience, the term EVs is used to refer to BEVs in this research. These types of EVs solely rely on the electrical grid and therefore on public charging infrastructure and are the main focus group for this research. When HEVs or PHEVs are meant they will be specifically mentioned.

2.4. EV Charging

Charging entails the storage of electrical energy in the battery pack which could be transformed into motion while driving later on. EVs could be charged every time the EV is parked for a while, no matter the state of the battery, only a charging point and a suitable charging cable are required. But which types of charging do exist? And which are convenient for charging EVs? In this section, 4 different charging modes are discussed according to a research project THEO (Thuis Elektrisch Opladen) from the Flemish Government (2015). A charging mode explains the way of charging and relates to which techniques are used. There is also mentioned which charging modes are suitable for EV charging. All findings are also applicable for PHEVs.

2.4.1. Mode 1 charging

The first mode is the easiest way of charging. Mode 1 charging uses the standard socket-outlets present in every house where all kind of household appliances are connected to. There is no single form of communication. This way of charging cannot assure the safety regulations, and is therefore no longer used for charging vehicles. In some countries it is even forbidden by law.

2.4.2. Mode 2 charging

Mode 2 charging solves the safety issues of mode 1 charging. In this type of charging also household socket-outlets are used, but the charging cable connecting the vehicle with the socket contains an In- Cable Control Box (ICCB) or In-Cable Control- and Protecting Device (IC-CPD) (Milieuvriendelijke voertuigen, s.d.-b). This “control” device serves as protection which makes it a suitable mode for charging EVs. Electronics in the box are regulating the current, it contains a safety system to avoid overheating and the box provides the communication.

A disadvantage is that the current needs to be somewhat limited, simply because household socket- outlets are not used to charge frequently during a long time at high-power. Therefore, the charging speed is only 2,3 kW. This makes EV charging possible but at a slow pace, which makes it a good method for charging at home during nighttime. For mode 2 charging no special equipment need to be installed, only the right charging cable with an ICCB or IC-CPD is required and an electrical socket.

2.4.3. Mode 3 charging

Mode 3 charging is another way to charge in a controlled manner which solves the low current and slow pace issue of mode 2 charging. Appropriate electrical sockets are developed especially for charging EVs. The electrical sockets (i.e. charging points) are built-in in a charging station that need to be installed if this way of charging is desired.

Several advantages arise with mode 3 charging. First of all, there is a continuous communication stream between the installation and the EV. Charging takes places only if an appropriate current is found, therefore the charging process is always safe. Secondly, charging is much faster due to the allowance of a higher current. Charging points can have a charging speed from 3,3kW to 22kW and even more. A disadvantage is that this type of charging requires installing an installation, but the advantages absolutely outweigh this effort and cost. Mode 3 charging is used for public charging infrastructure as home charging as well. The charging infrastructure could be placed against the wall or on a pole.

2.4.4. Mode 4 charging

Fast charging, DC charging or mode 4 charging is a last way of charging. Mode 4 charging also requires the use of especially developed charging points, but the big difference with mode 3 charging points is the implementation of a rectifier in the charging infrastructure. The previous three modes where types of AC charging, where a rectifier is found inside the vehicle. The power grid supplies alternating current and the task of the rectifier is to transform this alternating current into direct current. Unlike the AC charging modes, is with DC charging the rectifier located in the charging station, making it the charging station that leads the charging process.

The implementation of the rectifier in the charging equipment brings advantages and disadvantages. The biggest advantage is the speed by which charging is possible. A charging speed of 50kW and even more is possible. However, the implementation makes the charging stations very costly, which is therefore the biggest disadvantage. The high cost of the charging station makes that mode 4 charging is only used for public charging. Also, a too powerful electricity connection is needed to install at home.

2.5. Current situation analysis

2.5.1. Clean power for transport

Electric vehicles are no longer the future anymore, but a desirable alternative in the choice for an environmental friendly vehicle nowadays. Five years ago, it still was an emerging trend, but the future was bright. At the end of 2015 an action plan emanating from the Flemish government called ‘Clean power for transport’ was approved which was mainly focusing on the period up to 2020 (Vlaams Departement Omgeving, 2015). The main purpose of the plan was searching for the most suitable mobility and energy systems in which the reduction of the environmental impact plays an important role. The plan focused on greening the fleet and the use of renewable energy in doing so. An important job was thus to stimulate the adoption of (PH)EVs and therefore foreseeing a better charging infrastructure.

In the first place it was important to promote the great potential to charge at home or at work. This was for example done by stimulating businesses to foresee charging possibilities by providing an ecology bonus. Secondly, the plan was also responsible for the rapid development of (semi-)public charging infrastructure. Now the question arises: how was this done? One thing was clear from the beginning: charging station follows (PH)EV. In other words, the deployment of the charging infrastructure must go hand in hand with the growth in (PH)EVs. A European guideline recommended 1 charging point for every 10 (PH)EVs, or in other words the number of charging points needed equals approximately 10% of the (PH)EV fleet. The Flemish government estimated in 2015 an electric fleet of roughly 74.000 vehicles by 2020 in Flanders. This resulted in the need of at least 7.400 charging points or 3.700 charging stations (when each charging station contains two charging points) by then. Regarding the charging points already installed in 2015, 5.000 new charging points needed to be installed by 2020.

The distribution network managers Eandis and Infrax realized a ‘location plan for charging points’ in consultation with the local authorities. This location plan stated the number of public charging points each municipality needed to install by 2020, where each municipality has to install at least one charging point. The plan was, among other things, mainly based upon the number of inhabitants a municipality counted then. Every year the plan is updated according to the realized charging points, to monitor the remaining needed installations. For the exact location, local authorities played an important role for working towards a better charging infrastructure. They manage public domains and know the most suitable locations for new charging stations in their cities. Every municipality decides upon the best location for charging points in function of the local parking policy, the presence of locations attracting large numbers of visitors, public transport hubs and the capacity of the electricity network.

Every municipality can choose between two approaches: a proactive or a reactive approach. A proactive approach involves that they decide to install charging points on strategically interesting locations (e.g. sports centers, museums, shopping centers, …) which results in a core network of charging stations. The reactive approach is based on the demand for charging points, where the principle of ‘charging station follows (PH)EV’ comes up again. More precisely, this approach installs charging points nearby where (PH)EV drivers live. Based on their request charging station are placed which gives this approach a certain guarantee the charging station will be used. On top of that, municipalities have also the choice today to rely on the distribution system operators (Eandis and Infrax) to provide charging points or to implement the plan in-house.

2.5.2. Current charging point infrastructure in West Flanders

A charging station location map for Flanders is provided by the Flemish government. This can be easily consulted via the internet (Milieuvriendelijke voertuigen, s.d.-c) 2. Figure 1 shows a part of the map for a few regions in West Flanders (Roeselare, Izegem, Ingelmunster,…). Also some suburbs are shown on the map, for which the charging stations belong to the municipality from which they are part of. One spot on the map indicates the presence of a charging station. One charging station can contain multiple charging points. For the biggest part of the charging stations is real-time information about occupied charging points available. This information is constantly updated for the green and red spots on the map, a blue spots means no real-time information is available. Green means that some charging points might be occupied but there is at least one charging point available, red implies that all charging points are occupied. After choosing a spot, more specific information is provided from which an example is shown on Figure 2. The exact address, whether the equipment is public or semi-public and which type of sockets are present are shown.

2 https://www.milieuvriendelijkevoertuigen.be/laadpalen

Figure 1: Map of charging station locations in a few regions in West Flanders (Reprinted from Milieuvriendelijke voertuigen, s.d.-c)

Figure 2: More specific information about the chosen charging station in Roeselare (Reprinted from Milieuvriendelijke voertuigen, s.d.-c)

An overview of all the charging stations in West Flanders is made at the beginning of March 2020. Any new placed charging station hereafter is not incorporated in the analysis. The following could be deduced:

- West Flanders currently counts 488 charging stations from which 374 are public and 114 semi- public. - These charging stations all count together 1.106 charging points, 839 are public and 267 are semi- public. Meaning that on average a public charging station has 2,24 charging points and a semi- public charging station 2,34 charging points. - In this research the focus lies on the public charging stations, as the semi-public charging stations often belong to a company and are not always installed on request of the government. On top of that, from the 267 semi-public charging points are 60 charging points from Tesla (22,47%). Tesla enrolls an own charging station network where only Tesla EVs could charge. As these charging points could only serve a specific part of the demand, these charging points are not interesting for this research. - From the 839 public charging points, a categorization could be made as in Table 1. The biggest part of the charging points relate Type 2 Mennekes charging points with a charging speed of 11 kW, followed by Type 2 Mennekes and general sockets with a charging speed of 22 kW. As there is only 1 charging point with a charging speed of 4 kW, this is ignored in this research. The 6 Combo 50 kW, 6 Chademo 50 kW and the 6 Type 2 Mennekes 43 kW charging points always come together in one charging station. In other words, there are 6 charging stations in West Flanders containing one Chademo 50 kW plug, one Combo 50 kW plug and one Type 2 Mennekes plug. For convenience, there is assumed that public fast chargers always have a charging speed of 50 kW. This means that the 6 Type 2 Mennekes 43 kW charging points are counted together with the 50 kW charging points and all together are considered as fast chargers (i.e. with a charging speed of 50kW). The charging point type is important to know which charging cable fits into the socket, but lies outside the scope of this research. Therefore, in this research the type of the charging point refers to the charging speed it provides. Three types are considered, namely the three most common types in West Flanders : 11 kW, 22 kW and 50 kW. These are referred to as type 1, type 2 and type 3 respectively. Attachment 1 gives an overview how these charging points are divided across the different municipalities in West Flanders.

Charging point type Charging speed Number Type 2 Mennekes 4 kW 1 Type 2 Mennekes 11 kW 623 Type 2 Mennekes 22 kW 137 Socket 22 kW 60 Type 2 Mennekes 43 kW 6 Chademo 50 kW 6 Combo 50 kW 6 TOTAL 839 Table 1: Categorization of current public charging points in West Flanders according to type and provided charging speed

3. Literature review 3.1. Charging infrastructure planning models in current literature

As the use of EVs is increasing rapidly, the charging location problem is at the base of a wide range of research topics. A small overview of some solution methods for the planning of charging points is considered in this section. The existing literature can be divided into two major groups: deterministic solution approaches, which assume that all parameters and demand are known, and stochastic approaches, considering uncertainty (mainly regarding the charging demand). The stochastic element is therefore the element that involves uncertainty. For more details the reader is referred to the respective literature. 3.1.1. Deterministic approaches 3.1.1.1. Estimating the Required Density of EV Charging Stations (ERDEC) model

The first model is referred to as the ERDEC model by Ahn & Yeo (2015). This study derives the optimal density of charging stations and thus not necessarily solves the exact location problem. A study area is divided in a given number of unit square areas and the aim of the model is to determine the number of charging stations in each unit area. The purpose of the ERDEC model is therefore the same as for this research, but the biggest difference is that here all the parameters needed in the model are known. An analytical solution is provided and solved while minimizing total costs.

All parameters are known or at least given a fixed value by making assumptions. The charging demand is calculated based on the number of passing EVs in each unit area which is on his turn estimated by current traffic flow patterns or by the predicted number of future EVs. Sensitivity analysis is performed to compare results in different conditions. Correlation between the parameters and the costs, and the parameters and the density are described instead of giving the parameters exact values. So are for example the length of a unit area and the density negative and the length of a unit area and the costs positive correlated. The model is applied to Daejeon city (South Korea) where the number of passing vehicles could be easily calculated from the Daejeon taxi data. The ERDEC model is mainly designed to apply on a small urban area like a city.

3.1.1.2. Mixed integer linear programming (MILP)

Mixed integer linear programming (MILP) are problems where some decision variables (DVs) only can take integer values. The exact location of charging stations is defined instead of just the optimal density

for a given unit area, which makes them different from the ERDEC model. In literature there are some studies using MILP to solve the planning problem, some of which are described below.

A first example is a geographic information system (GIS) based MILP approach by Bian et al. (2019). The objective here is to maximize the total profits of all the new stations. Total profits are calculated as the revenues of charging EVs minus the costs of building and maintaining the charging stations. The study area is divided into grids and GIS is used to determine the charging demand based on the land-use classification. The model needs to be solved regarding three decision variables. The location of the charging stations : 1 , ", -ℎ/0/ "& 1 &-1-"2$ "$ 310%"$4 52- 6, ! = ) 6 = 1,2, . . . , ; , ' 0 , 2-ℎ/08"&/

the number of chargers in each station ($') and the charging demands met by each station (>'). The first two DVs need to be integers. The MILP model is derived from first implementing the objective function and secondly by creating the constraints.

A second study using MILP is one on the location of charging stations for an area of Lisbon performed by Frade, Ribeiro, Gonçalves, & Antunes (2011). The purpose is to define the number and locations of stations that need to be installed that optimize the demand covered within an acceptable level of service. This model is therefore referred to as the maximal covering model. The first step of the study includes an estimation of the demand for EV refueling in each census block for the area of Avenidas Novas, an important neighborhood in Lisbon consisting of 387 census blocks. This is done by assessing the number of charge-ups that are necessary each period of the day by regression analysis. The estimation exists of different steps where a lot of assumptions are made, for example on the future share of EVs in the fleet. The next step is to determine the location for the EV stations to be able to cover this estimated demand. A fixed set of possible locations for stations is taken into account. A mixed-integer optimization model can be made to solve the problem, namely decide upon the location of charging stations in order to maximize demand coverage.

Cavadas, Homem de Almeida Correia, & Gouveia (2015) propose a model for the optimal location of charging stations in a city while maximizing the satisfied demand under a fixed budget constraint. Three MILP models are represented by which each new model is an improvement of the previous model. A first model is one in which the demand for charging in each possible charging station location is calculated (local demand estimation). A second model is changed in a way that demand could be transferred between different charging stations (transferable demand estimation). A last model divides the day in

time intervals for calculating the demand at the sites instead of taking an average value for the demand of one day (estimating demand at a time interval). The area of application (Coimbra, Portugal) was divided in a grid with cells of 800 meters and a geocoded mobility survey to extract parking data was used to estimate the demand in each cell.

There could be given a lot more examples of studies using MILP to solve the EV charging station location problem. The works differ in for example the objective, the way data is processed, the used constraints, the assumptions made, etc. MILP problems can be easily solved by various software tools like for example CPLEX. The different possible objectives and the way in which constraints are developed are interesting to examine for this research.

3.1.2. Stochastic approaches 3.1.2.1. Two-stage stochastic programming

A second approach is two-stage stochastic programming, which is a commonly used method for planning problems under uncertainty. Therefore, a lot of research is already done using this approach for solving the EV charging point location problem. In this section, a concise review will be given of some authors with the main aspects of their research. The main differences between the studies are how the uncertainty is covered and the decisions made in the first and second stage. More details about the method of stochastic programming is given in Section 3.3. In the next section there will be mentioned that if necessary multiple stages could be repeated. This results in multi-stage stochastic programming, but is not further mentioned here because for this research two stages are enough. Also, the differences with this research are tackled.

The first research is one performed by Faridimehr, Venkatachalam, & Chinnam (2017) who applied their case study to Detroit midtown area in Michigan, U.S. All the installed public charging stations are of type 2. Based on Environmental Protection Agency (EPA) analysis which states that EVs represent between 3% and 5% of the light-duty vehicle fleet, two cases concerning the market share for BEVs and PHEVs are considered. In this research, 13% of total demand is not considered due to the lack of a parking lot within their walking distance preference.

- Objective: Maximizing coverage of demand (the expected access aims at serving as many people as possible with the public EV infrastructure). - Uncertainties: The demand for public EV charging stations is the stochastic element. A lot of uncertainties are considered affecting this demand. For the dwell time for example, six different

categories are defined (family, meal, school, shopping, social and work). Other uncertainties are state of charge, weekday vs. weekend, preference for charging away from home, EV market penetration and willingness to walk. - First stage: In a first stage need to be determined which parking lots from the potential locations for EV charging stations will be selected and how many charging stations will be installed on the selected parking lots. Just like in most location problems this is the location stage. - Second stage: The second stage in this problem is like in general location problems the allocation stage. Once real demand is revealed, EV drivers will be assigned to one of the selected parking lots based on their willingness to walk. - Solution approach: Sample Average Approximation (SAA) is a widely used method in stochastic programming where by use of case scenarios uncertainties are modeled. The purpose is to reduce the actual size of scenarios by which the optimal solution can be approximated by a sample of scenarios.

A second research is executed by Hosseini & MirHassani (2015). The case study is applied to the intercity network for Arizona. Not only the location problem is covered but also an innovative feature is introduced, namely the use of portable stations. Both the uncapacitated model where the capacity is sufficient to serve all flows passing through a node, regardless their volume, and the more realistic capacitated model are presented.

- Objective: The purpose of this model is also trying to respond as much as possible to the demand, or as described in the study: maximizing the sum of the expected values of the served flows. - Uncertainties: The traffic flow in the transportation network is the stochastic element, and therefore the quantities of traffic flow are modeled as random variables. This traffic flow results in a certain demand for refueling services and there are a lot of uncertainties affecting this demand. The adoption rate for the alternative-fuel vehicles (AFV) and the driving patterns of AFV users are examples of some of these uncertainties. - First stage: In the first stage the location and construction of permanent fueling stations are considered. There are a set of candidate facility nodes from which has to be decided in the first stage whether to place or not a permanent fueling station at each node. - Second stage: Based upon the decisions made in the first stage, and after the traffic flow and the demand are known, the locations of portable stations are determined in order to fulfill as much of the revealed demand.

- Solution approach: A gravity model based on the population in each node was used to determine the flow between origins and destinations. A finite set of scenarios is created that represents the uncertain parameters (12 randomly generated scenarios). Quantities of traffic flow are determined based on events that occur in each scenario. For example, in a first scenario traffic flow rises due to holiday plus good weather, while in the second scenario it decreases because of holidays in combination with bad weather. Furthermore, a heuristic algorithm is developed to simplify the problem. In a first step, a solution of the relaxed capacitated model leads to two core sets of potential location nodes, which reduce the size of the problem. In a second step, the location of stations is obtained by using a greedy iterative method on the restricted problem.

The third research is one in which the aim is to combine the transportation system with the power grid (Pan, Bent, Berscheid, & Izraelevitz, 2010). Instead of planning charging stations, exchange stations are planned. Exchange stations are large battery banks where PHEVs can change their empty battery by a new fully charged battery. On the one hand the exchange station can reduce the demand of vehicle-to- grid (V2G) on the grid by managing when to charge the batteries (e.g. during off peak moments). On the other hand the station may discharge batteries on the grid. Therefore, every battery can be used to satisfy PHEV demand or to supply power to the grid and a constant interaction between the power grid and the V2G system through the exchange stations is obtained.

- Objective: Where to site the exchange stations such that both the V2G system as well as the power grid benefit while minimizing the overall cost. - Uncertainties: The stochastic elements are the future demand for batteries on each traffic route, the load at buses, and production capacities of renewable generators. - First stage: Decide upon the location of exchange stations out of a number of possible locations and number of batteries stored at each station. - Second stage: Batteries are distributed such that PHEV demand is satisfied and power is discharged back to the grid. - Solution approach: For the second stage 100 independent scenarios are created where realizations for the random variables are specified. The PHEVs demand and the load at a bus are both the multiplication of a uniform random variable between two specified values with the average battery demand and the peak load respectively. The generation capacity for a renewable generator can be 0, 0,5 or 1 of its maximum generation capacity. The objective is then to minimize the overall cost over all the scenarios.

More examples could be given. They are all interesting and relevant in their own way, but they all differ in one way or another from this research. This research is applied to the study area of West Flanders which is divided in 64 unit areas (municipalities). The aim is to come up with the optimal number of charging points in a region, rather than provide a solution to the exact location problem.

- Objective: Minimizing total costs where only 3 cost parameters are taken into account: installation costs, waste costs and shortage costs. - Uncertainties: The demand for public charging stations is the stochastic element. The EV-to- vehicle ratio is the main source of uncertainty in the calculation of this demand. - First stage: Deciding upon the optimal number of charging points of each type in each unit area (municipality). - Second stage: The second-stage decision variables are pure resource responses for being able to calculate the expected cost, rather than actually suggesting actions when a certain scenario appears (e.g. assigning drivers to parking lots, locating portable stations, distributing batteries). The second-stage decision variables indicate whether there are built more charging points than required or too few. - Solution approach: A very simple method for calculating the different demand scenarios is provided based on the normal distribution of the stochastic EV-to-vehicle ratio. This makes it a suitable approach when little information is available.

3.2. Modeling under uncertainty

Stochastic programming is a widely used method for modeling under uncertainty. But which other approaches do there exist to cope with uncertainty, and why is stochastic programming preferred for the EV charging location problem? This section gives an overview of different approaches for modeling under uncertainty. The method of stochastic programming is described in detail in the next section.

3.2.1. Robust optimization

Gorissen, Yanıkoğlu, & den Hertog (2015) wrote a paper in which they are convinced that there are two big methods for modeling under uncertainty. The first one is stochastic optimization (SO), which assumes that the probability distribution of the stochastic element is known or can be easily estimated. SO is extensively discussed in the next section. A second method is robust optimization (RO), which instead of relying on the probability distribution for the stochastic element, assumes that the uncertain elements belong to a certain uncertainty set, i.e. a set of values for the uncertain parameter. On top of that, basic RO assumes hard constraints, which means that constraints may not be violated for any realization of the data in the uncertainty set. The general formulation of an uncertain linear optimization problem looks as follows: E min{D B ∶ GB ≤ I}(D,G,I)∈℧ B where D ∈ ℝN, G ∈ ℝO×N and I ∈ ℝOand are element of the specified uncertainty set ℧. Modeling under uncertainty means that a decision regarding the decision variables B ∈ ℝN needs to be taken before the true values of the uncertain elements are revealed. Because of the hard constraint assumption, the constraints must be satisfied for every possible pair of the uncertain elements.

Stochastic programming for planning charging points for electric vehicles is desired above robust optimization because the uncertainty is approached through real data from which the probability distribution is obtained. The EV-to-vehicle ratio displayed in terms of a probability distribution lies much closer to reality than creating a set of possible values. This makes the end results much more reliable.

3.2.2. Fuzzy optimization

Sometimes the value of the stochastic element is more of qualitative nature or the range depends on the person you ask. In other words, the boundary of information is not clear. This makes an unambiguous answer and therefore a single quantitative value for the stochastic element impossible. When for example someone asks whether the temperature T is suitable for swimming, the answer can never be totally yes (true) or no (false). It depends on the individual subjective feeling of the member you ask. This is exactly what fuzzy optimization all is about (Loucks & Beek, 2005). The interested reader is referred to Zadeh (1965), who has a main role in the emergence of fuzzy theory.

Fuzzy programming, as explained by Loucks & Beek (2005), makes use of a fuzzy set instead of a more crisp set of values. In a crisp set the answer really is black or white, an element may or may not belong

to the set. Unlike a crisp set, an element in a fuzzy set can have a partial degree of membership (Knapp, s.d.). In fuzzy optimization, membership functions are created to define the fuzzy set. In the temperature example, a group of members (e.g. potential swimmers) is asked to set up an interval which for them are suitable temperatures for swimming. Then, for each temperature T in the fuzzy set a membership value is determined, calculated as the number of times T is included in the range of all members divided by the total number of participating members. Every membership value lies in the interval [0,1], where one and zero mean that the element is or is not a member of the set respectively. A membership function can be obtained which shows the relationship between a value and its degree of membership. Figure 3 shows the degree of membership of 24°C in a crisp and in a fuzzy set. In Figure 4 the corresponding membership function for the fuzzy set is drawn.

Yes (1) Crisp set No (0) Is 24°C suitable for swimming? Yes (0,75) Fuzzy set No (0,25)

Figure 3: Degree of membership of 24°C in a crisp and in a fuzzy set

Membership function 1

0 0 5 10 15 20 25 30 35 40 45 50 Figure 4: Membership function of temperatures suitable for swimming

Fuzzy optimization is not suitable for this research, because the stochastic element is not a qualitative parameter and not depends on the subjective feelings of some members. Again, a probability distribution for the stochastic element relies much more on reality than creating a fuzzy set.

3.2.3. Probabilistic dynamic programming

Probabilistic or stochastic dynamic programming (SDP) is another widely used method to solve stochastic multistage optimization problems. SDP is all about dividing the main problem into several subproblems by which one or several parameters are modeled as stochastic elements (Haugen, 2016). A problem solved by using dynamic programming requires two characteristics (Gavis-Hughson, 2017):

1. Optimal substructure. It is possible to break the problem down into smaller and smaller subproblems. The optimal solution can be obtained by combining these solved subproblems. When it is possible to solve the problem recursively, it is likely that the problem has an optimal substructure.

2. Overlapping subproblems. Dynamic programming makes use of a memory which saves the solutions from all the subproblems such that every subproblem that appears several times needs to be calculated only once.

The problem will always contain stages, states, stochastic elements and an action space. The states are the possible values for the stochastic elements that could appear, and the action space are the possible decisions that could be made (Haugen, 2016). Once again, an example is the easiest way to explain the method.

The illustrative example is taken from the book ‘Stochastic Dynamic Programming’ from the author Haugen (2016). The problem is whether to sell a house or not, where the price of the house is the stochastic element. The objective is of course to maximize profit. In every stage the price for the house is revealed, after which there has to be decided whether to sell the house or to wait until the next stage. A decision tree can be obtained to visualize the problem and to get a better insight into the several subproblems. Figure 5 shows the upper branch of the decision tree of the problem for 2 stages. SDP has the advantage compared with the decision tree method that no full enumeration of all possible decisions and states is required. For the exact calculations of the numbers in the decision tree the interested reader is referred to Haugen (2016). The different elements in this problem are:

- Stochastic element: price of the house - States: high price, medium price, low price - Action space: sell, wait

- Probabilities, values and costs for the different states:

State Probabilities Prices Cost High price 0,25 200 100 Medium price 0,55 150 100 Low price 0,20 50 100

Table 2: Parameter values of the house selling problem (SDP)

100 sell

sell 100 wait P=0,2 0,2 0 5 wait P= sell 50 P=0,55 5P=0,55 wait 0 P=0,2 P=0,2 00 0 -50 0 sell wait 0 00 Figure 5: Upper branch of the decision tree of the house selling problem

It is possible to use SDP with a nondiscrete state space, which would be desired for this research because it is more reliable that the demand for charging points can be any value instead of predefining a set of possible values. Also a nondiscrete action space is possible, with the same reasoning that choosing a number of charging points out of an infinite possibility set is much more reliable compared to choosing from a limited set of possibilities. Nevertheless, both improvements are possible, this makes the model much more complex and making a decision tree is not possible anymore. Therefore, two-stage stochastic programming is much more convenient to use when having a nondiscrete state and action space. On top of that, the EV charging point planning problem regards making one decision and it is not possible to split up the problem in several overlapping subproblems. Doing this would make the problem unnecessarily complex. This leads to the conclusion that the problem tackled in this research has not the right characteristics to use DSP.

3.2.4. Bayesian methods

Modeling a scenario or a problem as a Bayesian model, can be done by representing it using Bayesian networks. Bayesian networks (BN) are another possibility which can be applied to model under uncertainty. Narayanan (2019) explains in an article the three main principles related with Bayesian thinking, where BN are based on :

1. Use prior knowledge 2. Use your observations wisely 3. Don’t make extra assumptions

Keeping these principles in mind, some daily unclear situations could be easily explained.

A Bayesian network explained by Narayanan (2019) is a graph with nodes which represent random variables (QR) and where arcs between the nodes indicate the direct relationships between the random variables. The network cannot have directed cycles in it which makes the network a Directed-Acyclic Graph (DAG). The joint probability distribution can also be easily derived from the graph using the following formula: N

S(QT, … , QN) = V S(QR|S10X(QR)) 8ℎ/0/ S10X(QR) 10/ -ℎ/ 310/$-& 2, $2Z/ QR. RYT

Figure 6 shows an example of a simple Bayesian network. The example is taken from Narayanan (2019). The uncertain scenario here is whether the grass in the garden will be wet or not. The wetness of the grass in this scenario can be due to 2 events: a sprinkler or the rain. This relationship results in the two arcs ending in the grass being wet. The arc going from rain to sprinkler, means that there is also a dependency between these two events. Indeed, the probability of the sprinkler being on is less when it is raining. In other words, the rain has an effect on the sprinkler. The network has no directed cycles and the joint probability can be given by:

S(X, [, \) = S(X|[, \) ∗ S([|\) ∗ S(\)

Grass wet (G)

Sprinkler Rain (R) (S)

Figure 6: Bayesian network for the garden problem

In this research the random variable is the demand for public charging points. Undoubtedly there are many other random variables that may have a direct impact on this demand, for example the price of an EV. However, the main purpose of this research is to enroll an optimal charging infrastructure instead of explaining why the EV market is evolving in a certain direction. Therefore, other random variables that may influence the demand have not been taken into account. No appropriate Bayesian network could be applied to the research question suggested in this research.

3.3. Stochastic programming 3.3.1. Concept

Unlike deterministic programming where all parameters are known, is stochastic programming a mathematical optimization framework that involves uncertainty. Uncertainty increases complexity because now the best possible solution has to be chosen while the exact values of some crucial information parameters on which the decision is based are missing. This makes it much closer to reality, because in practice decision making is usually based on unknown parameters. In some cases it is desirable and possible to wait until crucial information is revealed, but in most cases this is impossible and decisions need to be made before crucial information is known. The probability distribution of the variables from which the true values are unknown is often available. The stochastic programming approach can be used to address this type of optimization problems.

The examples and theory mentioned in this section are all reproduced from Sen & Higle (1999) who wrote an introductory tutorial to discuss some basics of linear programming-based models for planning under uncertainty. Stochastic Linear Programming (SLP) involves a linear program where one or more of

the parameters should be modeled as random variables because some necessary information is missing, these elements are referred to as the stochastic elements.

3.3.1.1. Infeasibility

One of the basic ideas underlying SLP is that uncertainty implies future infeasibility. In practice two types of infeasibility under uncertainty could appear, which can be shown by two approaches : the SLP with expected values approach and the wait-and-see approach. The following example will be considered throughout the remainder of this section:

^"$"_"`/ − !b

[cd6/e- -2

!T + !b + !g = 2

!T + !b + !h = 2 (1)

−1 ≤ !T ≤ 1

!' ≥ 0, 6 = 2, 3, 4

The stochastic elements that cause uncertainty will be the coefficients of the variables !T 1$Z !b in equation (1). Their value is not known with certainty, but their joint distribution is known:

3 1 n1, o 8"-ℎ 302d1d"5"-p (1l , 1l ) = m 4 2 bT bb 5 1 n−3, o 8"-ℎ 302d1d"5"-p 4 2

where 1lbT is the coefficient of !T and 1lbb of !b.This indicates that the probability that the combinations g t T (1l , 1l ) = r1, s and (1l , 1l ) = r−3, s both appear with probability . bT bb h bT bb h b

SLP with expected values

For the first approach the expected values of the stochastic elements (". /. 1lbT 1$Z 1lbb) are taken into consideration and the SLP problem is solved. This is -1 and 1 for 1lbT and 1lbb respectively (u[1lbT] = T T g t (1 + (−3)) = −1 , u[1l ] = r + s = 1 ). This results in the following model: b bb b h h

^"$"_"`/ − !b

[cd6/e- -2

!T + !b + !g = 2

−!T + !b + !h = 2

−1 ≤ !T ≤ 1

!' ≥ 0, 6 = 2, 3, 4

This can be easily solved with for example the solver function in Microsoft Excel and results in the solution

(!T, !b, !g, !h) = (0, 2, 0, 0). The main question now is if this solution is feasible under uncertainty. The constraint corresponding to (1) will under uncertainty not take the form with the expected values for the coefficients, but will take one of the following forms: 3 ! + ! + ! = 2 T 4 b h 20 5 −3! + ! + ! = 2 T 4 b h

When the obtained solution vector is taken into consideration, neither of these equations are satisfied

g g t t nr0 + r s ∙ 2 + 0 = ≠ 2 s 1$Z r(−3) ∙ 0 + r s ∙ 2 + 0 = ≠ 2 so and thus the solution is infeasible h b h b under uncertainty. In other words, taking the expected values for the random variables does not result in a feasible solution.

Wait and see The second wait and see approach implies that one has to wait to obtain additional information until all uncertainties have been resolved. This yields that for every possible combination of the stochastic elements a solution is obtained. In the example there are two possible realizations and the solution g t associated with (1l , 1l ) = r1, s is (−1, 3, 0, 0.75), while the solution for (1l , 1l ) = r−3, s is bT bb h bT bb h

b gb (− , , 0, 0.75). If one solution is implemented the chance of failing to satisfy a constraint is 50%, T{ T{ namely in the case the alternate outcome arises. Not satisfying a constraint indicates infeasibility.

3.3.1.2. Stochastic Linear Programming

Both types of infeasibility indicate the need for a framework to consider the future consequences of infeasibility. This is exactly where stochastic programming sets apart from deterministic programming. Stochastic programming literature refers to two approaches that are widely studied : probabilistic constraints and resource problems.

Probabilistic constraints In the first approach, indicated as probabilistic or chance constraints, is the probability that a constraint is violated, and thus makes the model infeasible, restricted to be not greater than a prespecified threshold. This method is less relevant for this research and is therefore not further explained in detail. The interested reader is referred to “An introductory Tutorial on Stochastic Linear Programming Models” from Sen & Higle (1999).

Resource problems The second approach are the resource problems, which are based on modeling future resources. Here two-stage resource models are discussed more in detail, where decision variables are classified in stages according to the timing when a decision is implemented. A decision that is implemented before the unknown parameters are known is called a first-stage decision. These decisions are seen more as proactive because they are taken before any uncertain element is revealed. Logically, second-stage decisions are decisions implemented after an outcome is observed. Second-stage decisions are regarded as being reactive because they allow you to act against the observed outcome coming from the stochastic element. In other words, a decision variable gets a value before the unknown parameter is known. In the second stage the outcome is observed after the stochastic elements got a value and second-stage decisions are further implemented to adapt to the revealed outcome and to avoid that constraints are becoming infeasible. Whenever the outcomes of the random elements are revealed sequentially, multistage planning is involved.

An example regarding inventory and production would provide more clarity. In the first stage the decision need to be made on how much to produce, without knowing the exact demand. The demand is in other words the unknown parameter or the stochastic element and is modeled using random variables. When later the exact demand is acknowledged, the demand could exceed the production quantity. Then in the

second stage, the policy is set up that the excess demand is backlogged, which occurs of course at a certain cost. The exact level that needs to be backlogged (this is a resource response) is the second-stage decision which depends on the decision made in the first stage (amount produced) and on the exact value of the stochastic element (the demand). The uncertainty regarding the different possible outcomes for the demand, makes it essential that under uncertainty a policy is adopted that accommodates alternative outcomes or to model a response for each possible outcome.

In short, two-stage stochastic programming implies : make decision in first stage à observe realization of stochastic element à react and make further decisions in second stage. Applied to the example: decide on how much to produce à observe demand à decide on how much need to be backlogged.

Now this is translated into a mathematical model, applying it to the same example as illustrated earlier.

The four variables (!T, !b, !g, !h) are all first-stage decision variables (e.g. the production quantities). The coefficients of constraint (1) are still the stochastic elements and can be represented as follows:

1lbT!T + 1lbb!b + !h = 2

As stated earlier, it is difficult to satisfy this constraint due to the stochastic elements. Suppose that a simple resource policy allows that per unit deviated from the right-hand-side value of 2 a penalty cost of 5 is incurred. The total penalty cost will thus comprise:

5|2 − (1lbT!T + 1lbb!b + !h)|

The objective is still a minimization function, and because this penalty cost is desired to be as low as possible, the problem can be rewritten:

^"$"_"`/

−!b + 5u[|2 − (1lbT!T + 1lbb!b + !h)|]

[cd6/e- -2

!T + !b + !g = 2

−1 ≤ !T ≤ 1

!' ≥ 0, 6 = 2, 3, 4

Due to the resource policy, first-stage decisions giving values to (!T, !b, !g, !h) which not satisfy constraint (1) are now acceptable, but higher deviations are leading to higher costs. Linear problems require linear relationships, thus u[|2 − (1lbT!T + 1lbb!b + !h)|] needs to be transformed in this way:

1 1 (p| + p}) + (p| + p}) 2 T T 2 b b

| | where the nonnegative variables pR , pR , " = 1,2 satisfy

3 ! + ! + ! + p| − p} = 2 T 4 b h T T

5 −3! + ! + ! + p| − p} = 2 T 4 b h b b

The first-stage variables (!T, !b, !g, !h) are applied to all possible outcomes of (1lbT, 1lbb). Now is in the second stage an additional set of resource variables created for each outcome (p|, p}). Depending on the first-stage variables values and the values for the stochastic elements, the appropriate levels of these variables are determined. So every resource variable will get a value, but only one will be implemented after the true values of the stochastic elements are known. The SLP problem can therefore be written as:

^"$"_"`/ 5 5 5 5 −! + p| + p} + p| + p} b 2 T 2 T 2 b 2 b [cd6/e- -2

!T + !b + !g = 2 3 ! + ! + ! + p| − p} = 2 T 4 b h T T 5 −3! + ! + ! + p| − p} = 2 T 4 b h b b

−1 ≤ !T ≤ 1 ~55 2-ℎ/0 10"1d5/& 10/ $2$$/41-"/

Let’s generalize this model. The constraints of this LP problem are forming the rows and can be written as ~! = d, where A and b are vectors containing the values for every row (i.e. every equation). Under uncertainty ~T and dT are a submatrix of A and a subvector of b containing only deterministic parameters and \ is the set of remaining rows containing at least one random element. The "th value in the vector A

is indicated as 1R and a ~ is used to present a random variable. A penalty cost of 4R > 0 is incurred per unit deviation from the target dÇR. Now a generalized stochastic programming problem with simple recourse can be obtained, where ÉR and ÑR are respectively a lower and an upper bound:

^"$"_"`/ e! + Ö 4RuÜádÇR − 1lR!áà R∈â &cd6/e- -2

~T! = dT

ÉT ≤ ! ≤ ÑT

Linearity is desired, so due to the absolute value this needs again to be transformed. This can be done äã1l , dÇ åç whenever the random vectors R R R∈â are discrete random numbers. All possible outcomes of the vector äã1lR, dÇRåç are represented by the set [R and 3Ré = Säã1lR, dÇRå = (1Ré, dRé)ç.

| } ^"$"_"`/ e! + Ö 4R èÖ 3Ré(pRé + pRé)í R∈â é∈êë &cd6/e- -2

~T! = dT | } 1Réx + pRé − pRé = dRé ∀ & ∈ [R, ∀i ∈ R

ÉT ≤ ! ≤ ÑT

Two remarks need to be made. First, a constant penalty cost is assumed disregarding dÇR − 1lR! is positive or negative. In some applications this may be not the case, and the model needs to be somewhat adapted. Secondly, here is assumed that the upper and lower bound are not subject to uncertainty which may also be the case in some applications. Again the model need to be somewhat extended if this is the case.

When the second stage is reached in a two-stage resource model, all uncertainties have disappeared, which may in reality of course not always be the case. Multistage resource models as been mentioned earlier are used when outcomes are revealed sequentially and decisions are made over multiple periods. As the planning problem in this research concerns a two-stage problem, multistage problems are not further discussed, but the general way of thinking is the same: First-stage decisions are made à observe in second stage the realization of some stochastic elements à decide on the values of the resource variables à second-stage decision are made à observe in third stage the realization of some stochastic elements à decide on the values of the resource variables, and so on and so on.

3.3.2. Applications for location problems

Due to the significance of uncertainty, stochastic programming is applied successfully on a lot of problems in various areas. As this research is all about two-stage stochastic programming concerning a location problem, some studies using two-stage stochastic programming for solving location problems are discussed here.

The first application concerns the location of air freight hubs and the planning of the flight routes introduced by Yang (2009). Hubs are special facilities to switch, transship and sort flows in transportation networks with the aim of minimizing the transportation costs. The purpose of this problem is to decide on the optimal hub locations and design a service network which makes it possible to transport the demand at the lowest possible cost under uncertainty. Uncertainty in this problem appears due to seasonal variations in the demand, therefore demand is the stochastic element. The discrete distribution of the demand is known, and only a finite number of scenarios are possible. Also, two stages can be recognized. In the first stage a decision need to be made on the number and location of the hubs. As this decision will not be influenced by the randomness of the stochastic element (the demand), this belongs to the first stage. The second stage involves the decisions of the flight routes to transport flows from origins to destinations. The flight routes and the corresponding flow allocation are second-stage decisions because they vary in response to the change of demand, thus they are based upon the first stage decision and the outcome of the stochastic element. The deterministic model would fix the hub location and the service network for every demand level, whereas the stochastic model adjusts the service network according to the observed demand level.

A second application of two-stage stochastic programming is also a facility location problem, namely a study conducted by Oksuz & Satoglu (2020) for modeling the location planning of temporary medical centers (TMCs) for disaster response. Some recent tragic events have increased the awareness for the importance of efficient location of medical centers for the purpose of being able to respond timely to casualties in case of disasters. TMCs are emergency medical centers which can be called on in time of disasters because the capacities of the existing hospitals are not sufficient. The study takes some considerations into account such as the capacity of the centers, the possibilities that roads and hospitals are damaged due to the disaster, the setup and transportation costs, etc . They conducted two studies, one in which the casualties are categorized according to the NATO triage system, and another one by considering only a single type of casualty. As only the relevance of the use of stochastic programming is mentioned here, the differences between these two studies are not further explained. The uncertainty is of course the unknown occurrence of disasters. And if a disaster appears, how tragic is it? So in other

words, how many casualties need help and which acuity class do the victims belong to? In this case study, where the model is applied for the district of Kartal in Istanbul which is prone to earthquakes, twenty different scenarios where taken into account. Each scenario contains some specific data like the magnitude of the earthquake, distribution of casualties, distance increase ratio of roads and capacity decrease ratio of hospitals. In the first stage a decision need to be made on the number of TMCs that need to be opened and where these are located. This is not affected by the unknown degree of severity of an earthquake. The second-stage decisions on their turn, do rely on the scenario that occurs and depends on the decision made on which TMCs to open. These decisions include which emergency medical center (EMC) serves casualties from which demand point and the number and type of casualties in each demand point that are assigned to each EMC. This all must be done while minimizing the total setup cost of the TMCs and the total expected transportation cost of the casualties.

A third and last application is somewhat in the same atmosphere as the topic of this research. Li, Wang, & Huang (2019) are using two-stage stochastic programming for the car-sharing problem. Car-sharing is gaining more popularity and involves reserving a vehicle by phone or Internet, pick the vehicle up at the appointed time and leave the car again at a car-sharing location. This problem contains different uncertainty parameters, like for example traveling time or supply, but for convenience in this application only the demand is considered as the stochastic element. For all stochastic programming models the probability distribution of the uncertain parameters are known. In this research the probability distribution information is obtained from the kernel density estimation, which is not relevant for this research and thus is not further explained. In the first stage the number of cars at each pick-up location needs to be determined, so without knowing the exact demand of the day. In a second stage, when the demand is known (which means that no new orders for the day will be accepted), a decision need to be made on how many vehicles that must be relocated between locations. This all must be done while maximizing the overall profit which equals the difference of total revenue and total holding cost.

Two-stage stochastic programming is widely adopted in literature to solve a lot of different practical problems and thus many more applications could be mentioned here. In general, as already mentioned, the overall structure is always the same. In a first stage the location must be determined under uncertainty. The stochastic element is often the demand, but it can also be something totally different like the occurrence of a disaster or traveling times. Anyway, when the stochastic element is revealed, decisions need to be made to avoid infeasibility of some equations and to optimize the objective function. Whether this relates to flow allocation decisions or reallocation of vehicles, the purpose is always the same. Some examples of two-stage stochastic programming used to solve the EV charging stations location problem were already provided in Section 3.1.2.1.

4. Methodology 4.1. Two-stage stochastic programming formulation

The study area of West Flanders can be divided into several regions, namely municipalities. The two- stage stochastic programming model will decide upon the optimal number of charging points of each type that need to be installed in every municipality based on the future demand of EVs in every municipality. This decision need to be made before the actual demand for public charging points is revealed, and therefore this relates a first-stage decision variable. Because the future is uncertain, different scenarios are created for each municipality. In every scenario there is a certain demand for charging points where each scenario occurs with a given probability. In the second stage, the decision variables will indicate for every possible scenario in each municipality if there is waste or shortage, which depend on the decisions made in the first stage. The resource actions that a municipality will have to take, will depend on the scenario that appears. Both possibilities involve consequences and therefore incur a certain cost. Building too many charging points entails unnecessary building costs and can be considered as waste. Building fewer charging points than demand also leads to a price for not covering the demand. The aim of the stochastic programming model will be to minimize the total cost over all the different demand scenarios.

First, the model sets and parameters which are used in the model are shown. Secondly, the first-stage and second-stage decision variables are introduced. Finally, the two-stage stochastic programming model formulation is presented followed by the meaning of the objective function and the different constraints.

Model sets and parameters: - N : Set of charging point types - I : Set of municipalities - S : Set of scenarios

- Sé : Probability of occurrence of scenario & ∈ [

- eN : Cost of installing a charging point of type $ ∈ ñ - 8 : Waste cost - & : Shortage cost

- ZR,é : Demand in municipality " ∈ ó in scenario & ∈ [

- ,N : Number of EVs a charging point of type $ ∈ ñ can serve in one day - ^: A very large positive number

Decision variables: 1st stage : Number and type of charging points in each unit area

!R,N = number of charging points of type $ ∈ ñ at municipality " ∈ ó

2nd stage : Waste or shortage for each scenario in each unit area

%R,é = 1, if total charging point capacity exceeds the demand at municipality " ∈ ó in scenario & ∈ [ 0, if demand exceeds total charging point capacity at municipality " ∈ ó in scenario & ∈ [

Model :

Minimize

ú õ ê ú õ õ

Ö Ö !R,NeN + Ö Ö Sé ù8 %R,é ûÖ !R,N,N − ZR,éü + & ã1 − %R,éå ûZR,é − Ö !R,N,Nü† (2) RYT NYT éYT RYT NYT NYT

Subject to

Ö !R,N ≥ 1 , ∀" ∈ ó (3) NYT

Ö !R,N,N − ZR,é ≤ ^%R,é , ∀i ∈ I, s ∈ S (4) NYT

ZR,é − Ö !R,N,N ≤ ^ã1 − %R,éå, ∀i ∈ I, s ∈ S (5) NYT

!R,N ∈ ℕ , ∀i ∈ I, n ∈ N (6)

%R,é ∈ {0,1} , ∀i ∈ I, s ∈ S (7)

Objective function : - (2) The objective is to minimize the total overall costs. The first-stage costs, the first part of the objective function, contain the number of each type of charging point installed multiplied by the cost of installing such a charging point over all the municipalities. These costs are fixed and will be the same in every scenario. The second part of the objective function are the second-stage costs and contain the expected cost of waste or shortage over all the scenarios. In every scenario a certain demand occurs and then there are two possible options, or there were built more charging points than required or there were built too few. Both options incur a specific cost, a waste and a shortage cost respectively. For every municipality and for every scenario only one of

both options will appear. When there are built too many, %R,é will get the value of one and the õ total capacity of all the installed charging points in that municipality (∑NYT !R,N,N) minus the demand will be positive. In that case a waste cost will be charged per EV that could be served more and the part calculating the shortage cost will be zero. When there are built too few, the

opposite will happen. The variable %R,é will be equal to 0, there will be no waste cost but instead a shortage cost will be charged per unserved EV. The probability by which every scenario appears

is known (Sé) and thus the objective function tries to minimize the total expected costs over all the scenarios.

Constraints : NOTE : Every constraint must always be satisfied for every municipality and if it belongs second-stage decision variables, also for every scenario.

- (3) There must be installed at least 1 charging point in every municipality. That is a requirement from the ‘Clean power for transport’ action plan from the Flemish government (Vlaams Departement Omgeving, 2015) to stimulate the further deployment of EVs (see Section 2.5.1). The type of the charging point does not matter, therefore the sum of the number of charging points installed of each type must be at least one.

- (4) This constraint, together with constraint (5), is for setting the right value for %R,é. When there

are built too many charging points (%R,é = 1), the total capacity exceeds the demand. In other words, the total number of EVs the charging points can serve minus the demand is bigger than zero. M is just a very big number, making sure that the difference is smaller than this very large number. The lower M, the stronger the model, but M has still to be large enough to give suitable solutions. Waste and shortage cost are chosen such that the model will always try to fit the demand as good as possible (see Section 5). When there is waste, it is highly unlikely that the number of EVs that could be served more would be double the demand. However, this could be

the case for municipalities with a very low demand (e.g. the demand is only 1 EV). A good value for M is therefore the maximum possible demand across all municipalities and across all scenarios, which is more than 200 EVs (see Attachment 2). In the opposite case when there are

built too few charging points (%R,é = 0), the demand is bigger than the total capacity which makes the difference negative and therefore smaller than or equal to zero. - (5) The same reasoning as in (4) can be made for this constraint. Building too many charging

points (%R,é = 1) results in the total capacity being bigger than the demand and makes the difference therefore negative. This is indeed smaller than or equal to 0. A shortage of charging

points (%R,é = 0) makes the difference positive and thus smaller than or equal to a very large number. Same reasoning as for constraint (4) can be made regarding the value for M. Also here M equals the maximum possible demand across all municipalities and scenarios. An important note is that when there are built just enough charging points to serve the demand, it does not

matter which value %R,é takes. The difference between the demand and the total capacity will always be zero and therefore also be smaller than or equal to either a very large number or zero. In the objective function this also results in nor a waste nor a shortage cost. - (6) The first-stage decision variables need to be non-negative integers. - (7) The second-stage decision variables are binary variables, meaning that they can only take a value of 1 or 0.

In what follows the different parameters needed as input for the model are explained. First, the calculation of the different demand scenarios with their corresponding probability will be explained

(ZR,é 1$Z Sé). The model will be applied to West Flanders, and the optimal charging infrastructure for 2020 will be determined. Therefore, possible demand scenarios for each municipality (I=64) in West Flanders for 2020 will be calculated, but the method could be easily applied to other regions. When the real demand for 2020 is revealed, the same exercise could be done for 2021 and so on. Next, the capacity of the different types of charging points considered in this research will be defined (,N). When in other case studies the same charging point types are examined, the same values for this parameter could be taken. Lastly, the cost parameters are defined (eN, 8 1$Z &). As will be explained later (see Section 4.4), do these cost parameters not reflect real costs. The aim of the research is to minimize the consequences of choosing a certain charging point infrastructure plan above another. This means that a higher shortage cost compared to the waste cost, indicates that the consequences of a shortage are worse than when there is observed waste, without indicating the real costs. When this model is applied to other regions, and the impact of the consequences are equal, the same values for the cost parameters could be easily adopted.

4.2. Demand

Demand for charging points can be seen as the number of EV drivers that need a public charging point per day. Because the future is uncertain, the demand is the stochastic element in this research, therefore a point estimation would not be appropriate and different scenarios must be created. In each scenario a certain demand appears in every municipality, and every scenario has its own probability of occurrence.

To calculate this demand two important things need to be known. First, the total number of EVs present in a municipality on a daily basis has to be determined. The global ratio between EVs and the total personal vehicle fleet will be referred to as the EV-to-vehicle ratio, or in what follows sometimes shortly referred to as ratio. When the total personal vehicle fleet registered in a municipality is multiplied by this ratio, the total number of EVs originating from inhabitants is known. In this study, it is assumed that EVs present in a municipality do not only originate from inhabitants but also from workers and tourists, whose vehicles are registered elsewhere. Therefore, personal vehicles coming from these two groups must also be multiplied by the ratio in order to obtain the total share of EVs daily present in a municipality. Secondly, this number has to be multiplied by the percentage of EVs that need a recharge at a public charging point. This leads to the total demand for charging points in each municipality and can be summarized in following formula :

(8) ≠2-15 Z/_1$Z ,20 eℎ104"$4 32"$-& "$ _c$"e"315"-p " = [(3/0&2$15 /ℎ"e5/& "$ℎ1d"-1$-& _c$"e"315"-p " + 3/0&2$15 /ℎ"e5/& 820%/0& _c$"e"315"-p " + 3/0&2$15 /ℎ"e5/& -2c0"&-& _c$"e"315"-p ") × uV to vehicle ratio] × 3/0e/$-14/ -ℎ1- $//Z& 1 0/eℎ104/ 1- 1 3cd5"e eℎ104"$4 32"$-

But how are different demand scenarios created? The scenarios depend on the uncertainty of the EV-to- vehicle ratio. The assumption is made that this ratio follows a normal distribution. Once the normal distribution is obtained, a simulation procedure can be set up to create possible outcomes for the ratio with a corresponding probability for each outcome. Depending on the number of different outcomes for the ratio, formula (8) will be applied several times to create different scenarios for the total demand in each municipality. In what follows the different parameters of formula (8) are explained.

4.2.1. EV-to-vehicle ratio 4.2.1.1. Normal distribution

Assigning a probability distribution to the EV-to-vehicle ratio tells something more about plausible outcomes and their corresponding probabilities. Afterwards the distribution can be used as input for the simulation procedure. Here the assumption is made that the ratio (Y) follows a normal distribution. This assumption is made because the point estimation for the ratio (which will serve as mean) has the highest probability of occurrence. The normal distribution is a symmetric distribution, resulting in equal probabilities of deviating values that are bigger or smaller, with most values around the mean. This a good assumption, because it is impossible to know what the future of the EV market will look like which makes it difficult to make statements about the direction of the deviation. A normal distribution is characterized by its parameters, namely its mean (¥) and variance (µb) and could be referred to as:

∂~(¥, µb)

The first step is to forecast the EV-to-vehicle ratio for 2020, which will be the mean of the normal distribution. On the website of Statbel data can be found about the vehicle fleet in Belgium over different years (Voertuigenpark Statbel, 2019). The past data is assumed to be reliable and it is also plausible to assume that the future EV-to-vehicle ratio can be predicted on the basis of the ratio in the past.

An Excel file with motor vehicle statistics for Belgium since 1980 has been available, from which the data can be obtained. One tab shows the number of motor vehicles classified according to fuel and type of vehicle registered in each year on the first of August since 2007. Description of the fuel could be petrol, diesel, gas, electricity or hybrid and type of vehicle could for example be passenger vehicles, buses, motorcycles, trucks, … . For the type of vehicle is chosen to focus on the passenger vehicles because this are the type of vehicles which are most dependent on public charging points. To calculate the EV-to- vehicle ratio in a year the number of EVs (fuel type electricity) in that year needs to be divided by the total number of personal vehicles in that year. Important to note is that this belongs pure EVs (BEVs) as hybrid vehicles (PHEV) are shown as a separate category in the overview. Table 3 gives an overview of the EV-to-vehicle ratio shown as a percentage for the years 2007 until 2019 rounded to four digits.

YEAR RATIO YEAR RATIO 2007 0,0002% 2014 0,0323% 2008 0,0002% 2015 0,0511% 2009 0,0002% 2016 0,0765% 2010 0,0007% 2017 0,1132% 2011 0,00030% 2018 0,1579% 2012 0,0119% 2019 0,2604% 2013 0,0167% Table 3: EV-to-vehicle ratio for the years 2007-2019 in Belgium (Voertuigenpark Statbel, 2019)

The data available clearly shows a times series. A time series is a sequence of observations at regular intervals over time, i.e. there is an equal unit of time between the observations (Hyndman & Athanasopoulus, 2018). In this case, every year on the first of August the ratio can be observed, thus between every observation there is exactly one year. The annual data is available for the last 13 years, from 2007 until 2019, and no year is skipped. Forecasting time series is about predicting which numbers might be expected in the future, or in other words which observations will continue the sequence.

One of the first things to do when analyzing data, is creating a time plot. Figure 7 shows the time plot with on the x-axis the units of time (years) and on the y-axis the variable which is being measured, namely the EV-to-vehicle ratio. A time plot provides a lot of information. Mostly it is immediately clear if there are any patterns, trends, outliers or seasonality present in the data (Hyndman & Athanasopoulus, 2018).

Time plot EV-to-vehicle ratio Belgium 0,3000%

0,2500%

0,2000%

0,1500%

0,1000%

0,0500%

0,0000% 2006 2008 2010 2012 2014 2016 2018 2020

Figure 7: Time plot EV-to-vehicle ratio Belgium 2007 – 2019

The forecast or dependent variable p is the variable of interest, and is assumed to have a relationship with the predictor or independent variable !. As no other variables than the past data are used to predict the future, it is common to set the predictor variable equal to -:

!∑ = - where - = 1, … , ≠ (Hyndman & Athanasopoulus, 2018). This would mean replacing the years on the time plot by t, so 2007 = 1 , 2008 = 2 and so on.

The observed trend on the time plot is clearly nonlinear. On the first sight, the relationship looks exponential. However, it is not ideal to approach the data by an exponential curve because an exponential curve is J-shaped, meaning that it never stops growing (Korstanje, 2020). It would be better to approach the data with a logistic growth curve, which is always S-shaped (Flom, 2017). A logistic growth curve has in the beginning an increasing growth, but a decreasing growth at a later stage (Korstanje, 2020). In the end the ratio may even reach an asymptotically stable value (which may however never actually be reached), represented by a theoretical maximum which is called the carrying capacity (Fischer, 2009). Imagine that in a bright future the EV-to-vehicle ratio reaches 100%, which is a maximum because any further increase is not possible anymore.

The three phases which could be recognized in a logistic growth model according to Flom (2017) can be easily applied to the EV-to-vehicle ratio : - Initial phase where growth is relatively stable or flat. This was the case in the very beginning, when the development of EVs was still in its infancy. - Intermediate phase where the rate of growth is increasing rapidly. EVs are now well developed and ready to conquer the world. It is still the beginning of the rising popularity of using EVs, which makes that the growth is at a rapid ascent stage. - Final phase where the ratio might stabilize. It is very plausible to assume that when the EV-to- vehicle ratio reaches a certain level, it will probably not grow a lot anymore.

According to Fischer (2009), the first step when you want to model logistic growth by regression, is to convert the y values to proportions by dividing them with the carrying capacity. As it is very difficult to predict the future stable share of EVs in the total personal vehicle fleet, the theoretical maximum value of 100% is taken. When the ratio is therefore divided by 1 and in the end multiplied by 1 again, same results will be obtained compared with if this would not be done. This makes it possible to move immediately to the second step, which is transforming the EV-to-vehicle ratio (y) to the peculiar-looking π “link function” 524 r s . Fischer (2009) indicates that when the EV-to-vehicle ratios could be T∏ T}π

approached by a logistic growth curve, the transformed variables would indicate linear behavior. The transformed y variables are therefore plotted and approached by a linear trendline using Microsoft Excel. The following functional form will be obtained :

pªºΩ 524 ∫ æ = ø∏ + øT!∑ 1 − pªºΩ Once this functional form is obtained, it would be easy to estimate EV-to-vehicle ratio for 2020 by setting

!∑ equal to 14 and transforming the peculiar-looking “link function” back to pªTh .

The second step in obtaining the normal distribution is calculating the variance. The standard deviation of the ratio is estimated and afterwards the square root is taken to obtain the variance. Hyndman & Athanasopoulus (2018) state that when a value is only forecasted one step ahead, the standard deviation of the forecast can be approximated by the standard deviation of the residuals. The residuals are calculated as follows :

pªºΩ − pºΩ = /∑

where pªºΩ is the fitted value and pºΩ the actual observation. A fitted value is the estimated value by the model, or the value that fits the equation (Hyndman & Athanasopoulus, 2018).

4.2.1.2. Simulation procedure

The obtained normal distribution serves as input for the simulation procedure. Simulation is performed in order to create different outcomes for the EV-to-vehicle ratio. In the end these different outcomes can be used in formula (8) and different scenarios are created. The simulation is executed in Microsoft Excel where the following steps are taken:

- A possible outcome for the future EV-to-vehicle ratio is calculated. As this ratio follows a normal distribution, there is made use of the NormInv function, which calculates the inverse of the cumulative normal distribution function. The three arguments the function needs include the probability, the mean and the standard deviation of the distribution. The mean and standard deviation are obtained from the corresponding normal distribution. The probability is realized by generating a random number in Excel. This calculation is the result of one simulation run, and each simulation run represents an outcome for the future EV-to-vehicle ratio. - The next step is to perform R simulation runs. Each calculation explained in the previous step represents one simulation run, and each simulation run on his turns represents an outcome for the ratio.

- The normal distribution is a continuous distribution, thus an infinite number of different outcomes for the ratio could be achieved. This also results in the existence of infinite different scenarios for the demand. This is not a desired outcome because the input for the stochastic programming model requires only a few discrete scenarios. This leads to the application of discretization, which involves the process of transferring the infinite number of scenarios (continuous probability function) to a finite set of scenarios (frequency distribution). Discretization explained by Gupta (2019) involves creating a set of contiguous intervals, also called bins, that represent the whole range of continuous variables. The procedure of equal width discretization is applied in this research (Gupta, 2019). This approach suggests creating N number of bins each with an equal width according to the following formula : width = (maximum value – minimum value) / N. Thus the first bin equals minimum value + width, the second bin equals minimum value + 2* width, and so on. - Now a frequency table can be created based on the formed bins. The frequency table tells how many simulations return a value for the ratio that lies between the minimum value and the first bin, how many between the first and the second bin, and so on. When dividing the number of occurrences in each interval with the total number of simulation runs in Microsoft Excel, the probability of obtaining a value in this interval is gained. - The final step is to create scenarios, which was the ultimate purpose of this simulation. The assumption is made that the boundaries of the intervals form the discrete values which are possible outcomes for the EV-to-vehicle ratio. When N bins are created, formula (8) has to be applied N times each time with a different value for the EV-to-vehicle ratio. N scenarios are created each with a probability equal to the probability of obtaining the corresponding EV-to- vehicle ratio. In other words, the scenarios are proportional to the acquired probabilities for the EV-to-vehicle ratio.

4.2.2. Inhabitants

A second parameter in formula (8) are the personal vehicles registered in each municipality for 2020. EVs are perfect city vehicles, therefore it is likely that most of the demand for public charging points will come from the inhabitants. Vehicles of inhabitants fall under the category of registered personal vehicles and Statbel released this data for the years 2017, 2018 and 2019 for all of the 64 municipalities in West Flanders (Voertuigenpark Statbel, 2019). Because it is not favorable to make estimations based on only 3 observations, there is assumed that the personal vehicle fleet in each municipality grows proportionally to the personal vehicle fleet on national level. The time plot of the personal vehicle fleet for Belgium is shown on Figure 8 where observations are available from the year 2007 until 2019. A linear trend can be

observed and therefore a linear regression is performed to forecast the personal vehicles in Belgium for 2020. The equation corresponding to the linear trendline in Excel equals p = 70.784! + 5.000.000. In 2020 the total personal vehicle fleet for Belgium is therefore estimated to be equal to 70.784 ⋅ 14 + 5.000.000 = 5.990.976. This entails a growth percentage of 1,1956% compared with 2019. The registered personal vehicles in 2019 for each municipality are therefore multiplied with 1,011956 to obtain the estimated number of registered personal vehicles in 2020. The exact numbers can be found in Attachment 2 under the column ‘Personal vehicles inhabitants’.

Time plot personal vehicles Belgium 6000000,00 5900000,00 5800000,00 5700000,00 5600000,00 5500000,00 5400000,00 5300000,00 5200000,00 5100000,00 5000000,00 2006 2008 2010 2012 2014 2016 2018 2020

Figure 8: Time plot personal vehicle fleet Belgium 2007 - 2019

4.2.3. Workers

People stay at their work for a while, therefore working hours seem like the ideal time to charge your EV. Statbel states that company cars which are in the name of a leasing company are registered at the address of the (main) seat of the company (Voertuigenpark Statbel, 2019). In other words, company cars are included in the category personal vehicles by the municipality of the company. Workers driving with a company car are therefore already indirectly incorporated by the registered personal vehicles in each municipality (Section 4.2.2). Because it is very difficult to obtain data about the workers in each municipality and about their way of commuting, workers at companies who do not have company cars in the name of a leasing company are not incorporated in this research. The assumption is made that whenever necessary charging points could always be installed at the company site by the companies itself. This results in no extra parameter regarding working people for estimating the future demand for charging points.

4.2.4. Tourists

A fourth parameter is the demand of tourists for charging points. This section tries to estimate the number of personal vehicles coming from daily tourists in each municipality. To obtain the number of EVs, this numbers has to be multiplied with the EV-to-vehicle percentage in formula (8). Numbers are gathered from ‘Toerisme Vlaanderen’ and ‘Westtoer’. They state that in terms of tourism in West Flanders three categories can be observed : tourism at the seaside, tourism in Bruges and tourism in Flemish regions.

West Flanders benefits from its nine seaside municipalities at the North Sea attracting every year a lot of tourists from both home and abroad. ‘Toerisme Vlaanderen’ divides the seaside in three big parts including following municipalities (Toerisme Vlaanderen, 2012):

- East Coast : De Haan, Blankenberge and Knokke-Heist - Middle Coast : Middelkerke, Oostende and Bredene - West Coast : De Panne, Koksijde and Nieuwpoort

Westtoer published in a coastal trend report for 2017-2018 that 36% of the 17,9 million day tourists came in July and August (Westtoer, 2018). Making extra expenses to place enough charging points for being able to respond to the EVs from tourists during peak months would maybe not be beneficial. This leads to the decision to spread the total day tourists at municipalities equally over the year (365 days). Westtoer published the amount of day tourists in every seaside municipality for the year 2018 (Westtoer, s.d.). Due to a lack of data of 2019, these 2018 numbers are taken as a starting point. A global report on tourism on Flanders coast released numbers on the average party size and percentage of people coming by car to the coast (Toerisme Vlaanderen, 2012) :

- East Coast : 3 (party size) and 82,8% (comes by car to the coast) - Middle Coast : 3 (party size) and 79,1% (comes by car to the coast) - West Coast : 3,6 (party size) and 87,1% (comes by car to the coast)

These numbers are not much changed since the previous report in 2005 and are therefore assumed to be still reliable for today. When the yearly day tourists are divided by 365, the average number of tourists per day are obtained. Multiplying this with the percentage of people coming by car, results in the daily number of personal vehicles coming from tourists assuming, however, that every tourist comes alone. There is assumed that people from the same party travel by one car, therefore this number need to be

divided by the average party size. This leads to the following formula to calculate the average number of personal vehicles coming from daily tourists in each seaside municipality :

Yearly day tourists / 365 / average party size x percentage coming by car

Secondly, beautiful Bruges lies in West Flanders, also attracting a lot of tourists. ‘Toerisme Vlaanderen’ set up the same kind of report as for the seaside municipalities in 2018 for Bruges where they reveal numbers about the average party size (2,29) and the percentage of visitors using a vehicle as means of transport to come to Bruges (46%) (Toerisme Vlaanderen, s.d.). Same formula as for the seaside municipalities is applied to calculate the extra personal vehicles in Bruges on one day coming from tourists.

Lastly, the same calculation are made for the Flemish regions. With a mean of 0,14 EV drivers extra at each municipality, these tourists are said not to play an important role and are not incorporated. Personal vehicles coming from tourists for each municipality can be found in Attachment 2 under the column ‘Personal vehicles tourists’.

4.2.5. Percentage that needs a recharge at a public charging point

A fifth and last parameter to calculate the different scenarios is the percentage of EV drivers that needs a recharge at a public charging point. It is not because there are 100 EVs in a municipality, that each one of these EVs requires a recharge during their daily trips. According to an article in de Tijd (Vanacker & Steel, 2020) said Langenberg that charging points in Flanders are only used on average 0,6 times a day. In December 2019 Flanders was provided with 3.655 public charging points (Vanacker & Steel, 2020). This results to the conclusion that on average in Flanders only 3.655 ⋅ 0,6 = 2.193 EVs are charged at a public charging point (assuming that no EV is charged more than once a day at a public charging point). Because personal vehicles per fuel type are known for Belgium but are not divided per region, there is assumed that the number of EVs is proportionally distributed against Flanders and Wallonia according to the total number of personal vehicles. So is estimated that Flanders counted 9.296 EVs in 2019 b.Tƒg (Voertuigenpark Statbel, 2019). This leads to only ≈ 24% of EV drivers using a public charging point, ƒ.bƒ≈ if every used charging point is used by another EV driver.

Two important notes could be made. Firstly, when no charging points are available, people do not have the possibility to use one but maybe someone would have charged his EV while shopping if there was one, even when it is not necessary to complete driving to later destinations. Maybe when more charging

points are available on strategic locations, people would charge more at public charging points. Secondly, due to range anxiety it is important to place public charging points, even when they are not used as much as hoped. It is a mental question that people would buy only an EV when they are sure that they will not be stranded anywhere with a dead battery. This could only be acquired when there are enough public charging points, even when a lot of people probably won’t even use them. Therefore, it is important to place more charging points than would be required to serve only the percentage of people that actually needs a public charging point to complete their daily routes.

Therefore, the percentage is set equal to 100%. This reflects that everybody driving an EV must be able to charge his EV once a day at a public charging point.

4.3. Capacity

The capacity of a charging point is expressed in the average number of EV drivers a charging point could cover per day. There are different factors playing an important role in determining this parameter :

- The capacity of the battery of the EV, expressed in kWh. Just as like the consumption of an ICE vehicle is expressed in litres per kilometer, is for every EV the energy consumption per kilometer expressed in kilowatt-hour (kWh). Energy consumption of 1.000 watts (=1kW) during one hour equals 1kWh. How much an EV consumes exactly depends on factors such as the model of the car, driving speed, weather conditions, and so on (Numobi, 2019). Numobi (2019) and ‘Milieuvriendelijke voertuigen’ (s.d.-d) both propose as rule of thumb a value of 17kWh per 100 kilometer, which will therefore be used in this research. The capacity of an EV expressed in kWh indicates how far an EV can reach without charging. For example, an EV with a capacity of 40kWh T∏∏»O can reach ⋅ 40%Àℎ ≈ 235,29%_ without the need to charge. According to an article of T{»… EV company (Jorg, 2019) the top 5 best sold EVs in 2019 were : Tesla model 3, Hyundai kona electric, kia-e-niro, Volkswagen e-golf and Nissan leaf. These EVs all have different capacities ranging from 35,8kWh to 75kWh3. In this research the mean of the capacities of this top 5 is taken as rule of thumb for the battery capacity of an EV which equals 54,35kWh. - The capacity of the charging point, expressed in kW (i.e. charging speed). As already mentioned earlier (see Section 2.4), there are different modes of charging. Only mode 2, 3 and 4 are suitable for charging EVs. Mode 2 is applied for charging at home, and mode 3 and 4 are convenient for

3 https://www.whattherange.com/elektrische-auto

public charging stations. In this research, public charging points are categorized according to their charging speed. In West Flanders there are three charging speed types commonly used for public charging stations (see Section 2.5.2) each with a specific power, which are therefore also used in this research: - Type 1, Normal charging : 11 kW (mode 3) - Type 2, Accelerated charging : 22kW (mode 3) - Type 3, Fast charging: 50 kW (mode 4)

This power indicates the amount of energy that can be transferred per unit of time. Once the power of the charging point and the energy consumption of the EV (17kWh per 100km) are known, the time it takes to charge an EV up to a certain level could easily be calculated. ‘Milieuvriendelijke voertuigen’ state that calculations must be made with an efficiency of 90% due to the fact that there is always a small part of the energy that is lost (Milieuvriendelijke voertuigen, s.d.-d). If you want to charge 17kWh, so you can drive for another 100km, at an T{»… T accelerated charging point (22kW) this would take ⋅ ≈ 0,8585ℎ ≈ 51,5151 _"$c-/&. bb»… ∏,ƒ∏ Important to note is that the charging process slows down a bit from the moment the battery is for 80%-90% charged. - The state of charge (SOC) when arriving and desired SOC when leaving. Not all EV drivers arriving at a charging point have a completely dead battery. Nor is every EV driver charging with the intention to leave with a fully charged battery. As people are using the charging points while parked, they could use the parking spot longer than required to fully charge the battery. Therefore different situations are possible, and three different situations are proposed here : 1. People are charging because they are running out of battery and there is no other option than charging if they want to drive further to their destination. The assumption is made that people arrive at the charging station with a SOC of 20% (because of range anxiety) and leave at 80%. This situation is most likely to happen between 6 AM and 23:59 PM, when people are on the road. 2. People are using the charging point while being parked for small activities that last 1-4 hours. Examples are a visit to the dentist, a walk in the city center with an ice cream in the summer, having diner, etc. There is assumed that for this reason of charging point use the charging point is only used between 10AM and 11PM. As the number of EVs that could be served here depend on the time EVs stay parked, the type of charging point does not matter. Every Tg charging point type can serve = 5,2 uÃ& when an average dwell time of 2,5 hours is b,t taken into account.

3. People stay at the location for 4-8 hours while staying parked on the charging point parking spot. City tripping or a shopping afternoon are examples of activities that last for a while. People who do not have the ability to charge at home will use public charging points to charge during the night. Therefore, the assumption is made that a charging point is taken during night (20 PM to 8 AM) by only 1 EV. This results that for this situation every charging point, Tb regardless the type, can serve + 1 = 3 uÃ& when an average dwell time of 6 hours is ≈ taken into account.

Important note is that it is not because for some situations the time at which the charging point could possibly be used does not include the whole day (24h), that the charging point is not 24 hours available. For every type of charging point the corresponding capacities are shown in Table 4. The assumption is made that the fast chargers are only used for the emergency charging situation (situation 1). Normal charging is not used for emergency charging as it takes more than 3 hours to charge the battery level from 20% to 80%. An example of how situation 1 is calculated for accelerated charging :

Charging from 20% of the EV capacity to 80% equals charging from 54,35%Àℎ ⋅ 20% = 10,87%Àℎ to 54,35%Àℎ ⋅ 80% = 43,48%Àℎ, this means charging 43,48%Àℎ − 10,87%Àℎ = 32,61%Àℎ. The gb,≈T»… T charging point has a power of 22kW, therefore it takes ≈ 1,6470ℎ ≈ 98,8182 _"$c-/& to bb»… ƒ∏% charge 32,61kWh. After this time the EV driver is leaving the charging spot, meaning the charging point T∏Õ∏ ORNŒ∑œé is every 98,8182 minutes ready to serve the next EV. This results in ≈ 10,93uÃ& that could ƒÕ,ÕTÕb ORNŒ∑œé be served by an accelerated charging point per day.

Normal charging Accelerated charging Fast charging 11kW 22 kW 50 kW Situation 1 / 10,93 EVs 24,84 EVs Situation 2 5,2 EVs 5,2 EVs / Situation 3 3 EVs 3 EVs / Table 4: Capacities of every type of charging point according to a certain situation

For this research, the mean of the calculated capacities is taken :

- Charging point type 1, normal charging, 11 kW : ,T = 4,1 uÃ& 3/0 Z1p

- Charging point type 2, accelerated charging, 22 kW : ,b = 6,3767 uÃ& 3/0 Z1p

- Charging point type 3, fast charging, 50 kW : ,g = 24,84 uÃ& 3/0 Z1p

4.4. Cost coefficients

The objective in this research is to minimize the total cost. However, the exact aim of this research is to determine a charging infrastructure that fits as best as possible the future EV demand and minimizes the consequences coming with that infrastructure. The costs in this research do thus not reflect real costs, but rather reflect consequences. The objective function cost gives therefore just an indication of the best charging infrastructure, but does not give the real cost for following the proposed decisions. This simply because these cost estimations are too difficult and are not the main objective of this research. The costs just indicate why a certain decision is preferred above another one. Therefore, the costs are not given a unit (euros). In the mathematical model, three cost parameters are important :

- eN : installation cost for charging point type $ ∈ ñ - & : shortage cost - 8 : waste cost

Installation cost (eN) - Every type of charging point has its own installation cost, therefore the index $ ∈ ñ is used to specify the type of charging point. As already mentioned in the previous section, three types of charging points are considered in this research, each with a corresponding power, capacity and cost:

- eT = installation cost for the normal charging point (11kW)

- eb = installation cost for the accelerated charging point (22kW)

- eg = installation cost for the fast charging point (50kW)

- According to ‘Milieuvriendelijke voertuigen’ there are a few factors playing a role in the installation cost of a charging point (Milieuvriendelijke voertuigen, s.d.-e). The placement cost will for example depend on the distance between the charging point and the electrical distribution board. Thus, this depends on the decision of the exact location of the charging points, which lies outside the scope of this research. The installation costs just give an indication that the different charging point types differ in price (due to differences in power), and therefore why one type would be desired above another type, without the need to approach the real cost. When the installation cost of a type 2 charging point is larger than for a type 1 charging point this means that the consequence of choosing a type 2 charging point above a type 1 charging point is a higher installation cost, without the need to specify the real costs.

- In reality, one charging station with two charging points is often less expensive relative to the number of EVs that could be served in comparison with one charging station with only one charging point. Once again, the aim is to decide upon the charging points needed to approach the future demand as best as possible. Whether 2 charging points are merged in one charging stations, or two charging stations with each one charging point are installed belongs to the responsibility of the municipalities itself. Therefore, the installation cost per charging point is considered in this research. - The assumption is made that for mode 3 charging the installation cost is linear with the provided power. Fast chargers (mode 4) are way more expensive because of the rectifier in the installation. The following costs are assigned to the different types:

- eT = 100

- eb = 200

- eg = 1.000

Shortage cost (s) - The second cost parameter charges the price for not covering the demand. Failing to meet the demand is unfavorable for the further emergence of EVs. The shortage cost is incurred per EV driver that could not be served. - The model will try to fit the demand as good as possible, because both a surplus as a shortage incurs a cost. However, only when the shortage cost per unserved EV is higher than the installation costs per EV, otherwise to minimize the objective function, it would be beneficial to never meet the demand. But when this cost is set too high, this will be avoided by the model and there will always be built too many charging points. What will be a good value for the shortage cost? That is a very difficult question. The average installation cost for one EV equals –—œ“–”œ RNé∑–‘‘–∑R’N ÷’é∑ hgg = ≈ 36,78 uÃ&. The consequences for building fewer charging –—œ“–”œ ÷–◊–÷R∑π TT,{{ ÿŸé points than demand are twofold. A price need to be incurred for not covering the demand (e.g. unhappy EV drivers resulting in bad word of mouth) and extra charging points need to be installed. The first cost is randomly said to be 20% more than the average installation cost per EV (i.e. ≈ 44). The second cost equals the average installation cost per EV. This leads to a default value for the shortage cost of : & = 44 + 36,78 = 80,78. - This value is only a default value. When solving the model, the impact of this parameter will be investigated and will therefore later set to another value.

Waste cost (w) - The third cost parameter incurs a cost for building too many charging points. When more charging points are installed than required, charging points are not used and this would mean that unnecessary costs have been made. Similar to the shortage cost, is the waste cost incurred per EV driver that could have been served more. - The model will try to fit the demand as good as possible, because both a surplus as a shortage incurs a cost. Similar to the shortage cost, only when the waste cost is high enough. When the waste cost is too low and the shortage cost is higher than the installation cost, the program will decide to install as many charging points to fulfill the demand in every possible demand scenario. The extra waste cost obtained in the scenario with the lowest demand due to the high number of charging points will be smaller than if there would be build fewer charging points and a shortage cost has to be charged in the scenario with the highest demand. But what is high enough? Because there is assumed that the future of EVs is bright and too many charging points will however stimulate the further deployment of EVs, building too many charging points is not that bad as building too few. Therefore, 8 is set equal to 110% of the average installation cost per EV to start with, 8 = 36,78 ⋅ 1,10 ≈ 40. - This value is only a default value. When solving the model, the impact of this parameter will be investigated and will therefore later set to another value.

5. Results and interpretation 5.1. Scenario creation 5.1.1. EV-to-vehicle ratio

First, the EV-to-vehicle ratio for 2020 is estimated by performing the suggested linear regression on the transformed EV-to-vehicle ratios as described in Section 4.2.1.1. Secondly, the standard deviation is estimated. Afterwards, these parameters can be used to describe the normal distribution which serves as input for the simulation procedure.

Figure 9 shows the results of plotting the transformed EV-to-vehicle ratio variables with a linear regression line. The corresponding equation is :

pªºΩ log ∫ æ = 0,2966!∑ − 6,1409 1 − pªºΩ

log(y/(1-y)) 2007 - 2019 with linear trendline 0 0 2 4 6 8 10 12 14 -1

-2

-3

-4

-5

-6

-7

Figure 9: Transformed EV-to-vehicle ratio variables approached by a linear trendline

When the fitted values (pªºΩ ) are compared with the actual observations, there can be seen that the model overestimates the ratio for the last two years:

- 2018 (t=12) : Fitted value equals 0,2613% where the actual value equals only 0,1579% - 2019 (t=13): Fitted value equals 0,5160% where the actual value equals only 0,2604%

Therefore, it is likely that this model would also overestimate the EV-to-vehicle ratio for 2020. Also when looking at Figure 9, it seems like the model does not fit the data very well. Fischer (2009) states that if

the data indicates logistic growth, the transformed y variables show linear behavior. Therefore, from the year the points on Figure 9 start to form a straight line, approaching the data with a logistic growth curve is appropriate. When looking at Figure 9, a clear linear relation can be observed from t=6 (2012). Meaning that if the observations from 2012 until 2019 would be separated from the other observations, a logistic growth curve could be applied and the linear regression line will give more accurate estimates. Therefore, the same procedure is performed, but now for only a part of the data. This leads to - ∈ 1, … ,8, where 2012 = 1 , 2013 = 2 and so on. Again, the transformed EV-to-vehicle variables are plotted in Excel and the linear trendline and corresponding equation are added (Figure 10):

πª‹Ω log n o = 0,1915!∑ − 4,1029 (9) T}πª‹Ω

log(y/(1-y)) 2012 - 2019 with linear trendline 0 0 1 2 3 4 5 6 7 8 9 -0,5

-1

-1,5

-2

-2,5

-3

-3,5

-4

-4,5

Figure 10: Transformed EV-to-vehicle ratio variables approached by a linear trendline for only a part of the available data (2012 – 2019)

Figure 10 shows that the linear trendline now fits the data much better. Equation (9) can now be used to estimate the EV-to-vehicle ratio in 2020. For 2020 t=9, so :

pªƒ log n o = 0,1915 ⋅ 9 − 4,1029 = −2,3794 1 − pªƒ

pªƒ ⇔ = 10}b,g{ƒh = 0,0041744571 1 − pªƒ 0,0041744571 ⇔ pª = = 0,0041571034 ƒ (1 + 0,0041744571)

≈ 0,4157%

The estimated EV-to-vehicle ratio (pªƒ) on the first of August in 2020 equals 0,4157% , which will form the mean of the normal distribution. The standard deviation of the residuals is calculated in Excel and equals 0,0068%. This serves as approximation of the standard deviation of the EV-to-vehicle ratio in 2020. Therefore, the variance equals 0,0068%b = 0,0000004625% and the EV-to-vehicle ratio following a normal distribution can be referred to as :

∂ ~(0.4157%, 0.0000004625%)

5.1.2. Simulation results 5.1.2.1. Discrete values for EV-to-vehicle ratio

Two main question arise when the simulation procedure is set up to create different outcomes for the EV-to-vehicle ratio: 1. How many simulation runs are required, or what is a suitable value for R? 2. How many bins must be created (N), or how many discrete values for the EV-to-vehicle ratio are desired?

1. Value for R To decide upon the number of simulations, the number of bins is set fixed to 17. Figure 11 shows the different graphs of the frequency distribution for simulation runs going from 10 to one million. There can be clearly observed that the higher R, the better the graph approximates the shape of a normal distribution. One million simulation runs is already quite a lot and gives the desired results, therefore R is set equal to 1.000.000.

Figure 11: Frequency distribution for simulation runs going from 10 to 1 million

2. Number of bins (N) The boundaries of the bins are the discrete values for the EV-to-vehicle ratio, this results in the number of N determining the number of scenarios. Figure 12 shows the graphs of the frequency distribution for 1.000.000 simulation runs where observations are divided in different bins going from 5 to 25 bins. On the x-axis the EV-to-vehicle ratio is shown and the data labels indicate the corresponding probability of occurrence. There can be seen that again more bins approach the normal distribution shape better. Nevertheless, taking as many bins as possible is not necessarily better. More bins are better to approach the normal distribution, but it is not necessarily better for the model. First of all, the more bins, the smaller the differences are between the different outcomes for the EV-to-vehicle ratio. When the EV-to-vehicle ratios are closer to each other, the computed demand over different scenarios will also be closer to each other. The closer the different demand values, the lower the

probability that another charging infrastructure will be proposed between different scenarios, and the solution remains the same. Secondly, the more bins, the more extreme values have a probability of occurrence lower than 1%. The model will take the demand in low probability scenarios less into account, because the incurred cost is much lower in comparison with scenarios which are more likely to occur. But what is a good value for N?

A lot of statistical packages and introductory statistics textbooks propose Sturges’ rule (Hyndman, 1995). This rule says that the number of classes when constructing a histogram from normal data has to be equal to (Hyndman, 1995):

% = 1 + 524b$ In the formula is n the number of observations, which is decided to be equal to 1.000.000. According to the formula, 1 + 524b1.000.000 ≈ 21 is a suitable number of bins.

Figure 12: Frequency distribution for number of bins going from 5 to 25

Table 5 gives an overview of the 21 different discrete values for the EV-to-vehicle ratio with their corresponding probability of occurrence, both rounded to 4 digits.

Scenario EV-to-vehicle Probability Scenario EV-to-vehicle Probability ratio ratio Scenario 1 0,3864% 0,0007% Scenario 12 0,4202% 16,3269% Scenario 2 0,3894% 0,0046% Scenario 13 0,4233% 12,1358% Scenario 3 0,3925% 0,0279% Scenario 14 0,4264% 7,3294% Scenario 4 0,3956% 0,1252% Scenario 15 0,4295% 3,6776% Scenario 5 0,3987% 0,4618% Scenario 16 0,4325% 1,5005% Scenario 6 0,4018% 1,4082% Scenario 17 0,4356% 0,4909% Scenario 7 0,4048% 3,4774% Scenario 18 0,4387% 0,1393% Scenario 8 0,4079% 7,0696% Scenario 19 0,4418% 0,0299% Scenario 9 0,4110% 11,7776% Scenario 20 0,4448% 0,0055% Scenario 10 0,4141% 16,1113% Scenario 21 0,4479% 0,0009% Scenario 11 0,4171% 17,8990% Table 5: The 21 discrete values for the EV-to-vehicle ratio with corresponding probability of occurrence

5.1.2.2. Different scenarios

≠2-15 Z/_1$Z ,20 eℎ104"$4 32"$-& _c$"e"315"-p " &e/$10"2 & (10) = (3/0&2$15 /ℎ"e5/& "$ℎ1d"-1$-& _c$"e"315"-p " + 3/0&2$15 /ℎ"e5/& -2c0"&-& _c$"e"315"-p ") × uÃ -2 /ℎ"e5/ 01-"2 2020 &e/$10"2 &

Formula (8) (see Section 4.2) is now applied 21 times for each municipality with the parameters calculated in the methodology section and with the 21 different EV-to-vehicle ratios. Workers are not incorporated and are therefore left out. The percentage that needs a recharge is equal to 100% which means multiplying by one thus can also be eliminated in the formula. This leads to formula (10), which is a small simplification of formula (8). These calculations result in 21 different scenarios for the demand in each municipality, with for each scenario a corresponding probability of occurrence. Some results are available in Attachment 2, where values are rounded to two digits. Not all scenarios are shown, but same calculations (i.e. formula (10)) are made for the other scenarios.

5.2. Optimal charging infrastructure West Flanders for 2020

Now for every municipality the 21 different demand scenarios (ZR,é) with their corresponding probability

(Sé) are known, the stochastic programming model can be solved for optimality. All other parameters are set equal to the values as described in the methodology section. West Flanders counts 64 municipalities (i.e. I = 64), there has to be decided upon the number of three different types of charging points (i.e. N = 3) and the cost has to be minimized across 21 possible demand scenarios (i.e. S = 21). In Attachment 2 there can be seen that the highest possible demand over all the municipalities and scenarios appears in Brugge and equals 279,05. This is rounded up to 280 which is the value for big M.

An overview of the model sets and parameters other than ZR,é and Sé is shown in Table 6.

Parameter Value N 3 I 64 S 21 eN eT = 100 , eb = 200,eg = 1.000 8 40 & 80,78 ,N ,T = 4,1 ; ,b = 6,3767; ,g = 24,84 M 280 Table 6: Overview of the different model parameters and their values for a first solution

The model is implemented in the optimization software package IBM ILOG CPLEX Optimization Studio. The code of the implemented model can be found in Attachment 3 (the model file). The appropriate values for the parameters can be assigned in the data file. The results for the !R,N decision variables are shown in Table 7. Municipalities are just numbered according to alphabetic order (i.e. i=1= Alveringem, i=2=Anzegem, i=3 = Ardooie, …). In total there are 631 type 1 charging points (power of 11 kW), 17 type 2 charging points (power of 22 kW) and 0 type 3 charging points (power of 50 kW). A few interesting conclusions can be made.

11 kW 22 kW 50 kW 11 kW 22 kW 50 kW n=1 n=2 n=3 n=1 n=2 n=3 Alveringem 1 1 0 Lendelede 3 0 0 Anzegem 8 0 0 Lichtervelde 5 0 0 Ardooie 5 0 0 Lo-Reninge 2 0 0 Avelgem 4 1 0 Menen 17 0 0 Beernem 8 0 0 Mesen 1 0 0 Blankenberge 10 0 0 Meulebeke 6 0 0 Bredene 9 0 0 Middelkerke 9 1 0 Brugge 63 0 0 Moorslede 6 0 0 Damme 5 1 0 Nieuwpoort 7 0 0 De Haan 8 0 0 Oostende 32 0 0 De Panne 6 1 0 Oostkamp 13 0 0 Deerlijk 12 0 0 Oostrozebeke 4 0 0 Dentergem 3 1 0 Oudenburg 5 0 0 Diksmuide 9 0 0 Pittem 4 0 0 Gistel 5 1 0 Poperinge 10 0 0 Harelbeke 15 0 0 Roeselare 35 0 0 Heuvelland 3 1 0 Ruiselede 3 0 0 Hooglede 4 1 0 Spiere-Helkijne 1 0 0 Houthulst 4 1 0 Staden 6 0 0 Ichtegem 6 1 0 Tielt 11 0 0 Ieper 19 0 0 Torhout 11 0 0 Ingelmunster 6 0 0 Veurne 5 1 0 Izegem 14 1 0 Vleteren 2 0 0 Jabbeke 8 0 0 Waregem 23 0 0 Knokke-Heist 21 0 0 Wervik 8 1 0 Koekelare 5 0 0 Wevelgem 17 0 0 Koksijde 14 0 0 Wielsbeke 4 1 0 Kortemark 7 0 0 Wingene 8 0 0 Kortrijk 44 0 0 Zedelgem 11 1 0 Kuurne 7 0 0 Zonnebeke 7 0 0 Langemark-Poelkapelle 4 0 0 Zuienkerke 0 1 0 Ledegem 5 0 0 Zwevegem 13 0 0 Table 7: Optimal solution for the decision variables !R,N with parameters equal to Table 6

1. Evaluation criteria

The impact of changing the shortage and waste cost will be investigated. As for every different solution another shortage and/or waste cost is taken into account, it makes no sense to compare different solutions according to their objective function value (i.e. the total cost). Only when all the same costs are taken into account, a comparison regarding the costs could be made. Therefore, some other evaluation criteria need to be investigated to decide upon suitable values for the shortage and waste costs. In this research, the focus will lie on two criteria : the charging point type 2 share and the total cases in which a waste could be observed. The first criteria is the ratio between all the type 2 charging points placed in West Flanders and the total number of charging points placed in West Flanders. The second criteria is the sum of all the kﬂ,‡ decision variables. One scenario in one municipality is referred to as a case, so when there are 64 municipalities and 21 scenarios, the model counts 1.344 cases and thus 1.344 kﬂ,‡ decision variables.

2. No fast chargers

In the initial optimal solution (Table 7) most charging points of type 1 are placed, as opposed to fast chargers (i.e. type 3) of which none are placed. This could be explained by the installation cost per served T∏∏ EV. For type 1 the installation cost per served EV equals = 24,39/uÃ , while for a fast charger this h,T ÿŸé T.∏∏∏ cost equals = 40,26/uÃ. The model will only assign a fast charger to a municipality when the bh,Õh ÿŸé high installation cost per served EV is justified because the waste and shortage cost are very high. This happens because placing a fast charger leads to a better match between supply and demand in cases where otherwise this high shortage or waste would be incurred. In other words, a fast charger leads to a total charging point capacity that better fits the charging point demand. The high installation cost required to obtain this better fit is lower than that the waste or shortage cost would be if the capacity would fit the demand worse.

An example where shortage and waste cost both are randomly multiplied with 1.000 (& = 80.780 1$Z 8 = 40.000) is solved to clarify this. The model decides now to place 1 fast charger and 1 type 1 charging point in the municipality Kortemark instead of the 7 type 1 charging points from the initial solution. This leads to a total capacity of 24,84 uÃ& + 4,1uÃ& = 28,94 uÃ& instead of 7 ⋅ 4,1uÃ& = 28,7 uÃ&. This higher total capacity fits the demand better in scenarios where otherwise a very high shortage cost would be charged. For both charging point infrastructure plans in Kortemark the same

shortage, waste and installation costs are taken into account. The expected shortage/waste cost for the 7 type 1 charging points equals 22.312,86 and for the 1 type 3 and 1 type 1 charging point 20.751,34 , which results in a saving of 22.312,86 − 20.751,34 = 1.561,52. This saving is bigger than the extra required installation costs (i.e. (1.000 + 100) − 7 ⋅ 100 = 400), which leads to the decision to place a type 3 charging point.

If this is beneficial, the model will always decide to replace a few type 1 or type 2 charging points by a type 3 charging point. This results in a lower total amount of charging points. This is not desired for stimulating the EV market. The range anxiety problem will mainly be solved if people see a big amount of charging points on different places in the city. A potential EV driver would like to see increasing the number of charging points instead of seeing fewer charging points with a higher capacity. Therefore, there is decided to drop the type 3 charging points in the model, and only decide upon the type 1 and type 2 charging points. Fast chargers are currently placed in the bigger cities in West Flanders (Brugge, Kortrijk, Oostende and Jabbeke). The choice to place a fast charger is rather done to offer extra convenience to those EV drivers that require a quick charging stop instead of serving the biggest part of the demand. Therefore, the assumption is made that the municipalities itself decide upon placing fast chargers on top of the type 1 and type 2 charging points required to serve the demand, if enough budget to do so is available.

When the model is solved for two types of charging points instead of three (i.e. N=2), while all other parameters remain the same, the solution does not change. This is of course because in the first solution the model did not assign any type 3 charging points. Therefore, in the next point, the same solution as in Table 7 is further analysed.

3. Increasing shortage (s) and waste (w) cost

An important note is that the same conclusion as regarding to the fast chargers could be made for type b∏∏ 2 charging points. The installation cost per EV is for a type 2 charging point also bigger = ≈,g{≈{ ÿŸé 31,36/uÃ compared to a type 1 charging point. This leads again to a type 2 charging point only being placed if the higher installation cost could be justified because of the high waste and shortage cost. However, there is a big difference. 6 charging points of type 1 will be replaced by 1 charging point of type 3 (capacity of 24,6 EVs against 24,84 EVs). But, 6 type 1 charging points shall be replaced by at least 4 type 2 charging points when at least the same capacity has to be reached (capacity of 24,6 EVs versus 25,5 EVs). This leads to a better fit between supply and demand in scenarios where otherwise a high

shortage cost would be charged, and a total amount of charging points that is not that much smaller. Another possibility that could arise is that one type 1 charging point is replaced by one type 2 charging point. Now approximately two EVs could be served more, indeed at a higher cost per served EV, but this may incur less shortage costs. The opposite case in which a lower total capacity is achieved by replacing some type 1 charging points with type 2 charging points can of course also arrive. In that case the higher installation cost is justified by the high waste cost that would be charged otherwise. On top of that, a capacity of 22 kW could be desired above a capacity of 11 kW for an EV driver, justifying the higher installation cost once again. Leaving type 3 charging points out but incorporate type 2 charging points can also be deduced from the current situation analysis. There can be seen that 23,50% of the total charging points has a capacity of 22 kW and only 2,15% a capacity of 50kW. Type 2 charging points represent a large proportion of the total current charging point infrastructure, while type 3 charging points can be neglected.

This leads to the conclusion that the higher the shortage and waste costs are set, the better the model shall try to fit the demand as best as possible to avoid high shortage or waste costs. This in as many scenarios as possible, or at least in the scenarios with a high probability of occurrence. This better fit could be achieved by placing more type 2 charging points leading to higher installation costs but less total expected shortage and waste costs. Now the question arise : how high should these & and 8 parameters be? A good approach could be to rise the shortage and waste cost until the proportion of type 2 charging points equals the proportion as it is in the current situation in West Flanders (i.e. 23,50%). In the initial T{ solution, the type 2 charging point share equals only 2,62% r s. Shortage and waste costs need to ≈gT|T{ change to increase this percentage. 23,50% is roughly achieved when s equals 18.013 and w 8.920. Solving the model with this changed shortage and waste costs results in a total of 451 type 1 charging points and 139 type 2 charging points, leading to a 23,56% charging point type 2 share. This solution differs from the solution obtained in Table 7, and more details about the values of the !R,N decision variables can be found in Attachment 4.

4. Changing the &/8 ratio

In the previous solution, & and 8 are increased to better fit supply and demand, but the ratio between ‚ h∏ Õ.ƒb∏ both costs remained the same ( = = ). Of course, the solution might change further if this é Õ∏,{Õ TÕ.∏Tg ratio is adapted. Increasing the shortage cost could result in placing more charging points because it is ‘more expensive’ to have charging points short instead of having charging points in surplus.

In the last solution, the sum of all the kfl,‡ equals 776 (i.e. cases in which waste is observed). A 1 means that for that municipality in that particular scenario the total charging point capacity exceeds demand, a zero appears in the opposite case when the demand exceeds total capacity. In other words, in 776 cases there is a waste observed. When demand is exactly equal to the total charging point capacity, kfl,‡ can take a value of 0 or 1. In what follows this is every time checked to be sure that all cases in which waste is observed is correct. This will never occurs, and therefore the model can be kept as it is. If this would not be the case, in constraint (5) of the model (see Section 4.1) the ≤ inequality could be replaced by the strict inequality <. This could not be solved by CPLEX, and therefore the definition of kfl,‡ would have to change such that when the capacity exactly equals the demand, kfl,‡ will get a value of 0. This means that in 776 cases too many charging points are placed and in 568 cases too few. What happens with the number of cases in which a waste could be observed if the gap between shortage and waste cost is increased?

For convenience, all costs are divided by 100. This is possible because the costs do not reflect real costs, and if the proportions remain the same the decision variables will be given the same values. The model is therefore further analysed starting with values for the parameters as in Table 8. To investigate the effects of changing the gap between w and s, the shortage cost is stepwise increased with 5 units, while the waste cost is kept constant. For 10 different values for s, results are studied and shown in Table 9. Column 1 shows the parameter values. Column 2 and 3 are showing the total number of type 1 and type 2 charging points respectively across all municipalities in West Flanders. The sum of both, and thus the total number of charging points in West Flanders, is shown in column 4. Column 5 shows the total capacity over all municipalities, and column 6 the sum of all kﬂ,‡ decision variables (i.e. the total cases in which a waste could be observed).

Parameter Value N 2 I 64 S 21 eN eT = 1 , eb = 2 8 89,20 & 180,13 ,N ,T = 4,1 ; ,b = 6,3767 M 280 Table 8: Overview of the different model parameters and their values as a starting point to decide upon the optimal values for w and s

1 2 3 4 5 6 Â Â Â Ë Â Ë Â Ï Parameter values Ö B„,‰ Ö B„,Ê Ö Ö B„,Á Ö Ö B„,Á ⋅ ÈÁ Ö Ö Í„,Î „Y‰ „Y‰ „Y‰ ÁY‰ „Y‰ ÁY‰ „Y‰ ÎY‰ 8 = 89,20 ; & = 180,013 451 139 590 2.735,461 776 8 = 89,20 ; & = 185,013 453 138 591 2.737,285 781 8 = 89,20 ; & = 190,013 447 142 589 2.738,191 785 8 = 89,20 ; & = 195,013 447 142 589 2.738,191 785 8 = 89,20 ; & = 200,013 447 142 589 2.738,191 785 8 = 89,20 ; & = 205,013 447 142 589 2.738,191 785 8 = 89,20 ; & = 210,013 444 144 588 2.738,645 787 8 = 89,20 ; & = 215,013 455 137 592 2.739,108 788 8 = 89,20 ; & = 220,013 452 139 591 2.739,561 789 8 = 89,20 ; & = 225,013 454 138 592 2.741,385 801 Table 9: Solution results for different values of the shortage cost parameter s

Every time the shortage cost is increased with 5 units, the sum of all the %R,é increases or remains the same (column 6 Table 9). Because it becomes ‘cheaper’ to have charging points in surplus, two things can happen :

1. The amount of type 1 and/or type 2 charging points is changed such that an increase of the total capacity is obtained. A total capacity which increases, means more cases in which charging points

are over, resulting in an increase of the total sum of %R,é. An increase in capacity can be obtained by increasing the number of type 1 charging points, resulting in a total number of charging points which increases. Or by replacing some type 1 charging points by type 2 charging points, because they have a higher capacity. The latter leads not to a higher amount of total charging points, but it does lead to a higher total capacity. 2. The outcome does not change when the saving to have more charging points in surplus than short does not outweigh the extra installation cost. For example the solutions where s=190,013 and s=195,013 are giving the same results.

All these findings can be clearly observed in Table 9 and on Figure 13. In Figure 13 are on the x-axis the different values for the shortage cost shown. On the primary y-axis the blue bars indicate the cases in which waste is observed and on the secondary y-axis the orange line shows the total capacity. There can be clearly seen that when the shortage cost increases both the total capacity and the cases in which waste is observed increase or remain the same.

Figure 13: Solution results for different values of the shortage cost parameter s

Now the effects of widening the gap between both costs are known, the question is of course how large the gap should be. In this research, there will be focused on the cases in which waste is observed. The objective is to achieve a certain percentage of cases in which waste is observed. The waste cost is kept constant and the shortage cost is changed such that different percentages are achieved and could be compared with each other. Results are shown in Table 10 and Figure 14 where the different solutions coming from different shortage costs are compared with one another. For the stimulation of the EV market it is desired to have more cases in which charging points are in surplus, therefore the percentage of cases in which waste is observed has to be at least 50%. This means that the sum of the %R,é decision variables has to be at least 1.344 ⋅ 0,5 = 672. To keep things simple, the percentage is stepwise increased with 5%. The first value for the shortage cost where a certain percentage is achieved, is taken.

1 2 3 4 5 6

Percentage of Shortage cost (s) Â Ï Â Â Ë Charging point Ö Ö Í Ö Í Ö Ö B cases in which „,Î „,‰‰ „,Á type 2 share „Y‰ ÎY‰ „Y‰ „Y‰ ÁY‰ waste is observed 50% 84,20 672 34 587 0,2266 55% 163,20 740 54 589 0,2343 60% 258,20 805 59 596 0,2215 65% 462,20 874 62 592 0,2483 70% 736,70 943 64 590 0,2695 Table 10: Solution results for different percentages of cases in which waste is observed

How can these different solutions be compared with each other, and which percentage is a good objective? In this research, there is aimed to achieve in as many municipalities as possible waste or at least in the scenario with the highest probability of occurrence. Scenario 11 is the scenario with the ú highest probability of occurrence (see Table 5), so the objective is to maximize ∑RYT %R,TT. But is it suitable ú to keep increasing s until this number is maximized (i.e. ∑RYT %R,TT = 64 )? Figure 14 visualises for the different percentages the sum of the %R,é decision variables for each municipality. The municipalities in Figure 14 shown on the x-axis are now ordered from smallest to largest demand. The orange line shows when for a municipality in at least 11 scenarios waste is observed. As there are 21 possible demand scenarios, the sum of the %R,é decision variables for a municipality can be maximum 21, which is indicated by the green line. Following conclusions are made :

- For 50% and 55% there are municipalities in which zero scenarios waste is observed, or in other words no matter which scenario appears, there will always be a shortage. Therefore, these percentages with corresponding waste and shortage costs will not be chosen. The shortage cost will be further increased to avoid that in some municipalities there will always be a shortage. - If the shortage cost is increased as such that in 70% of all the cases across all municipalities and scenarios waste is observed, in every municipality there is waste in the scenario with the highest probability of occurrence. For 65% in two municipalities (Zuienkerke and Oudenbrug) and for 60% in 5 municipalities (Zuienkerke, Alveringem, Langemark-Poelkapelle, Lichtervelde and Oudenburg) this is not the case.

Figure 14: Sum of the %R,é decision variables for each municipality for different percentages of total cases in which waste is observed

Figure 15 shows for the different percentages the total number of charging points the model decides to place (primary y-axis, the blue bars) and the charging point type 2 share (secondary y-axis, the orange line). The objective of 23,50% charging point type 2 share is indicated by the green line. In this research there is chosen to set the waste and shortage cost equal to values such that in 60% of the cases waste is observed (i.e. w= 89,20 and s=258,20). This mainly because of two reasons :

- For this percentage the most charging points are placed which is beneficial for the EV market (Figure 15). However, this seems logical because also the charging point type 2 share is the lowest (22,15%). The shortage cost is stepwise increased while the waste cost was kept constant. It is of course possible to increase also the waste cost in such a way that both objectives are achieved (i.e. charging point type 2 share of 23,50% and the desired % of cases in which waste is observed). As it is impossible to predict exactly how the model will react on changing the costs, the efforts to further change the s and w parameters do not outweigh the benefits of achieving the exact values. The obtained charging point type 2 shares are for every percentage really close to the objective, and therefore one of the presented solutions will be chosen. For the solution in which 65% of the cases waste is observed, the share equals 24,83% which is an equally large deviation from the objective, but in the opposite direction. Therefore, 60% is chosen because this leads to more total charging points. - Figure 14 clearly shows that when the shortage cost increases (increasing percentage of cases in which waste is observed), the effects on municipalities with a lower demand are more pronounced compared to municipalities with a higher demand. For the larger municipalities

(right side of the figure) the cases are increasing gradually by one or two units at a time. When there occurs a change for the smaller municipalities (left side of the figure), the shift in cases in which waste is observed is much larger. For example for the second municipality on Figure 14 (Spiere-Helkijn) the total cases in which waste is observed is zero for 50% but jumps immediately to 21 for 55%. For Brugge, the largest municipality, the increase in cases occurs gradually, namely 10 cases for 50%, 12 cases for 55% and 60% and 13 cases for 65% and 70%. This can be logically explained. The demand in the various scenarios for smaller municipalities lies much closer to each other than for larger municipalities. Thus, when the capacity is increased, the chance of having waste in more scenarios is much larger for the smaller municipalities. When shifting from 60% to 65%, the cases in which waste is observed for the three municipalities extra reaching the orange line (Alveringem, Langemark-Poelkapelle and Lichtervelde) jump immediately from 6, 7 and 8 cases to 21, 21 and 18 cases respectively. The same observation could be made when jumping from 65% to 70%. Because it belongs small municipalities, the number of EVs served in 7 cases differs not much from the number of EVs served in 21 cases. Therefore, focusing on the larger municipalities is more important and having only 5 municipalities in which the boundary of 11 cases is not reached is still acceptable.

Figure 15: Total number of charging points and charging point type 2 share for different percentages of total cases in which waste is observed

5. Optimal solution Now all the parameters have an appropriate value, the model can be solved to obtain the optimal solution for the number of charging points in each municipality for 2020. An overview of the optimal

values for the different parameters is shown in Table 11. The values for the decision variables !R,N when the model is solved in CPLEX is shown in Table 12.

Parameter Value N 2 I 64 S 21

eN eT = 1 , eb = 2 8 89,20 & 258,20 ,N ,T = 4,1 ; ,b = 6,3767 M 280 Table 11: Overview of the different model parameters and their optimal values 11 kW 22 kW 11 kW 22 kW n=1 n=2 n=1 n=2 Alveringem 1 1 Lendelede 0 2 Anzegem 7 1 Lichtervelde 0 3 Ardooie 4 1 Lo-Reninge 2 0 Avelgem 4 1 Menen 14 2 Beernem 2 4 Mesen 1 0 Blankenberge 10 0 Meulebeke 3 2 Bredene 3 4 Middelkerke 9 1 Brugge 64 0 Moorslede 0 4 Damme 5 1 Nieuwpoort 1 4 De Haan 5 2 Oostende 31 1 De Panne 6 1 Oostkamp 4 6 Deerlijk 12 0 Oostrozebeke 3 1 Dentergem 3 1 Oudenburg 2 2 Diksmuide 6 2 Pittem 4 0 Gistel 5 1 Poperinge 9 1 Harelbeke 3 8 Roeselare 26 6 Heuvelland 3 1 Ruiselede 0 2 Hooglede 4 1 Spiere-Helkijne 0 1 Houthulst 4 1 Staden 0 4 Ichtegem 6 1 Tielt 2 6 Ieper 16 2 Torhout 11 0 Ingelmunster 0 4 Veurne 2 3 Izegem 11 3 Vleteren 2 0 Jabbeke 5 2 Waregem 17 4 Knokke-Heist 12 6 Wervik 5 3 Koekelare 5 0 Wevelgem 11 4 Koksijde 8 4 Wielsbeke 1 3 Kortemark 4 2 Wingene 8 0 Kortrijk 40 3 Zedelgem 8 3 Kuurne 6 1 Zonnebeke 7 0 Langemark-Poelkapelle 1 2 Zuienkerke 0 1 Ledegem 4 1 Zwevegem 12 1 Table 12: Optimal solution of the model for the decision variables !R,N and for the parameters equal to Table 11

5.3. Evaluation current charging point infrastructure

In this section, there will be investigated if the current charging point infrastructure in West Flanders is in line with the optimal infrastructure for charging points in 2020 (Table 12). For convenience the current fast chargers are ignored in the analysis. An important note is that the current charging point infrastructure is meant to serve the BEV market as well as the PHEV market. ‘Clean power for transport’ estimated a BEV fleet of 60.500 for 2020 and a PHEV fleet of 13.600, where for every 10 vehicles 1 charging point needed to be installed (Vlaams Departement Omgeving, 2015). As BEVs and PHEVs had an equal share in the demand for charging points, 81,64% of the charging points was intended to serve ≈∏.t∏∏ the pure EV market r = 0,8164s. Therefore, the current numbers of charging points in each {h.T∏∏ municipality (see Attachment 1) are multiplied by 0,8164 to obtain the charging infrastructure meant to serve the BEVs. This makes it possible to compare the optimal charging point infrastructure with the current charging point infrastructure, because for the optimal solution only the BEV demand is taken into account. This results in Attachment 5 which shows the current number of installed charging points in each municipality meant to serve the BEV market (only for type 1 and type 2).

For every municipality the waste or shortage cost in each scenario can now be calculated based on the current number of charging points and the future demand scenarios. In other words, calculating the shortage and waste consequences for 2020 when the current charging point infrastructure would be maintained. This is achieved by giving the !R,N variables the values of the current number of type 1 and type 2 charging points (i.e. as in Attachment 5), instead of letting them be decision variables. ‘Clean power for transport’ suggested one charging point for every 10 EVs, therefore in the plan the capacity of both types of charging points is set equal to 10. To be able to compare results, the model is solved for more realistic values of the capacity for both types of charging points (i.e. ,T = 4,1 and ,b = 6,3767).

Figure 16 gives an overview of the sum of all the %R,é variables for each municipality, if the current charging point infrastructure would not change for 2020. Following conclusions can be made:

- A value of 21 means that for every possible future demand scenario there are currently too many charging points in that municipality. - A value of 0 means that for every possible future demand scenario there are currently too few charging points in that municipality. - A value somewhere between 0 and 21 means that for some future demand scenarios there are currently too many and for some future scenarios there are currently too few charging points.

Figure 16: Sum of %R,é for every municipality according to the current charging point infrastructure and the future demand scenarios (2020)

This would mean that for 29 municipalities there are currently too few charging points and extra charging points need to be built to serve the demand in 2020. For 23 municipalities there are more than enough charging points and in every scenario waste is observed. This results that in 2020 there is no need to built extra charging points for these municipalities. For the remaining 12 municipalities it could be beneficial to built extra charging points or not. Despite the large overestimation of the EV fleet for 2020, there are still municipalities with a lack of charging points to meet demand in 2020. This can be explained by following reasons :

- Planned charging points in 2015 are not all realised yet. - This research suggests approximately twice as many charging points due to a smaller capacity. ‘Clean power for transport’ suggested 1 charging point for every 10 EVs, while this research h,T|≈,g{≈{ suggests 1 charging point for every = 5,23835 uÃ&. b - ‘Clean power for transport’ was based, among other things, on the number of inhabitants, in each municipality while this research is based on the number of EVs daily present in each municipality.

To investigate the number of charging points that need to be added to the current charging point infrastructure to serve the demand in 2020 as appropriate as possible while minimizing the costs, another model is created. The current charging points are taken into account in the new model and therefore it slightly differs from the original model. The first-stage decision variables are now to decide upon the

optimal number of each type of charging points that need to be installed on top of the current charging points in every municipality. The biggest difference is that to calculate the total capacity of all the charging points both the new as the current charging points need to be taken into account. The model sets, parameters, decision variables and the model itself are presented below.

Model sets and parameters:

- N : Set of charging point types - I : Set of municipalities - S : Set of scenarios

- Sé : Probability of occurrence of scenario s

- eN : Cost of installing a charging point of type n (installation cost) - 8 : Waste cost - & : Shortage cost

- ZR,é : Demand in municipality i in scenario s

- 3R,N: Current number of charging points of type n at municipality i

- ,N : Number of EVs a charging point of type n can serve in one day - ^: a very large positive number

Decision variables:

!R,N = number of charging points of type $ ∈ ñ at municipality " ∈ ó that need to be installed to serve the demand in 2020

Model : Minimize ú õ ê ú õ õ

Ö Ö !R,NeN + Ö Ö Sé ù8 %R,é ûÖ(!R,N + 3R,N),N − ZR,éü + & ã1 − %R,éå ûZR,é − Ö(!R,N + 3R,N),Nü† RYT NYT éYT RYT NYT NYT

Subject to õ

Ö(!R,N + 3R,N) ≥ 1 , ∀" ∈ ó NYT õ

Öã!R,N + 3R,Nå,N − ZR,é ≤ ^%R,é , ∀i ∈ I, s ∈ S NYT õ

ZR,é − Öã!R,N + 3R,Nå,N ≤ ^ã1 − %R,éå, ∀i ∈ I, s ∈ S NYT

!R,N ∈ ℕ , ∀i ∈ I, n ∈ N

%R,é ∈ {0,1} , ∀i ∈ I, s ∈ S

The model is again implemented and solved using CPLEX and results are shown in Table 13. For each municipality where in every scenario charging points were short, extra charging points need to be installed. For the municipalities which have in some scenarios waste and in other scenarios shortage is only for Kortemark and Ardooie one extra charging point of type 1 built. For those municipalities that have waste in all future demand scenarios, there is of course no need to install any additional charging points and things will remain as they are. Therefore, the decision variables !R,N for these municipalities are 0 and are not included in Table 13. Figure 17 shows the number of cases in which waste is observed for each municipality for the optimal solution when the current charging point infrastructure is taken into account.

11 kW 22 kW 11 kW 22 kW n=1 n=2 n=1 n=2 Anzegem 2 0 Meulebeke 0 1 Ardooie 1 0 Moorslede 0 4 Avelgem 1 0 Oostkamp 7 1 Beernem 5 0 Oostrozebeke 3 0 Damme 0 1 Pittem 1 1 Deerlijk 4 3 Ruiselede 0 1 Dentergem 3 0 Torhout 3 0 Gistel 2 1 Vleteren 1 0 Harelbeke 4 0 Wervik 0 2 Houthulst 4 0 Wevelgem 6 1 Ichtegem 6 0 Wielsbeke 1 0 Jabbeke 0 2 Wingene 0 3 Kortemark 1 0 Zedelgem 5 1 Langemark-Poelkapelle 1 0 Zonnebeke 2 0 Ledegem 2 1 Zwevegem 7 0 Lichtervelde 0 2 Table 13: Number of charging points of each type that need to be installed in the municipalities where there are currently too

few charging points to serve the demand in 2020 (values !R,N)

Figure 17: Cases in which waste observed for the optimal solution when the current charging point infrastructure is taken into account

6. Discussion 6.1. Conclusions arising from the research

In this research, a model is proposed to plan the optimal charging point infrastructure in a study area based on the future demand. The study area can be divided into several unit areas and the number of different types of charging points needed in each unit area is calculated. Rather than investigating the exact location for charging points, the optimal number of charging points to be able serve the future demand is investigated by the model. This all must be done while minimizing the consequences of choosing one plan above another, referred to as costs. Building too many charging points brings waste, but building less than demand leads to a cost for not covering the demand.

Literature shows that already a lot of researches about the charging point location planning problem exist. A lot of different approaches are presented, but after investigating different solution methods for planning under uncertainty, two-stage stochastic programming could be best applied on the problem suggested in this research. Moreover, two-stage stochastic programming is already applied a lot on various different planning problems in literature, also on the charging point planning problem. The existing works often propose a model to determine the exact location, while that is in this research not the case. A lot of specific difficult to obtain information is not needed here which makes this research a lot easier and therefore more applicable on large study areas. Although the exact location is also of big importance for the adoption of the EV market, the model proposed in this research gives already a clue about the amount of charging points needed to serve demand.

A two-stage stochastic programming model is set up with the demand for public charging points as the stochastic element. The model is applied to the study area of West Flanders, which can be divided into different unit areas according to the municipalities. The demand in each municipality is based on the number of EVs daily present. This number is on his turn estimated by multiplying the sum of the personal vehicles coming from inhabitants and tourists with the EV-to-vehicle ratio for 2020. This EV-to-vehicle ratio is the main source of uncertainty and follows a normal distribution from which different scenarios are subtracted. Furthermore, three cost parameters are important : the installation, waste and shortage costs. The installation costs get a fixed value according to the charging mode and the power they deliver. The shortage and waste cost are given a value taken two objectives into account : the charging point type 2 share need to be approximately 23,50% and in 60% of the cases there need to be observed waste. The capacities of the different types of charging points needed in the model are all given suitable fixed values.

The proposed model is perfect to apply on the different municipalities in Flanders, and could therefore be easily applied to other regions. The ‘location plan for charging points’ realized by Eandis and Infrax in 2015 to decide the optimal number of charging points in each municipality in Flanders, was less or more done in the same way. The biggest difference is that they provided a deterministic approach. Simply stated, they followed following steps :

1. Estimate the future EV fleet for Flanders in 2020 2. Count a capacity of 1 charging point for 10 EVs 3. Divide the total number of charging points needed across the different municipalities according to, among other things, the number of inhabitants

The general thoughts are largely the same in this research. The number of charging points needed in the municipalities is calculated according to the number of EVs driving around and the number of EVs a charging point can cover (i.e. the capacity). To do so, the future EV fleet also needs to be estimated. Biggest difference: the future EV fleet is uncertain and different scenarios need to be taken into account. Today, five years after the action plan was approved, there can be concluded that in 2015 the EV fleet for 2020 was largely overestimated. Now that more data is available from previous years, and there need to be estimated only one year in advance, more accurate estimations can be made. Therefore, this model can serve to estimate the optimal charging point infrastructure for next year. This plan can be compared with the current charging point infrastructure to check if it is still on track to meet next year’s demand. Or in other words, how many charging points need to be installed on top of the current points now to meet next year’s demand.

In summary, this model is compared with the approach in ‘Clean power for transport’ :

- More realistic because future uncertainty is taken into account (<-> deterministic approach) - More accurate and reliable because estimations need to be made only for one year in advance (<-> estimate five years into the future) - More accurate because the model is based on the number of EVs (<-> inhabitants) - Every year again applicable (<-> a one time plan)

Of course the research has some drawbacks, which are explained in the following section.

6.2. Limitations of the research

In this research some limitations are recognized. Each paragraph in this section tackles a limitation.

Predicting the future is always difficult, no matter what. Here the logistic growth forecasting method is based on data from only 8 years (2012-2019). The more data there is available, the more accurate estimations could be made. Therefore, in a few years, when it will be more clear in which direction the EV market is developing and numbers from more years are available, forecasting will be easier and more reliable.

The carrying capacity of the EV-to-vehicle ratio in this research is said to be 100%. This would mean that in the future, every personal vehicle driving around will be an EV. This is of course unrealistic and another percentage could lead to other forecasting results. But once again, the more data and information about the EV market will be available in the future, the easier it will be to make accurate estimations about the carrying capacity.

To decide upon the number of bins, Sturges’ formula is applied. Hyndman (1995) states that Sturges’ rule lead to oversmoothed histograms and this especially when samples are large. With a sample of 1 million in this research, the formula is not ideal to decide upon the number of bins. However, Dogan & Dogan (2010) propose some other methods resulting in many more bins for large samples. A large amount of bins is not beneficial due to the small EV-to-vehicle ratio mean and small standard deviation. This justifies the choice for 21 bins, nevertheless the effect of taking a different amount of bins (and thus scenarios) on the optimal solution could be investigated.

The results of the model strongly depend on the values for the parameters. If for example the capacity would be halved, twice as many charging points would be needed. The solution is also very much influenced by the waste and shortage cost. It is very difficult to express the difference in costs coming from both consequences. Also, different objectives could be important by deciding on the optimal value for the different costs. Depending on the region and situation in which the model is applied, the parameters could be given different values.

The shortage and waste cost are increased such that the charging point type 2 share approximates the current share. This might be a limitation because it is impossible to predict exactly how the model will react in the different municipalities. In other words, the obtained share does not assure the same

proportion of type 2 charging points in each municipality separately. So can be seen that in the current infrastructure, in the 24 municipalities with the lowest demand zero charging point type 2 are placed, which is the case in the optimal solution. For the 6 municipalities with the largest demand, at least 11 charging point type 2 are placed, which is not the case in the optimal solution. An alternative way of incorporating type 2 charging points taking into account the size of the demand needs to be explored.

An optimal charging point infrastructure to serve only the BEV fleet is investigated in this research. PHEVs also rely on public charging points, albeit to a lesser extent. Therefore, the model could be extended to also incorporate this specific demand. This could be for example done by giving priority to pure EVs by giving them a higher weight in the model as PHEVs still can go to a normal gas station.

6.3. Directions for future research

This research can serve as basis and inspiration for some further research.

First of all, there could be investigated what the relation between the different types of charging points is. These findings could then be used to create a model in which there is decided upon the optimal number of charging points of each type (i.e. type 1 and type 2, but also fast chargers) based on other parameters than solely costs and capacity.

Secondly, as already mentioned in the previous section, the model could be extended such that also the PHEV demand would be taken into account.

Other objectives could be taken into account like for example minimizing traveled route, maximizing the amount of EVs served, maximizing utilization, etc.

Finally, the exact location problem of charging points for a municipality in Flanders could be investigated. This research could than serve as continuation on this research. The model could then be applied to each municipality separately after the exact amount of charging points that need to be installed is known. A combination in which the optimal amount and the exact location is investigated is of course also a possibility for future research.

References

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Attachments

Attachment 1: Current public charging points in every municipality in West Flanders according to charging speed (March 2020)

11 kW 22 kW 50 kW TOTAL Alveringem 6 0 0 6 Anzegem 8 0 0 8 Ardooie 6 0 0 6 Avelgem 6 0 0 6 Beernem 4 0 0 4 Blankenberge 6 10 0 16 Bredene 8 6 0 14 Brugge 81 27 3 111 Damme 6 0 0 6 De Haan 8 8 0 16 De Panne 8 8 0 16 Deerlijk 4 0 0 4 Dentergem 2 0 0 2 Diksmuide 14 4 0 18 Gistel 4 0 0 4 Harelbeke 14 0 0 14 Heuvelland 6 0 0 6 Hooglede 7 0 0 7 Houthulst 2 0 0 2 Ichtegem 2 0 0 2 Ieper 20 2 0 22 Ingelmunster 7 1 0 8 Izegem 16 2 0 18 Jabbeke 6 0 6 12 Knokke-Heist 14 22 0 36 Koekelare 6 0 0 6 Koksijde 12 10 0 22 Kortemark 8 0 0 8 Kortrijk 50 14 6 70 Kuurne 6 2 0 8 Langemark-Poelkapelle 4 0 0 4 Ledegem 2 0 0 2

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Lendelede 4 0 0 4 Lichtervelde 2 0 0 2 Lo-Reninge 6 0 0 6 Menen 18 2 0 20 Mesen 2 0 0 2 Meulebeke 6 0 0 6 Middelkerke 22 0 0 22 Moorslede 0 0 0 0 Nieuwpoort 10 10 0 20 Oostende 42 20 3 65 Oostkamp 6 0 0 6 Oostrozebeke 2 0 0 2 Oudenburg 8 0 0 8 Pittem 2 0 0 2 Poperinge 12 2 0 14 Roeselare 26 20 0 46 Ruiselede 2 0 0 2 Spiere-Helkijn 2 0 0 2 Staden 8 0 0 8 Tielt 8 4 0 12 Torhout 10 0 0 10 Veurne 8 4 0 12 Vleteren 2 0 0 2 Waregem 10 18 0 28 Wervik 8 0 0 8 Wevelgem 12 0 0 12 Wielsbeke 6 0 0 6 Wingene 4 0 0 4 Zedelgem 6 1 0 7 Zonnebeke 6 0 0 6 Zuienkerke 2 0 0 2 Zwevegem 8 0 0 8 TOTAL 623 197 18 838

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Attachment 2: Values of the demand for some scenarios for all the municipalities

SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO 1 2 3 4 5 6 16 17 18 19 20 21

Probability 0,0007% 0,0046% 0,0279% 0,1252% 0,4618% 1,4082% 1,5005% 0,4909% 0,1393% 0,0299% 0,0055% 0,0009% …

EV-to- 0,3864% 0,3894% 0,3925% 0,3956% 0,3987% 0,4018% 0,4325% 0,4356% 0,4387% 0,4418% 0,4448% 0,4479% … vehicle ratio

Personal Personal Total EVs Total EVs Total EVs Total EVs Total EVs Total EVs … Total EVs Total EVs Total EVs Total EVs Total EVs Total EVs vehicles vehicles SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO SCENARIO Municipality inhabitants tourists 1 2 3 4 5 6 16 17 18 19 20 21 Alveringem 2596,68 0 10,03 10,11 10,19 10,27 10,35 10,43 … 11,23 11,31 11,39 11,47 11,55 11,63 Anzegem 8212,02 0 31,73 31,98 32,23 32,49 32,74 33,00 … 35,52 35,77 36,03 36,28 36,53 36,78 Ardooie 5144,78 0 19,88 20,03 20,19 20,35 20,51 20,67 22,25 22,41 22,57 22,73 22,88 23,04 Avelgem 5297,59 0 20,47 20,63 20,79 20,96 21,12 21,29 … 22,91 23,08 23,24 23,40 23,56 23,73 Beernem 8058,21 0 31,14 31,38 31,63 31,88 32,13 32,38 … 34,85 35,10 35,35 35,60 35,84 36,09 Blankenberge 8430,60 1285,48 37,54 37,83 38,14 38,44 38,74 39,04 … 42,02 42,32 42,62 42,93 43,22 43,52 Bredene 8632,99 361,19 34,75 35,02 35,30 35,58 35,86 36,14 … 38,90 39,18 39,46 39,74 40,01 40,28

Brugge 57734,11 4567,80 240,73 242,60 244,54 246,47 248,40 250,33 … 269,46 271,39 273,32 275,25 277,12 279,05

Damme 6355,08 0 24,56 24,75 24,94 25,14 25,34 25,53 … 27,49 27,68 27,88 28,08 28,27 28,46

De Haan 6777,07 1134,25 30,57 30,81 31,05 31,30 31,54 31,79 … 34,22 34,46 34,71 34,95 35,19 35,43

De Panne 5385,63 1988,58 28,49 28,72 28,94 29,17 29,40 29,63 … 31,89 32,12 32,35 32,58 32,80 33,03

Deerlijk 11639,52 0 44,98 45,32 45,69 46,05 46,41 46,77 50,34 50,70 51,06 51,42 51,77 52,13 Dentergem 4456,65 0 17,22 17,35 17,49 17,63 17,77 17,91 … 19,28 19,41 19,55 19,69 19,82 19,96 Diksmuide 8831,34 0 34,12 34,39 34,66 34,94 35,21 35,48 … 38,20 38,47 38,74 39,02 39,28 39,56

Gistel 6382,41 0 24,66 24,85 25,05 25,25 25,45 25,64 … 27,60 27,80 28,00 28,20 28,39 28,59 Harelbeke 15018,44 0 58,03 58,48 58,95 59,41 59,88 60,34 … 64,95 65,42 65,89 66,35 66,80 67,27

Heuvelland 4368,61 0 16,88 17,01 17,15 17,28 17,42 17,55 … 18,89 19,03 19,17 19,30 19,43 19,57 Hooglede 5431,17 0 20,99 21,15 21,32 21,49 21,65 21,82 … 23,49 23,66 23,83 23,99 24,16 24,33

Houthulst 5310,74 0 20,52 20,68 20,84 21,01 21,17 21,34 … 22,97 23,13 23,30 23,46 23,62 23,79

Ichtegem 7367,04 0 28,47 28,69 28,92 29,14 29,37 29,60 … 31,86 32,09 32,32 32,55 32,77 33,00 Ieper 18546,12 0 71,66 72,22 72,79 73,37 73,94 74,52 80,21 80,79 81,36 81,94 82,49 83,07

Ingelmunster 6092,99 0 23,54 23,73 23,91 24,10 24,29 24,48 … 26,35 26,54 26,73 26,92 27,10 27,29 Izegem 15246,13 0 58,91 59,37 59,84 60,31 60,79 61,26 … 65,94 66,41 66,88 67,36 67,81 68,29 Jabbeke 7870,99 0 30,41 30,65 30,89 31,14 31,38 31,63 … 34,04 34,29 34,53 34,77 35,01 35,25 Knokke-Heist 18752,56 1966,03 80,06 80,68 81,32 81,96 82,60 83,25 … 89,61 90,25 90,89 91,53 92,16 92,80 Koekelare 4762,26 0 18,40 18,54 18,69 18,84 18,99 19,13 … 20,60 20,74 20,89 21,04 21,18 21,33 Koksijde 12496,64 1325,72 53,41 53,82 54,25 54,68 55,11 55,54 … 59,78 60,21 60,64 61,07 61,48 61,91 Kortemark 6876,24 0 26,57 26,78 26,99 27,20 27,42 27,63 … 29,74 29,95 30,17 30,38 30,59 30,80 Kortrijk 43574,83 0 168,37 169,68 171,03 172,38 173,73 175,08 … 188,46 189,81 191,16 192,51 193,82 195,17 Kuurne 7235,48 0 27,96 28,17 28,40 28,62 28,85 29,07 31,29 31,52 31,74 31,97 32,18 32,41 Langemark- 4146,99 0 16,02 16,15 16,28 16,41 16,53 16,66 … 17,94 18,06 18,19 18,32 18,45 18,57 Poelkapelle Ledegem 5166,03 0 19,96 20,12 20,28 20,44 20,60 20,76 … 22,34 22,50 22,66 22,82 22,98 23,14 Lendelede 3012,59 0 11,64 11,73 11,82 11,92 12,01 12,10 … 13,03 13,12 13,22 13,31 13,40 13,49 Lichtervelde 4662,08 0 18,01 18,15 18,30 18,44 18,59 18,73 … 20,16 20,31 20,45 20,60 20,74 20,88 Lo-Reninge 1674,79 0 6,47 6,52 6,57 6,63 6,68 6,73 … 7,24 7,30 7,35 7,40 7,45 7,50 Menen 16596,08 0 64,13 64,63 65,14 65,65 66,17 66,68 … 71,78 72,29 72,81 73,32 73,82 74,33

Mesen 503,95 0 1,95 1,96 1,98 1,99 2,01 2,02 … 2,18 2,20 2,21 2,23 2,24 2,26

Meulebeke 5983,70 0 23,12 23,30 23,49 23,67 23,86 24,04 … 25,88 26,06 26,25 26,44 26,62 26,80

Middelkerke 9518,46 794,61 39,85 40,16 40,48 40,80 41,12 41,44 44,60 44,92 45,24 45,56 45,87 46,19

Moorslede 6014,05 0 23,24 23,42 23,61 23,79 23,98 24,16 … 26,01 26,20 26,38 26,57 26,75 26,94 Nieuwpoort 6010,01 1060,58 27,32 27,53 27,75 27,97 28,19 28,41 … 30,58 30,80 31,02 31,24 31,45 31,67

Oostende 28879,20 2672,78 121,92 122,86 123,84 124,82 125,80 126,78 … 136,46 137,44 138,42 139,40 140,34 141,32 Oostkamp 12928,75 0 49,96 50,34 50,75 51,15 51,55 51,95 … 55,92 56,32 56,72 57,12 57,51 57,91

Oostrozebeke 4301,82 0 16,62 16,75 16,88 17,02 17,15 17,28 … 18,61 18,74 18,87 19,01 19,13 19,27

Oudenburg 5076,98 0 19,62 19,77 19,93 20,08 20,24 20,40 … 21,96 22,12 22,27 22,43 22,58 22,74 Pittem 3813,05 0 14,73 14,85 14,97 15,08 15,20 15,32 … 16,49 16,61 16,73 16,85 16,96 17,08

Poperinge 10180,28 0 39,34 39,64 39,96 40,27 40,59 40,90 … 44,03 44,35 44,66 44,98 45,28 45,60 Roeselare 34420,67 0 133,00 134,03 135,10 136,17 137,24 138,30 148,87 149,94 151,00 152,07 153,10 154,17

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Ruiselede 2990,33 0 11,55 11,64 11,74 11,83 11,92 12,02 … 12,93 13,03 13,12 13,21 13,30 13,39 Spiere-Helkijn 1201,19 0 4,64 4,68 4,71 4,75 4,79 4,83 … 5,20 5,23 5,27 5,31 5,34 5,38

Staden 6109,18 0 23,61 23,79 23,98 24,17 24,36 24,55 … 26,42 26,61 26,80 26,99 27,17 27,36 Tielt 11061,69 0 42,74 43,07 43,42 43,76 44,10 44,45 … 47,84 48,18 48,53 48,87 49,20 49,55 Torhout 10688,28 0 41,30 41,62 41,95 42,28 42,61 42,95 … 46,23 46,56 46,89 47,22 47,54 47,87 Veurne 6482,59 0 25,05 25,24 25,44 25,65 25,85 26,05 … 28,04 28,24 28,44 28,64 28,83 29,04 Vleteren 1885,27 0 7,28 7,34 7,40 7,46 7,52 7,58 … 8,15 8,21 8,27 8,33 8,39 8,44 Waregem 22624,30 0 87,42 88,10 88,80 89,50 90,20 90,90 … 97,85 98,55 99,25 99,95 100,63 101,33 Wervik 9421,31 0 36,40 36,69 36,98 37,27 37,56 37,85 40,75 41,04 41,33 41,62 41,91 42,20 Wevelgem 16794,42 0 64,89 65,40 65,92 66,44 66,96 67,48 … 72,64 73,16 73,68 74,20 74,70 75,22 Wielsbeke 5511,11 0 21,29 21,46 21,63 21,80 21,97 22,14 … 23,84 24,01 24,18 24,35 24,51 24,68 Wingene 7785,99 0 30,09 30,32 30,56 30,80 31,04 31,28 … 33,67 33,92 34,16 34,40 34,63 34,87 Zedelgem 12322,59 0 47,61 47,98 48,37 48,75 49,13 49,51 … 53,30 53,68 54,06 54,44 54,81 55,19 Zonnebeke 6745,70 0 26,07 26,27 26,48 26,69 26,90 27,10 … 29,18 29,38 29,59 29,80 30,00 30,21 Zuienkerke 1597,88 0 6,17 6,22 6,27 6,32 6,37 6,42 … 6,91 6,96 7,01 7,06 7,11 7,16 Zwevegem 13131,14 0 50,74 51,13 51,54 51,95 52,35 52,76 … 56,79 57,20 57,61 58,01 58,41 58,81

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Attachment 3: Model file of the implemented model in CPLEX int N = 3; /* Model set N*/ int I =64; /* Model set I*/ Int S =21; /* Model set S*/ int M=280; /* Parameter M*/ range chargingPointType=1..N; range municipality =1..I; range scenario = 1..S; float Ps[scenario]=...; /* Parameter !"*/ float wasteCost=...; /* Parameter #*/ float shortageCost=...; /* Parameter $*/ float installationCost [chargingPointType]=...; /* Parameter %&*/ float chargingPointCapacity [chargingPointType]=...; /* Parameter '&*/ float demand[municipality][scenario]=...; /* Parameter (),"*/ dvar int+ numberOfCPs [municipality][chargingPointType]; dvar boolean k[municipality][scenario];

/*minimize total cost*/ minimize sum(i in municipality, n in chargingPointType) numberOfCPs[i][n] *installationCost[n] + sum(s in scenario, i in municipality)Ps[s] *(wasteCost*k[i][s]*(sum(n in chargingPointType) numberOfCPs[i][n]*chargingPointCapacity[n]- demand[i][s]) + shortageCost*(1-k[i][s])*(demand[i][s]-sum(n in chargingPointType) numberOfCPs[i][n]*chargingPointCapacity[n]));

/* constraints*/ subject to { forall(i in municipality) sum(n in chargingPointType) numberOfCPs [i][n]>=1; /* Constraint (3)*/ forall(i in municipality, s in scenario) sum(n in chargingPointType) numberOfCPs [i][n]*chargingPointCapacity[n]-demand [i][s] <= M* k [i][s]; /* Constraint (4)*/ forall(i in municipality, s in scenario) demand [i][s]- sum(n in chargingPointType) numberOfCPs [i][n]*chargingPointCapacity[n] <= M* (1- k [i][s]); /* Constraint (5)*/

}

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Attachment 4: Optimal solution for the decision variables +),& for s = 18.013 and w = 8.920

11 kW 22 kW 11 kW 22 kW n=1 n=2 n=1 n=2 Alveringem 1 1 Lendelede 0 2 Anzegem 7 1 Lichtervelde 0 3 Ardooie 2 2 Lo-Reninge 2 0 Avelgem 4 1 Menen 17 0 Beernem 2 4 Mesen 1 0 Blankenberge 10 0 Meulebeke 3 2 Bredene 3 4 Middelkerke 9 1 Brugge 53 7 Moorslede 3 2 Damme 5 1 Nieuwpoort 1 4 De Haan 5 2 Oostende 23 6 De Panne 6 1 Oostkamp 7 4 Deerlijk 12 0 Oostrozebeke 3 1 Dentergem 3 1 Oudenburg 2 2 Diksmuide 9 0 Pittem 4 0 Gistel 5 1 Poperinge 1 6 Harelbeke 3 8 Roeselare 29 4 Heuvelland 3 1 Ruiselede 0 2 Hooglede 4 1 Spiere-Helkijne 0 1 Houthulst 4 1 Staden 0 4 Ichtegem 6 1 Tielt 2 6 Ieper 19 0 Torhout 11 0 Ingelmunster 0 4 Veurne 2 3 Izegem 11 3 Vleteren 2 0 Jabbeke 5 2 Waregem 17 4 Knokke-Heist 15 4 Wervik 5 3 Koekelare 5 0 Wevelgem 11 4 Koksijde 11 2 Wielsbeke 1 3 Kortemark 7 0 Wingene 8 0 Kortrijk 40 3 Zedelgem 8 3 Kuurne 6 1 Zonnebeke 7 0 Langemark-Poelkapelle 1 2 Zuienkerke 0 1 Ledegem 4 1 Zwevegem 1 8

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Attachment 5: Current public charging points (type 1 and type 2) in every municipality in West Flanders meant to serve the BEV market (March 2020)

11 kW 22 kW 11 kW 22 kW n=1 n=2 n=1 n=2 Alveringem 4,8984 0 Lendelede 3,2656 0 Anzegem 6,5312 0 Lichtervelde 1,6328 0 Ardooie 4,8984 0 Lo-Reninge 4,8984 0 Avelgem 4,8984 0 Menen 14,6952 1,6328 Beernem 3,2656 0 Mesen 1,6328 0 Blankenberge 4,8984 8,164 Meulebeke 4,8984 0 Bredene 6,5312 4,8984 Middelkerke 17,9608 0 Brugge 66,1284 22,0428 Moorslede 0 0 Damme 4,8984 0 Nieuwpoort 8,164 8,164 De Haan 6,5312 6,5312 Oostende 34,2888 16,328 De Panne 6,5312 6,5312 Oostkamp 4,8984 0 Deerlijk 3,2656 0 Oostrozebeke 1,6328 0 Dentergem 1,6328 0 Oudenburg 6,5312 0 Diksmuide 11,4296 3,2656 Pittem 1,6328 0 Gistel 3,2656 0 Poperinge 9,7968 1,6328 Harelbeke 11,4296 0 Roeselare 21,2264 16,328 Heuvelland 4,8984 0 Ruiselede 1,6328 0 Hooglede 5,7148 0 Spiere-Helkijne 1,6328 0 Houthulst 1,6328 0 Staden 6,5312 0 Ichtegem 1,6328 0 Tielt 6,5312 3,2656 Ieper 16,328 1,6328 Torhout 8,164 0 Ingelmunster 5,7148 0,8164 Veurne 6,5312 3,2656 Izegem 13,0624 1,6328 Vleteren 1,6328 0 Jabbeke 4,8984 0 Waregem 8,164 14,6952 Knokke-Heist 11,4296 17,9608 Wervik 6,5312 0 Koekelare 4,8984 0 Wevelgem 9,7968 0 Koksijde 9,7968 8,164 Wielsbeke 4,8984 0 Kortemark 6,5312 0 Wingene 3,2656 0 Kortrijk 40,82 11,4296 Zedelgem 4,8984 0,8164 Kuurne 4,8984 1,6328 Zonnebeke 4,8984 0 Langemark-Poelkapelle 3,2656 0 Zuienkerke 1,6328 0 Ledegem 1,6328 0 Zwevegem 6,5312 0