Optimal Sizing of Energy Storage System to Reduce Impacts of Transportation Electrification on Power Distribution Transformers Integrated With Photovoltaic

Transportation systems are one of the leading sectors that contribute to greenhouse gas emissions that lead to enhance global warming. The electrification of vehicles is a promising solution to this widespread problem; however, integrating electric vehicles (EVs) into existing grid systems on a large scale creates several problems, both for consumers and for utilities. Accelerated aging of expensive grid assets, such as power transformers, is one of the primary issues that these utilities are facing. This problem can be addressed with battery energy storage systems (BESS), which acts as buffer between demand and supply. Accordingly, this paper proposes a novel strategy for optimal sizing of BESS based on thermal loading of transformers. This paper also investigates issues associated with high penetration levels of rooftop photovoltaics (PVs), determining the synergy between EV charging load and BESS. The proposed solution is treated as an optimization problem, in which a new time of use (ToU) tariff is utilized as a demand response signal to reduce the accelerated aging of transformers. Extensive simulation results show that the size of BESS can be considerably reduced based on the proposed methodology, thereby avoiding accelerated aging of transformers without the need to augment existing grids.


INDEX TERMS
Number of households. P BESS BESS size (kWh). P EV EV load (kVA). P PV PV generation (kVA). P R Residential load (kVA).

P total
Total load on transformer (kVA). r Ratio of rated load loss to no-load loss.

S nom
Nominal power of transformer (kVA). S t Apparent power of transformer (kVA).

SOC min
Minimum SOC of EV battery (%). T Time horizon. t Index time. th min θ H to start off-peak price ( • C). th peak θ H to start peak price ( • C). th sdr_1 θ H to start shoulder-1 price ( • C). th sdr_2 θ H to start shoulder-2 price ( • C). X pen EV penetration level.

I. INTRODUCTION
Electric vehicles (EVs) have become a popular choice, as they emit far less carbon than conventional vehicles, even when their electricity originates from non-renewable sources [1], [2]. Further, the use of renewable energy (like PV) and EVs are emerging as the most viable strategy to address growing environmental concerns and energy scarcities, where this trend is likely to expand in the future [3]. Electric vehicle penetration levels are expected to skyrocket in the coming decades, with estimates predicting that by 2040, roughly 30% of the worldwide passenger fleet will be electric [4]. There is a much current research and development in the integration of EVs into transportation systems, mainly focusing on EV owner perspectives. However, reducing the impact of the eventual integration of EVs from a utility standpoint is just as important. In this regard, negative effects of EVs on power distribution system are one of the most significant barriers [5]- [7]. The inherent coincidence of projected EV demand and conventional peak load in particular, can generate severe distribution overload [8]- [10]. Further, the diversity of load in the distribution level is relatively lower than in the transmission level, making this more dramatic [11], [12]. The authors of [5] and [6] have determined that charging electric vehicles during peak load periods overburdens distribution system. Further, with EV penetration level of 60%, augmentation investment costs can grow by 15%, where energy losses can approach 40% [7]. As most EVs are charged on the low-voltage side of the grid, their adverse effects are greater. At AC level 2, the power demand for traditional EV loads is about 19.2 kW [13], which is nearly 20 times that of household appliance power demand [14]. This has the potential to create voltage and frequency deviations, resulting in an unstable system with a real-time power mismatch. A system's distribution grid should be able to accommodate additional EV charging load without compromising network stability, where grid expansion often takes decades due to the long life of grid assets [15]. The effect of uncoordinated charging on a power system, in particular on its transformers, can be catastrophic. Transformers are seen as the most critical and expensive element of an electrical grid, where it is very costly to replace them [16], [17].
There are numerous studies that have investigated the benefit of BESS coupled with charging stations [18]- [20]. The use of energy storage devices to control renewable generation and load fluctuation has been investigated in [21]. Gimelli et al. [22] and Martins et al. [23] have also investigated optimal BESS size and design in the context of cuttingedge peak shaving. An incentive-based demand response program was used in one study to maximize the reliability of a microgrid by selecting an optimal BESS size [24]. Real time pricing, using a fuzzy logic controller and swarm optimization has also been used to optimally size hybrid energy system in [25], [26]. These references have also investigated different price elasticity of demand and dynamic pricing, based on the state and characteristics of a BESS. However, the idea of charging EVs in conjunction with demand response programs integrated with roof-top PV systems and BESS without impacting the grid has not yet been explored. Further, by purchasing electricity from the grid during off-peak times, a BESS can reduce system (transformer and feeder) upgrade costs [18], [27]. Finally, BESS can help EVs to be more resilient, by supplying them with the required energy to travel to safe charging stations in the event of a system failure.
The authors in [28] have proposed a system design for a grid-tied PV system to charge EVs and support existing household load. Bedir et al. [29] have experimentally shown that a PV combined with a BESS can be used to reduce the overall cost of electricity to charge an EV. Authors of papers [30] and [31] have tried to determine if the addition of roof-top PV can help in reducing the accelerated aging of transformers due to EV load. They observe that although the additional generation from PV has the potential to improve the LoL of transformers, due to a lack of chronological coincidence, this effect is negligible. The works of [31], and [32] have also studied the LoL of distribution transformers for charging EVs when PV is present. However, the thermal time constant of transformers has not been taken into account above, which leads to minimal synergetic relations between EV load and PV generation.
Authors in [33] have developed an approach for determining the impact of high EV adoption on distribution transformer thermal aging, showing that transformer LoL is mostly influenced by ambient temperature and transformer loads. The authors of [34] have tried to address this problem using ToU tariffs to minimize the LoL of distribution transformers. They solve this as an optimization problem, where demand response based on price elasticity is used to shift the electrical demand of both residential load and EV load based on the thermal loading of the transformer. This paper was successful in lowering the LoL of transformer, even for 50% of EV penetration. However, not all loads were supplied by 1900 hrs the next day. A maximum of 20% percentage of 'load not supplied' was used as a constraint. As per Fig. 1, the percentage of unsupplied load varied from 6.2% to 18%. This is due to fact that not all residential loads are deferrable. Accordingly, this also means that to have all load supplied, the size of the battery should match to supply this additional EV charging load. Further, it is apparent that normal residential load not supplied is smaller compared to EV load, as EV load can only be shifted to a later time after its arrival time. Accordingly, the above paper did not take roof-top PV into consideration, where ways to minimize the percentage of load not supplied was not discussed.
This article explores the detrimental effects of EV integration on distribution assets, specifically LoL of distribution transformers. This happens mainly due to irreversible damage to insulating papers and oil due to overloading of transformers [35]. To address the aforementioned problems without leaving any load unsupplied, this paper proposes a solution for sizing BESS to support the combined load of additional EVs and residential demand. The key contributions of this article are as follows.
• This paper proposes a novel sizing strategy of BESS based on thermal loading of the transformer to ensure that all EVs are charged before 1900 hrs for next day trips while avoiding accelerated aging of transformers.
A new concept of average time of use (ToU) tariff is introduced as an optimization constraint, thereby minimizing the impact of demand response on consumers.
• This paper also investigates the influence of rooftop PVs and ambient temperature on the sizing of BESS. The synergy between the thermal loading of the transformer and rooftop PV is investigated as an optimization problem. This problem is solved by introducing a new ToU pricing signal based on the thermal load of transformers.
• Several case studies and comprehensive analyses have been conducted to validate the proposed solution. The proposed approach is successful in reducing the size of BESS up to 15%. The positive impact of rooftop PV allows further reductions up to 35%. The remainder of this paper is organized as follows. The proposed system is introduced in Section II. Section III defines the proposed solution to decrease the impact of EV integration by introducing a system model and recommended method for addressing the problem of LoL reduction of the distribution transformer. Section IV summarises the simulation's findings and examines the case studies presented, followed by suggestions for future work.

II. PROPOSED SYSTEM
The proposed system is shown in Fig. 2. A new BESS sizing method is proposed based on the thermal loading of the transformer to ensure that all EVs are charged before 1900 hrs the next day. A new ToU pricing mechanism based on hot spot temperature of a transformer is utilized to reduce the accelerated aging of the distribution transformer in the presence of roof-top PV systems. ToU tariff can be easily declared at least a day ahead based on past residential load profile and weather forecasts from the local Bureau of Meteorology (BoM). A detailed dynamic model of the transformer has been considered to investigate the influence of thermal time constant of the transformer. The solution presented in this study does not require any changes to the physical infrastructure already in place.

III. SYSTEM MODELLING A. EV LOAD MODELING
The aggregated EV load curve for uncoordinated charging was generated using Monte Carlo Simulation (MCS) [36]. This was utilized to calculate the overall load demand of the EV fleet for the 24-hour study period. Data on EV charge start time and length was obtained from National Household Travel Survey (NHTS 2017), including 129,696 households [37]. Out of 222,183 vehicles surveyed by the NHTS, 4,766 were hybrid or electric.
The EV charging duration was calculated based on the daily distance traveled. It was also assumed that EV owners begin charging as soon as they arrive home, as 80% of EVs are charged at home [38]. Home arrival time and daily miles were calculated based on cumulative distribution function (CDF) [39] and [40]. The number of EVs connected to the grid can be calculated using (1). According to [4] and [41], EV penetration levels range from 0% to 50%. Based on results from the 2017 NHTS [37], the number of EVs per household (µ) was estimated to be 2, where N EVs is number of EVs, X pen is EV penetration level and N House is the number of households. Accordingly, The algorithm outlined in [32], and [42] was used to estimate EV charging load with a charging capacity of 3.7 kW (charging level 2). The EVs that have been investigated are the Chevy Volt (16 kWh) and the Nissan LEAF (24 kWh).

B. RESIDENTIAL LOAD MODELING
For the results to be valid, the existing load must be properly modeled. To date, most researchers have represented existing load with a single load curve depicting an average load demand. This model does not account for seasonal variations in load. To overcome this problem the load model developed in the Australian National Feeder Taxonomy Study (NFTS) [43] has been used in this paper, and Fig.3 shows the load profiles used.

C. MODELING OF AMBIENT TEMPERATURE AND PV GENERATION
Ambient temperature (θ A ) data was obtained from the Australian Government's Bureau of Meteorology [44]. Ambient temperature clustering was determined using the Euclidean K-mean method, as shown in Fig. 4. The suitable number of clusters was based on [45].
Three PV generation scenarios have been used to study the influence on distribution transformer aging (Fig. 5). Similar to ambient temperature, solar radiation data was taken from the Australian Government's Bureau of Meteorology.

D. MODELING DISTRIBUTION TRANSFORMER LoL
Distribution transformers are the most vital and expensive node in the distribution system; therefore, it becomes important for a utility to manage accelerated aging. The LoL of a transformer is directly dependent on its hot spot temperature, where its elevated temperature can cause irreversible damage [46].  In the case of increasing load step, top oil temperature ( O ) and hot spot temperature ( H ) rise, based on the load factor (L t ). O,t is given by (2), where θ Oi is rise of top oil temperature over ambient temperature, θ OR is rise of top oil temperature over ambient temperature and r is ratio of rated load loss to no-load loss.
The hot spot temperature rise ( H ,t ) is given by (3), where θ Hi is rise of winding hot spot temperature over top oil temperature, H is hot spot factor, κ is rise of average winding temperature over average oil temperature, k 11 , k 22 , k 21 , k 12 are thermal model constants, and m is exponent of winding gradient vs. load squared.
For decreasing load step, the O and winding H reduces corresponding to the L t . The equation of the top oil temperature ( O,t ) is given by (4) where, The H increase is given as: Finally, the lifetime aging of transformer is dependent on hot spot temperature ( H ,t ) and is given by (6): O,t and H ,t were calculated as differential equations with transformer's loading as input, where ρ is the exponent of top oil temperature rise vs. loss function, and τ O is rated oil thermal time constant.
The differential equation for H was solved as (8), where τ W is winding time constant at hot spot location.
The differential equations (7)-(10) can be further approximated by difference equation, where (7) becomes: A difference in the related variable Dt is represented by the operator D. From the (n − 1) th value, the n th value of D O can be determined using: Eqs. (9) and (10) become: and The n th values of each of H ,(t) and H ,(t−1) can be calculated in a way similar to (12). The final H rise at the n th time step is given by: In the case of the thermally upgraded paper, the equation of the aging rate (F AA ) and equivalent aging rate (F EQA ) were expressed as follows [46]: The differential equation for aging rate F AA and loss of life LoL are given by: implying: and:

IV. PROPOSED SOLUTION TO SIZE BESS AND REDUCE IMPACT ON TRANSFORMERS
The main idea explored in this research paper involves lowering the negative impact on distribution transformer aging by shifting the load on it. This can be achieved by determining optimal ToU pricing to shift the load, with proper sizing of BESS to support the remaining load. Table 1 provides an overview of the input, output, and decision variables. The relationship between customer demand and electricity price, which is based on [47], is given in (23). This paper presents two demand response models, one based on ToU and the other on a demand response technique for emergencies.
In [48] and [49], the same model was expanded upon and used. The demand-price elasticity idea, which is centered on psychological and economic concepts, is used in this model, where E t is self elasticity, E t,k is cross elasticity, β t is spot electricity price in t th hour, β k is spot electricity price in k th hour, A t is incentive in t th hour and A k is incentive in k th hour.
where t, k = 1, . . . , 24 The percentage thermal loading of the transformer can be used to determine the start time and duration of various electricity ToU prices, as they are described by (24). Based on the work in [50], the self and cross elasticity used in order to determine the ToU tariff is given in Table 2 is off-peak price, th peak is θ H to start peak price, th sdr_1 is θ H to start shoulder-1 price, th sdr_2 is θ H to start shoulder-2 price and th min is θ H to start off-peak price. (24) where th sdr_1 = th peak − th min 2 3 + th min th sdr_2 = th peak − th min 1 3 + th min The optimization problem is defined by the following objective function and accompanying constraints, where the goal is to maximize the life of the transformer, as determined by existing residential load, PV generation and increased EV load.
Nameplate insulation (L normal ) is considered to be 180000 hours at rated load. As given in (17), LoL is dependent on F AA , which further depends on hot spot temperature. The hot spot temperature of a transformer is dependent on ambient temperature, top oil temperature of the transformer and the total loading on the transformer. Total loading on the transformer is given by the summation of residential load and additional EV load. This total load is also supported by roof top PV generation and storage, such as BESS. The total demand/load is given by (26), where P total is total load on transformer, P EV is EV load, P R is residential load, P PV is PV generation and P BESS is BESS size.
The constraints that must be met during this process of optimization are as follows: 1) Load not supplied: The demand response based on ToU tariff pushes the load towards off peak periods. Deferrable loads can be supplied at a later time based on the price signal. As a constraint, the total load not supplied is given by (27)- (29), where L NS is load not supplied, L total is total load and C avg is average ToU tariff.
Average ToU tariff: where C avg = $0.2, $0.25, $0.3 2) Transformer Capacity Limit: Due to high temperatures, total apparent power after adding EV charging load must not exceed a transformer's rated capacity, which is calculated as given in (30), where S t and S nom are apparent and nominal power of transformer, respectively.
3) EV Battery State of Charge: The constraint (31) gives the state of charge (SOC) of the n th EV at time t over a certain duration t. The initial SOC n ini of the n th EV is determined by (32) and is dependent on the prior driving distance, where E batt is capacity of battery, η is efficiency of the charger, SOC min is minimum SOC of EV battery and E cons is energy consumed by EV.
Constraint (33) specifies that an EV must be adequately charged to be used the next day, which is considered as 98%.
4) Lithium-ion Battery Charging Characteristics: Fig. 6 shows the typical charging characteristics of EVs, and it is included by simplifying it by piecewise linearization [33], [51], and [52]. The overall optimization model is shown in Fig. 7. In this paper, one hundred and eight charging scenarios are considered as given in Table. 3. This includes three real representative residential loads, three levels of EV penetrations, three-levels of PV penetration, and four real representative ambient temperatures. The Simplicial Homology Global Optimization (SHGO) algorithm has been used to optimize the values of the decision variables. This is a potential derivative-free global optimization (GO) approach based on integral homology and combinatorial topology [53], [54]. SHGO creates a simplicial complex from a selection of vertices and uses it to approximate a function's surface. To begin local optimization, a collection of locally convex regions is identified. These areas are then individually given a preliminary guess. When compared to other optimization techniques, SHGO has the advantage of being able to find unique local minima that are locally convex (roughly) with relative simplicity. The challenges for practical implementation of the proposed method are mainly related to the collection of real and accurate data for EV load (e.g., number of EVs, EVs/house, EV arrival/departure and daily miles), residential load (e.g., summer, winter, and threshold), transformer load, PV generation, and incentive.

V. NUMERICAL SIMULATION AND RESULTS
The size of BESS without ToU tariff-based demand response is shown in Fig. 8. It is important to note here that without any smart charging strategy, the size of additional energy demand grows up to 372 kWh for 50% EV penetration. In order to avoid accelerated aging of transformers, either the size of the transformer or the size of the BESS should match the  additional power and energy demand. In implementation, this incurs huge economic and technical constraints.
One better way of sizing BESS is based on the thermal loading of the transformer. The advantage of sizing the BESS this way is illustrated in Fig. 9. This compares the BESS size with the kVA based method and the thermal loading method. It can be seen that the additional load drops to 330 kWh from 372 kWh for winter loading and from 315 kWh to 290 kWh for threshold loading. This shows the advantage of sizing the BESS based on thermal loading of a transformer.
The influence of PV penetration in the distribution network is shown in Fig. 10. The hot spot temperature profiles with various PV penetrations for 10% and 50% EV charging load are shown in Fig. 11, and Fig. 12, respectively. The inclusion of PV generation in the distribution system introduces a delay/buffer time of 30 minutes to 85 minutes to reach the designated transformer threshold hot spot temperature of 110 • C. For example, with 50% EV penetration, the time to reach the hot spot threshold of 110 • C degrees is postponed from 15:00 hrs ( Figure 11, green profile with 0% PV generation) to 16:10 hrs (Fig. 12, red profile with 50% PV generation). This buffer time helps the transformer to take on additional EV load during peak hours from 1700 hrs to 2100 hrs. While it can be argued that the PV is not present during peak periods, it helps to keep the transformer cooler for a longer period of time and additionally helps in lowering the peak hot spot temperature up to 8%. Note that the transformer's active power loading above 1 p.u is mainly due to the combination of residential load and additional EV load. This occurs for EV charging load when the penetration level of EVs is 50%. As per the NHTS (2017), the number of vehicles owned by each household is approximated to be 2. So, when 50% of the cars are replaced by EVs and when they are charged as they come home, the additional EV load together with residential   peak load will load the transformer beyond its capacity, going up to 1.4 p.u. Similarly, Fig. 13 and Fig. 14 show the reduction in aging of transformer for 10% and 50% of EV charging load for various PV penetration levels. The reduction in the accelerated aging rate (F AA ) is more drastic since it has an exponential behavior defined by (17).    15 shows the demand response of the total load including 50% EV penetrations based on ToU tariff with 0% and 50% penetration of PV. The figure also shows the hot spot temperature of the transformer with uncoordinated charging of EV. The hot spot temperature of the transformer for uncoordinated charging goes beyond the threshold temperature of 110 • C from 15:15 hrs until 21:00 hrs, and reaches a peak of 168 • C. The hot spot temperature for both 0% and 50% PV with ToU tariff shows that it only crosses the threshold temperature of 110 • C for a very short period of time, thereby avoiding any additional LoL. The advantage of having more PV in the system is its ability to allow the transformer to cool down before the peak period begins, which allows it to supply more load. This can be seen in the time between 17:00 hrs to 18:00 hrs, where average ToU tariff with 50% PV penetration is lower than the case with no PV generation making the tariff more affordable.
The average ToU tariff (C avg ) concept is used in this paper as a constraint, where it varies between $0.2 and $0.3 per kWh. A higher ToU tariff can be used to shift the additional load, but this becomes very unaffordable to consumers. A compromised approach to apply a ToU tariff may be to   limit the C avg within $0.3 per kWh. The impact of C avg on the equivalent aging of transformer (F EQA ) is given in Fig. 16.
The reduction in size of BESS is considerable when the sizing is done based on the hot spot loading of the transformer. The BESS size further reduces with PV penetration in the distribution network in form of the rooftop PVs. Fig. 17 shows the size of BESS based on [34] without any restriction on C avg , and based on 20% and 50% rooftop PV penetration with C avg less than $0.3 per kWh. The size of BESS with 50% PV is less than 29% on average in comparison to sizing based on [34]. The maximum value of BESS corresponds to 116 kWh with 50% EV penetration for summer load and can be easily charged with the rooftop PV.

VI. CONCLUSION
This study explores the notion of EV load shifting to lower the negative impact on distribution transformers. A comprehensive methodology to size BESS in a PV integrated distribution network along with optimal ToU pricing is investigated to minimize the adverse impact of EV charging load, particularly in lowering the loss of life of power transformers. Comprehensive and realistic data were employed to model EV load, PV generation, and applied to the thermal model of the transformer. The robustness of the model was tested by implementing one hundred and eight charging scenarios with three real representative residential loads, three levels of EV penetrations, three levels of PV penetrations, and four real representative ambient temperatures. The main conclusions based on detailed analysis of simulation results are: 1) For up to 10% of EV penetration, the requirement of BESS can be eliminated altogether if the transformer is loaded based on its hot spot temperature as proposed in this paper. Furthermore, the BESS size can be reduced if PV is integrated into the distribution network. For example, for 10% to 50% of PV integration, the BESS size can be reduced by an additional 20% to 35%, respectively, without leaving any load unsupplied while considering transformer thermal loading. 2) Despite the common understanding of PV not being available during the peak load periods. The findings in this paper show the synergy between PV and EV charging load which helps in extending the life of transformers. This provides crucial delay time (e.g., 30 to 85 minutes in Figs. [10][11] for the distribution transformers to cool down before reaching their hot spot temperature limits. 3) A new concept of average time of use tariff (C avg ) is used in this paper as an optimization constraint. It is shown that higher C avg results in lower equivalent aging of transformer and vice versa. Higher C avg corresponds to higher peak tariff resulting in more load being shifted to off-peak periods. However, a compromised approach to apply ToU tariff may be to limit C avg within $0.3 per kWh. The size of the BESS can be reduced substantially (up to 35%) even with the C avg $0.3 per kWh. Overall, this paper has shown that a demand response method (ToU tariff), based on thermal loading of transformers can be used to effectively reduce BESS size while maintaining up to 98% of EV charging for next day trips.
Future investigations including, for example, the sensitivity of price elasticity on the proposed algorithm could be investigated. Demand response based on incentive-based programs could also be included to further understand the impact of sizing BESS based on the thermal loading of transformer.