MINIMIZING THE NUMBER OF DEPOT CHARGING POINTS FOR ELECTRIC BUSES OF SEVERAL ROUTES

1. MINIMIZING THE NUMBER OF DEPOT CHARGING POINTS FOR ELECTRIC BUSES OF SEVERAL ROUTES B. Rozin, M.Y.Kovalyov, N. Guschinsky United Institute of Informatics Problems of NAS of Belarus, Minsk, Belarus Talk outline: 1. PLATON project 2. Charging configurations 3. Problem statement 4. Brief review 5. Solution techniques 6. Conclusion 1

2. 1. PlanningProcessandToolforStep-by-StepConversionofthe ConventionalorMixedBusFleettoa 100 % ElectricBusFleet 2018-2020, 30 months Horizon-2020: ERA-NET Co-fund Objective: defineaplanningprocessfortheconversionofagivendieselormixedbusfleettoa 100% electricbusfleetandimplementthisprocessintoaweb-basedsoftwaretool. Tasks: Relevantreallifecasesandrequirementswillbecollectedfromelectricbusmanufacturers(busmodels, electricalpowerstoragedevices, powerchargingsystems,etc.) andpublictransportoperators(characteristicsofbusfleetsandroutes, operatingandmanagementcostofbuses,etc.). Themostcomplexpartoftheprojectismathematicalmodellingofthewholetransportationsystemoptimaldesign, aswellastheimprovementtheefficiencyofexistingbasicmethodsusingcomputersciencealgorithms. Impact: reliableandfastconversionofconventionalbusestoelectricbusesandthereforeanaccelerationofenvironmentandclimateprotection. Effiziente, Graz BKM, JIME, UIIP IFAK, Magdeburg Politechnika, Katowice

3. 2. Electric bus charging configurations in EU (based on analysis of data from (ZeEUS report) and other sources. (Platon project. Deliverable 3.1) 3

4. 3. PROBLEM STATEMENT 3.1.Consider a set R of routes to be served by e-buses that are charged in the same depot by thecharging stations of the same type(hereinafter type c). 2 A B 3 1 4 D 5 7 E C 6 Routes cycle (slow charging in the depot) Scheme of the routes from R 4

5. 3.2 ASSUPTIONS • Each of the e-buses serves the route (or sequence of routes) prescribed to it. • E-buses are equipped with high-capacity batteries (hundreds of kWh) • that provide them the opportunity to operate the whole day without • recharging. • The initial state of charge (SOC) level of each e-bus before its first • departure from the depot should be defined within the range. • 4) The daily schedule of each e-bus of the e-fleet is given by a set of pairs of time moments of departing from/ arriving to the depot. • 5) All e-buses of the e-fleet are charged in a single depot equipped by a slow charging stations of the same type (2-8 hours for charging a completely discharged battery). The output power of this charging station is given and remains invariable during its operating. • 6) Providing the depot with charging stations should ensure the cyclically repetitive DecisiveDaily Traffic (DDT). This implies recovery in the depot of the initial SOC levels of all e-buses of the e-fleet for DDT by the beginning of the next day. . 5

6. 3.2 ASSUPTIONS (continuation) 7) The DDT is compiled for the most representative day in terms of traffic intensityandenergy consumption. 8) It is assumed to be given: the charge loss functions by the e-buses during their trips in the course of the dayas well as the functions of restoring the e-bus SOC level at the charging station depending on charging time and on the e-bus battery. 9) The SOC level loss of the idle e-bus in the depot is considered to be negligible. 10) The durations of the replacement at the charging station of one e-bus with any other one is considered to be negligible. 11) The time varying power supplied to the depot by the city power grid is taken into account in the form of the maximum number of charging stations operating in parallel in the depot for each time moment. . 6

7. 3.3 INPUT DATA • Set R of routes served by the e-fleet. • Type c of identical charging stations in the depot, cC. •  Set J={1,2,…, n}of indexes of all e-buses of the e-fleet serving the routes of the set R, each e-bus jJ is equipped by the battery bjBc compatible with charging station c. • is the given segment of feasible values of the e-bus j SOC level, jJ; • Daily schedule of the e-bus j, where is the time interval between p-th departure from /arrival to the depot of this e-bus serving its respective routes from R, p=1,…, nj, jJ; •  Functions jp(s) defining SOC levels of the e-buses jJ after the trip p in the time interval with its starting SOC level s, p=1,…, nj, jJ; • Functions fjc() defining the resulting SOC levels of the e-buses jJ after their charging at the charging station during time from the initial SOC level . . jp(s) fbc() s  s> 0 7

8. 3.3 INPUT DATA (continuation) • costcap(c)is a present value (per year) of capital cost for one charging station cC; • costope(c)is a present value (per year) of operating cost for one charging station cC; • costbj isa cost of the battery bj Bc; • Pc is a nominal power of the charging station c; • ce(t)is a time-varying piecewise constant electric power rates; • cost pH is a contract value of the power supplied to the depot (per year); • Nj( ) is the maximal number of charge/discharge cycles of battery bjlifetime for discharge ; • is the required number of battery charge/discharge cycles per year; • Function P(t) of the power supplied by the city power grid during the day and night. . Nj () 1105 1104 s LTO battery 1103 8

9. Available electrical power in the depot, upper bound of the number of charging stations 1.3 INPUT DATA P(t) k(P) . 6 5 4 … … 3 8 t t1 t2 t5 t3 t9 t8 t7 t10 t4 t11 … … … City power grid 9

10. 3.4. Scheme of charge loss during trips and recharging at the depot (example for 2 e-buses and 1 charging point) T={t1,t2,…, t8, 24} s t t1 t2 t3 t8 t5 t6 t7 24 t4 24+t1 24+t2 trip1 trip2 e-bus 1 trip2 trip1 e-bus 2 10

11. 1.4 PROBLEM FORMULATION . The problem is to select cost-effective charging infrastructure in the depot, options of batteries for the e-buses as well as distribution of e-buses charging durations in a depot that provide cyclically repeating daily passenger traffic of several routes in accordance with given daily e-buses schedule on the most representative day. Minimize (pH,c,b,K,uc,sa)=cost pH+K[costcap(c)+costope(c)]+ +350 s.t. pHpH , cC, b=(bj| jJ), bjBc, jJ, K pH/Pc, uc=( |jJ)U, , , sa=( | jJ), = ( | p=1,...,nj), , p=1,…, nj, jJ. The problem solution: pH*,c*,K*,b*, uc*,sa*. 11

12. 2. Brief review (Gao, et al. ,2017) evaluates the energy consumption and battery performance of city transit electric buses operating on real day-to-day routes and standardized bus drive cycles, based on a developed framework tool that links bus electrification feasibility with real-world vehicle performance, city transit bus service reliability, battery sizing and charging infrastructure. (Leou and Hung, 2017) studied the problem of optimal planning the contracted power capacities and charging schedule of an charging station for e-buses considering the different electric power rates for three time categories (peak hours, semi-peak hours, regular hours) is studied. (Montoya et al., 2017) have shown that the SOC level is the concave function of the charging time. (Olsson, Grauers and Pettersson, 2016) compares different systems of electric buses together with their charging infrastructure (charging at the depot, charging at the terminal stations, charging during movement and opportunity charging at the bus stops). It was stated that electric buses designed for charging at the depot have a battery range of up to 300 km on one charge under favorable conditions, which could be enough to complete an entire transport work needed during one day. This bus type has a usage characteristic similar to a combustion engine bus in the sense that charging is needed only a few times per day. No chargers are necessary along the route. (ZeEUS-report 2017-2018) An updated overview of electric buses in Europe. 2018. http://zeeus.eu/uploads/publications/documents/zeeus-report2017-2018-final.pdf A large number of options of such e-buses and respective charging stations for charging them in the depot are listed. 12

13. 3. SOLUTION TECHNIQUES 3.1 Three-level decomposition scheme of the problem . 13

14. 3. SOLUTION TECHNIQUES 3.2 Sub-problems of the decomposition scheme . At the lower level the sub-problem D(c,K,b) to minimize the present value 2(uc,sa)= + 350 s.t. ucU, , p=1,…, nj, jJ, for a fixed type cC of charging station, battery options b=(bjBc|jJ), and the number K of these stations in the depot is solved. At the medium level the sub-problem B(pH) to minimize the present value  1(c, K, b)=K[costccap(c)+ costcope (c)]+ 2 *(c,K,b) , s.t. cC,bBc and KpH/Pc for fixed value pH of supplied power is solved. At the upper level the sub-problem C a one-dimensional search over a given segment pHpH is performed to minimize the total present value (pH) =cost pH+ 1*(pH) of charging stations in the depot, batteries of the e-fleet and consumed electrical energy is performed. 14

15. 3. SOLUTION TECHNIQUES 3.3 Sub-problem D(c,K,b) is formulated as mixed integer linear programming problem. . 15

16. 4. CONCLUSIONS • The problem of minimization of the total present value of charging stations in the depot, battery options of the e-buses of several routes and supplied electrical energy is considered. Daily schedules of the e-buses are given. It is assumed that stations in the depot should provide the recovering until the next day the SOC levels of all the e-buses. The upper bound of the power provided by the city power grid in the depot is taken into account. The mathematical model of the problem is formulated. • The three-level decomposition scheme for solving this problem is proposed. • At the lower level, for a fixed type c of charging stations, the number K of these stations and e-buses battery options, the distribution of recharging durations for discharged e-buses in the depot and levels of batteries discharge are selected to minimize the present value of batteries and consumed energy providing • the restoring the initial charge levels of all e-buses in the depot up to the next day. This sub-problem is reduced to the MIP problem. • At the middle level the sub-problem of selecting the type of charging stations, their minimal required number as well as the options of e-buses batteries to minimize the present value of charging stations, batteries and consumed energy is solved. The method for this problem is based on the combination of directed search and heuristics. • At the upper level a one-dimensional search over a given segment of feasible values of supplied power is performed to minimize the total present value of supplied power, charging stations, batteries of all e-buses and consumed energy. • Possible topics for future study: • the stability of the solution of the problem to possible fluctuations of the input data; • - the more general problem of selecting the fleet of e-buses and their schedules as well as the type of charging stations in the depot to minimize the total present value. 16

17. Thank you for attention