Day ahead scheduling of PHEVs and D‐BESSs in the presence of DGs in the distribution system
2019; Institution of Engineering and Technology; Volume: 10; Issue: 2 Linguagem: Inglês
10.1049/iet-est.2018.5096
ISSN2042-9746
AutoresBablesh Kumar Jha, Amit Singh, Abhishek Kumar, Dharmendra Kumar Dheer, Devender Singh, Rakesh Misra,
Tópico(s)Advanced Battery Technologies Research
ResumoIET Electrical Systems in TransportationVolume 10, Issue 2 p. 170-184 Research ArticleFree Access Day ahead scheduling of PHEVs and D-BESSs in the presence of DGs in the distribution system Bablesh Kumar Jha, Corresponding Author Bablesh Kumar Jha bableshkj.rs.eee15@itbhu.ac.in orcid.org/0000-0001-6475-9145 Electrical Engineering Department, IIT(BHU) Varanasi, Uttar Pradesh, IndiaSearch for more papers by this authorAmit Singh, Amit Singh Electrical Engineering Department, IIT(BHU) Varanasi, Uttar Pradesh, IndiaSearch for more papers by this authorAbhishek Kumar, Abhishek Kumar Electrical Engineering Department, IIT(BHU) Varanasi, Uttar Pradesh, IndiaSearch for more papers by this authorDharmendra Kumar Dheer, Dharmendra Kumar Dheer Electrical Engineering Department, NIT Patna, Bihar, IndiaSearch for more papers by this authorDevender Singh, Devender Singh Electrical Engineering Department, IIT(BHU) Varanasi, Uttar Pradesh, IndiaSearch for more papers by this authorRakesh Kumar Misra, Rakesh Kumar Misra Electrical Engineering Department, IIT(BHU) Varanasi, Uttar Pradesh, IndiaSearch for more papers by this author Bablesh Kumar Jha, Corresponding Author Bablesh Kumar Jha bableshkj.rs.eee15@itbhu.ac.in orcid.org/0000-0001-6475-9145 Electrical Engineering Department, IIT(BHU) Varanasi, Uttar Pradesh, IndiaSearch for more papers by this authorAmit Singh, Amit Singh Electrical Engineering Department, IIT(BHU) Varanasi, Uttar Pradesh, IndiaSearch for more papers by this authorAbhishek Kumar, Abhishek Kumar Electrical Engineering Department, IIT(BHU) Varanasi, Uttar Pradesh, IndiaSearch for more papers by this authorDharmendra Kumar Dheer, Dharmendra Kumar Dheer Electrical Engineering Department, NIT Patna, Bihar, IndiaSearch for more papers by this authorDevender Singh, Devender Singh Electrical Engineering Department, IIT(BHU) Varanasi, Uttar Pradesh, IndiaSearch for more papers by this authorRakesh Kumar Misra, Rakesh Kumar Misra Electrical Engineering Department, IIT(BHU) Varanasi, Uttar Pradesh, IndiaSearch for more papers by this author First published: 01 June 2020 https://doi.org/10.1049/iet-est.2018.5096Citations: 5AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The rapid growth of plug-in hybrid electric vehicles (PHEVs)/electric vehicles (EVs) and their capability of providing a vehicle to grid power support in distribution network needs in-depth studies for the effective operation of the distribution system. Charging/discharging of EV from/to the distribution system has significant impacts on the load demand, network congestion, voltage rise/dip, and other operational issues. Power supply from distributed generators (DGs) is utilised during the peak demand hour to avoid the need for upgradation of the distribution systems. In this study, 24-hour day ahead power scheduling of PHEVs (in between arrival and departure time), distributed-battery energy storage system (D-BESS) and DGs is proposed to mitigate its effect on the distribution system. Four objective functions including system operating cost, CO2 emission, energy losses, and load flattening are considered to examine the effect of distributed sources on the 38-bus distribution system. An effective butterfly optimiser is implemented to minimise single weighted objective function. To understand individual as well as combined effect of unscheduled PHEVs charging, scheduled charging/discharging of PHEVs, D-BESS, and DGs various case studies is performed. On the basis of these case studies, optimal scheduling of PHEVs, D-BESS, and DGs are proposed to improve the overall system performance. Nomenclature charging efficiency discharging efficiency bus voltage angle at the ith bus at the hth hour bus voltage angle at the kth bus at the hth hour line susceptance between the ith and the kth bus (p.u.) electrical energy capacity by D-BESSs (kWh) electrical energy capacity by the eth PHEVs battery (kWh) electrical energy cost produced by CPG at the hth hour (€/kWh) electrical energy cost produced by the dth DG at the hth hour (€/kWh) discharging electrical energy cost of PHEVs and D-BESS at the hth hour (€/kWh) electrical energy curtailment cost of the dth DG at the hth hour (€/kWh) distance travel by PHEV (km) charging electrical energy of the bth D-BESS at the hth hour (p.u.) charging electrical energy of the eth PHEV at the hth hour (p.u.) emission due to CPG (kg) emission due to DG (kg) emission due to PHEV (kg) electrical energy produced by CPG at the hth hour (p.u.) maximum limit of electrical energy produced by the dth DG at the hth hour (p.u.) minimum limit of electrical energy produced by the dth DG at the hth hour (p.u.) electrical energy produced by the dth DG at the hth hour (p.u.) discharging electrical energy of the bth D-BESS at the hth hour (p.u.) discharging electrical energy of the eth PHEV at the hth hour (p.u.) maximum possible G2V energy limit of the eth PHEV electrical curtailment energy of the dth DG at the hth hour (p.u.) electrical energy stored by the bth D-BESS at the hth hour (p.u.) electrical energy stored by the eth PHEVs battery at the hth hour (p.u.) electrical energy used by the bth D-BESSs at the hth hour (p.u.) electrical energy used by the eth PHEVs at the hth hour (p.u.) electrical energy cost produced by CPG during 24-h (€) electrical energy cost produced by D-BESS during 24-h (€) electrical energy cost produced by DG during 24-h (€) electrical energy curtailment cost produced by DGs during 24-h (€) electrical energy cost produced by PHEVs during 24-h (€) line conductance between the ith and the kth bus (p.u.) active component of the lth line current active component of current produced by DG at the lth line emission in (kg/kWh) due to CPG emission in (kg/kWh) due to DG emission in (kg/km) due to PHEV number of branches number of buses number of D-BESSs at each residential bus number of DGs number of PHEVs at each residential bus lth branch loss component before DG's installation lth branch compensated loss component after DG's installation conventional active power load at the ith bus at the hth hour (p.u.) active power losses at the hth hour (p.u.) conventional reactive power load at the ith bus at the hth hour (p.u.) reactive power losses at the hth hour (p.u.) line resistance between the ith and the kth bus (p.u.) resistance of the lth line state of charge of the bth D-BESS at the hth hour state of charge of the eth PHEVs battery at the hth hour SOC of the eth PHEV at arrival time SOC of the eth PHEV at departure time arrival time of PHEV departure time of PHEV bus voltage at the ith bus at the hth hour (p.u.) bus voltage at the kth bus at the hth hour (p.u.) line impedance between the ith and kth bus (p.u.) b D-BESS index d DG index e PHEV index i,j system buses index. l system branch index. 1 Introduction Over the last few decades, global warming is the most alarming issue for the entire human kind as well as for nature. Emission of CO2 is the major cause of global warming and its major sources are conventional power plants and the transportation sector [1]. To reduce the contribution to global warming from the conventional electric power generation system, it is necessary to move forward to the clean energy generation system. The contribution from the conventional transportation system can be reduced by shifting the transportation system to zero emission vehicles, i.e. the electric vehicle (EV). In the last few years, the penetration of EV into the distribution system is increased, which brings the increased energy storage capacity in the system. This increased energy storage capacity reduces the stress on the grid during the peak load hour. It is required to effectively utilise the potential of EVs in vehicle to grid (V2G) mode for the grid support applications [2, 3]. On the other hand, charging EVs brings significant consequences on the existing distribution system including increased peak load demand, deterioration in power quality, increment in network losses, overloading of transformers, excessively heavy line loads and larger voltage deviations [4, 5]. In the modern era of the smart grid, the usage of battery energy storage system (BESS) also plays an important role in the electrical power system. BESS can be installed by either distribution system operator (DSO) or individual customer. BESS owned by DSO is a centralised battery installed on the secondary side of the distribution transformer for the off-peak shaving. BESS ensures reliable services to customers during power congestion. It also supports the grid during peak demand and stores energy at a low tariff period during the off-peak hours [6, 7]. The control strategies, management strategies, sizing and siting of BESS are reported in [8]. The optimal charging schedule of BESS by considering the EV travel characteristics is presented in [9, 10]. In the current scenario, renewable energy sources (RES) become an important part of the power system structure. In the near future, the integration of RES and BESS into the distribution system will be utilised to support the grid when the distribution system will experience the EVs as a significant load to the system. A two-step procedure to determine the sizing and siting of RESs and the sizing of EVs by minimising the overall system cost meeting the relevant technical constraints is presented in [11]. Simultaneous allocations of EVs and RESs in the distribution system are addressed in [12]. Scheduling of EVs and RES for the microgrid perspective is presented in [13]. The possible solutions to mitigate the effect of plug-in EVs (PEVs) on the distribution system are suggested in the literature [14, 15]. It includes the time variant pricing scheme, the demand response management, V2G discharging, renewable energy resource integration and utilisation of the battery storage system into the grid. The effect of EVs in the presence of distributed generators (DGs) on the distribution system is studied in [16-19]. The study proposes optimal coordination of PEV charging schedule, the penetration level of PEV, sizing, and siting of DG units to mitigate the effect of PEVs on the distribution system. A role-based method to minimise the domestic peak load using an EV, BESS, and renewable sources is proposed in [20, 21]. Optimal utilisation of renewable energy resources, EV and BESS to manage operating cost of utility is proposed in [22-25]. The potential of BESS to accommodate high penetration of PVs is investigated in [26]. For the peak shaving and valley filling, peak-to-average ratio (PAR) minimisation problem considers the optimal use of RESs, BESS and integration of EV in G2V and V2G mode in the distribution system. In recent years, BESS and V2G operation mode of EV manage the residential loads at a higher scale. The utilisation of EV with photovoltaic (PV) units to support the residential load demand is presented in [27, 28]. A dynamic adjustment of EVs charging/discharging is proposed by controlling the charging rate to support the load demand by effective use of available battery capacity [29]. In the literature, studies have been carried out by considering the coordinated effect of PHEVs with DGs or PHEVs with BESS on distribution networks. A summary is presented in Table 1. Table 1. Classification of similar work Ref. DG PHEV V2G BESS COST Load flattening Loss [20] Y Y Y Y — — Y — [15] Y Y — Y — — Y — [23] Y Y — Y Y — — — [16, 17] Y Y Y Y Y — — Y [24] Y Y Y Y Y — — — [30] Y Y — Y Y — — Y [31] Y Y — Y Y Y — — [11] Y Y — — — — — Y [32] — Y — — Y — Y — [26] — — — Y Y — Y — present work Y Y Y Y Y Y Y Y In the papers cited in Table 1, formulations of the objective function are either based on the cost analysis or on the load flattening. In [16], the cost-based objective functions consider two times the cost of PHEV charging which leads the inconsistency to calculate the total cost . Apart from the inconsistency in the cost calculation, the authors have considered the PHEVs as deterministic load demand on distribution networks, which does not realise the real scenario. The proper scheduling of PHEVs (between start trip time and last trip arrival time), distributed-battery energy storage system (D-BESS) and DGs are required to overcome the above-mentioned research gap. To the best of authors’ knowledge, the combined objective of cost and load flattening-based optimisation in distribution system with PHEV, D-BESS, and DGs is not found in the literature. In this study, combined formulation of the cost analysis and load flattering by considering the combined integration of PHEVs (G2V and V2G modes), D-BESS and DGs is proposed. The method to minimise the PAR along with cost, emission and losses by scheduling PHEVs, BESSs, and DGs by keeping the other consumer loads intact is also proposed. The main contributions of the study are summarised as follows: (i) The stochastic SOC profile of PHEVs is proposed by using MCS with consideration of uncertainties related to the driving pattern of PHEVs based on NHTS 2009 data. (ii) Selection of candidate buses has been performed for all dispatchable DGs in the IEEE-38 bus system using a non-linear programming approach. (iii) 24-h day-ahead scheduling of PHEVs, DGs, and D-BESSs to optimise four contradictory objectives (i.e. cost minimisation, CO2 emission minimisation, real power losses minimisation, and load flattening) have been proposed simultaneously by keeping the consumer loads intact. (iv) A study based on the setting of weights is presented which reflects relative importance of the individual objective function on distribution system planning and operation problem. The organisation of the paper is as follows: Stochastic modelling of PHEV is presented in Section 2. In Section 3, the selection of candidate bus for DGs is presented. In Section 4, the problem formulation is presented. The methodology to solve the problem is presented in Section 5. The test system description and system model are given in Section 6. Result and discussion are presented in Section 7 and Section 8 presents the conclusions of the research. 2 Stochastic model of PHEVs 2.1 Vehicle characteristics In this study, based on all electrical range (AER), three types of PHEVs are considered and its percentage share in the market is depicted in Table 2 [33]. For example, PHEV-40 represents the vehicle that can travel 40 miles in electric mode under full charged condition. Furthermore, under PHEV-x category, different types of vehicles are classified based on different types of energies consumed per mile and battery capacity, which are shown in Table 3 [34]. The vehicle state of charge (SOC) is the battery's level of charge similar to a fuel gauge in internal combustion cars, usually expressed as a percentage of full capacity. The measurement of SOC is on-board estimation and it cannot be measured during PHEV operation. Accurate knowledge of SOC is required for calculating the energy required from the grid to charge the battery and the amount of energy that can be injected into the grid. A battery having higher value of SOC is charged in shorter time. There are several methods to determine the SOC of the battery. However, the coulomb counting method [35] is most commonly used. Table 2. Percentage of the share of PHEVs with different AERs PHEV30 PHEV40 PHEV60 percentage 21% 59% 20% Table 3. Size of battery for PHEVs (kWh) Type Vehicle PHEV30 PHEV40 PHEV60 1 compact sedan 7.8 10.4 15.6 2 mid-size sedan 9 12 18 3 mid-size sports utility vehicle (SUV) 11.4 15.2 22.8 4 full size SUV 13.8 18.4 27.6 Mathematically, SOC for PHEVs can be expressed as follows: (1) where is the percentage of distance that PHEV travelled in electric mode and d is the total travelled distance in miles. 2.2 Obtaining PHEVs SOC profile The driving habits of the vehicle such as daily distance travelled, last trip arrival time, and start trip time are extracted from the NHTS 2009 transportation report of the U.S. [36]. NHTS 2009 data base consists of 1,048,575 single trips and each trip has 150 attributes. The sum of all the trips during a day is used to generate the daily distance travelled and its departure time is considered as start trip time and its arrival time is considered as last trip arrival time. The daily distance travelled by the vehicle is shown in Fig. 1a and it is described by lognormal distribution ( and ). The last trip arrival time and start trip time of vehicle are shown in Figs. 1c and b, respectively. The normal distribution corresponding to last trip is and while for start trip is and [37]. Fig. 1Open in figure viewerPowerPoint Histograms of PHEVs parameters (a) Daily miles driven by PHEV, (b) Start trip time of vehicles, (c) Last trip arrival time of vehicles The SOC profiles of PHEVs are generated by Monte–Carlo simulation. In every iteration, a sample of SOC profile is generated using (1) by randomly considering the type of vehicle, battery capacity, distance travelled by vehicle, last trip arrival time and start trip arrival time. The generation of distance travelled by vehicle, last trip arrival time, and start trip arrival time for a given number of PHEVs is taken according to its pdfs. The simulation is iterated several times for all PHEVs and the output of every iteration is stored. The average output of all iterations is obtained to generate the SOC profile of each vehicle between the last trip arrival time and the start trip time. 3 Selection of candidate bus for DGs The candidate bus selection for DGs in the distribution system plays a significant role in mitigating the negative effects on the distribution system including reduction in energy losses, voltage profile, and energy balance problem. In this work, the main aim of the selection of the candidate bus for DGs placement is to maximise the value of loss saving in distribution system. Mathematically this can be formulated as: (2) Where, Subject to (3) Where, (4) (5) Equation (3) is linked with the limit on the total maximum number of candidate buses for the DGs integration in the system. Furthermore, next equation ensures that more than one DG will be not be integrated at a time on the same node of the distribution system, i.e. if select the jth bus as a candidate bus then next will be installed on the kth bus . Equation (4) forces the limit regarding a number of DGs, i.e. the DGs are selected in discrete manner. 4 Problem formulation In this section, the mathematical model of utility operating cost of (CPG, DG, BESS, and PHEV), emission, losses, and load flattening in the distribution network is formulated. Four objective functions are considered in this study, which includes CPG, DGs, D-BESS, and PHEVs (G2V/V2G mode). The time step is taken one hour throughout the problem formulation and any changes in PHEV DGs and D-BESSs behaviour within an hour are neglected. 4.1 Objective function The proposed optimisation model aims to minimised objective function (F), which consists of the cost of energy , emission , losses , and load flattening . The main objective function (F) is given as The cost of energy is calculated as the sum of the cost of CPG's energy, cost of DGs power, curtailment cost of DGs, cost of discharging of PHEVs and cost of discharging of D-BESS. It is to be noted that the charging cost of PHEVs and D-BESS is already included in . Thus, the cost of energy can be expressed as (6) where The emission is calculated as the sum of emission due to energy generation of CPG , fuel cell (FC) DGs and shaving off due to PHEVs (7) where The energy losses are calculated as the sum of total energy loss in the system (8) where is set of all the buses that have been directly connected to the ith bus. For the load flattening , a flat load curve is desirable for the system which is formulated as (9) where and are total demand and average demand at the point of common coupling at the hth h, which is supplied by CPG is the average power demand for 24 h and can be defined as The multi-objective function is formulated as the weighted sum approach of , , and which is shown as (10) where , , , and are user supplies weights, which correspond to the relative importance of one's prefer objective function. Each set of weights generate one optimal solution at a time. However, in this work, there are four sets of weights as listed in Table 4 are considered to quantify the relative effect of the objective function with respect to each other. For example, in set-A, when the cost of energy is treated as 45% relative importance, whereas emission, energy losses and load flattening-based objective function get weights of 25, 15, and 15% respectively. The problem is to determine the optimal values of , , , , and for a given pattern of , , , and . Table 4. Variation in weighing factor Weight Set A Set B Set C Set D 0.45 0.25 0.15 0.15 0.25 0.45 0.25 0.25 0.15 0.15 0.45 0.15 0.15 0.15 0.15 0.45 4.2 Constraints Several constraints including power flow constraint, bus voltage magnitude, maximum and minimum DGs power limit, a limit on number of DGs, CPG maximum limit and battery technical limit for PHEV and D-BESS are considered for the optimisation problem formulation in this research. The details of the constraints are as follows. 4.2.1 Power flow constraints at time h (11) (12) where is considered as and here we assume that PHEVs and DGs do not consume or produce reactive power from/to the distribution system. Equations (11) and (12) represent the active and reactive power balance on the distribution system. These equations ensure the generation and load demand on distribution system should be matched all times. 4.2.2 Bus voltage magnitude (13) Constraint (13) ensures that the bus voltage will be always within the specified limit. 4.2.3 Maximum and minimum DG limit (14) (15) where is the binary number (0,1), which represents the connection status of DGs on candidate bus. So that if , which means there is no exchange of power, whereas if , which means there is an exchange of power. DGs maximum and minimum power range is restricted in constraints (14) and (15). 4.2.4 PHEVs and D-BESS technical constraints at the ith bus Constraints related to the technical limit of PHEV's battery and D-BESS are given in (16)–(26) (16) (17) Constraints (16) and (17) ensure that the charging and discharging of PHEV's battery and D-BESS will not take place simultaneously at the ith bus (18) (19) Constraints (18) and (19) show the energy balance equation for PHEV battery and D-BESS (20) (21) (22) (23) Constraints (20)–(23) restricted the battery charging and discharging limit considering battery balance for PHEVs and D-BESS (24) (25) where and are minimum possible limits for PHEVs and D-BESSs. and are possible maximum limits for PHEVs and D-BESSs. Constraints (24) and (25) ensure that the SOC of PHEVs and D-BESSs at the hth hour restricted within the limit (26) where Constraints to get the maximum possible SOC of the eth PHEVs at departure time are imposed in (26). 4.3 Analysis of the modified objective function According to [16], consists of both charging and discharging costs, which is given as (27) where and charging and discharging cost of PHEVs according to [16]. It is to be noted that the net PHEV's energy cost for utility is the same as described in (27). To schedule PHEVs charging and discharging, if is considered the same as (27) then it brings unnecessarily charging and discharging of PHEVs to minimise the objective function. It is obvious that and may be less than or greater than , depending upon dynamic pricing. Since charging cost of PHEVs has already been considered in as a positive term and if, it is considered as negative term in then the net impact of charging and discharging cost imposed on objective function will be (28) Equation (28) clearly shows that the net value of the first term is either zero or negative and the second term varies with the difference between and . To minimise the objective function, charging will be maximised in such a way that the first term will become more negative. will be added in consumer electricity bill to minimise . This will reflect as maximisation of for consumer point of view. Therefore, the charging term is eliminated from (27) for optimisation purposes which are modified in (29). However, the cost calculation is based on (27) (29) Similarly for BESS, the can be written as follows: 5 Problem solving methodology 5.1 Power flow analysis The single phase current injection method [38] is applied to perform power flow analysis. In this method, the 2n set of current injection equations is written in rectangular coordinates and the Jacobian matrix associated with them has the same structure as the nodal admittance matrix [38]. This will be the input to the system which will be further used to perform the power flow analysis. The step-by-step procedure of the modified current injection load flow algorithm is shown in Algorithm 1 (see Fig. 2). The constant power load model is considered for PHEV load to obtain the power flow solution. Fig. 2Open in figure viewerPowerPoint Algorithm 1 5.2 Optimisation methodology Butterfly optimiser (BO) is a population-based global optimisation technique based on the mate locating behaviour of male butterflies [39]. This algorithm is efficient and easy to implement, compared with other bio-inspired algorithms. However, it may sometime converge to a local optimum solution in hard problems. To address this issue, Kumar et al. added a binomial mutation to effective BO (EBO) to improve the global convergence [40]. This global improved algorithm called EBO. As a consequence, in practice, it might be hard to validate the performance derived by EBO. In an attempt to address the validation of performance, a variant of EBO, EBOwithCMAR has secured the first position and outperformed all the participated algorithms in most of the optimisation problems in CEC-2017, special session and competitions on real-parameter single objective optimisation [40]. EBO is a dual population-based algorithm, where two different populations are initialised within the search space of the problem. In every iteration, populations update themselves by using patrolling or perching strategies of the algorithm in such a way to reach the optimum solution. The main procedure of EBO is shown in the form of a flowchart in Fig. 3a. The process of EBO is divided into five steps: initialisation, condition-I, perching, patrolling, and condition-II. Fig. 3Open in figure viewerPowerPoint Schematic diagram of EBO (a) Flow chart diagram of EBO, (b) Process of patrolling and perching 5.2.1 Initialisation In the initialisation process, the population and all the required parameters are initialised. The initialised population covers the entire search space uniformly distributed numbers. These random variables are within the prescribed lower and upper boundary limits (30) (31) The initial location of the jth index of the ith individual of population-I can be generated as (32) where rand[0,1] is a uniformly distributed random number within the range [0,1]. Similarly, the initial value of the jth index of the ith individual of population-II is generated as (33) The initial velocity vector of the ith individual is calculated using the following equation: (34) After initialisation, all the individuals are required to proceed for iteration until condition-II is satisfied. Two variable crisscross and attractive neighbours of all individuals are re-initialised at the beginning of every iteration before entering the main process of EBO. Crisscross and most attractive neighbour variables are used in perching and patrolling strategy, respectively. The crisscross vector is generated by: (35) where is a random permutation of a number between 1 and N. In the original BO [39], the most attractive neighbours of all individuals are the same and the individuals having lower fitness values are selected as the most attractive neighbours. In every iteration, EBO employs the perching or patrolling operation to update the positions of individual in both populations. Condition-I is a criterion that selects the update strategy of individuals out of the two updating methods namely perching and patrolling. Condition-II is applied as the termination criteria for the optimisation proce
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