Modeling and forecasting the load in the future electricity grid

Transcription

1 Modeling and forecasting the load in the future electricity grid Spatial electric vehicle load modeling and residential load forecasting Mahmoud Shepero

2 Abstract The energy system is being transitioned to increase sustainability. This transition has been accelerated by the increased awareness about the adverse effects of the greenhouse gas (GHG) emissions into the atmosphere. The transition includes switching to electricity as the energy carrier in some sectors, e.g., transportation, increasing the contribution of renewable energy sources (RES) to the grid, and digitalizing the grid services. Electric vehicles (EVs) are promoted and subsidized in many countries among the sustainability initiatives. Consequently, the global sales of EVs rapidly increased in the recent years. Many EV owners might charge their EVs only at home, thereby increasing the residential load. The residential load might further increase due to the initiatives to electrify the heating/cooling sector. This thesis contributes to the knowledge about the operation of the future energy system by modeling the spatial charging load of private EVs in cities, and by proposing a forecasting model to predict the residential load. Both models can be used to evaluate the impacts of both technologies on the local electricity grid. In addition, demand response (DR) schemes can be proposed to reduce the adverse effects of both the charging load of EVs and the residential load. A case study of the EV model on the Herrljunga city grid showed that 100% EV penetration with 3.7 kw (charging rate of 14.8 km/h) chargers will not cause voltage violations in the grid. Winter load is responsible for 5% voltage drop at the weakest bus, and EVs add only 1% to this drop. In a Swedish city, charging EVs will require adding extra 1.43 kw/car to the grid capacity assuming 22 kw (charging rate of 88 km/h) residential chargers. If the EV charging is not restricted to residential locations, an increase of 1.23 kw/car is expected. The proposed forecasting model is comparable in accuracy to previously developed models. As an advantage, the model produces a probability density function (PDF) describing the model s certainty in the forecast. In contrast, many previous contributions provided only point forecasts.

3 To my wife, Sue, with whom each day is fresh and new, a truly Markovian relationship. Lipsky, L. (2008). Queueing Theory: A linear algebraic approach. Springer Science & Business Media.

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5 List of papers This thesis is based on the following papers, which are referred to in the text by their roman numerals. I Shepero, M., Munkhammar, J., Widén, J., Bishop, J. D.K., Boström, T. (2018). Modeling of photovoltaic power generation and electric vehicles charging on city-scale: A review. Renewable and Sustainable Energy Reviews, 89, II III Luthander, R., Shepero, M., Munkhammar, J., Widén, J. Photovoltaics and opportunistic electric vehicle charging in the power system a case study on a Swedish distribution grid. Submitted to IET Renewable Power Generation (2018). Shepero, M., Munkhammar, J. Spatial Markov chain model for electric vehicle charging in cities using geographical information system (GIS) data. Submitted to Applied Energy (2018). IV Shepero, M., van der Meer, D. W., Munkhammar, J., Widén, J. (2018). Residential probabilistic load forecasting: A method using Gaussian process designed for electric load data. Applied Energy, 218, Reprints were made with permission from the publishers. Publications not included in the thesis V VI VII van der Meer, D. W., Shepero, M., Svensson, A., Widén, J., Munkhammar, J. (2018). Probabilistic forecasting of electricity consumption, photovoltaic power generation and net demand of an individual building using Gaussian processes. Applied Energy, 213, Widén, J., Shepero, M., Munkhammar, J. (2017). On the properties of aggregate clear-sky index distributions and an improved model for spatially correlated instantaneous solar irradiance. Solar Energy, 157, Widén, J., Shepero, M., Munkhammar, J. (2017). Probabilistic load flow for power grids with high PV penetrations using copula-based

6 modeling of spatially correlated solar irradiance. IEEE Journal of Photovoltaics, 7(6), VIII IX X XI Shepero, M., Munkhammar, J. (2017). Probabilistic modeling of public electric vehicles charging based on travel survey data. In proceedings of the European Battery, Hybrid and Fuel Cell Electric Vehicle Congress Geneva, Switzerland, March Shepero, M., Munkhammar, J. (2017). Modelling charging of electric vehicles using mixture of user behaviours. In proceedings of the 1st E-mobility Power System Integration Symposium, Berlin, Germany, 23 October Luthander, R., Shepero, M., Munkhammar, J., Widén, J. (2017). Photovoltaics and opportunistic electric vehicle charging in a Swedish distribution grid. In proceedings of the 7th International Workshop on Integration of Solar into Power Systems, Berlin, Germany, October Munkhammar, J., Shepero, M. (2017). Autonomous electric vehicle fleet charging in cities: optimal utility estimates and Monte Carlo simulations. In proceedings of the 7th IEEE International Conference on Innovative Smart Grid Technologies, ISGT Europe 2017, Torino, Italy, September Notes on my contributions I contributed the following to the appended papers: Paper I, I did the electric vehicle (EV) literature survey and wrote Sections 3 and 4. Paper II, I developed the EV charging model, did the EV charging simulations, and wrote Section 2.5. Paper III, I developed the model, did the simulations and wrote the paper. Paper IV, I co-developed the model, did the simulations and wrote the paper.

7 Contents 1 Introduction Aims of the thesis Overview of the appended papers Background Electric vehicles Sales and barriers Demographics of current EV owners Cost of ownership EV batteries Charging infrastructure Modeling the charging load of EVs Grid impacts of EVs Controlled charging Charging with RES Residential electrical load Modeling Demand response potentials Forecasting Research gaps Methodology Electric vehicle charging model Extract charging stations Markov chain for EV mobility Spatial charging load Gaussian process forecasting Gaussian process Covariance functions Gaussian processes in forecasting Log-normal process Error metrics Results Electric vehicles charging load Grid study Load of parking lots... 32

8 4.2 Forecasting using Gaussian process Discussion and future work Important results Future work Conclusion Acknowledgments Bibliography... 45

9 List of abbreviations AC ANN ARD ARIMA BEV DC DR EV GDP GHG GIS GP GPS ICEV LP MAE OSM PDF PHEV PI PICP PINAW PLF PNP pu PV RES RMSE SE SVR V2G Alternating current Artificial neural network Automatic relevance detection Auto regressive integrated moving average Battery electric vehicle Direct current Demand response Electric vehicle Gross domestic product Greenhouse gas Geographical information system Gaussian process Global positioning system Internal combustion engine vehicle Log-normal process Mean absolute error OpenStreetMap Probability density function Plug-in hybrid electric vehicle Prediction interval Prediction interval coverage probability Prediction interval normalized average width Probabilistic load forecast Peak of the normalized power Per-unit Photovoltaics Renewable energy sources Root mean square error Squared exponential Support vector regression Vehicle to grid

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11 1. Introduction In the year 2017, the global CO 2 emissions due to fossil fuels were estimated to be a record high 32.5 billion tons as heavy as the maximum takeoff weight of 57 million Airbus A380 planes [1]. The impacts of these large quantities of carbon emissions will extend for centuries after the emissions terminate [2, 3]. In the Kyoto protocol in 1997, an initial reaction to limit the CO 2 emissions was taken by 37 industrialized countries [4]. Later in December 2015, 195 countries 1 agreed to combat climate change and take actions to promote sustainable future in what is known as the Paris agreement [5, 6]. The parties agreed to take appropriate actions to keep the global temperature rise below 2 C, to reach a global peak of greenhouse gas (GHG) as soon as possible, and to reduce the GHG emissions thereafter. Several countries have taken measures to fulfill the agreements; however, the effectiveness of these measures has been questioned [7]. As a part of a larger aim to reduce the GHG emissions by 80% 95% below 1990 levels by the year 2050, the EU aims to decarbonize the energy demand mainly by electrification in both the transportation and the heating/cooling sectors [8]. This is expected to increase the demand for electricity by 2050 [8]. Moreover, the EU aims to supply this demand by almost emission free electricity. Such a transition is expected to come with several advantages such as less dependency on fossil fuel imports, and expansion of the energy system leading to economic growth. The EU aims to halve the use of the internal combustion engine vehicles (ICEVs) in cities by 2030, and to completely ban them by 2050 [9] thereby placing electric vehicles (EVs) 2 in the core of every climate initiative. EVs, unlike ICEVs, have zero tailpipe emissions, produce less noise and if charged with carbon-free fuels can reduce GHG emissions [10]. Globally, the average annual electricity consumption per capita increased from 2.1 MWh/capita in 1995 to 3.1 MWh/capita in 2014 [11]. In the EU, however, the average household s consumption of electricity fell by 0.9% from 2005 to 2015 [12]. Even though increases were experienced in 18 countries the highest of which was Romania with a 31% increase other countries witnessed a decrease, such as Belgium with a 27.6% decrease [12]. As regards energy efficiency, the global energy intensity in kwh/gross domestic product (GDP) decreased by 2.1% annually from 2010 to 2016, 1 Later on 1 June 2017, the USA announced its withdrawal from the agreement. 2 EVs in this document include both battery electric vehicles (BEVs) and plug-in hybrid electric vehicles (PHEVs) operating in electric mode. 1

12 which reflects adopted measures to improve efficiency since the annual rate of reduction was on average 1.3% from 1981 to 2010 [13]. There is, still, a large improvement potential in the energy efficiency, globally, as it is estimated that 68% of the global energy use is not covered by efficiency standards [13]. The previous policies and initiatives have stimulated a transition to a modern electricity system. Several trends were identified as cornerstones of this transition. Among these trends are extensive electrification of different sectors such as the transportation sector, decentralization through distributed generation from renewable energy sources (RES), and digitalization of network services such as smart grid services [14, 15]. The World Economic Forum proposed four recommendations to, potentially, accelerate the transition to the future electricity system [14]. The four recommendations are redesigning the regulations governing the electricity system, deploying the necessary infrastructure, improving customer experience, and adopting new business models. Due to the electrification of the transportation sector and the increase in the RES penetration, the modern electricity system might need enhancements to the existing infrastructure or even building new ones, e.g., smart grid communication infrastructure [14, 16]. Some of these enhancements might be alleviated if EV scheduling and demand response (DR) were widely employed especially in grids with high penetrations of variable RES. Even without DR, accurate models of the future electricity system might help avoiding unnecessary expensive investments in the infrastructure [16]. 1.1 Aims of the thesis The overarching aim of this thesis is to contribute to the knowledge regarding the operation and performance of the future electricity system through 1) developing a model to estimate the charging load of private EVs in cities, and 2) providing a probabilistic load forecast (PLF) model for the residential electricity demand. The EV charging model can be used along with RES and load models to perform a spatial study to identify the weak locations in the grid infrastructure. The forecasting model is of value to for example electric utilities, short-term electricity traders, and grid operators. A forecasting model for the EV charging load in a possible future work is a good complement to the residential electricity demand PLF model. 1.2 Overview of the appended papers The appended papers were chosen to cover the methods developed to fulfill the aims of the thesis. Papers employing the same method were ranked based 2

13 on the author s contribution and the accordance of the case study with the aims of the thesis. Paper I provides a literature review of the previous research in city-scale photovoltaics (PV) generation and EV charging modeling. The review concluded by the remark that the city-scale studies on the synergies between EVs and PV are scarce and more contributions are needed. Paper II presents a grid study that analyzes the impacts of PV and private EVs on a distribution grid in Sweden. Paper III formulates a spatial model to estimate the charging load of private EVs in cities. Unlike the previous contributions in the literature this model employed geographical information system (GIS) data to provide a more spatially accurate charging patterns of parking lots. Paper IV provides an analysis of the performance of Gaussian processes (GPs) in residential load forecasting. The conventional GP was compared to an improved model the log-normal process (LP). 3

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15 2. Background This chapter provides a background for the research done in the thesis. Section 2.1 introduces the reader to EVs and the recent progress done in the related research field. A background on the residential electrical load is provided in Section 2.2. Finally, research gaps are identified in Section Electric vehicles Technological advancements in the second half of the 19th century led to the successful introduction of EVs [17]. During the first decade of the 20 century, the market share of EVs peaked at 38% in the USA, which was the second largest market share after steam vehicles with 40% market share [17]. This trend continued until the introduction of the Ford model T and the invention of the assembly line, which resulted in the rapid uptake of ICEVs and the downfall of EVs [17] Sales and barriers Globally, the sales of EVs and fuel cell EVs exceeded one million in 2017, thereby making the global stock exceed 3 million cars [10]. Sweden was the third largest market with EVs representing 6.3% of the sales of cars [10]. China alone had 40% of the global stock of EVs, while the EU and USA accounted for approximately 25% each [10]. With the currently announced polices and incentives, it is estimated that the stock of EVs could reach 125 million cars globally by 2030 [10]. In Norway, incentives which started in 1990 were not sufficient back then to promote the mass adoption of EVs [18]. The situation improved when Li-ion batteries were mass-employed in the EVs batteries [18], possibly due to the higher energy density of Li-ion batteries which resulted in EVs with longer ranges. This is to say that EV usability, and the public awareness of the environmental benefits are important factors in the wide adoption of EVs [19]. On the other hand, the high purchase price, driving range, and the lack of strong charging infrastructure are considered among the main barriers to the rapid adoption of EVs [19 21]. Car dealers are considered one of the barriers to the wide penetration of EVs [22 24]. In the Nordic countries for example, car dealers were observed turning potential buyers away from EVs to ICEVs, providing wrong information 5

16 about EVs, and even avoiding to mention them [22]. Misinformation which conflicted with the specifications of the sold EVs regarding the range of the EVs were often provided. It is, however, important to note that there is a plethora of estimates for the range of EVs. The estimates vary based on the assumed driving cycle and other factors [25, 26]; amongst these factors is the ambient temperature [27]. The direct current (DC) consumption was estimated to average 0.20 kwh/km in [25], and to range between kwh/km in [27]. By 2020, the alternating current (AC) consumption of EVs was assumed to be kwh/km in [28] Demographics of current EV owners Currently, EV owners tend to be younger, more likely to have higher education, live in populated areas, have higher income, and have more cars per household than ICEV owners [29]. Both EV owners and ICEV owners commute equally long, though EV owners perform long trips more than 100 km a day more frequently [29]. The authors in [29] explained this by the lower operating costs of EVs compared with ICEVs. However, it was not clear, in the paper, whether these long trips were performed using EVs. It might be that since EV owners are richer they perform longer trips more frequently than the ICEV owners. As the penetration level of EVs increases and more affordable EVs enter the market, the demographic difference between EV and ICEV owners is expected to shrink Cost of ownership The high purchase cost of EVs is considered among the barriers to the wide penetration of EVs [19]. The purchase price of EVs is generally higher than that of similar ICEVs. However, the running cost of EVs is cheaper than similar ICEVs. The low running cost makes EVs a better choice, economically, for car fleets owned by companies and governments [30]. Based on 2014 fuel prices in Europe, the fuel costs of EVs were 3% 69% cheaper than that of ICEVs [31]. The saving percentage depended on both the cost of electricity and the cost of fossil fuel in the country. The electricity prices ranged between EUR per kwh, and the fossil fuel prices ranged between EUR per liter [31]. A chart presenting the relation between the running costs of both EVs and ICEVs for different fuel and electricity prices is provided in [32]. Smaller EVs are penalized by the high cost of the battery more than larger EVs [31], which results in them being less cost competitive in comparison with similar ICEVs. Weldon et al. [21] concluded that large EVs are more economical than smaller EVs when compared with a similar sized ICEV. Moreover, 6

17 the fuel cost makes EVs a more economical option, compared with ICEVs, for drivers with longer more than 15,904 km a year annual driving distance EV batteries One of the reasons for the high price of EVs is the high price of the battery [33]. For example, a 100 kwh Li-ion battery pack is estimated to cost $25,000 to produce [34]. Early EVs relied on lead acid batteries for energy storage [35], which are 60% cheaper than Li-ion batteries [33, 35]. Nevertheless, lead acid batteries have a low energy content when compared to Li-ion batteries 40 Wh/kg and 125 Wh/kg, respectively [36]. The economies of scale and advancements in the manufacturing technology are expected to lower the price of the battery pack to be as low as $125 per kwh by [34, 37]. The lifetime of the batteries of EVs is usually rated to 150,000 km or 8 10 years [38, 39]. The lifetime is, however, dependent on certain factors such as the charging/discharging rate and temperature [40]. The current battery technology needs improvements to withstand fast charging. Ahmed et al. [41] provided a detailed analysis of the impacts of fast charging 400 kw on the Li-ion batteries. The results indicate safety challenges combined with battery degradation due to fast charging. Using the batteries of EVs after degrading below the standards of the automotive applications is commonly known as the second life of the EV batteries [42, 43]. The economic viability of the second life of EV batteries, however, depends on the underlying assumptions such as the purchase cost of the degraded battery, and the fluctuations in the electricity price [44, 45] Charging infrastructure The EV charging infrastructure is often portrayed as the chicken egg problem ; where investments in charging stations require high penetration of EVs simultaneously a large penetration of EVs requires a strong charging network [46 48]. Some argue that access to charging at home might reduce the severity of this problem, at least for early adopters [47]. In Norway for example, 75% of the population park their vehicles in their own property, and 74% of the households have sufficient power capacity due to electric heating systems to charge their EVs [18]. The EU recommends having at least one publicly accessible charging point per 10 EVs in the city by the year 2020 [49]. Sweden notified the EU with their estimate of EVs per one public charging port as of 2016, which is slightly below the EU 2020 requirement [50]. Numerous countries have currently achieved the EU 2020 goal, but they expect that by 2020 the rapid increase in EV penetration will surpass the expansion of the charging infrastructure. Germany, for example, estimated in 2016 that there are 4.86 EVs per 7

18 publicly accessible charging port, which will increase to 23 EVs per charging port by 2020 [50]. This is to say that the publicly accessible charging ports per EV in Germany will be approximately 5 times scarcer by 2020 compared with On the other hand, the Netherlands predicts to meet the EU requirement and to have a network of one publicly accessible charging port per 7.85 EVs by France claimed that the requirement of TEN-T Core Network at least one fast recharging point every 60 km of highways was already achieved in Targets for the distance between fast chargers on highways for the year 2020 were proposed to be 45 km and 115 km for China and the USA, respectively [10]. The lack of strong charging infrastructure was often mentioned as a barrier to the purchase of EVs, e.g., Germany [20]. The current German infrastructure, however, is stronger than both the EU s 2020 goal and Germany s forecast for 2020 [50]. Moreover, Norway the country with the highest EV sales share [10] have EVs per publicly accessible charging port which is worse than Germany [51]. This is to say that the effects of the soon to deteriorate infrastructure, in Germany for example, on the public appeal of EVs needs further investigation. To the best of my knowledge, these effects were not studied before. As regards the fast charging infrastructure, Bryden et al. [52] estimated that a fleet of 1 million EVs with 322 km range in the USA would need 5,000 fast charging sessions a day, i.e., 0.5% of the EVs use fast charging each day. Moreover, they showed that an EV with 322 km range need fast charging at a rate of 32.2 km/min around 400 kw to suffice 80% of the trips without extending the resting time. Gnann et al. [53] estimated the need of an infrastructure such that the number of EVs per fast charger to range between and 147 1,429 for Sweden and Germany, respectively. The wide range of results is attributed to the variations of charging power and battery capacity and to the differences in the specifications of the long trips between the two countries. The higher the charging power and the longer the range of the EVs the larger the number of EVs per fast charger [52, 53]. Fast charging, however, comes with extra challenges such as high costs for both charging stations and EVs, and high load intermittency combined with in some cases low utilization [54] Modeling the charging load of EVs As shown in Paper I, numerous methodologies have been used in modeling the charging load of EVs. Among the widely used methods are the Markov process in e.g. [55 57], Monte Carlo sampling in [58 60], Copula in [61], basic physical models in [62] based on mechanics fundamentals such as equations of drag, friction, etc. 8

19 Many papers rely on travel survey data for ICEVs in their model development. The underlying assumption is that future EVs, with long enough ranges, will not force drivers to adapt their driving behaviors. As shown in [63], ninety-five percent of the American drivers with an EV with a 350 mile range 563 km will have to adapt only one week a year. This is to say that the inconvenience due to the limited range of EVs is trivial with the currently available technology, e.g., Tesla Model S 100D. One thing to note here, is that the previous study according to the authors provided a top-estimate of the driving requirements in the USA. Moreover, it did not account for the possibility of fast charging during the long trips. Different types of data have also been employed in EV charging models, e.g., global positioning system (GPS) and mobile phone data [62, 64] and data from road cameras [65]. Currently, with the slight increase in the penetration of EVs, mobility data from EVs have become available along with data from charging stations regarding charging sessions. Such recently recorded data were used in [53, 58, 66, 67]. It was noted in [68] that the charging profiles of EVs can be categorized into several categories based on the charging location. For example, an early morning charging profile was observed at workplaces. On the other hand, a late evening charging profile was observed at residential locations. Such findings were used in recent models, e.g., [57, 64], to model the spatial load of EVs in cities. The electricity grid is spatially heterogeneous. This is to say that the strength of the grid is not spatially constant, and that the impacts of load/generation on the grid depend on the connection location [69, 70]. Consequently, spatial estimates of the EV charging load are essential to better evaluate the impacts of EVs on the grid. As regards modeling the spatial mobility of EVs, several approaches have been proposed, e.g., origin destination matrices in [71], Markov chains with rank-based exploration and preferential return in [64], and using spatial data from trip records in [72] Grid impacts of EVs The current electricity grid was not designed to supply the charging load of EVs. Unlike the residential load, fully charging an EV consumes large amounts of energy at high powers. Depending on the grid design and the supplied loads, EVs can have a wide range of impacts on the voltages, losses, and components loadings. Both the penetration level and the charging power heavily affect the impacts on the electricity grid. The penetration level is commonly defined as the number of EVs as percentage of the total number of vehicles in the studied location. Muratori [73] studied a distribution transformer with six customers in the USA. The results indicated that for the 100% penetration case the transformer 9

20 would operate 2.8% and 9.4% of the time above the nominal capacity for charging powers 1.92 kw and 6.6 kw, respectively. In the 6.6 kw case, the peak load was estimated to be 84% higher than the nominal capacity. A similar study was performed on a workplace transformer and a residential grid with 17 households in the UK [55]. As regards the workplace transformer, it was largely over-sized for the building, 1 MVA transformer for a 0.4 MVA peak load. As a result, the 100 simulated EVs charging with 7.4 kw did not overload the transformer. On the other hand, the residential grid suffered from under-voltage, less than 0.94 per-unit (pu), for 9 hours a week within 99% confidence interval. This under-voltage took place during peak hours. Charging with 15 kw chargers and in a different grid, Mu et al. [71] showed that a 50% EV penetration could cause under-voltage problems where bus voltages would reach 0.86 pu. In addition, two branches exceeded their loading capacity at 50% penetration rate. Given that the damaging effects can occur due to the simultaneous charging of a large number of EVs especially during peak hours, controlled charging schemes, such as off-peak charging, have been presented as a solution to such a problem Controlled charging During the early days of EVs in the late 19th century, the potentials of using controlled, or smart, charging were observed [74], as late evening EV charging flattened the load curve for utilities back then home appliances were not as prevalent as today and increased revenues from selling more electricity. The load curve has changed since then, yet improving the load factor has encouraged researchers as early as the 80s to evaluate the potentials of off-peak EV charging [75]. Recent research showed that controlled charging can improve grid voltage in [71, 76], grid components loadings in [71, 77, 78], grid losses in [76], peak load in [66], charging costs in [79], valley filling in [80], and RES integration in [81]. One concept connected to smart charing is the vehicle to grid (V2G) concept, in which a bi-directional power flow between the grid and the EV is enabled [82, 83]. Vehicles are parked on average 22 hours a day with 16 hours, on average, of uninterrupted parking after the last trip of the day [84]. These long parking durations encourage the usage of the, otherwise unused, EV batteries to provide ancillary services, such as frequency regulation reserves, to the electricity grid [85]. Controlled charging schemes can be categorized into two categories, centralized and decentralized [86]. In the centralized, a single controller manages the charging of multiple EVs, unlike the decentralized in which individual EVs take the smart charging decisions. In recent years, there has been a trend to- 10

21 wards the aggregation of several decentralized controllers such that they represent an aggregator [87]. The role of an aggregator is to communicate between EVs and energy market players [88, 89]. Aggregators increase the economic and technical benefits of controlled charging by increasing the size of the managed car pool [90]. Will and Schuller [91] reviewed the user acceptance of the concept of smart charging by surveying EV early adopters in German. The majority of the respondents, 76%, expected to be allowed to override the smart charging scheme, i.e., to charge opportunistically. The results also showed that the user acceptance of smart charging is positively correlated with the possibility of increasing the RES penetration in the grid and with improving the grid stability. On the other hand, the monetary compensation did not affect the owners acceptance of smart charging. The authors explained this by indicating that the EV owners valued more their flexibility than the saved expenses. Other concerns, such as concerns regarding EV battery degradation, privacy, and range anxiety are among the factors that limit the acceptance of smart charging [87] Charging with RES Charging EVs using RES reduces the carbon footprint of EVs [92], and thereby contributes to reducing the carbon emissions from transportation. In fact, electricity supplied from dirty energy sources, such as coal, can result in ICEVs becoming environmentally friendlier than EVs [93]. Depending on the mixture of energy sources of the electricity grid, off-peak charging can reduce or increase the EV charging emissions [92, 94]. High shares of PV in the grid will encourage midday charging to increase the solar energy utilization. On the other hand, high shares of wind in the grid supply might favor late evening charging [95, 96]. Nonetheless, the diurnal profile of wind speed, and thus wind generation, is both location and season dependent. For example, the average diurnal wind profile has a midday peak in Sweden [97], a late afternoon peak in Italy [96], and a flat curve in Finland [97]. One potential benefit of midday charging is that it increases the daily range of EV through charging twice a day [98]. EVs can be charged during the day and reduce the curtailment of PV. Denholm et al. [98] showed that EV charging can almost halve 11% to 6% the PV curtailment for the case of 50% and 30% penetrations of EVs and PV, respectively. One limitation of RES charging of EVs arises from the seasonality of RES and the seasonal correlations with both the EV and the grid loads. For example, PV production in Sweden is lowest in winter, while the EV consumption is highest due to e.g., the heating load of the car. Moreover, off-peak charging of EVs is mostly needed during winter evenings, which is the time of the peak load in the Swedish grid. In another warmer country, the peak load in the grid 11

22 and peak EV consumption can be better correlated with the PV production both occur in summer, e.g., in [98]. There is an inverse relation between the population density and both the per-capita PV production and the per-capita transportation energy requirement [99, 100]. This means that in rural locations, rooftop yields are larger and energy spent on transport are larger than that of urban locations if both are measured per person living under the roof. In the study made on the city of San Francisco, California, Ko et al. [99] showed that for all population densities, the rooftop solar yield is enough to supply the transportation requirements both per-capita if EVs with consumption less than 0.22 kwh/km and PV with efficiency higher than 13.5% were used. A similar finding was observed in the city of Auckland, New Zealand [100]. 2.2 Residential electrical load On-site electric lighting systems have been installed from as early as 1878 [101]. By 1885, the business of electric lighting systems quickly expanded to reach 1,500 installations in the USA, owing to the initial development of the incandescent light bulb by Thomas Edison in 1880 [101]. In the year 1888, Westinghouse electric company bought the patents of the AC system from Nikola Tesla, and after 5 years an AC lighting system was used to light the World s Columbian Exposition in Chicago [102]. Currently, electricity lies at the heart of both the residential and the industrial sectors. Both sectors in Sweden are supplied through 15,000 km of electricity transmission lines delivering 140 TWh of electricity a year [103, 104]. Almost half, 51%, of this energy is used by both the residential and the service sectors [105]. In comparison, if EVs were used in all the private car trips in Sweden totalling 68 billion km in 2017 [106] an increase of 15.6 TWh, or 11%, in electricity generation and transmission will be required assuming a consumption of 0.23 kwh/km [28] Modeling There are two broad categories of electricity demand models: top-down and bottom-up models [107]. The top-down assumes that the residential electricity consumption is an energy sink where the individual behaviors are trivial [107]. Instead such models rely on long term changes in the residential sector and on macroeconomic indicators such as the GDP. On the other hand, bottom-up models rely on data such as the activity patterns of the appliances in the household to model the electricity consumption [107]. Top-down models were developed in e.g., [ ] and bottom-up models in e.g., [ ]. In addition to the previously described categories, some models rely on prob- 12

23 ability density functions (PDFs) of known distributions or mixtures thereof, e.g., [ ]. Kavousian et al. [118] analyzed data from smart meters in the USA and observed that the weather and the floor area were the most important predictors of the minimum daily load. Nonetheless, the peak daily load was best modeled using large loads such as electric heaters [118] Demand response potentials According to the US Department of Energy, DR is a program to incentivize changes in electricity usage behavior in response to price signals where high prices correspond to times when the grid reliability is jeopardized [119]. This definition makes the aim of DR similar to the aim of controlled charging of EVs. In fact some authors consider EVs as part of the residential load which reacts to price signals or RES availability. DR incentives can be categorized into two categories: price-based DR, and incentive-based DR [120]. The price based DR motivates customers to shift their load to times with lower price signals. On the other hand, in the incentivebased DR utilities or grid operators reward participants financially based on the gained benefits. Both the customers and the utilities or grid operators benefit from DR [120]. Customers reduce their costs by using the electricity grid more efficiently, and simultaneously utilities benefit from a better matching of supply and demand and from an improved grid reliability. The benefits of the DR are expected to increase with the increase of the share of RES in the energy supply since RES, such as PV and wind, are variable by nature. Such a variability, if not managed properly using e.g., DR, could cause an economic barrier to a high RES penetration due to the high integration costs [121]. In some DR programs, the participants engagement decreased after the new technology hype diminished [122, 123]. Such a finding indicates the importance of understanding the human behavior in order to maximize both the engagement of participants and the benefits of the DR programs. An important study in this field was done by Sintov and Schultz [123] who reviewed the models in behavioral science and connected them to the results of the applied smart grid programs such as DR Forecasting In order to plan a day ahead DR schedule, accurate forecast of the load and RES generation is essential [124, 125]. In this thesis, forecasting and modeling are differentiated based on the type of predictors used in the model. In forecasting and unlike modeling, previous values of the time series are used 13

24 as predictors sometimes with other exogenous predictors such as weather information, hour of the day, etc. to forecast future values. Forecasting loads with higher variability is more difficult than loads with low variability, see e.g., [126, 127]. Consequently, as the time resolution increases e.g., hourly instead of daily and the number of forecasted households decrease, forecasting becomes more challenging. Forecasting methods can be classified into two categories based on their output: deterministic forecasts and probabilistic forecasts [128]. In a deterministic forecast, the model produces a point result representing the forecast. On the other hand, the probabilistic forecast produces a PDF within which the future value is expected to be. The deterministic forecast, however, can be understood as the mean of the PDF of the probabilistic forecast. Various forecasting techniques have been successfully employed in the literature, e.g., auto regressive integrated moving average (ARIMA) models in [129], artificial neural networks (ANN) models in [130], support vector regression (SVR) models in [131], and GP models in [ ]. The usage of hybrid methods, which combine two or more techniques, have been steadily increasing lately [135], see e.g., [136]. 2.3 Research gaps The work that has been done so far in the fields of EV modeling and load forecasting is comprehensive. Nevertheless, there are some research gaps that need to be complemented. Regarding the synergies between EVs and PV, there is a scarcity in the city-scale studies. Moreover, many city-scale studies used a deterministic EV charging model and PV assumptions. A city-scale grid study was missing using stochastic PV and EV models. Paper II tries to contribute to filling this research gap. Multiple EV models have been proposed in the literature. These models required as an input the locations of the charging stations and the number of parking lots in each station. Some models attach the load of the charging EVs to the electrical load of the buildings with little regard to the locations of parking similar to our implementation in Paper II. A more realistic model could assume that charging occurs in a parking location, e.g., public parking lot with EV chargers. Paper III fulfills this research gap by relying on the GIS data to spatially estimate the charging load in the parking locations. It is expected that some parking lots in a big city might be visited by multiple different drivers with different trip purposes during the day, e.g., work and leisure trips. These parking lots, if they have EV chargers, might have a charging profile that is different from a similar parking lot visited only be drivers going to work. This phenomenon 14

25 has not been included in any of the previous EV models, and Paper III provides a method to account for this phenomenon. Several previous studies have employed GPs in forecasting the electrical load. Many of these implementations treated the GP as a deterministic forecast. Such a treatment excluded one of the main advantages of GPs, which is that they provide a PDF of the forecast making them probabilistic by nature. In addition, the residential load of households is not normally distributed the load cannot be negative without RES generation. Normal GP assumes a normally distributed forecast. Paper IV utilized the probabilistic nature of the GP and evaluated the forecasts using probabilistic error metrics. Moreover, a new method was implemented to account for the problem of the GP and the non-normality of the residential load. 15

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27 3. Methodology This chapter presents the methods used in the thesis. The methods used to develop the EV charging model and the GP forecasting model are presented in Sections 3.1 and 3.2, respectively. 3.1 Electric vehicle charging model This model is divided into three parts as shown in Figure 3.1. Part I, described in Section 3.1.1, uses GIS maps to extract the information about parking lots or charging stations. Section presents part II of the model, which models the mobility of EVs in the city using a Markov chain. Part III of the model estimates the spatial charging load due to the mobility of the EVs, and it is described in Section The EV charging model, presented here, was used in Papers II and III Extract charging stations The information about parking lots and thus potential charging stations are extracted from GIS maps. The model is designed to utilize spatial information from OpenStreetMap (OSM) [137], or other proprietary maps to extract the features of parking lots. Areas of parking lots and information about neighboring buildings are extracted from the GIS data to cluster the parking lots based on the usage profile. Figure 3.1. A layout of the three components of the EV charging model. 17

28 Figure 3.2. An imaginary parking lot with imaginary surrounding buildings. The buildings located within the buffer distance the black solid line are assumed to be visited by the parking lot users. The model assumes three distinct usage profiles of parking lots: Work, Home, and Other. Each profile reflects parking to visit a category of buildings, e.g., Home represents residential buildings. Each parking lot is expected to be used by users adhering to one or multiple profiles. The underlying assumption is that in a large city the usage profile of the parking lots is similar to the usage profile of the nearby buildings. In other words, car drivers will park near the visited locations [138, 139], especially if the parking fees are neglected [139]. The model draws a buffer distance around each parking lot. The buffer distance is used to resemble the walking distance between the parking lot and the surrounding buildings. The building types located within this buffer distance are assumed to be visited by the users of the parking lot. Consequently, the types of these buildings within a certain walking distance determine the usage profile/profiles of the parking lot. Buffer distances or air distances were used before in the parking model developed in [140] and in the optimization of taxi charging stations in [141]. In case of multiple usage profiles for a parking lot, multiple charging stations are created with surface areas proportional to the building footprint area of the different building types. If the buffer distance does not intersect any buildings, the parking lot is divided equally on the three usage profiles, i.e., three charging stations were created with equal areas. Figure 3.2 depicts an imaginary parking lot surrounded by imaginary buildings, as an example. In this example, two building types are located within the assumed buffer distance which are workplaces and other buildings. As a result, two charging stations, Work and Other, are created such that the area of each charging station is proportional to the building areas of the same type that are located within the buffer distance Markov chain for EV mobility A Markov chain is a stochastic process in which the conditional probability of the future states depends only on the current state [142, 143]. For example, a stochastic process {Y t } t=0 is a Markov chain in state space S and transition 18

29 Figure 3.3. A diagram depicting the three Markov states of the model and the transition probabilities between the states. Note that the probabilities of remaining in the same state are not presented in this diagram, i.e., p 11, p 22, and p 33. The three probabilities are estimated from the equations 3 j=1 p ij = 1, for i in {1,2,3}. matrix T if for all i and j S we have P(Y t+1 = j Y t = i,...,y 0 )=P(Y t+1 = j Y t = i)=p ij, (3.1) where p ij is the probability of transitioning from state i to state j [142]. A transition matrix T might be formed for a Markov chain with M states, p 11 p 12 p 1M p 21 p 22 p 2M T =......, (3.2) p M1 p M2 p MM such that the M j=1 p ij = 1, for all i. The probabilities of transition can be estimated from the maximum likelihood as N ij p ij = M j=1 N, (3.3) ij where N ij is the number of transitions from state i and j [143]. In Equations (3.1) and (3.2), a homogeneous Markov chain is defined where the transition probability between states is time independent. In practical implementations, the time-homogeneity assumption might not be valid, especially in applications where the transition probabilities are expected to change with time. For example, in a traffic model the transition probabilities between two states say street junctions might be time dependent [65, 144]. In the model, three Markov states are defined: Work, Home, and Other. Each state represents a parking profile in the city as described before in Section The model states and the transition probabilities are presented in Figure 3.3. In the developed model, the transition probabilities are assumed to be timedependent such that they change on minute basis and based on whether the 19

30 transition time is on a weekday or a weekend. In other words, the transition matrices are T δ =((p δ ij )) M M where δ is a variable that signifies the time of transition the minute of transition and whether the transition takes place on a weekend or a weekday. Thus there are, in total, transition matrices instead of the one shown in Equation (3.2) Spatial charging load Each parking lot, or a charging station, in the city is assumed to belong to a unique state. As stated before in Section 3.1.1, a parking lot might be used according to multiple parking behaviors, e.g., by workplace and residential drivers. In case of a mixture usage behaviors, the parking lot is divided into multiple parking lots each belongs to a unique state. When an EV transitions from one state to another it is randomly assigned to a new parking lot which belongs to the new parking state. Grahn et al. [145] defined the instantaneous capacity Et v (kwh) of the battery of the vehicle v at time t as E Et v t 1 v +Cψ Δt if charging, = Et 1 v η d if driving, (3.4) else, E v t 1 where C ψ is the charging power (kw) of station ψ, d is the driving distance (km) driven by an EV during Δt, and η is the specific energy consumption (kwh/km) which is the AC energy needed to drive one km. The driving states are excluded from this model, as it was also done in [57]. This is to say that in this model the driving occurs instantaneous, Δt = 0, and the driving distance d is sampled from the recorded trip distances between similar states. This assumption will cause the model to over-estimate the charging time in the origin location by a duration which equals the driving duration. In Sweden, the average trip takes 44±2 minutes (95% confidence interval) [146]. The load in each station P (kw) of station ψ at time t is defined by Pt ψ = C ψ mt ψ, (3.5) where mt ψ is the number of charging EVs in station ψ at time t. A normalized power P t (kw/car) is also defined such that P t = 1 n EV Pt ψ, (3.6) ψ n st where n EV is the number of EVs in the city and n st is a set of stations. This metric is of importance to evaluate the total load per vehicle in the city or in some parking states in the city, for example Home. In addition, the peak value of the normalized power P t is estimated and named the peak of the normalized power (PNP). 20

31 3.2 Gaussian process forecasting This section starts by describing the mathematical foundations and forecasting equations of the GP in Section 3.2.1, then the role of the covariance functions in forecasting is outlined in Section A toy-example presenting the usage of the training data to train and forecast using the GP is provided in Section The newly employed method, the LP, is presented in Section Finally, the error metrics used to evaluate the accuracy of the forecast are provided in Section The methods described in this section were used in Papers IV and V Gaussian process In this section, a summary of the mathematical representation of the GP is provided. The summary provided here follows Rasmussen and Williams [147], who provided a detailed description of the GP. A GP is a collection of random variables, any finite number of which have a joint Gaussian distribution. The GP can be defined as f (x) GP(m(x),k(x,x )), (3.7) where m(x) is the mean function, k(x,x ) is the covariance function or kernel, and f (x) is the value of the function at the location x. The random variables represent the value of the function. In a general case, the location x is a vector of D predictors, i.e., x R D. Provided a set of training observations (X,y) of size n where X R n D and y R n, and a set of test points (X,y ) of size n where X R n D and y R n, a joint distribution between the training and test outputs f(x) =y and f(x ) can be estimated as [ ] ( f(x) N f(x ) 0, [ ] ) K(X,X) K(X,X ), (3.8) K(X,X) K(X,X ) through incorporating the knowledge available in the training data to constraint the functions to the ones resembling the training data and through assuming the mean function m(x) to be zero as it is commonly assumed [147]. Note that this assumption does not constraint the mean of the posterior process to be zero [147]. The covariance matrix between all the pairs of test and training locations K(X,X) is defined to be k(x 1,x 1 ) k(x 1,x 2 ) k(x 1,x n ) k(x 2,x 1 ) k(x 2,x 2 ) k(x 2,x n ) K(X,X)=......, (3.9) k(x n,x 1 ) k(x n,x 2 ) k(x n,x n ) 21