Statistical charging load modelling of PHEVs in

Statistical charging load modelling of PHEVs in electricity distribution networks using National Travel Survey data 1

Statistical charging load modelling of PHEVs in electricity distribution networks using National Travel Survey data Rautiainen, A., Repo, S., Järventausta, P., Mutanen, A. Tampere University of Technology, P.O. box 692 FIN-33101 Tampere Finland (e-mail: [email protected]) Abstract In this report, statistical charging load modelling of plug-in hybrid electric vehicles in electricity distribution networks using National travel survey data was investigated. National travel survey data was used because it offers valuable information about car use habits, which have major impact on the network effects of PHEVs, of Finns. The modelling problem was investigated and some preliminary results are presented. 1. Introduction Transportation has a very important function in today‟s society. Globally, the energy production of transportation systems is highly dependent on oil, and there are strong expectations that the price as well as the volatility of the price of oil will increase in the future. The transportation sector is also a significant consumer of energy and a significant source of greenhouse gases and other emissions (Davis et al. 2009). Today‟s climate and energy policies imply strongly towards diversification of transportation fuels, improving energy efficiency and reducing emissions. The use of electrical energy in a broader manner by means of plug-in hybrid electric vehicles (PHEV) and electric vehicles (EV) offers a potential to partly fulfil these challenging requirements. Emission reductions and the amount of primary energy conservation due to plug-in vehicles are, however, highly dependent on the energy system. Plug-in vehicles are only a single way to contribute to reduction of oil dependency, reduction of primary energy consumption and reduction of CO2 emissions. It seems obvious that to achieve sustainable transportation system many other ways are also needed. Such ways are for example reduction of fuel consumption of conventional internal combustion engine based cars, development of biofuels, development of other alternative fuels and development of public transportation such as electrical rail traffic. There are some barriers related to high penetration of plug-in vehicles (PHEV and EV). It is, however, widely believed, that PHEVs and EVs will become common at some time frame, but there are differences of opinion about when and at what rate the market penetration will happen. The most important barrier is the battery technology. Technologically batteries are fairly good at the moment, but batteries suitable for transportation appliances are very expensive. However, the prices are expected to go down in the near future (Lache et al. 2010). Secondly, a lack of adequate charging infrastructure is a major barrier. It is fairly expensive to construct wide charging infrastructure especially in densely populated areas.

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Vehicle chargers affect the power system in many ways. Impacts on the energy production capacity, transmission networks, medium voltage networks, low voltage distribution networks and residential low voltage networks are very different in nature. Plug-in vehicles are not very big loads (when compared to electricity consumption in Finland) when considering the amount of energy absorbed. Rough upper limit estimation of energy need can be easily carried out. For example, there are about 2.5 million registered passenger vehicles in Finland today. According to latest National travel survey (NTS) conducted in Finland an average yearly mileage of Finnish passenger cars is about 18 000 km. If the average specific electricity energy consumption of the vehicles were 0.2 kWh/km and if all passenger vehicles were plug-in vehicles which use only electrical energy, the total yearly need for electrical energy of the vehicle fleet would be 9 TWh, which is roughly about 10 % of the today‟s total electricity consumption of Finland. However, plug-in vehicles can be big loads when considering instantaneous power. A remarkable penetration level of plug-in vehicle increases the loading level of the power system, which might influence the dispatch of power plants and thus the specific CO2-emissions of energy production. The impact on the dispatch depends on the timing of charging and the level of charging load. In the transmission network level the impacts of plug-in vehicles are probably minor, being mostly a small reduction in stability margins due to load increase. In medium voltage and low voltage networks the impacts are, without counter actions, probably the rise of peak load levels in some parts of the network (Lassila et al. 2009) and possible temporary over loading situations. In residential low voltage networks impact of plug-in vehicles can be in the case of high power charger and without counter actions the rise of the rating of the main fuses in some cases. To assess the impacts of plug-in vehicles on power system, the effect on the electrical load of a plug-in vehicle fleet in a power system has to be modelled. In this paper, a method which is used to construct a statistical load model for plug-in hybrid electric vehicles especially in Finnish transportation system is developed. In addition to the contribution to the academic discussion, this study offers a tool for network companies for practical studies. Modelling could be used to assess impact of different PHEV penetration levels on the existing networks and as a tool for future network planning. Vehicle-to-grid (V2G) and Vehicle-to-home (V2H) functionalities of plug-in vehicles are very interesting because their possibility to store fairly big amount of electrical energy for the needs of a power system or an individual household. For example, if 50 % of Finland‟s 2.5 million cars were plug-in vehicles which have an average effective energy capacity of 20 kWh, the total energy storage formed by these vehicles is about 25 GWh, which is fairly big amount of energy in Finnish power system. Also, the initial cost of this storage can be thought to be fairly low because these vehicles are purchased primarily for driving purposes, and a possible electricity storage use is only an ancillary service. However, this paper excludes V2G or V2H functions and concerns only regular charging, i.e. a situation where chargers only draw active power from the grid. The modelling in this paper is restricted only to PHEVs. This is because it is assumed that these vehicles will penetrate widely to the market sooner than EVs which do not have internal combustion engines.

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Using PHEVs a fairly high proportion of driving can be done using electrical energy. Fig. 1 illustrates cumulative shares of driving of Finnish people as a function of length of a trip. Data of fig. 1 is conducted using data from Finnish National travel survey 2004–2005. It can be seen, that about half of driven kilometres are driven as trips shorter than 50 km. Depending on the charging opportunities, PHEVs having electrical range under 100 km can reach very high proportion of kilometres driven using mainly electrical energy.

Fig. 1. Cumulative share of number of trips and driven kilometres as a function of a length of a trip The paper is organized as follows. In chapter 2 issues which have to be taken into account when assessing PHEV load are presented and discussed. In chapter 3 the method which is used to build up the load model is presented. In chapter 4 some conclusions are made and future work is proposed. 2. Issues affecting the PHEV load There exist many issues which have an effect on the impacts of PHEVs on the load levels of an electricity network. Such issues are for example driving habits, specific electricity consumption of vehicles, charging opportunities, battery capacities, available charging powers and electricity tariff applied by the vehicle users. Driving habits is a very crucial issue affecting to PHEV load. For example, in different countries in Europe driving habits of people are investigated in forms of different types of national travel surveys (Marconi et al. 2004). As different types of travel survey information is available, it is an interesting to do some research concerning the use of this type of data to model possible charging habits of people. In Finland, the latest National Travel Survey (NTS) was conducted in Finland during the years 2004–2005. Survey was made for Finish Ministry of Transport and Communications, the Finnish National Road Administration and the Finnish Rail Administration. NTS includes very specific data regarding when people are driving their vehicles, what are the starting places and the destinations of an individual trips etc. Based on 3


this type of data, an algorithm which calculates the charging profiles (basis for load models) of PHEV load was developed. Specific electricity consumption of a PHEV is dependent on many things. Specific electricity consumption (typical unit is kWh/km) is defined as the electrical energy need per driving distance. Typical value of regular passenger car is of the order of 0.15...0.30 kWh/km, but the consumption is dependent on the driving cycle, need for electrical energy for cooling or heating purposes etc. Also, the design of the energy management system of a PHEV has an impact on the specific electricity consumption. PHEVs have two different driving modes: charge depleting (CD) mode and charge sustaining (CS) mode (Axsen et al. 2008, Kromer&Heywood 2007)). When the state of charge (SOC) of the battery pack is above a certain value, vehicle operates in CD mode using primarily electrical energy from the battery pack for propulsion. In CS mode PHEV works as a regular hybrid electric vehicle thus using the battery pack only as an energy buffer. In CS mode all net energy is produced by ICE. CD mode can be divided in two different types: all-electric and blended mode (Axsen et al. 2008). In all-electric mode vehicle uses only electrical energy from the battery pack during CD operation. In blended mode vehicle uses also ICE in some situations. Thus, the type of the CD mode and its design affects also to the need of electrical energy of a PHEV. Charging opportunities and battery capacities have also impact on the PHEV load. If charging spots are available in many places such as at homes, work places, public parking places, shopping centres etc., charging would carried out in many places and a greater portion of driving could be done using electrical energy. From this point of view bigger battery capacities can also be thought as a substitute of wider charging infrastructure. Wide spread charging infrastructure would also change the charging profile of the vehicles so that charging would distribute more evenly along a day. Available charging power affects also the PHEV loads. Lithium-ion batteries can be charged using different charging rates which are usually expressed as C values. A rate of nC corresponds to a full charge in (approximately) 1/n h. In general level the behaviour of charging power during the charging process is dependent on the battery chemistry. Fig. 2 presents the behaviour of charging power of a lithium-ion (C-FePO4 chemistry) battery as a function of time with two different approximate charging rates: 0.5 C and 0.15 C. Data of the graphs of fig. 2 is obtained from European Batteries Inc. C-FePO4 battery chemistry is a promising option for vehicle appliances due to its high specific energy and high safety characteristics. It can be seen, that the power profile is fairly flat, and if the power is assumed to be constant during the charging process, the error is fairly small (the order of 10 % at the maximum). Available maximum charging power in different places can vary significantly especially in the future. It is expected, that in Finland charging powers used in domestic environment are usually of the order of 2...10 kW. These limits correspond approximately to one-phase 10 A and three-phase 16 A feeders in a 230 V network, respectively. In the future, there might have opportunities for fast charging (having maximum power of some dozens of kW and above) which enable charging of a battery pack in a few minutes. This requires a high power electricity network connection, and it sets high requirements for battery materials, battery design and heat management systems (Zaghib et al. 2009, Ceder&Kang 2009). 4


However, if these challenges are tackled, fast charging would solve a fundamental problem of slow recharging of the vehicle batteries, which is usually seen as a severe problem related especially to penetration of EVs.

Fig. 2. The behaviour of charging power of a single 42 Ah lithium-ion (C-FePO4) battery cell with two different charging rates: 0.5 C and 0.15 C (data of the curves is obtained from European batteries Inc.). Electricity tariffs applied by electricity users may have some influence on the PHEV load. If a dual tariff policy is applied, part of the charging, whose proportion is dependent on the behaviour of a customer, is probably shifted to night time, where electricity is cheaper than in day-time. This definitely has some impact on the charging profiles. If more dynamic pricing or other electricity market related services are applied, the timing of charging is more difficult to forecast and model. Such pricing principles or services might be different kinds of demand response programs offered by electricity retailers or dynamic transfer tariffs offered by distribution network companies. The functions and services of the electricity market and the power system related services in the context of plug-in vehicle charging are overviewed in (Rautiainen et al. 2010). Fig. 3 illustrates by means of a simplified example the impacts of different issues on the charging profile. The figure presents different charging profiles of a single day of a person who arrives at work place at 8:00, comes back to home at 17:00, is at home for one hour, visits a shop and finally comes back to home at 19:00. First profile presents situation when charging is carried out only at home. In the second profile charging opportunity is also at work place. In the third profile all charging is carried out at home but is shifted to night time. Fourth profile includes the effect of a more dynamic electricity tariff or electricity market related service, in which charging is controlled in accordance of electricity price on the market (control by electricity retailer) or the state of the network (control by a distribution network company). Fourth profile can be thought to be a result of for example an unexpected event in the power system or an unusual situation in electricity market. It can be seen, that the timing of charging and thus load curves for PHEV loads are highly dependent on charging opportunities, applied electricity tariffs, and the functions of electricity market.

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Fig. 3. A simplified example which illustrates the effect of different types of charging on the load of an electricity network 3. A method to build up PHEV load models Network planning of today in Finnish distribution network companies is based strongly on load curves. Curves which are mostly constructed in 1990‟s (Seppälä 1996) in accordance of long-lasting measurements are widely used. These curves include models for mean values and standard deviations for electrical energy consumption of customers in all hours of a year. Customers are grouped in many customer types, and to model a certain customer, the customer type specific curve is scaled in accordance of the customer‟s yearly electricity consumption. It is also possible to make an outer temperature correction. These curves present fairly well the total consumption of large amount of customers. In addition to these load curves, the rapid increase in automatic metering infrastructure has brought lots of data on electricity consumption of different consumers, and this data is also used in network planning by some network companies. For practical reasons, it would be desirable to model PHEV load in such way, that the models could be used as easily as possible in existing network information systems (NIS) and other related calculation software. PHEV load curves built in this work are somewhat similar with the curves mentioned above. In this work PHEV load curves are designed to cover only energy which is charged at home and thus the curves can be used only to model electricity consumption of households. The load curves used in network planning include nearly always an assumption that hourly energies of different consumers are normally distributed. In power flow calculations of NISs different confidence levels can be used. In this application a certain confidence level is defined so that by a certain probability a value of a real load is equal to or below the value used in the calculation. If the load is assumed normally distributed, the value of load in a calculation which is carried out with a certain confidence level is quantified using the cumulative probability density function of normal distribution. For example, to obtain a confidence level of 50 %, corresponding load level is the mean load of different customers. To obtain 95 % confidence level, mean load values added to standard deviation multiplied by approximately 1.65 are used. Typical used confidence levels are 99%, 95%, 90% and 50%. 6


99% and 95% values are used typically for example in maximum capacity calculations of lines, 90% is used for example in voltage reduction calculations, and 50 % is used for example in loss energy calculations (Lakervi&Partanen 2008). If the load is not normally distributed then a cumulative density function corresponding to assumed probability distribution should be used. The aim of this work is to produce models for an electrical load component of PHEV charging for households. 3.1 Source data To model PHEV load, it would be ideal if long lasting measurements of charging of large number of test PHEVs could be carried out in large number of different types of charging spots. At this time, data of such a research is not available, and to perform such a research a large number of modern PHEVs and extensive experimental arrangement including charging infrastructure and appropriate measurement would be needed. Thus, to assess today the effect of PHEVs on the load of electricity networks, some other approaches have to be applied. In this work, the results of National travel survey of Finland were exploited. This approach brings some uncertainty to the results as many justified and heuristic assumptions are made. PHEV load curves were built based fairly strongly on the raw data of Finnish National Travel Survey (NTS) 2004–2005. NTS data gives plenty of information about the travelling habits of Finns. NTS data was collected by means of telephone interviews covering time interval 1.6.2004–31.5.2005, and there were about 13 000 people answering the survey. Fig. 4 presents the data structure of the NTS relational database for those parts which are essential for construction of load curves. Four different data tables are shown in the figure: Background information, Daily trips, Cars and Family.

Fig. 4. Structure of the essential parts of the NTS relational data base. Background information table includes the information about the respondent of the survey. In addition to the ID identifying the respondent, data regarding for example the survey date, type of dwelling place (for example detached house, row house and apartment building), existence of driving licence and driven kilometres during the last year is included in the table.

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Daily trips table includes all the trips made by a respondent during a 24 h period. Period begins 04:00 at the date of survey and ends 04:00 of the next day. Data regarding for example departure time, duration of trip, type of starting place of the trip (18 different options, for example home and work place), type of destination place (the same options as in starting place), length of the trip and the way of travel (for example driving a passenger car) are included in the table. Cars table includes information about the cars of the households of the respondents. Table includes data about driven kilometres during the last year of each car. Family table includes information about the respondent‟s family members. Table includes data about the existence of a driving license for each family member. There are also some errors in the NTS data which had to be filtered off before further data processing. For example, a typical error was that an arrival time of a trip of a person was recorded to be after a departure time of the next trip. National travel survey includes data which can be used to sketch PHEV load models. All the trips of the respondents made by cars (trips where respondents is driving) are documented in detailed manner. However, the use of NTS data is also somewhat problematic. One problem is that NTS data describes the driving behaviour and driving habits of individual people, and it does not describe the driving patterns of individual cars. Because of this, an assumption is made: an individual driver (in NTS data) uses the same vehicle whole day. This assumption brings some error to the results, because to some extent people do drive using different cars along a day and a car can be driven by many drivers during a day. Also, NTS includes no information about driving of the other members of the respondent‟s family during the date of survey or neither data concerning the use of the cars of the respondent‟s family during the date of survey. In this work respondents of the NTS were classified in a few customer groups and an important generalization was made: people in different groups were assumed to present more or less similar driving behaviour. After driving of individual people is modelled, the data has to be extended or generalized to describe single household. Here some assumptions have to be made. 3.2 NTS data processing In this paper, case in which charging is started immediately when vehicle is parked at a charging place is considered. This concept is sometimes called as “dumb charging”. Another interesting case includes the applying of dual tariff charging, in which all charging at home is shifted to night time having lower price of electricity. This is not treated in this paper and belongs to further work. When constructing PHEV load models many background assumptions have to be made. Some of the most essential assumptions are as follows.

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1. Driving habits do not change when a conventional internal combustion based vehicle is changed to a PHEV. This assumption can be thought fairly justified, because PHEVs do not have such a strict range limitations as EVs have. If the state of charge of the battery goes low, driving can continue using the ICE, and the vehicle can be refuelled very quickly in a regular gas-station in a conventional manner or in fast charging spots in the future. Of course, there are many psychological factors in customers‟ behaviour which are hard to predict. 2. Vehicles have battery packs whose effective capacities are formed randomly and are normally distributed having a mean value of 18 kWh and standard deviation of 1 kWh. The selected capacities are somewhat overestimated when compared to state of the battery technology of today. Thus, it is assumed that specific energies of battery packs are increased due to research and development, which is widely expected to realize in the future. 3. The specific energy needs of the vehicles are formed randomly and are normally distributed having a mean value of 0.2 kWh/km and standard deviation of 0.02 kWh/km. Specific energy need is dependent on nature of the driving cycle. If an appropriate data is available, specific energy need could be approximated in accordance of average velocity of the trip. 4. All the PHEVs operate in all-electric CD mode until battery SOC has decreased to a certain level. In this point battery is treated as “empty” in from charging point-ofview. 5. Two different charging powers to be available in individual households were assumed: 10 kW and 3 kW. In the case of detached houses, semi-detached houses and farms a charging power is 10 kW. In other dwelling places power is 3 kW, which is somewhat overestimated value in city areas. Another option, which is also treated in this work, is that charging powers in all places are assumed to be 3 kW. 6. Because charging rate is usually below 0.5 C it is fairly safe to assume that charging power is constant during a charging process (see chapter 2). 7. Charging can be made in two different places: at home and at work place. Today, in Finland there are lot of work places in which employers have sockets in parking places which are used for preheating the engines of the vehicles at winter. These sockets can be used also for charging purposes. Charging power at home is defined by the assumption 5 (see above) and charging power at work places is 3 kW. 8. One-phase chargers are treated as symmetrical loads. When considering load flow calculations in electricity distribution networks, most of the network parts include enough customers, so that due to random variation of the phase to which one-phase chargers are connected, the load becomes approximately symmetrical in most of the lines and transformers. Driving habits of people vary to some extent according to day of week and season. It is therefore reasonable to divide the investigation of driving habits and hence charging habits into different time windows. In this work charging profiles are divided in summer (May– August) and winter (September–April) profiles, and both summer and winter profiles are divided in three parts: workdays (Monday–Friday), Saturdays, and Sundays. The law which 9


regulates the business hours of stores etc. in Finland changed at the beginning of the year 2010, and this will probably change the behaviour of people, especially on Saturdays and Sundays, when comparing to time (2004–2005) when the latest NTS was conducted. Charging behaviour of people is dependent on available charging power. In this study, available charging power at homes of people is dependent on the type of the dwelling place. It is therefore reasonable to form different load models for different types of household in accordance of dwelling places. In addition to available charging power, division to different types of households may also include some other type of factors which lead correlation between driving habits of different households of a certain group. Here load models are divided in three types in accordance dwelling place and charging power (see also assumption 4 above): first type includes detached houses, semi-detached houses and farms having 10 kW charging power available, second type includes the previous dwelling places having 3 kW charging powers, and the third type includes other types of dwelling places having 3 kW charging powers. Figure A1 in Appendix 1 presents a simplified presentation of an algorithm which is used to model charging patterns of individual drivers based on NTS data. The algorithm produces a data regarding hourly charged energies of set of drivers. The figure presents the case where charging is started immediately when a vehicle is parked at home or at work place. It is also assumed, that the battery pack of the vehicle is fully charged at the beginning of the first trip. Another option for this is that state-of-charges would be set to be below the full value defined randomly obeying a certain probability distribution. Also, it is assumed that the battery is charged full after the last trip. Using the algorithm, charged energies of different drivers at different hours are calculated. To illustrate the main principle of the algorithm, a simple example is presented in Table 1. The table presents driving trips of a person who participated to NTS. The driver makes six car trips during the day. Fig. 5 presents the driving trips of table 1 (1 means that the respondent is driving and 0 means that he is not driving) and corresponding charging of the driver having charging power off 3 kW at work place and home and having 0.2 kWh/km specific electrical energy consumption. Also the assumptions presented above are valid. First charging period starts at 06:55 when the driver arrives at work place and charging lasts until the battery is full again at 08:47. Second charging event begins when the driver arrives home at 15:20. Battery is again charged to a full charge. After this the driver visits very shortly his friends or relatives (type 15) and comes back at home for five minutes. During these five minutes some charging is again made. It is assumed, that drivers charge their vehicles always when there is even a very short time for charging. In reality this would not probably be always the case. However, the error caused by this assumption is small. In this stage the battery is not charged to full charge. The final visit is made to a summer cottage (type 17) and the arrival at home is at 19:27. After this the battery is charged to full charge.

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Table 1. Car trips of an individual respondent of NTS Departure time 06:35 15:00 18:00 18:20 18:35 19:25

Duration of the trip (min) 20 20 10 10 2 2

Length of the trip (km) 28 28 12 12 2 2

Type of the starting place 1 3 1 15 1 17

Type of the destination 3 1 15 1 17 1

Fig. 5. State of the car (1 refers to driving and 0 to parking) and computed charging behaviour of an individual respondent of NTS When a calculation of a set of drivers is carried out, different statistical figures such as mean values and standard deviations can be calculated. Figure 6 presents an example of a calculation result. It presents mean values and standard deviations of charged energies of a winter work days, Saturdays and Sundays concerning the people who have driving licences and who live in detached houses, semi-detached houses and farms having charging power of 3 kW. It can be seen, that the standard deviations are very big when compared to mean values. Some charging is carried out at work place and is not included in the figures. However, on average about 22 % of total energy was charged at work place. Although figure 6 presents two different statistical numbers for each hour, it does not present the statistical distributions of energy values of different hours.

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Fig. 6. Mean values and standard deviations of individual people who have a driving licence and who are living in detached houses, semi-detached houses or farms having 3 kW charging power for winter work days (WD), Saturdays (Sa) and Sundays (Su). Fig. 7 presents a histogram of charged energies at the peak hour 18 (time interval 17:00– 18:00) of the work day drivers of fig 6. The mean value of charged energies is 0.51 kWh, and standard deviation is 0.99 kWh. It can be seen, that the histogram does not seem to remind any of the most common probability density functions such as normal distribution. Most of the people, approximately 74 % of them, do not charge their vehicles during this hour. Also, there is another clear peak (9 % of all values) in the histogram at interval [2.85 kWh, 3.0 kWh]. This is due to plenitude of people who have started the charging process in previous hours and charging continues after the hour under inspection. Because of this, these people draw the maximum charging energy 3 kWh from the network.

Fig. 7. Charged energies at winter work days of people who have driving licence and who are living in detached houses, semi-detached houses or farms having 3 kW charging power regarding hour 18 Fig. 8 presents, as an example, six histograms corresponding to hours 16, 17, 19, 20, 21, and 22. From the network impact calculation point of view, the most interesting parts of a load curve are the high load hours, and the selected hours are the ones having the highest mean values (in addition to 18th hour) as presented in fig 6. These histograms present the similar thing as fig 7 but for the hours mentioned above. The histograms of fig 8 have also the same 12


group division as in fig 7 although not showed on the vertical axes. It can be seen, that the forms of the histograms seem to be fairly similar to form of the histogram of fig. 7.

Fig 8. Histograms of six peak hours 16, 17, 19, 20, 21 and 22 (hour 18 is already presented in fig 6). Group division is the same as in fig 7. Previous results included an assumption, that the maximum charging power was 3 kW. Fig. 9 presents a case similar with previous case, but charging power is now 10 kW. It can be seen, that when compared to fig. 6, most of the charging is spread to a narrower time slot. Standard deviations have increased dramatically and some increase can be seen in the mean values of the peak hours. These results are pretty much such as expected.

Fig. 9. Mean values and standard deviations at winter work days of individual drivers living in detached houses, semi-detached houses or farms having 10 kW charging power for.

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Fig. 10 presents a histogram for the hour 17 (16:00–17:00), which is now the hour of highest mean value, of the data of fig. 9. The mean value of charged energies is 0.65 kWh, and standard deviation is 1.71 kWh. It can be seen, that there is no as clear peak in the upper end of the distribution as in the case of 3 kW charging power. This issue can be noticed also in the fig 11 in which histograms of other peak hours are presented.

Fig. 10. Charged energies at winter work days of drivers living in detached houses, semidetached houses or farms having 10 kW charging power regarding hour 17

Fig. 11. Histograms of six peak hours 15, 16, 18 19, 20, 21 and 22 (hour 17 is already presented in fig 10). Group division is the same as in fig. 10. Because load models are specific for people who have driving licences, it is necessary to expand the model for a load model of a household. According to NTS, Finnish households include on average about 1.9 people with driving licence. Here, it is assumed, that charging 14


pattern of a single household consists of two independent charging patterns of two typical people who have a driving licence. Thus, charging distribution of a household consists of a sum of two independent driver specific distributions. As distributions are independent, there must have also two PHEVs. In this work, sum distribution is obtained simply by summing up two equal but independent (no correlation between distributions) distributions. In practice this means, that a sum distribution of a certain hour is obtained so that the vector containing the charged energies (during the certain hour) of individual people is summed up with a vector containing the same values but in random order. Fig. 12 presents a sum distribution of two distributions of the data of fig. 6 (3 kW charging power, detached houses, semi-detached houses and farms, winter work day, hour 18). The maximum charging power is now 6 kW (2 3 kW). The mean value of this distribution is 1.02 kWh and standard deviation is 1.38 kWh.

Fig. 12. Sum distribution of two distributions of the data of fig. 6 (3 kW charging power, detached houses, semi-detached houses and farms, winter work day, hour 18). If it is necessary to apply values of different confidence levels, a cumulative probability function should be defined. As the histogram presented in fig. 12 does not remind normal distribution or either very well any of the most typical distributions, some other type of approach has to be chosen. One possibility is to treat the data of figure 12 directly as probability density function. Then cumulative probability density function could be computed and values corresponding to different confidence levels can be computed for different types of network calculations. Fig. 13 presents load values of different confidence levels for the case of 2 3 kW, winter work day and detached houses, semi-detached houses and farms. It can be seen, that the load values are very high at some hours when a big confidence levels are used. It can be also noticed, that with confidence level of 50 % load value is zero kilowatts for every hour. The reason for this can be seen from the fig. 12: about 56 % of the values are zeroes at the peak hour 18. Always when this share is equal to or greater than 50 %, the load value corresponding to 50 % confidence level is zero. Appendix 2 includes the data for every type of customers for every parameter combinations.

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Fig. 13. Mean values and load values of different confidence levels at winter work days for different hours of day. Data concerns of sum of two drivers living in detached houses, semidetached houses or farms having 3 kW charging power 4. Conclusions and future work In this report, charging load modelling of PHEVs from electricity distribution networks‟ point-of-view using NTS was investigated. National travel survey data was used because it offers valuable information about car use habits, which have major impact on the network effects of PHEVs, of Finns. Statistical modelling is needed to obtain more accurate results for networks of lower amount of customers. The results the study presented in this paper are more or less an “educated guess”. This study includes many assumptions which make the investigation more or less a case study and increase the error of the results. However, it has to be remembered that it is still uncertain how people would use their PHEVs. Also locations, amount and features of charging spots available in the future and other important aspects presented in chapter 2 are uncertain, and these issues have major impact on the network effects. This study induced many development ideas and interesting questions for the future studies. The scaling technique presented in chapter 3 could be improved in many ways to obtain more realistic and scalable results. Grouping of NTS respondents could also be developed. Also, different sensitivity studies could and should be made. Such studies could be for example the average share of driven kilometres using electrical energy as function of vehicle fleet‟s mean battery capacity or mean specific electrical energy consumption. Also, the effect of driving cycle on the specific energy consumption could be modelled for example modelling the consumption as a function of average driving velocity of a trip. Using the algorithm of the studies, possible CO2 reduction, primary energy consumption reduction and crude oil consumption reduction by PHEVs could be assessed. The impact of dual tariff policy on the load models and other results would be interesting to investigate. And of course, different network calculations in which loading levels of different network components is assessed using the load models are the most important future studies.

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References Axsen J., Burke A., Kurani K. 2008. “Batteries for Plug-in Hybrid Electric Vehicles (PHEVs): Goals and the State of Technology circa 2008”. Instute of Transportation Studies, University of California. 26 p. Available: http://pubs.its.ucdavis.edu/publication_detail.php?id=1169 Ceder, G., Kang, B. 2009. „Response to “unsupported claims of ultrafast charging of Li-ion batteries”‟, Journal of Power Sources 194 (2009), pp. 1024–1028. Davis, S. C., Diegel, S. W., Boundy, R. G. 2009. “Transportation energy data book: Edition 28”. Oak Ridge National Laboratory, 379 p. Available: http://cta.ornl.gov/data/index.shtml Kromer M. A., Heywood J. B. 2007. “Electric Powertrains: Opportunities and Challenges in the U.S. Light-Duty Vehicle Fleet”. Sloan Automotive Laboratory, Laboratory for Energy and the Environment, Massachusetts Institute of Technology. Publication No. LFEE 2007-03 RP. 153 p. Available: http://web.mit.edu/sloan-autolab/research/beforeh2/files/kromer_electric_powertrains.pdf Lache R., Galves, D., Nolan, P. 2010. “Vehicle Electrification, More rapid growth; steeper price declines for batteries”. Deutsche Bank, Global Markets Research, Available: http://www.scribd.com/doc/28104500/Deutsche-Bank-Electric-Car-Analysis-Batteries Lakervi, E., Partanen, J. 2008. “Sähkönjakelutekniikka” (Electricity distribution Technologies). Otatieto. 285 p. (In Finnish) Lassila J., Kaipia T., Haakana J., Partanen J., Järventausta P., Rautiainen A., Marttila M. 2009. “Electric cars – challenge or opportunity for the electricity distribution infrastructure?”. European Conference SmartGrids and Mobility, Würzburg Germany. 8 p. Marconi, D., Simma, A. & Gindraux, M. 2004. “The Swiss Microcensus 2005: An International Comparison on Travel Behaviour” Swiss Transport Research Conference. 19 p. Available: http://www.strc.ch/conferences/2004/Marconi_Simma_Gindraux_SwissMicrocensus2005_S TRC_2004.pdf Rautiainen A., Repo S., Järventausta, P. 2010. “Intelligent charging of plug-in vehicles”. Accepted for NORDAC 2010. Seppälä A. 1996. “Load research and load estimation in electricity distribution”. Dissertation. Technical Research Centre of Finland. 137 p. Available: http://www.vtt.fi/inf/pdf/publications/1996/P289.pdf Zaghib, K., Goodenough, J. B., Mauger, A., Julien, C. 2009. “Unsupported claims of ultrafast charging of LiFePO4 Li-ion batteries”, Journal of Power Sources 194 (2009), pp. 1021–1023.

17


Appendix 1

Fig. A1. Simplified description of the algorithm which is used to produce charging pattern of an individual driver.

18

Statistical charging load modelling of PHEVs in electricity distribution networks using National Travel Survey data

19

Appendix 2 Load curve data as tables and figures are presented here. Case 1: Detached houses, semi-detached houses and farms, 2

3 kW, winter

Table A2.1. Mean values and standard deviations for case 1 Work day 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value (kWh)

0.25 0.16 0.09 0.05 0.02 0.01 0.02 0.03 0.06 0.10 0.14 0.21 0.26 0.31 0.47 0.62 0.94 1.02 0.88 0.80 0.81 0.73 0.58 0.39

Standard deviation (kWh)

0.81 0.68 0.50 0.37 0.19 0.18 0.22 0.25 0.33 0.46 0.50 0.67 0.74 0.82 0.97 1.09 1.28 1.38 1.34 1.27 1.32 1.28 1.17 0.97 Saturday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value (kWh)

0.27 0.10 0.03 0.00 0.06 0.04 0.04 0.02 0.01 0.06 0.12 0.19 0.36 0.50 0.60 0.73 0.69 0.63 0.67 0.59 0.48 0.41 0.42 0.34


0.80 0.52 0.27 0.05 0.40 0.34 0.30 0.23 0.12 0.33 0.47 0.59 0.80 0.97 1.14 1.27 1.27 1.18 1.24 1.18 1.12 1.04 1.04 0.92 Sunday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value (kWh)

0.20 0.14 0.10 0.06 0.03 0.02 0.07 0.07 0.07 0.03 0.08 0.14 0.25 0.29 0.33 0.37 0.54 0.68 0.83 0.84 0.81 0.71 0.70 0.60


0.72 0.62 0.52 0.41 0.29 0.21 0.41 0.40 0.43 0.20 0.40 0.46 0.66 0.72 0.84 0.85 1.05 1.23 1.37 1.38 1.39 1.28 1.29 1.17

Fig. A2.1. Mean values and standard deviations for case 1. 19


20

Table A2.2. Load values corresponding to different confidence levels for case 1 Work day 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value 0.25 0.16 0.09 0.05 0.02 0.01 0.02 0.03 0.06 0.10 0.14 0.21 0.26 0.31 0.47 0.62 0.94 1.02 0.88 0.80 0.81 0.73 0.58 0.39 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.20 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.75 1.05 1.50 2.00 2.90 3.00 3.00 3.00 3.00 3.00 3.00 3.00 2.50 95 % 3.00 2.15 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.65 1.20 2.00 2.25 2.65 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 99 % 3.00 3.00 3.00 3.00 0.00 0.00 0.25 1.50 2.00 3.00 3.00 3.00 3.00 3.00 3.25 3.95 5.00 5.50 5.25 5.00 5.10 5.25 3.80 3.00 Saturday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value 0.27 0.10 0.03 0.00 0.06 0.04 0.04 0.02 0.01 0.06 0.12 0.19 0.36 0.50 0.60 0.73 0.69 0.63 0.67 0.59 0.48 0.41 0.42 0.34 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.90 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.75 1.75 2.25 3.00 3.00 3.00 3.00 3.00 3.00 3.00 2.85 3.00 1.55 95 % 2.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.50 2.25 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 99 % 3.00 3.00 1.25 0.00 3.00 2.45 2.20 0.50 0.65 2.00 3.00 3.00 3.00 3.00 4.25 4.50 5.65 4.00 4.05 4.75 3.20 3.00 3.00 3.00 Sunday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value 0.20 0.14 0.10 0.06 0.03 0.02 0.07 0.07 0.07 0.03 0.08 0.14 0.25 0.29 0.33 0.37 0.54 0.68 0.83 0.84 0.81 0.71 0.70 0.60 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.25 1.00 1.20 1.65 2.00 2.85 3.00 3.00 3.00 3.00 3.00 3.00 3.00 95 % 3.00 0.60 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.45 2.05 2.25 3.00 2.55 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 99 % 3.00 3.00 3.00 3.00 1.60 0.50 3.00 3.00 2.75 0.75 2.00 2.10 3.00 3.00 3.00 3.00 3.00 4.50 5.75 5.70 6.00 3.60 3.80 3.00

20


Fig. A2.2. Load values for work days corresponding to different confidence levels for case 1

Fig. A2.3. Load values for Saturdays corresponding to different confidence levels for case 1

Fig. A2.4. Load values for Sundays corresponding to different confidence levels for case 1

21


22

Case 2: Detached houses, semi-detached houses and farms, 2 10 kW, winter

Table A2.3. Mean values and standard deviations for case 2 Work day 1 Mean value (kWh)

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

0.06 0.00 0.00 0.00 0.01 0.02 0.03 0.03 0.08 0.12 0.19 0.29 0.36 0.42 0.64 0.87 1.30 1.26 0.90 0.80 0.66 0.50 0.34 0.15

Standard deviation (kWh) 0.58 0.08 0.00 0.00 0.32 0.43 0.39 0.25 0.56 0.58 0.88 1.19 1.36 1.46 1.78 2.08 2.39 2.65 2.29 2.09 1.85 1.67 1.46 1.00 Saturday 1 Mean value (kWh)

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

0.00 0.00 0.00 0.00 0.04 0.00 0.02 0.01 0.01 0.13 0.16 0.29 0.52 0.77 0.98 0.89 0.79 0.68 0.65 0.48 0.30 0.31 0.34 0.23

Standard deviation (kWh) 0.00 0.00 0.00 0.00 0.60 0.00 0.22 0.15 0.07 0.76 0.71 1.13 1.34 2.10 2.34 2.23 2.24 1.96 2.25 1.63 1.37 1.44 1.46 1.37 Sunday 1 Mean value (kWh)

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

0.10 0.00 0.00 0.00 0.05 0.05 0.08 0.04 0.02 0.03 0.11 0.25 0.29 0.44 0.37 0.57 0.90 0.90 1.14 0.99 0.66 0.56 0.50 0.36

Standard deviation (kWh) 0.85 0.00 0.00 0.00 0.60 0.56 0.53 0.40 0.15 0.22 0.56 0.94 0.95 1.45 1.19 1.81 2.27 2.45 2.74 2.62 2.20 1.89 1.96 1.65



23


2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value 0.06 0.00 0.00 0.00 0.01 0.02 0.03 0.03 0.08 0.12 0.19 0.29 0.36 0.42 0.64 0.87 1.30 1.26 0.90 0.80 0.66 0.50 0.34 0.15 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.17 0.67 1.00 2.17 3.33 4.50 5.00 3.50 3.33 2.50 1.33 0.00 0.00 95 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.67 1.17 1.67 2.83 3.17 4.67 5.00 6.67 7.50 6.50 5.83 5.00 4.00 2.17 0.00 99 % 2.17 0.00 0.00 0.00 0.00 0.00 0.00 1.33 2.33 3.50 5.00 6.67 7.67 8.33 10.0 10.0 10.0 10.0 10.0 10.0 10.0 9.83 9.33 6.50 Saturday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value 0.00 0.00 0.00 0.00 0.04 0.00 0.02 0.01 0.01 0.13 0.16 0.29 0.52 0.77 0.98 0.89 0.79 0.68 0.65 0.48 0.30 0.31 0.34 0.23 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.33 2.50 2.00 4.83 4.17 3.33 2.50 1.17 0.83 0.00 0.00 0.00 0.00 95 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.83 2.50 4.00 5.50 6.17 6.00 6.83 5.50 4.50 4.00 1.67 1.67 1.83 0.00 99 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.50 4.17 5.17 6.00 10.0 10.0 10.0 10.0 10.0 10.0 8.50 8.33 10.0 7.50 9.83 Sunday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value 0.10 0.00 0.00 0.00 0.05 0.05 0.08 0.04 0.02 0.03 0.11 0.25 0.29 0.44 0.37 0.57 0.90 0.90 1.14 0.99 0.66 0.56 0.50 0.36 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.17 1.67 1.17 1.67 3.83 4.17 5.00 3.50 1.67 0.83 0.00 0.00 95 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.50 2.17 2.50 3.17 4.67 5.83 5.50 8.33 7.50 6.33 5.67 4.50 2.33 99 % 5.33 0.00 0.00 0.00 0.00 0.00 2.50 0.50 0.00 0.83 2.83 5.00 4.50 6.67 5.50 8.33 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

23





24


25

Case 3: Detached houses, semi-detached houses and farms, 2 3 kW, summer

Table A2.5. Mean values and standard deviations for case3 Work day 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value (kWh)

0.37 0.25 0.15 0.05 0.03 0.02 0.05 0.04 0.04 0.09 0.19 0.24 0.32 0.38 0.41 0.54 0.85 0.90 0.82 0.75 0.70 0.71 0.64 0.49


0.98 0.80 0.58 0.38 0.27 0.25 0.34 0.32 0.30 0.39 0.62 0.73 0.80 0.94 0.93 1.06 1.25 1.39 1.28 1.23 1.22 1.26 1.24 1.11 Saturday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value (kWh)

0.55 0.43 0.23 0.13 0.05 0.04 0.06 0.06 0.08 0.12 0.14 0.21 0.47 0.54 0.59 0.67 0.68 0.83 0.64 0.49 0.53 0.40 0.44 0.33


1.19 0.99 0.75 0.58 0.36 0.36 0.43 0.43 0.46 0.53 0.48 0.58 0.96 1.06 1.08 1.17 1.30 1.39 1.26 1.14 1.15 0.99 1.05 0.94 Sunday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value (kWh)

0.24 0.16 0.14 0.06 0.01 0.07 0.07 0.05 0.05 0.14 0.09 0.23 0.24 0.23 0.33 0.60 0.89 0.94 0.95 0.97 0.88 1.03 1.02 0.84


0.82 0.67 0.61 0.43 0.08 0.45 0.45 0.35 0.33 0.56 0.42 0.70 0.71 0.66 0.86 1.18 1.31 1.42 1.62 1.53 1.47 1.54 1.47 1.43



26


2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value 0.37 0.25 0.15 0.05 0.03 0.02 0.05 0.04 0.04 0.09 0.19 0.24 0.32 0.38 0.41 0.54 0.85 0.90 0.82 0.75 0.70 0.71 0.64 0.49 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 2.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.50 0.75 1.35 2.00 2.00 2.75 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 95 % 3.00 3.00 1.50 0.00 0.00 0.00 0.00 0.00 0.00 0.65 1.55 2.25 2.45 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 99 % 3.00 3.00 3.00 3.00 1.15 0.40 2.45 2.00 1.05 2.25 3.00 3.00 3.00 3.00

3.0

3.8

4.8

5.8

4.8

4.2

4.4 4.95 4.75 3.25

15

16

17

18

19

20

21

Saturday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

22

23

24

Mean value 0.55 0.43 0.23 0.13 0.05 0.04 0.06 0.06 0.08 0.12 0.14 0.21 0.47 0.54 0.59 0.67 0.68 0.83 0.64 0.49 0.53 0.40 0.44 0.33 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 3.00 2.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.25 1.00 2.25 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 2.55 3.00 1.40 95 % 3.00 3.00 2.55 0.00 0.00 0.00 0.00 0.00 0.00 0.45 1.10 1.60 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 99 % 3.00 3.00 3.00 3.00 2.30 2.65 3.00 3.00 2.75 3.00 2.40 2.25 3.50

3.0

3.2

3.0

4.5

6.0

5.5 3.50 4.40

3.0 3.00 3.00

14

15

16

17

18

19

22

Sunday 1

2

3

4

5

6

7

8

9

10

11

12

13

20

21

23

24

Mean value 0.24 0.16 0.14 0.06 0.01 0.07 0.07 0.05 0.05 0.14 0.09 0.23 0.24 0.23 0.33 0.60 0.89 0.94 0.95 0.97 0.88 1.03 1.02 0.84 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.70 1.25 0.65 1.75 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 95 % 2.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.50 0.35 2.00 2.40 2.00 3.00 3.00 3.00 3.00 3.00 4.05 3.00 3.75 3.00 3.00 99 % 3.00 3.00 3.00 3.00 0.30 3.00 3.00 1.50 0.85 3.00 1.75 3.00 3.00 3.00 3.00 3.00

3.0

5.0

6.0

6.0

6.0

5.9

6.0

6.0

26





27


28

Case 4: Detached houses, semi-detached houses and farms, 2 10 kW, summer Table A2.7. Mean values and standard deviations for case 4 Work day 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value (kWh)

0.04 0.00 0.00 0.00 0.02 0.01 0.05 0.02 0.04 0.15 0.27 0.36 0.45 0.47 0.59 0.72 1.19 0.97 0.81 0.67 0.69 0.79 0.58 0.24


0.45 0.00 0.00 0.00 0.38 0.17 0.52 0.27 0.30 0.73 1.12 1.32 1.49 1.62 1.82 1.82 2.35 2.23 2.06 1.90 2.01 2.17 2.00 1.26 Saturday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value (kWh)

0.17 0.07 0.00 0.00 0.12 0.10 0.02 0.00 0.05 0.07 0.22 0.38 0.87 0.83 0.61 0.78 0.69 0.98 0.39 0.44 0.35 0.18 0.50 0.41


1.19 0.71 0.00 0.00 0.84 1.02 0.17 0.00 0.51 0.44 1.04 1.31 2.23 2.19 1.65 2.10 1.87 2.55 1.23 1.82 1.15 0.82 1.94 1.71 Sunday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value (kWh)

0.00 0.00 0.00 0.00 0.03 0.18 0.08 0.00 0.02 0.15 0.16 0.48 0.33 0.36 0.74 0.80 1.47 1.30 1.02 0.63 0.75 1.25 1.03 0.37


0.00 0.00 0.00 0.00 0.27 1.22 0.73 0.00 0.12 0.68 0.91 1.82 1.35 1.49 2.34 2.34 3.28 2.95 2.68 1.72 2.33 2.99 2.78 1.75

Fig. A2.13. Mean values and standard deviations for case 4.

28


29


2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value 0.04 0.00 0.00 0.00 0.02 0.01 0.05 0.02 0.04 0.15 0.27 0.36 0.45 0.47 0.59 0.72 1.19 0.97 0.81 0.67 0.69 0.79 0.58 0.24 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.17 0.67 1.17 1.17 1.67 2.50 5.00 3.67 3.33 2.50 2.67 2.83 0.83 0.00 95 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.67 2.67 3.33 3.83 5.00 5.00 7.50 6.67 5.33 5.00 5.00 6.50 5.00 0.67 99 % 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.67 1.67 3.33 5.83 7.50 7.50 10.0 10.0

8.7

10.0 10.0 10.0

9.5

10.0 10.0 10.0 7.83

Saturday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value 0.17 0.07 0.00 0.00 0.12 0.10 0.02 0.00 0.05 0.07 0.22 0.38 0.87 0.83 0.61 0.78 0.69 0.98 0.39 0.44 0.35 0.18 0.50 0.41 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 3.00 2.50 2.00 2.50 2.50 3.17 0.83 0.00 0.00 0.00 0.00 0.00 95 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.83 2.50 7.50 5.00 3.33 7.00 3.83 9.17 2.83 2.33 3.33 0.83 2.50 1.67 99 % 6.17 0.00 0.00 0.00 5.00 0.00 0.00 0.00 0.00 2.50 4.00 5.83 10.0 10.5

7.8

10.0

9.2

10.0

5.8

15

16

17

18

19

10.0 5.33

4.3

10.0 8.50

Sunday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

20

21

22

23

24

Mean value 0.00 0.00 0.00 0.00 0.03 0.18 0.08 0.00 0.02 0.15 0.16 0.48 0.33 0.36 0.74 0.80 1.47 1.30 1.02 0.63 0.75 1.25 1.03 0.37 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.50 2.50 2.83 7.83 5.67 4.00 3.00 2.00 6.17 2.17 0.00 95 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 4.50 1.33 1.67 5.17 4.67 10.0 8.50 10.0 4.17 7.50 10.0 7.67 1.17 99 % 0.00 0.00 0.00 0.00 0.00 5.83 0.00 0.00 0.83 2.67 3.50 10.0 7.00 8.33 10.0 10.0 10.0 10.0 10.0

6.7

10.0 10.0 10.0 9.83

29





30


31

Case 5: Row houses, apartment buildings and other types of dwelling places (other than Detached houses, semi-detached houses and farms), 2 3 kW, winter Table A2.9. Mean values and standard deviations for case 5 Work day 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value (kWh)

0.18 0.11 0.06 0.02 0.01 0.02 0.01 0.01 0.04 0.03 0.05 0.08 0.10 0.16 0.22 0.37 0.54 0.59 0.50 0.48 0.50 0.48 0.39 0.26


0.68 0.55 0.41 0.22 0.20 0.22 0.15 0.11 0.26 0.25 0.32 0.38 0.45 0.58 0.65 0.82 0.97 1.09 1.02 0.98 1.08 1.10 1.01 0.82 Saturday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value (kWh)

0.12 0.06 0.03 0.02 0.03 0.03 0.03 0.05 0.04 0.02 0.05 0.09 0.12 0.21 0.20 0.37 0.44 0.34 0.31 0.28 0.28 0.24 0.23 0.20


0.56 0.40 0.27 0.23 0.32 0.32 0.27 0.35 0.32 0.17 0.24 0.34 0.42 0.67 0.64 0.89 0.95 0.90 0.85 0.79 0.83 0.76 0.82 0.75 Sunday 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value (kWh)

0.16 0.12 0.08 0.05 0.03 0.02 0.03 0.01 0.02 0.01 0.03 0.08 0.09 0.16 0.27 0.44 0.50 0.45 0.59 0.60 0.58 0.55 0.42 0.29


0.68 0.57 0.49 0.33 0.27 0.25 0.30 0.06 0.15 0.11 0.21 0.41 0.40 0.57 0.78 0.89 1.05 1.01 1.12 1.17 1.16 1.18 1.05 0.89


31


32


2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value 0.18 0.11 0.06 0.02 0.01 0.02 0.01 0.01 0.04 0.03 0.05 0.08 0.10 0.16 0.22 0.37 0.54 0.59 0.50 0.48 0.50 0.48 0.39 0.26 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.75 1.60 2.10 2.85 2.65 2.25 2.60 3.00 2.25 0.75 95 % 2.40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.60 0.80 1.50 1.95 2.50 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 99 % 3.00 3.00 3.00 0.85 0.00 0.00 0.00 0.00 1.65 1.00 2.00 2.25 3.00

3.0

3.0

3.0

3.3

3.8

3.2

3.2

4.5

4.3

3.5

3.00

14

15

16

17

18

19

20

21

22

23

24

Saturday 1

2

3

4

5

6

7

8

9

10

11

12

13

Mean value 0.12 0.06 0.03 0.02 0.03 0.03 0.03 0.05 0.04 0.02 0.05 0.09 0.12 0.21 0.20 0.37 0.44 0.34 0.31 0.28 0.28 0.24 0.23 0.20 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.70 0.50 2.00 2.00 1.75 1.25 0.95 0.75 0.35 0.00 0.00 95 % 0.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.25 0.75 0.75 2.00 1.45 3.00 3.00 3.00 2.90 2.85 3.00 3.00 3.00 3.00 99 % 3.00 3.00 1.95 0.00 3.00 3.00 0.20 2.05 0.85 0.50 1.25 1.75

2.2

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.00

3.0

3.0

3.00

13

14

15

16

17

18

19

20

21

22

23

24

Sunday 1

2

3

4

5

6

7

8

9

10

11

12

Mean value 0.16 0.12 0.08 0.05 0.03 0.02 0.03 0.01 0.02 0.01 0.03 0.08 0.09 0.16 0.27 0.44 0.50 0.45 0.59 0.60 0.58 0.55 0.42 0.29 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.40 1.00 2.00 2.50 2.50 3.00 3.00 3.00 3.00 3.00 0.60 95 % 2.70 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.75 1.25 3.00 3.00

3.0

3.00

3.0

3.00 3.00

3.0

3.00 3.00

99 % 3.00 3.00 3.00 2.20 0.00 0.00 2.50 0.25 1.30 1.00 1.50

4.2

3.2

4.0

4.5

6.0

3.6

2.9

2.75 3.00

3.0

3.0

3.8

3.00

32





33


34

Case 6: Row houses, apartment buildings and other types of dwelling places (other than Detached houses, semi-detached houses and farms), 2 3 kW, summer

Table A2.11. Mean values and standard deviations for case 6 Work day 1 Mean value (kWh)

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

0.24 0.16 0.10 0.04 0.02 0.01 0.03 0.02 0.03 0.04 0.05 0.08 0.11 0.12 0.19 0.36 0.51 0.58 0.49 0.49 0.48 0.44 0.37 0.25

Standard deviation (kWh) 0.85 0.70 0.51 0.30 0.22 0.17 0.25 0.19 0.27 0.24 0.27 0.38 0.45 0.47 0.60 0.81 1.00 1.11 1.04 1.04 1.04 1.03 0.97 0.78 Saturday 1 Mean value (kWh)

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

0.26 0.13 0.08 0.00 0.04 0.02 0.00 0.00 0.00 0.00 0.05 0.09 0.06 0.14 0.24 0.28 0.22 0.33 0.37 0.44 0.41 0.46 0.43 0.30

Standard deviation (kWh) 0.88 0.60 0.44 0.00 0.33 0.14 0.00 0.00 0.00 0.00 0.29 0.36 0.26 0.55 0.73 0.77 0.62 0.83 0.95 1.01 1.06 1.07 1.05 0.85 Sunday 1 Mean value (kWh)

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

0.23 0.17 0.12 0.11 0.04 0.02 0.00 0.00 0.00 0.04 0.06 0.10 0.07 0.17 0.26 0.30 0.46 0.55 0.56 0.47 0.47 0.68 0.75 0.64

Standard deviation (kWh) 0.86 0.68 0.58 0.57 0.35 0.19 0.00 0.00 0.00 0.28 0.39 0.44 0.40 0.51 0.74 0.76 1.01 1.10 1.12 1.02 1.08 1.18 1.28 1.23


34


35


2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Mean value 0.24 0.16 0.10 0.04 0.02 0.01 0.03 0.02 0.03 0.04 0.05 0.08 0.11 0.12 0.19 0.36 0.51 0.58 0.49 0.49 0.48 0.44 0.37 0.25 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.50 1.50 2.25 2.90 2.50 2.50 2.50 3.00 2.25 0.55 95 % 3.00 1.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.40 1.05 1.05 1.75 2.75 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 99 % 3.00 3.00 3.00 1.55 0.00 0.00 1.00 0.65 1.75 1.15 1.50 2.25 2.50

3.0

3.0

3.0

4.0

4.0

3.9

3.4

3.8

3.0

3.0

3.00

14

15

16

17

18

19

20

21

22

23

24

Saturday 1

2

3

4

5

6

7

8

9

10

11

12

13

Mean value 0.26 0.13 0.08 0.00 0.04 0.02 0.00 0.00 0.00 0.00 0.05 0.09 0.06 0.14 0.24 0.28 0.22 0.33 0.37 0.44 0.41 0.46 0.43 0.30 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.50 1.35 1.00 1.50 2.50 3.00 3.00 3.00 2.95 0.70 95 % 2.85 0.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.85 0.50 1.25 2.50 2.45 1.50 3.00 3.00 3.00 3.00 3.00 3.00 3.00 99 % 3.00 3.00 3.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.25 1.50

1.3

2.3

3.0

3.0

3.0

3.0

3.0

3.0

3.00

3.0

3.0

3.00

13

14

15

16

17

18

19

20

21

22

23

24

Sunday 1

2

3

4

5

6

7

8

9

10

11

12

Mean value 0.23 0.17 0.12 0.11 0.04 0.02 0.00 0.00 0.00 0.04 0.06 0.10 0.07 0.17 0.26 0.30 0.46 0.55 0.56 0.47 0.47 0.68 0.75 0.64 50 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90 % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.80 0.90 1.35 2.50 3.00 3.00 2.95 2.25 3.00 3.00 3.00 95 % 3.00 1.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.40 1.15 2.25 2.50

3.0

3.00

3.0

3.00 3.00

3.0

3.00 3.00

99 % 3.00 3.00 3.00 3.00 3.00 1.15 0.00 0.00 0.00 2.25 3.00

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.00 3.00

3.0

3.0

4.5

3.00

35





36

Statistical charging load modelling of PHEVs in

Statistical charging load modelling of PHEVs in

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