Feasibility study of an EV management system to provide Vehicle-to-Building considering battery degradation

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Feasibility study of an EV

management system to provide Vehicle-to-Building considering battery degradation






Feasibility study of an EV management system to provide Vehicle-to-Building considering battery degradation

Sofia Gon¸calves

Master’s Thesis at School of Electrical Engineering & Computer Science Supervisors: Meng song & Xue Wang

Examiner: Mikael Amelin Date: November 2018



The recent increase of electric cars adoption will influence the electricity demand in the distribution networks which risks to be higher than the maximum power available in the grid, if not well planned. For this reason, it is on the DSOs and TSOs’s interest to plan carefully coordinated charging of a bulk of EVs as well as assess the possibility of EVs acting as energy storages with the Vehicle-to-Grid (V2G) or Vehicle- to-Building (V2B) capability. When parked and plugged into the electric grid, EVs will absorb energy and store it, being also able to deliver electricity back to the grid/building (V2G/B system).This can be an optimized process, performed by an aggregator, gathering multiple EVs that discharge the battery into the grid at peak time and charge when there is low demand i.e. overnight and off-peak hours.

Numerous studies have investigated the possibility of aggregating multiple EVs and optimizing their charging and discharging schedules for peak load reduction or energy arbitrage with participation in the electricity market. However, no study was found for optimizing a shared fleet of EVs with daily reservations for different users trying to perform V2B. In this study an optimization modelling algorithm (mixed integer linear problem - MILP) that manages the possible reservations of the shared fleet of EVs, coordinates the charging and discharging schedules, and provides V2B (Vehicle-to-Building), with the objective of minimizing energy costs and accounting with battery ageing has been developed. A case study with real data for a building is carried out modelling different number of EVs for two different days in year 2017, one in March and other in June.

Results show that the profits are higher for all cases when introducing V2B as compared to a no opti- mization scenario: V2B with battery degradation (50 ¨ore/kWh) has decreased daily variable electricity costs between 54 and 59% in March and 60 and 63% for June when compared without smart charging. Integra- tion of battery degradation cost in V2B applications is necessary and influences significantly the charging and discharging strategies adopted by EV and finally the total daily costs: The total daily cost increase by maximal 10% for the day in March and 13% for the day in June when comparing the scenario that has stationary battery and uses only-charging model for EVs with the scenario applying V2B mode considering a degradation cost of 80 ¨ore/kWh.

Key words: Energy flexibility, Electric Vehicle (EV), Vehicle-to-grid (V2G), Vehicle-to-building (V2B), Local system operator, Residential distribution, Distributed energy resources, Energy storage;



Okningen av antalet elbilar kommer att p˚¨ averka lasten i eln¨atet som riskerar att bli h¨ogre ¨an kapacitet om det inte ¨ar v¨al planerat. D¨arf¨or ¨ar det i eln¨atsf¨oretags intresse att samordna laddningen av de flesta elbilarna samt att utv¨ardera m¨ojligheterna att anv¨anda elbilar som energilager gentemot eln¨atet (Vehicle- to-Grid,V2G) eller byggnader (Vehicle-to-Building, V2B). Vid parkering och anslutning till eln¨atet kommer elbilar att ladda energi och lagra den, samtidigt de kan leverera el tillbaka till eln¨atet eller byggnaden (V2G/V2B). Detta kan vara en optimerad process som utf¨ors av en aggregator genom att ladda flera elbilar i l˚aglasttimmar och ladda ur dem under h¨oglasttimmar.

M˚anga studier har unders¨okt m¨ojligheten att aggregera flera elbilar och optimera laddnings- och ur- laddningsplaner f¨or topplastreduktion eller energiarbitrage p˚a elmarknaden. Ingen studie har dock hittats f¨or att optimera en gemensam flotta av elbilar med dagliga reservationer f¨or olika anv¨andare som f¨ors¨oker utf¨ora V2B. Denna studie har utvecklat en optimeringsmodell (blandad heltalsprogrammering - MILP) som hanterar m¨ojliga reservationer av en flotta av elbilar, koordinerar laddning och urladdning planering, och utf¨or V2B f¨or att minimera energikostnader med h¨ansyn till batteriets ˚aldrande. En fallstudie f¨or en byggnad genomf¨ordes modellering av olika antal elbilar f¨or tv˚a dagar 2017, en i mars och andra i juni.

Resultaten visar att vinsten ¨ar h¨ogre i samtliga fall d˚a man introducerar V2B j¨amf¨ort med scenario utan optimering: V2B med batteriladdningskostnad 50 ¨ore/kWh minskade dagliga r¨orliga elkostnader mellan 54%

och 59% i mars och mellan 60% och 63% i juni j¨amf¨ort med utan smart laddning. Att inkludera batteriladd- ningskostnaden i V2B-applikationer ¨ar n¨odv¨andigt och har en signifikant inverkan p˚a laddningsstrategierna och de totala kostnaderna: De totala dagliga kostnaderna ¨okar med upp till 10% i mars och upp till 13% i juni d˚a man j¨amf¨or scenariot att bara ladda elbilar och ha station¨art batteri med scenariot V2B med h¨ansyn till batteriladdningskostnad 80 ¨ore/kWh.



Firstly, I would like to thank my supervisors Meng Song and Xue Wang for all their help, dedication and strong support during all these months. Without you, this would not be possible. I would also like to thank everyone in Power2U that helped me in this project and contributed with their knowledge. To Arshad Saleem for giving me the opportunity to work in this incredible project.

To my SELECT friends and colleagues, for accompanying me during our journey of this two year’s master and all the adventures that came with it. It was an amazing journey!

To my dear family that has always been very supportive during these two years and pushed me to aim for greater things everyday. Without you this would not be possible!

Last but not least, to Agust´ın, thank you for being present everyday and give me the strength to go through.



• ACC - Achievable Cycle Count

• BEV - Battery Electric vehicle

• BMS - Battery Management System

• CHP - Combine Heat and Power

• DSO - Distribution System Operator

• DER - Distributed Energy Resources

• DOD - Depth of Discharge

• EV - Electric Vehicle

• EVSE - Electric Vehicle Supply Equipment

• HVAC - Heating, ventilation, and air conditioning

• ICV - Internal Combustion Vehicle

• I2V - Infrastructure to Vehicle 1item LiFePO4 or LFP - lithium iron phosphate

• LSO - Local System operator

• MILP- Mixed integer linear problem

• PHEV - Plug-in Hybrid Electric Vehicle

• PPA - Power Purchase Agreement

• RMSE - Root mean squared error

• SOC - State of Charge

• VAT - Value Added Tax

• V2B - Vehicle to Building

• V1G - Grid-to-vehicle

• V2G - Vehicle to Grid

• V2H - Vehicle to Home

• V2I - Vehicle to Infrastructure

• V2L - Vehicle to Load

• TSO - Transmission System Operator



1 Introduction 1

1.1 Background . . . 1

1.2 Purpose of the study . . . 2

1.3 Thesis structure . . . 3

2 Literature review 4 2.1 Nordic electricity system . . . 4

2.2 Vehicle-to-Grid and to Building . . . 8

2.3 Battery Degradation . . . 11

2.4 Studies developed . . . 13

3 Methodology and Case study 15 3.1 Methodology . . . 15

3.1.1 Objective Function . . . 16

3.1.2 Constraints . . . 16

3.1.3 Battery degradation model . . . 18

3.2 Case study . . . 21

3.2.1 Building data . . . 21

3.2.2 Vehicles data . . . 23

3.3 Assumptions . . . 23

4 Results 25 4.1 EVs ’Just charging’ . . . 25




4.1.1 Scenario 1.1 - No battery storage and grid limits . . . 25

4.1.2 Scenario 1.2 - No battery storage and imposed grid limits . . . 26

4.1.3 Scenario 1.3 - With battery storage and imposed grid limits . . . 28

4.2 Vehicle-to-Building . . . 31

4.2.1 Scenario 2.1 - No battery storage . . . 31

4.2.2 Scenario 2.2 - With battery storage . . . 33

4.2.3 Scenario 2.3 - With battery storage and EVs battery degradation . . . 36

4.2.4 Sensitivity Analysis . . . 39

5 Discussion 41 6 Future Work and Conclusion 44 6.1 Future Work . . . 44

6.2 Conclusions . . . 45


List of Figures

2.1 Overview of Local System Operator mode of operation for this study case . . . 7

2.2 Peak electricity demand in Norwegian houses (detached) with home charging.(Power connec- tion for the small house is the lowest blue line) source: [1] . . . 11

3.1 Diagram flow of optimization process . . . 15

3.2 Cash flow diagram for the model of battery degradation (dc is a cost). [2] . . . 19

3.3 Iterative process based on [2] . . . 20

3.4 Building Loads for one day in January and in May . . . 21

3.5 Hourly prices (¨ore/kWh) for one day in March 17 and for June 2017 . . . 22

4.1 Total power and effects on building for 2 EVs (upper-left), 4 EVs (upper-right), 10 EVs (lower-left) and 20 EVs (lower right) of scenario 1.2 for one day in March . . . 27

4.2 Total power and effects on building for 2 EVs (upper-left), 4 EVs (upper-right), 10 EVs (lower-left) and 20 EVs (lower right) of scenario 1.2 for one day in June . . . 28

4.3 Total power and effects on building for 2 EVs (upper-left), 4 EVs (upper-right), 10 EVs (lower-left) and 20 EVs (lower right) of scenario 1.3 for one day in March . . . 29

4.4 Total power and effects on building for 2 EVs (upper-left), 4 EVs (upper-right), 10 EVs (lower-left) and 20 EVs (lower right) of scenario 1.3 for one day in June . . . 30

4.5 Total power and effects on building for 2 EVs (left), 4 EVs (right) of scenario 2.1 for one day in March . . . 31

4.6 Total power and effects on building for 10 EVs (left) and 20 EVs (right) of scenario 2.1 for one day in March . . . 32

4.7 Total power and effects on building for 2 EVs (upper-left), 4 EVs (upper-right), 10 EVs (lower-left) and 20 EVs (lower right) of scenario 2.1 for one day in June . . . 33




4.8 Total power and effects on building for 2 EVs (upper-left), 4 EVs (upper-right), 10 EVs

(lower-left) and 20 EVs (lower right) of scenario 2.2 for one day in March . . . 34

4.9 Total power and effects on building for 2 EVs (upper-left), 4 EVs (upper-right), 10 EVs (lower-left) and 20 EVs (lower right) of scenario 2.2 for one day in June . . . 36

4.10 Total power and effects on building for 2 EVs (left) and 4 EVs (right) of scenario 2.3 for one day in March. . . 37

4.11 Total power and effects on building for 10 EVs (left) and 20 EVs (right) of scenario 2.3 for one day in March. . . 37

4.12 Total power and effects on building for 2 EVs (upper-left), 4 EVs (upper-right), 10 EVs (lower-left) and 20 EVs (lower right) of scenario 2.3 for one day in June . . . 38

4.13 Degradation costs for all cases in March . . . 39

4.14 Total costs dependent on degradation costs for all cases in March . . . 39

4.15 Degradation costs for all cases in June . . . 40

4.16 Total costs dependent on degradation costs for all cases in June . . . 40

5.1 Total costs for the 2 and 4 EVs case in all scenarios in March . . . 41

5.2 Total costs for the 2 and 4 EVs case in all scenarios in March . . . 42

5.3 Total costs for the 2 and 4 EVs case in all scenarios in June . . . 42

5.4 Total costs for the 10 and 20 EVs case in all scenarios in June . . . 42


List of Tables

2.1 Main differences between V2G, V2B and V2H [3] . . . 9

3.1 Case description: Number of EVs and accepted reservations . . . 23

3.2 Scenarios description . . . 24

4.1 Results Scenario 1.1 for all cars for one day in March . . . 25

4.2 Results Scenario 1.1 for all cars for one day in June . . . 26

4.3 Results Scenario 1.2 for all cars for one day in March . . . 26

4.4 Results Scenario 1.2 for all cars for one day in June . . . 27

4.5 Results Scenario 1.3 for all cars for one day in March . . . 28

4.6 Results Scenario 1.3 for all cars for one day in June . . . 29

4.7 Results Scenario 2.1 for all cars for one day in March . . . 31

4.8 Results Scenario 2.1 for all cars for one day in June . . . 32

4.9 Results Scenario 2.2 for all cars for one day in March . . . 34

4.10 Results Scenario 2.2 for all cars for one day in June . . . 35

4.11 Results Scenario 2.3 for all cars for one day in March . . . 36

4.12 Results Scenario 2.3 for all cars for one day in June . . . 38



Chapter 1


1.1 Background

With current concerns about climate change, governments and institutions all over the world are taking action in order to tackle this challenge. Since the transportation sector is one of the major sources of CO2 emissions within the EU, the need to reduce emissions in this sector is inevitable. Cars and vans represent the majority of transport emissions and are responsible for 15% of overall CO2 emissions in the EU [4].

Thus, for transportation, the European Commission stated the goal to reduce the greenhouse gas emissions by around 20% until 2030 compared to emissions in 2008, and by 60% until 2050 compared to 1990 [5].

One of the broadest accepted solutions is the electrification of the transportation sector in order to reduce CO2 emissions and fossil fuel dependency. For these reasons, investments in developing electric vehicles are booming and these are gaining increasing shares all over the world. Especially, in the Nordic countries, the share of EV went up by 46% in 2017 compared to 2016, hitting a new record in absolute numbers of new sales[1]. Also, energy storage solutions were recognized to be a key element in helping to accommodate the grid with the growing number of distributed energy resources (DER): battery storage is among the most efficient and compatible technologies for an improved power system operation and control with large renewable-based electricity generation. The operation of storage systems is complementary to the stochastic nature of renewable energy. They can charge whenever there is an excess of electricity in the connected system and discharge when required.

The new relationship between the electric vehicles and the distribution networks will also impose a number of challenges to system operators ( planning, operation, and control of the electric grid) that needs to be taken into account to avoid undesirable effects, such as increased power losses and degraded power quality. Denmark estimates that its network can handle 100 000 EVs, translating to a stock share of 5%, after which grid reliability issues may start to arise [6]. To prevent this impact on the performance, it is necessary to avoid uncoordinated charging and to plan the charging and discharge properly, since these will definitely introduce a change in the overall load profile of a power system.

For the utility, the EVs are seen as dynamic loads hard to schedule but also as a potential back up for the electric grid. And for the EV owners, they have a notion that will considerably decrease the operating costs when compared with owning an internal combustion vehicle, nonetheless most people are not willing



1 Introduction 2

to pay for the higher up-front cost when they are not completely aware of the full benefits that the EV can provide.

EV fleets were recognized as an opportunity to play a big role as dynamic energy storage systems when they are aggregated and controlled smartly, allowing energy savings. On top of that, multiple studies show EVs should be used in idle times (using the extra energy in their batteries when is not needed for driving or when the EV is just parked (90% of the time accordingly to studies [7]) . The energy can be discharged from a vehicle to grid (V2G), to a building (V2B), or even to another vehicle (V2V) [3]. V2G enables the EV to both charge and discharge electricity to the grid, but is only possible with a bi-directional power converter, which has been commercialized by some manufacturers but still in development/testing phase for most Electric vehicle brands [8]).

It is expected that enabling the V2G capability will help to increase the efficiency, reliability and perfor- mance of the system in a near-term future. The battery of an EV can be charged when the other demand in the grid is low, and the stored power can be fed back to the grid during the peak hours. Aggregating the batteries of a fleet of many EVs, will gather a representative battery capacity and help to stabilize the grid’s voltage and frequency, by providing ancillary services to the grid and therefore improve the reliability of the system. Also, through V2G, EV owners can potentially generate revenues while charging their cars and at the same time alleviate the negative impacts on the grid from charging. In order to implement effective smart charging and discharging strategies for EV fleets, new actors are appearing in the market, such as ag- gregators and also local system operators (LSO), which will be explored further in this work. Despite having many recognized advantages, the V2G/V2B capability brings concerns relating the batteries, since these can experience premature battery degradation, due to limited cycle life of actual batteries. When performing V2G, there is a loss of capacity in the battery produced by the repetitive process of charging and discharging and depends on number of cycles, deep of discharge level (DOD), temperature and charging/discharging rate (C-rate). Studies suggest that nowadays, the cost of battery degradation resulting from discharging is high enough to make V2G unprofitable [9]. Accounting with battery wear will allow measuring the financial and technical feasibility of these applications in a realistic way.

This increasing importance of the EVs and their value has been explored both by industry and academia and in recent years, more and more studies continue to be published about the best charging/discharging strategies and their impact on the grid operation ([10, 11, 12]), local load profiles ([7, 13]), buildings/homes ([14, 15]).

1.2 Purpose of the study

This thesis project was developed in line with a project of EVs implementation in the residential sector with

”Power2U”, a local system operator based in Stockholm, Sweden. The LSO partners with a Residential real-estate, that owns a building, where the LSO installs a shared fleet of EVs with its respective charging stations directly connected to the building. These buildings are also being loaded with power from a PV system and have a stationary battery storage system. This project intends to develop an optimization modelling algorithm that manages the possible reservations of the shared fleet of EVs, coordinates the charging and discharging schedules, and provides V2B (Vehicle-to-Building) with the objective to minimize electricity costs for the residential building. The study will answer the following research questions:


1 Introduction 3

1. How to manage the energy storage that a shared EV fleet can provide to control peak loads for the facility in a residential community, coupling it with battery storage and PV panels?

2. Until which degree, using EVs as distributed energy storages, the V2B capability will help to increase the efficiency and performance of the system?

• Would it be possible to decrease the present peak facility load of a residential building by using V2B capability and satisfying the same number of reservations as in the charging only mode?

• How are the charging and discharging profile for multiple reservations in one day?

• Accounting with the EVs battery degradation, will there be any profits in using the cars for the reservations and discharging extra energy for the building?

3. Feasibility: What will be the most feasible Technical and/or Economical scenarios/solutions for com- mon household types (Multi-apartment) with integrated EV charging?

1.3 Thesis structure

This report is organized in: chapter 2 describing the relevant concepts of the electricity market in Nordic countries, Vehicle-to-Building and other important studies for the project. Chapter 3 provides the description of the methodology (section 3.1), including the mathematical formulation, followed by the Case study (section 3.2). Chapter 4 presents all the results divided in three sections. Finally, chapter 5 and 6 contains the discussion and future work and conclusions, respectively.


Chapter 2

Literature review

This chapter intends to sum up the important information needed to understand completely: the electricity market in the Nordic countries, the state of art of Vehicle-to-Building implementation and relevant studies for this project.

1. Description of the value chain electricity system and different actors: Electricity Market structure and organization in Nordic countries;

2. Describe V2B and opportunity for using EV as energy storages for peak load at Residential level:

Requirements, advantages and disadvantages; Aggregator concept;

3. Analysis of studies of EVs/V2B connected to Residential Buildings: Analysed parameters, Implemented methodologies and models, benefits achieved.

2.1 Nordic electricity system

In this section, an introduction to the Nordic electricity system is given: Firstly, a general overview of how it is organized physically and organizational, secondly who are the actors of the Nordic electricity market (in Sweden) and which roles do they have;

Power has become a vital part of our lives and nowadays the electricity market is a complex system for purchase and sale of energy between multiple stakeholders- producers, retailers, and consumers. Transmission System Operators (TSO) and Distribution System Operators (DSO) are crucial to facilitate the interactions between all the stakeholders and ensure that final consumers receive a reliable and secure supply of electricity.

On the market side, producers can sell their electricity to large consumers, Retailers -which in turn sell it to the consumer, or to the Power Exchange market.

Grid Operators

In conventional electricity grids, the energy is generated in large power plants and electric power is transmitted through the transmission system and from there to the Distribution system in one-way flow. In Sweden, the power grid is divided into three categories: the national grid (which is part of the transmission grid), regional and local grids (Distribution grids)[16].

The transmission system usually deals with high or very-high voltages, covering power lines and cables



2 Literature review 5

of 220 kV or 400 kV (in Sweden). The transmission system connects to the distribution system through a substation which transforms the electricity from high voltage to medium voltage. The regional grid, with a voltage between 20 kV and 130 kV, is the interlink that connects the national grid to the local grids, some generation plants, and large power intense industries. The local grids support a voltage between 0.4 kV and 20 kV and transfer the electricity to the end customers, such as Residential and commercial buildings. there is one state-owned Transmission System Operator (TSO) in Sweden - Svenska kraftn¨at which manages the national grid and is responsible for maintaining the balance between production and consumption of the electricity in the whole country. The TSO must ensure the reliability of the electricity system at a national level and the ability to cope with critical situations.

As for the distribution side, there are around 170 DSOs that own and operate local and regional distri- bution grids and operate as local monopolies varying in each region in the country. Electricity generated at a small scale is also fed directly into to the local grid.

Nordic Power Exchange market

Nord Pool is the formal marketplace, having three markets: the spot market, the intra-day market and the real-time balancing market. In the spot market/day-ahead, electricity is traded on an hourly basis and the price of power is determined accordingly to the balance between supply and demand. The day-ahead market receives bids and offers from producers and consumers and calculates an hourly price, as a balance between supply and demand. Nord Pool publishes daily the energy price for each hour of the coming day, the spot price, which is used by the players within the Nordic electricity market. The Elspot market, where the day-ahead prices are defined, provides price transparency, since is publicly available online, and reliability[5].

In addition to this, there is a final balancing process for fine adjustments in the real-time balancing market.

This market operator is also responsible for creating the rules and formulates agreements and procedures for trading electricity in the country, and between the Nordic and Baltic countries.

Nord Pool integrates Sweden, Norway, Denmark, Finland, Estonia, Latvia, Lithuania, Germany and the UK in the largest and leading electricity market in Europe[17]. The users of Nord Pool Spot are energy producers (public and private), energy-intensive industries/large consumers, distributors, funds, investment companies, banks, brokers, utility companies who have chosen to trade on this power exchange market.

Power Retailers

In Sweden, the electricity market was deregulated in 1996, to create competition in the production and retail within the electricity market. The retailers buy electricity through Nord Pool and supply it directly to the consumers, having a commercial agreement with them. In other words, the retailers are responsible to deliver to other retailers and to the end users only the prices and the electricity bills.


The introduction of the prosumers on the electricity market shifts the traditional structure and poses opportunities and threats to existing players on the market. The decentralized energy market that is being built already, with prosumers taking bigger roles, will oblige the traditional market players to rethink their business models. As a prosumer, one of the most typical examples is having installed solar panels in the household roof, coupled with battery storage or not: the household generates solar power and consumes or stores the electricity generated accordingly to the needs of the household. There are multiple types of


2 Literature review 6

contracts but the most typical ones in Sweden are PV ownership by prosumer, power purchase agreement (PPA) or leasing contract.

If the prosumer owns their PV system, the household generates solar power and consumes the electricity generated if the consumption at that given time is greater than the solar production. When solar production is not sufficient to power the house, electricity is bought directly from the grid via a standard contract with an electricity company. If the production is greater than the consumption, electricity will be sold to the grid. When the PV system is coupled with Battery storage, instead of selling the excess electricity generated by the solar cells directly to the grid, the electricity is stored in batteries to be used or sold later when the electricity spot price is higher.

Through a power purchase agreement (PPA) that is signed between two parties, usually an energy company (retailer) and an individual or other company. The energy company installs the PV system on the customer’s household and connects it to the building’s energy supply, being responsible by the installation, design, financing and permitting of the PV system. Under the PPA agreement, the prosumer is obliged to buy all the power generated by the PV system[18], typically at a lower price than the local utility’s retail rate.

This lower price and the low risk investment are the incentives to the customer to adopt a PPA solution. As for the energy company, it receives the incomes from the generated electricity and also tax credits and other incentives which might be generated from the system. Eneo Solutions is one of the first energy companies to adopt the PPA solution in Sweden for businesses. J¨arf¨alla Municipality signed a PPA agreement with Eneo binding the energy company to supply ten properties with a total of 745 kW of PV [19].

Another type of contract is leasing, where an energy company leases the PV system to the property owner. The energy company is usually responsible for installation, operation and maintenance. The prop- erty owner, an individual or a housing cooperative, pays a monthly fee which is calculated by estimating the amount of electricity the system will produce and the contract often runs over 20 years [18]. The prosumer, in this case, does not pay for any power that the PV systems generate. Instead, the energy can be used in the facility or it can be sold to the grid to generate revenue.

Local System Operator

Local System Operator (LSO) is a new concept that consists of an energy operator which links the energy consumers and the DSO and the main objective is to manage an aggregated load of a specific building/s or area. With the conventional retail contract, customers will buy or sell electricity at a predefined price (flat or spot-price) from a typical retailer.

With an LSO acting as a local retailer, creating local energy & flexibility contracts and ensuring clarity and transparency, all consumers, prosumers and producers can buy or sell electricity through the LSO which then negotiates with an energy retailer, as can be seen in Figure 2.1 .


2 Literature review 7

Figure 2.1: Overview of Local System Operator mode of operation for this study case

Alternative local Peer-to-Peer contracts are introduced to complement the conventional retail contract by introducing more favourable energy prices for local producers and prosumers to sell the renewable generation to the local market [20].

The LSO has multiple roles: can perform optimization of flexibility loads (as an aggregator), energy planning, energy storage scheduling (as an energy storage manager) and EV scheduling (as an EV operator) to provide grid and community services. It operates using Information Communication Technology (ICT) to connect the data control automation system with the DSO meter. The LSO uses the DSO electricity meter data and acts as smart sub-meter, that functions ‘behind-the-meter’, as represented in figure 2.1 .

In this concept, the whole building will have a single aggregated load that will be read by a single meter, that could possibly change the fuse size and reduce the overall grid fee.


2 Literature review 8

2.2 Vehicle-to-Grid and to Building

This section is intended to describe: General definition of V2B system, differences between unidirectional and bidirectional, benefits and disadvantages/barriers for EVs adoption and the types of charging strategies.

EVs offer a unique technological advantage as flexible energy storages since they can use one of their many features: Charging service- commonly referred to as the grid-to-vehicle (V1G) or discharging service known as Vehicle-to-Grid (V2G).

The V2G enables the EV to both charge and discharge electricity to the grid, facilitated by a bi-directional power converter which is purchased by the Electricity utility. The main difference of V2G in comparison to regular smart charging (‘V1G’) is the discharge functionality. By having the possibility to discharge, avoids the situation where the battery is full and the car just stands idle, 90% of the day according to studies [21].

EVs having V2G system can be seen as a source of backup for renewable resources. These features can enable ancillary services including spinning reserve and control of voltage and frequency ([10, 22, 23]).

Despite EVs multiple benefits, there are a number of significant barriers to car owners’ adoption of an EV such as: travel needs, charging infrastructure, up-front and ownership costs.

Related to the infrastructure, the low availability of recharging stations outside urban areas forces the EV owners to be always looking for charging places when they want to make a longer trip (especially on freeways) and causes the effect known as range anxiety, which is the fear that a vehicle has insufficient range to reach its destination. Despite that, range anxiety is becoming a lesser problem: accordingly to a 2016’s study by the MIT it was shown that a car with a mere range of 80 miles, the Nissan LEAF, for example, was sufficient to cover 84 to 93% of the daily trips of a regular citizen in a developed country[24]. Furthermore, as the batteries kWh capacity increase and cell’s cost decreases, 90% of existing vehicles can be replaced by Electric Vehicles by 2020”. Range anxiety and low availability of charging infrastructures are seen as the most decisive factors that make consumers reluctant to buy EVs. In the UK a network of rapid chargers was deemed the most efficient way to complement overnight charging at home [25].

Currently nearly (90%) of the charges from an EV during its lifetime actually takes place in buildings: at home overnight or daily at the workplace. This creates an opportunity of accordingly equipping the Euro- pean buildings with EV charging possibilities to make them the preferred choice for families and commuters.

Measures are taking place,and the European Commission passed on regulations on Building’s directive which states that larger new and renovated commercial buildings and residential buildings with more than 10 park- ing spaces require at least one charging point or are equipped with ducting infrastructure, respectively[26].

As for the economic reasons, it is widely known that battery costs currently determine that EVs are more expensive to produce than internal combustion vehicles (ICVs), although battery prices are falling more rapidly than anticipated at a rate of around 8% annually [27]. To fight high up-front costs, incentives for electric car purchases have been created by governments to reduce barriers for customers related to the high upfront costs of electric vehicles. The purchase price of cars is high due to the VAT and registration tax structures. Purchase prices for BEVs and PHEVs are reduced in several Nordic countries with support mechanisms, such as direct purchase subsidy (super green car rebate) in Sweden[1].

With the development of EVs, new applications for using BEVs and PEVs are coming up, with the same principle as V2G, such as: EVs discharging the energy surplus from the battery back to residential houses called Vehicle-to-home (V2H) or back to buildings, called Vehicle-to-Building (V2B), vehicle-to-load (V2L),


2 Literature review 9

and vehicle-to-vehicle (V2V). V2H includes using the EV as a home generator during periods of electrical outages and for increasing self-generated renewable energy consumption.

The Vehicle-to-Building (V2B) concept was introduced in 2008 [28] as a subclass of the V2G idea, where EVs would exchange electrical energy with a building and provide demand-side management features to either reduce electricity costs and/or optimize the building energy consumption. In this case, the energy delivered back from the vehicle is limited to the building, not going to the main grid. The main differences between the three most known kinds of Vehicle-to-X, are presented in Table 2.1.

Vehicle-to-Grid (V2G) Vehicle-to-Building (V2B)

Vehicle-to-Home (V2H)

Scale Operation at large scale Building level Home level

Fleet size Large fleets (100EVs) Small fleets Normally one

Market Ancillary services market:

Frequency regulation and op- erating reserve

Currently no market

Reduced peak loads and valley-filling at building

Provide backup power/ Pro- vide energy to off-grid homes

Advantages Large scale RES integration Increase local DER integra- tion

Reduce their vehicle/home operating costs; Increase power reliability

Barriers Complex operation:software platforms and equipment to control distributed vehicles

Legal barriers and complex- ity with interaction with DSO

Simpler operation since each consumer can choose it’s re- tailer

Projects NewMotion V2G[29] SMART Solar Charging[30] SEEV4City[31]

GridMotion[32] Solar-powered bidirectional EV charging station [33]

Nissan to Home[34]

Table 2.1: Main differences between V2G, V2B and V2H [3]


2 Literature review 10

Main barriers for V2G/V2B technology:

Currently the majority of the work and projects in the V2G/V2B field, are at the trial stage with the objective to improve the user interface and commercial agreements [3]. The main barriers are:

1. V2G/V2B technology needs to allow bi-directional charging which requires additional hardware not currently included in most EVS produced. For this reason, the standardization of this technology is still lacking, with currently, only one type of connector is capable of V2G, the “CHAdeMO” DC connector and it is not used in homes but in public charging points [35].

2. V2G/V2B requires advanced metering and information and communication control systems that assure real-time communication between charging points, EVs, aggregators and grid operators to control the charging/discharging of EVs. One concern in this context is the security of communications and the interoperability required to maximize the number of actors the vehicle will be able to communicate with.

3. To avoid undesirable effects to the grid, such as overloading or decrease in power quality , the load of vehicles should be carefully controlled and anticipated earlier. However, the uncertainty surrounding the number of parked vehicles and the total energy and power they can commit delivering to the grid at any given time due to the lack of aggregation is still a barrier.

4. The battery lifetime for batteries providing V2G is shorter since these go through extra degradation than G1V.

Characteristics of charging stations and charging points

With the evolution of electric vehicles, the charging technologies also continue to innovate and several standards which vary from region to region have become commonly adopted across the industry. The charging time depends on multiple factors such as the capacity and type of battery of the EV, the capacity and efficiency of the on-board charger and the temperature of the battery. On the charging equipment side, depends on the charging power, the cable size, and the supply circuit.

The charging power can vary by different orders of magnitude depending on the electric vehicle supply equipment (EVSE) outlet. An EVSE is part of the charging station providing energy for an EV via an outlet and which is connected to a smart meter. One charging station can have two different or more EVSEs that is able to charge two EVs at the same time, each with an unique EVSE ID. Also, one EVSE can have one or more outlets (different charging modes as CHAdeMO or Type 2)[36]. Plug-in charging is when vehicles are physically connected to a charging point, using a cable and a plug, and it’s the most common method for the majority of BEVs and PHEVs across Europe. The charging power depends on the type of plug, socket and connectors: a household outlet alone can charge as slow as 3.7 kW whereas the most advanced fast charging stations can charge up to 350 kW. Home chargers of the newest electric car models, with a power rating that is typically 3-7 kW, add a significant load to the electricity consumption of a household, if not charged smartly (see figure 2.2).


2 Literature review 11

Figure 2.2: Peak electricity demand in Norwegian houses (detached) with home charging.(Power connection for the small house is the lowest blue line) source: [1]

2.3 Battery Degradation

Most electric vehicles batteries nowadays are lithium-ion based due to its high energy capacity, the possibility of fast charging and long lifetime. When the battery is charged and discharged once, it is named a cycle. The battery’s capacity degrades as the number of cycles increases. For this reason, the battery life is sometimes provided by manufacturers with reference to a standard of cycles, that the battery can perform before its normal capacity falls below 80% of its initial rated capacity.

The State of Charge (SOC) and Depth of Discharge (DOD) are two ways of describing the charge level of the batteries. The SOC is the remaining capacity of a battery and is affected by its operating conditions such as current and temperature, and when the cell is fully charged is 100%. DOD is the percentage of battery capacity that has been discharged expressed as a percentage of maximum capacity. A discharge to at least 80 %DOD is referred to as a deep discharge. Also, a very common term when talking about batteries is the C-Rate, which is a measure of the rate at which a battery is discharged relative to its maximum capacity. A 1C rate means that the discharge current will discharge the entire battery in 1 hour[37]. The voltage goes up as the lithium-ion battery is charged, achieving full charge when the battery reaches the voltage threshold and the current drops to 3 % of the rated current [38]. Overcharging the battery cells above the maximum voltage of the cell terminal should be avoided because it ruins battery life, can cause battery destruction or overheating and even fires[39].

The monitoring and regulation of the battery SOC is done by a Battery Management System (BMS) that uses a battery analytical model and consists of hardware and software installed in the EV itself. The BMS has several features to control and monitor the states of the battery at different battery cell, battery module, and battery pack levels[40].The batteries of an EV must deliver a specific amount of energy to the drive-train during operation but also provide power in different types of roads (depending on the slope or type of road). For this reason, it is crucial to know the maximum power that can be delivered to and from the battery, by charging/discharging, together with the knowledge about SOC in order to decide on the operation of the EV.

With the increasing interest in EVs, one of the most important issues for manufacturers is to optimize the EVs battery longevity ensuring the safety simultaneously and for this reason, the batteries go through


2 Literature review 12

strenuous life cycle testing. Accounting for battery degradation in charging and discharging optimization models is important because Li-ion batteries represent the major component of the vehicle cost. Despite the incentives that V2G brings, a key concern has been the impact of discharging operations on the degradation of Lithium-ion batteries – which is central to both EV and V2G operations.

There are two main criteria to estimate the real-life cycle of a battery: calendar or storage life that estimates the retainable duration without considering the cycling of the battery. The second is cycle life, that represents the achievable number of charge-discharge cycles that the battery can go through before its capacity goes below 80% of the initial rated capacity. Since the calendar life is independent of the charging strategies and only affected by the storage conditions, this parameter won’t be taken into account in this study. The loss in cycle life is linked to the decrease of active lithium ions due to the electrochemical parasitic reaction and rise of the anode film resistance.

The rate of battery degradation depends on how the battery is used, which is typically influenced by the following ageing stress operational factors:

1. Magnitude and rate of charging and discharging current (C-Rate): studies have defended that high charge and discharge currents accelerate the degradation of batteries. However, in case the charging power is limited to small kilowatts, as home charging (3-7 kW), when compared to the batteries capacity (24-100 kwh), the current rate would be less than 0.1-0.2 C, which is negligible, when compared to other parameters [41].

2. Average State of Charge(SOC): studies defend that the loss of capacity of the battery is different depending on the operating SOC. Bashash et al. concludes that there is an exponential relationship between calendar ageing and SOC: battery internal resistance increases as SOC increases. Thus, keeping battery levels always at high SOCs, can increase battery degradation in some cases[42].

3. The depth of discharge (DOD) is considered as one of the major factors that limits the cycle life for certain lithium-ion batteries is DOD due to reactions with deposited lithium. The Depth of Discharge shows the percentage of the total battery capacity that has been discharged. The relation of DOD and SOC is given by: DOD = 1 − SOC. Li-ion batteries can be partial discharged, there is no memory and the battery does not need periodic full discharge cycles to prolong life. Usually, manufacturers suggest that in order to achieve higher life cycle, 100% DOD must be avoided and that cycling the battery at a extremes DOD can dramatically reduce the number of lifetime cycles for lithium-ion batteries.The relation between cycle life and the depth of discharge appears to be logarithmic, meaning that the number of cycles yielded by a battery goes up exponentially the shallower the DOD, as suggested by ([43]). The cycle life increases faster that the DOD reduction. This is important since it means that using a larger battery at a smaller DOD can become more economic than using a smaller battery capacity with 100% depth of discharge.

4. The total energy throughput: the total amount of energy charged and discharged from the cell, is usually one typical parameter used to measure battery degradation. This approach links capacity fade to the severity of charge occurrences and assumes a finite amount of energy which can be processed by the battery [44]. Research indicates that charging and discharging at high currents, cause different degrees of battery degradation and the deterioration level associated with charging is more noticeable[2].

5. Temperature: Elevated ambient temperatures have direct effect on the battery wear since they acceler- ate the growth of electrode film resistance which causes the loss of charging capacity. However, working


2 Literature review 13

within normal operating conditions, the life cycle would not change significantly, according to research [2]. On the other hand, the charge current is small in EVs applications (as explained before),and so the temperature variation will be negligible.

Despite batteries with identical chemistries show similar characteristics, the exact wear behaviours differs from battery to battery and therefore can only be identified by manufacturer specifications. These spec- ifications are mostly based on the experimental data, which is costly and time-consuming. Consequently, the manufacturers provide very limited data. The most typical cycle life specification is in the form of the achievable cycle count (ACC) with respect to the DOD for several temperature conditions [9]. The actual battery degradation is only known by experimenting various DOD levels, by repeating thousands of charging and discharging, and estimating the battery cycle life. The battery chemistries influence to a great extent how the different factors are affected by the operation mode and in consequence, the degradation. For this reason, it is critical to create individual models that reflect the unique characteristics of each battery and not generalize a model for all EV batteries.

2.4 Studies developed

Multiple studies address the issues around EV charging scheduling in Residential distribution systems, considering RE sources or not and also including V2G or not. Usually, the renewable energy sources are PV panels, small wind turbines or biomass based CHP. The focus on the research related to electric load management is on the coordination of the charging of EVs where the goal is typically either the reduction of the peak load caused by uncoordinated charging operations or the minimization of total costs. This is achieved through different optimization methods which usually focus on finding a proper scheduling of charging operations. Existing work on EV charging and its impacts are usually divided into two groups:

1. EVs scheduling for charging only;

2. Scheduling for both charging and discharging.

Due to the scope of this project, the option 2 was investigated deeper than number 1, despite the relevance that the first has for the topic. The following studies have proved helpful to assess the main advantages and disadvantages of using V2G/V2B:

Mets et al.[14] have assessed an optimal discharging schedule for PHEVs to achieve peak shaving and reduction of the variability of loads of multiple households in a residential distribution grid. This model considers two types of loads in the residential system, uncontrollable and controllable (in which EVs are included) and tries to minimize the distance between a target load profile and the household load profile, achieving between 32% to 70% peak load reduction with V2B.

Igualada et al.[15] has proposed an optimization model to manage a residential microgrid including a charging station with V2G system and RE sources, taking into account EV owners range anxiety and manageable domestic devices with controllable loads. This model also considers the EV as a shiftable load that can be allocated during the off-peak hours in line with energy prices. This study is very interesting since it concludes that the savings coming from V2G are highly dependent on the system flexibility which is directly related to the range anxiety.


2 Literature review 14

Mahmud et al.[45] has formulated a smart control algorithm for coordinating a system of households, coupled with battery storage, EVs with V2G capability and photovoltaic generation, that plans the EV’s charging-discharging process. The decision algorithm is based on the EV battery SOC that was divided into several bands and the discharge would only be possible when the SOC of EV is above a certain defined SOC. Although this study presents promising results, such up to 37% of peak shaving on the electricity distribution grid under realistic conditions, it is not known if the result is universal and an economic analysis was not performed.

Yoon et Al.[7] proposes a V2G coordinated scheme for office buildings with EV charging stations, con- sidering the integration of distributed energy resources such as PV and BES (Battery energy storage). This algorithm uses an integer linear programming assuming perfect information of schedules of visiting EVs at the station. The coordinated scheme showed the potential of reducing energy costs by ca. 15.7 USD/Day or 14.3% reduction compared to the first come first served approach.

Ortega-Vazquez [46] presents an optimal scheduling algorithm for EVs charging and V2G at the household level under a real-time price scheme and takes into account the cost of battery degradation. The study shows the scheduling of V2G is sensitive to electricity prices uncertainty and is also influenced by the degradation costs.

The degradation of battery capacity is proved to be accelerated in vehicles providing V2G services and influences the frequency of battery replacement and associated costs. In the past few years, several research studies have come up with models for EV charging and discharging, already trying to minimize battery wear within their model [9, 46, 44, 41] or to estimate long-term Li-ion battery degradation [47, 48] after running their simulations. Usually, these works are based on experiments with a specific type of battery chemistry and applied to the respective EV, since the study is focused on calculating the overall economical impacts on EVs. Hoke et Al.[9] concludes that the cost of battery degradation resulting from discharging is high enough to make V2G unprofitable, in some situations. The authors estimate that simply delaying charging can extend life of an EV battery by up to 1.5 years, while adopting an optimised charging regime can extend the life by up to 2.6 years.

To conclude on the state of V2G development, it can be implemented from a purely technical point of view however, there are still some remaining issues that are delaying its widespread adoption: the battery degradation and reliable aggregation strategies. For the degradation issue, more research is needed on developing degradation model for different battery chemistries, charging and discharging strategies that limit battery degradation. As for the aggregators/local operators strategies, it is necessary to define the rules in a strict and transparent way for the interactions between all the players (Household,Retailer, DSO,TSO...) to work and allow for participation in the electricity markets. All these operations must be done, ensuring the security of communication between vehicle owners and grid operators.


Chapter 3

Methodology and Case study

3.1 Methodology

The purpose of this study, as explained before, is to evaluate the potential of a shared fleet of EVs to provide V2B to a residential building, while assuring a specific number of reservations per day and also considering the existence of local PV and battery storage. The work developed during this project was divided into two main parts: Optimization Model development and EV Battery Degradation analysis. Matlab was used to generate data files to be read in (GAMS- General Algebraic Modelling System) software where the optimization algorithm was performed. And also later, GAMS results were transformed to plots and tables using Matlab. Figure 3.1 illustrates the flow-in of data with main inputs and outputs.


Residential Building

User Behavior

-Nº of EVs and clusters - Battery capacity -Charging and discharging power and efficiency -Max and min SOC limits

Software GAMS: Optimization


MATLAB: Generate data and plotting .wgdx

Input .rgdx output - Load Profiles

- PV Data

- Battery: capacity, charge and discharge power

- Grid Feed-in price - Electricity price - Grid Peak tariff


Accumulated load of the building for a

24h period + EV charging and

discharging schedule -Desired SOC of reservation

-Required starting time of reservation

-SOC of charging cycle i when it arrives at the charging station -Arrival time of charging cycle i in cluster n

Evs data

Figure 3.1: Diagram flow of optimization process

The basic scheme for deriving the optimal control algorithm without consideration of the V2B function or battery degradation is borrowed from the authors’ previous works[49]. The cost function was then modified to include the wear cost of the battery per day, which will be explained further. The algorithm used Mixed integer linear programming to perform for a 24 hour period, the following:

1. For different number of reservations, decide which EV is assigned to each reservation;

2. Plan the charging and discharging of the EVs schedule while optimizing the assignment of reservations;



3 Methodology and Case study 16

3. And at the same time, minimizing the total building electricity cost per day.

3.1.1 Objective Function

The approach was to formulate a suitable optimization problem for minimizing electricity costs for the residential building/community. The residential building buys electricity from a retailer, paying a time- varied fee λAt and can also feed back to the grid the surplus power produced through a ’feed-in’ tariff, λFt. Considering the two factors, the objective function can be written as (3.1):

M inimize




(PtAλAt − PtFλFt)∆t (3.1)

The load balance, in equation ((3.2)), takes into account the net load as behind-the-meter, and that the power taken from grid is positive and power given back to the grid as negative for every time step, t. The algorithm assumes that whichever the number of EVs in the community, these are divided into N clusters (in this case 2) and for each cluster, there are In charging cycles for the planning horizon.



n=1 In



(Pi,n,tEVc+ PtB++ Ptbuilding− PP V − PtB−− Pi,n,tEVd) = PtA− PtF, ∀t (3) (3.2)

in which

Pi,n,tEVc - Power of EV charging (kWh per hour)

PtB+- Power of stationary battery charging (kWh per hour) Ptbuilding - Building power load (kWh per hour)

PP V - PV power production input (kW)

PtB+- Power of stationary battery discharging (kWh per hour) Pi,n,tEVd - Power of EV discharging (kWh per hour)

3.1.2 Constraints

It is necessary to set a grid limit to assure the total load never exceeds what the grid can actually accom- modate, given by equation (3.3):

− Gt≤ PtA− PtF ≤ Gt , ∀t (3.3)

Battery constraints

The SOC of the stationary battery is given by equation (3.4) and has minimum and maximum limits expressed in (3.5)

SOCtB= SOCt−1B + (αPtB+−PtB−

β )∆t , ∀t (3.4)

in which

SOCtB - Stationary Battery State of Charge α - Battery charging efficiency

β - Battery discharging efficiency

SOCB ≤ SOCtB ≤ SOCB, ∀t (3.5)


3 Methodology and Case study 17

A binary variable cBt was introduced to indicate if the battery is charging (1) or discharging (0). The charging and discharging powers have limits too, expressed in

0 ≤ PtB+≤ cBtPB+, ∀t (3.6)

0 ≤ PtB−≤ (1 − cBt)PB−, ∀t (3.7)

EV constraints

The SOC, charging and discharging power of the EV are subject to a number of constraints, in order to not only control their physical limits but to make sure the EVs can be assigned for reservations. The SOC for each EV charging cycle (i), within the cluster (n) and for each time step (t) is calculated by equation ((3.8)) :

SOCi,n,tEV = SOCi,n,t−1EV + αci,nPi,n,tEVc∆t −Pi,n,tEVd

βi,nd ∆t, ∀i, n, t ≥ t0i,n (3.8) where αci,n and αdi,n represent respectively, the charging and discharging efficiencies. The charging require- ments must be satisfied in order to the reservation to be confirmed and for these reason [49] introduces the binary variables: yi,n,m and ai,n,m. A new set is introduced now, (mn) which represents the number of accepted reservations per day. If an EV does not satisfy the requirements of a reservation (mn) at the required leaving time of the respective reservation, RTm,n, the variable yi,n,m = 0. The condition imposed, is then, that SOC at RTm,n needs to be higher than the required SOC of the reservation m in cluster n, Qm,n, being yi,n,m= 1 and the reservation satisfied. This conditions is given by the constraints in equations (3.9) and (3.10):

Qm,n− SOCi,n,tEV ≤ L1(1 − yi,n,m) (3.9) Qm,n− SOCi,n,tEV ≥  − L2yi,n,m ∀i, n, m, t = RTm,n (3.10) The binary variable ai,n,m indicates if the EV in is assigned to the reservation mn: 1 is assigned and 0 not.

The number of EVs assigned is lower or equal to the number of EVs that satisfy the reservation, meaning that only the EV satisfying SOC requirement can be assigned (equation (3.11)).

ai,n,m≤ yi,n,m, ∀i, n, m (3.11)

A charging cycle in can only be assigned once (to one reservation m at most) during the planning horizon of 24 hours (equation (3.12)). The algorithm also makes sure that every reservation should be assigned with an EV at least (equation (3.13)).




ai,n,m≤ 1, ∀i, n (3.12)




ai,n,m= 1, ∀m, n (3.13)

Finally, if an EV arrives ( t0i,n is the charging cycle arrival time) to the charging station later than the required reserve leaving time RTm,n, it cannot be assigned to the respective reservation (equation (3.14) )

ai,n,m = 0, ∀i, n, m where t0i,n≥ RTm,n (3.14)

The charging/discharging powers and the SOC of EVs, are also submitted to physical limits, such as maxi- mum charging/discharging power (equation (3.15) and(3.16)) and maximum and minimum SOC (equation


3 Methodology and Case study 18

(3.17) ). For the algorithm to understand if the EV is charging or discharging, a binary variable (di,n,t) is introduced to indicate if the EV is charging=1 or discharging=0.

0 ≤ Pi,n,tEV c≤ PEV ci,n,t(di,n,t), ∀i, n, t ≥ t0i,n (3.15) 0 ≤ Pi,n,tEV d≤ PEV di,n,t(1 − di,n,t), ∀i, n, t ≥ t0i,n (3.16) SOCEVi,n,t≤ SOCi,n,tEV ≤ SOCEVi,n, ∀i, n, t ≥ t0 (3.17) Additionally, the charging and discharging power are set to zero after the leaving time RTm,n, the charging and discharging powers are set as always lower than their maximum, respectively in equations (3.18) and (3.19).

0 ≤ Pi,n,tEV +≤ (1 − ai,n,m)PEV +i,n,t ∀i, m, n, t where t ≥ RTm,n (3.18) 0 ≤ Pi,n,tEV −≤ (1 − ai,n,m)PEV −i,n,t ∀i, m, n, t where t ≥ RTm,n (3.19)

3.1.3 Battery degradation model

After identifying the major contributing factors of the battery degradation process, it is known that there are two apparent ways to ensure a long battery life:

The first is to restrict cycle life degradation over the planning period, by for example restricting its maximum daily DOD [50] or number of daily cycles [51].

The second is to attribute a cost to the objective function reflecting the cost of degradation. In order to develop an algorithm that would take into account the battery degradation cost within the algorithm itself, a great extent of literature review was performed and it was possible to develop it based on a study by [2]

that proposed a practical wear cost model for EVs charge scheduling applications.

The reasoning behind the model has to be first explained, so we can later understand the model formu- lation. The loss of cycle life for a lithium-ion battery cycled at a specific DOD is described by the general equation (3.20):

∆Ei= Ei− Ei−1= KD(2EiDOD) (kW.h) (3.20) The Ei denotes the battery energy capacity at the beginning of the charge-discharge cycle i. The KD is named as the discharge coefficient that accounts for the capacity lost in the cycle life at different operating SOCs, in terms of processes energy so measured in kW.h/kW.h. A cycle consists of both discharge and charge so a factor of 2 is considered in 3.20. Taking into account the ACC-DOD characteristics[52] (achievable cycle count (ACC) as a function of operating DOD) provided by battery manufacturers, it is possible to predict the achievable cycle count as function of DOD: usually the battery decrease to 80% of E0 after N cycles.

Once,the value of KD is determined for all operating DODs,through the method described by [2] the loss of energy capacity from a discharging or charging process between two arbitrary SOCs is evaluated by equation 3.20. Since DOD is equivalent to (1-SOC), this equation can be transformed to (3.21) where Diniand Df in

are the initial and final DODs of the charge or discharge process:

∆E = |E(DiniKDini− Df inKDf in)| (kW.h) (3.21) By assuming common ACC-DOD characteristics, the capacity loss is calculated for various initial and final SOCs which resulted in a linear relationship, represented by a linear function. This linear relationship is translated by the global wear coefficient, Kwexpressed in (kW.h/kW.h). Using the root mean squared error (RMSE), the author calculated the value of 0.00015 (kW.h/kW.h) for Kw, giving the best approximation.


3 Methodology and Case study 19

This value means that for every 1 kWh of charge/discharge, the total capacity of battery will be reduced by approximately 0.00015 kWh. This value was confirmed with other studies [53] and is considered the same for all Li-ion batteries with identical ACC-DOD characteristics. Assuming the average daily amount of energy processed with charge and discharge and used in driving is given by EV 2B and EDRV , the average daily battery wear (dw ) can be calculated through equation (3.22):

dw = Kw∗ ((1 + c) ∗ EDRV + EV 2B) (kW.h/day) where EV 2B= Echarging+ Edischarging (3.22) with coefficient c accounting for the higher capacity loss during driving mode compared to that of V2B mode, as a result of more rapid cycling. In this study, its value is set to 2.22 as the literature reference.

Taking into account that the battery reaches the end of its life cycle when it has decrease 20% of its initial rated capacity, the cycle life Ncycles of the battery can given by (3.23):

Ncycles =0.2E0

dw (days) (3.23)

Accordingly to economics principles, the degradation cost can be calculated as a series of equal payments during Ncycles, as represented in figure 3.2. The daily wear cost (dc) can be calculated with equation (3.24):

dc = rd(CC(1 + rd)Ncycles− SV )

(1 + rd)Ncycles− 1 euro/day (3.24)

Figure 3.2: Cash flow diagram for the model of battery degradation (dc is a cost). [2]

Where CC and SV are respectively the capital cost and salvation value of the battery at the end of cycle life, and rd is the daily interest rate. The values considered for these three parameters are: 2000 SEK/kWh for the battery cost, SV as 60% of CC and an interest rate of 0.4%.

Having the daily wear cost, it is possible to calculate the cost per 1 kWh (wp) of processed energy, as follows (equation (3.25)):

wp = dc

dw/Kw euro/kW.h (3.25)

These equations (3.20 to 3.25) were used in this study after calculating the daily energy charged and discharged per EV in the GAMS optimization model(explained in next section). This process is iterative,as shown in figure 3.3 since the actual wp depends on the EV utilization pattern which is unknown before solving the simulation. This study wanted to be the most close to reality as possible and also check how the battery degradation cost would affect the algorithm choosing to perform V2B or not. For these reasons, the cost of battery degradation was developed in this study in order to be included inside the objective function of the optimization problem. It should be noted that as both charge and discharge actions cause battery wear, their contributions are summed in equation (3.26) after taking into account the charging/discharging efficiencies:

T =24h




βi,nd )wp∆t (3.26)




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