En-Route Charging Strategy for Wirelessly Charged Electric Bus Considering Time-of-Use Price

To mitigate the range anxiety problem of electric bus system, wireless power transfer is regarded as one of the emerging technologies for long-term range extension. Previous studies have discussed the optimization problem of the power track deployment. However, the en-route charging strategy also significantly influences the operation cost besides the power track, which is yet to be investigated sufficiently. To fill this gap, a new wireless charging model for optimizing the energy cost is proposed. In particular, the cost of battery and the time-of-use electricity price are taken into account. Firstly, a microscopic power consumption model considering passenger flows and automobile dynamics is developed to estimate the charging cost. Then, a relaxation approach based on penalty function and grey wolf optimization (GWO) algorithm is developed to solve the non-deterministic polynomial-hard (NP-hard) problem with complex multidimensional variables and multiple inequality constraints. And the performance of the proposed charging strategy is verified in a real-world bus line via numerical simulation. A sensitivity analysis is conducted to quantify the marginal impact of the unit cost of battery capacity on the total energy cost. Finally, the computational performance of the proposed algorithm (GWO) is validated by comparing other outstanding methods such as genetic algorithm (GA), particle swarm optimization (PSO) and CPLEX solvers.

issue of range anxiety still hampers the promotion of electric 23 bus (EB) system [2], [3], [4], [5]. Electric vehicles (EVs) 24 with wireless power transfer (WPT) technology have been 25 introduced to solve this problem [6], [7]. However, the cost of 26 operating a wireless charged electric bus (WCEB) line is still 27 The associate editor coordinating the review of this manuscript and approving it for publication was Tariq Umer . expensive. The cost mainly includes power track deployment 28 cost, battery cost and charging cost [8]. Previous studies have 29 focused on optimizing the cost of the power track deployment 30 [9], [10], [11], [12], but the optimization of the battery cost 31 and charging cost during operation is yet to be investigated 32 sufficiently. 33 The total cost of battery and charging are defined as the 34 energy cost in this study, which are mainly related to the 35 battery capacity, the electricity price and the charging strat-36 egy. Due to the limitation of battery capacity, the range 37 anxiety problem has plagued many electric vehicle users 38 [13], [14], [15]. Several  management [18], and eco-driving in mixed connected traffic 41 [19], [20], [21]. However, the limited coverage of charging 42 stations and the charging waiting time remain the primary 43 barriers to long-distance driving. For EBs, equipping with 44 large-capacity battery might be a possible solution for the 45 range anxiety problem, but it is not economical and environ- 46 mentally friendly [22]. The larger the capacity is, the longer charging time will be, which might result in higher operation 48 cost [23]. Compared with the traditional plug-in charging 49 technology, WPT allows EBs to be connected to the grid 50 for charging en-route. Besides, it is possible to decentralize 51 charging times for better adaption to the profile of the time- 52 of-use (TOU) electricity price. 53 TOU price is a typical price-based demand response mech- to adapt to the TOU pricing mechanism [11]. Wirelessly 74 charged EVs using WPT technology has also been proven 75 to be better in reducing battery capacity specifications and 76 mitigating the range anxiety [33]. Though the cost of deploy-77 ing WPT may be higher than that of the wired charging 78 device [34], it is acceptable to the future transit system 79 because it helps to mitigate the range anxiety, reduce the 80 weight of battery, and optimize the long-term operation cost 81 [35]. In [33], the authors developed an integrated life cycle 82 assessment model to evaluate the cost of an all-EB sys-83 tem with plug-in or wireless charging technology. Korea 84 Advanced Institute of Science and Technology (KASIT) 85 reported that the WCEB was possible to achieve the power 86 efficiency of 83% at an output power of 60 kWh [12]. Simi-87 larly, the PRIMOVE system for WCEB made by Bombardier 88 enabled a charging power of up to 200kWh with a conversion 89 efficiency of more than 90% [36]. They all found that the 90 WCEB system is more economically competitive than the 91 plug-in charging EB system.

92
The total cost of WCEB system is mainly contributed by 93 the power track, the vehicle battery and the charging strategy 94 [8]. Previous research has focused on the optimization of 95 the cost of power track [7], [9], [12], [37] and [38], but the 96 battery capacity and charging strategy are yet to be studied 97 sufficiently. A summary of selected works on optimizing the 98 charging cost of wirelessly charged EVs is given in Table 1. 99 In [7], the cost of battery and power tracks with the constraint 100 of energy consumption and the driving range were optimized 101 by using the continuous Meta-heuristic approach. In [38], 102 a bi-level mixed integer nonlinear programming (MINP) was 103 proposed to optimize the total cost including the battery, the 104 power tracks and the EBs. A similar approach was imple-105 mented to minimize the cost of the transmitters and battery 106 was proposed in [9]. In [11], the authors quantified the ben-107 efits of three charging methods, i.e., static wireless charg-108 ing, dynamic wireless charging (DWC) and quasi-dynamic 109 wireless charging. The optimal charging strategy for various 110 market conditions and initial investment cost was discussed 111 in [12]. They concluded that the dynamic charging strategy   The rest of this paper is organized as follows.   Notations used in this study are given in Table 2.

151
The charging mode for the WCEB system is shown in

171
Min where W e is the battery cost, W c is the charging cost per day, 180 and d is the number of the operation days.
where u e is the unit battery cost, referring to the cost of per 183 kWh capacity [49].
where y (t) is the charging price at time t and p c is the 186 charging power.

187
The remaining battery power during the whole operation 188 period cannot exceed the rated battery capacity E o , nor can it 189 be lower than the minimum remaining power, which can be 190 presented by the following constraint.
where E (t) is the remaining battery power at each moment 193 during operation, and E min is the minimum remaining power.
The stopping time at a bus station depends on the number 215 of passengers getting on and off the bus. Thus, the stopping 216 time (t ε ) can be represented by Eq. (13).
where q refers to the station number between the (i − 1) th 220 and i th power track. ε j on and ε j off are the number of passengers 221 getting on and off at the j th bus station, ϕ is the number of bus 222 station passed.

223
Eq. (6) and Eq. (7) are the boundary conditions. Eq.(6) 224 means that the initial battery power is set to the battery 225 capacity E 0 . In Eq. (7), the remaining power of the WCEB 226 is set to a fully charged state at the end of the one-day cycle. 227

228
To facilitate the optimization of the TOU based charging strat-229 egy, a dynamic time-dependent energy consumption model is 230 necessary to estimate the power consumption [39]. Consider-231 ing that the power consumption p x (t) in Eq.(2) consists of 232 the engine power (p d (t)) and other energy consumption (p u ), 233 p x (t) can be presented by Eq.(15).
where β is the conversion factor of the engine power.

236
In Eq.(15), the effective power (p d (t)) of the generator 237 can be estimated by the sum of the rolling resistance power, 238 the slope resistance power, the air resistance power and the 239 acceleration resistance power [40]. Thus, the effective power 240 can be formulated by Eq.(16).
where m is the weight of the bus, g is the gravitational acceler-244 ation, θ is the inclination of the road, a (t) is the acceleration 245 of the EB at time t, v (t) is the vehicle speed at time t, A f is the 246 area of the vehicle subject to the air resistance, ρ air is the air 247 mass density, C D is the air resistance coefficient of the bus, 248 and r is the rolling resistance coefficient given by Eq. (17).    original problem can be transformed to an unconstrained 300 minimization problem by Eq.(24).

305
To improve the search efficiency, the penalty factor can be 306 updated iteratively by Eq.(25).
where σ (k) is the ratio of feasible solution to unfeasible solu-309 tion for the unconstrained problem in the k th iteration [51]. 310

311
GWO is a searching method inspired by the prey activity 312 of grey wolves [43]. It has strong convergence perfor-313 mance on solving multi-peak and multi-dimensional NP-hard 314 problems [44].
315 Figure 2 shows the calculation process of the GWO algo-316 rithm. First, it divides the wolves into four levels, i.e., λ, µ, 317 δ and , according to the size of the fitness value. λ, µ and δ 318 are the wolves in top three levels, while the is the remaining 319 wolves. The wolf pack realizes the optimization process 320 of the whole algorithm. The three high-level wolves λ, µ 321    The specific formulation of the GWO algorithm can be 336 expressed by the following equations.    [45]. As shown in Figure 3, the length of bus line is 360 32,960 meters and the bus service begins at 5.30 a.m. There 361 are 5 wireless power tracks and 33 bus stops along the bus 362 line. The bus runs 15 cycles in one day, thus the total number 363 of charging opportunities (n) is 75. Accordingly, the total 364 stopping times at bus stops (ϕ) is 495. Table 3 shows the 365 location of the power track. According to [46], the local TOU 366 price is given in Table 4.

367
According to the vehicle parameters provided by Yutong 368 Bus Company, road surface coefficients and resistance 369   constants provided by [47] and [36], the parameter setting of 370 the energy consumption model is given in Table 5.    delayed charging strategy, which enables to select a charging 381 chance with relatively lower electricity price. With the above 382 experiment setting, the optimized charging strategy T n is 383 shown in Figure 4. It demonstrates that the WCEB decides 384 to charge at the current power track or defer charging until 385 arriving at the next power track. The instant charging strategy 386 is used as the benchmark for comparison, which means that 387 when the remaining power of the battery falls below a certain 388 level, the WCEB decides to charge at the current power track 389 instantly.

390
As shown in Figure 5, the battery charging amount dis-391 tribute relatively balanced in the whole operation circles with 392 the instant charging strategy, while it is concentrated in the 393 period of lower electricity price with the delayed charging 394 strategy which is guided by the TOU electricity price. We also 395 explore the energy consumption pattern of the two charging 396 strategies.

397
According to the battery charging amount in Figure 5, 398 we compare the curves of the remaining power in Figure 6. 399 The turning points shows the time when the TOU price 400 changes. The turning points A, B, and C on the curve of 401 the delayed charging strategy indicate that when the charg-402 ing price rises from the off-peak price to the peak price, 403 the WCEB decides to reduce charging to save the energy 404 cost unless the remaining power is lower than the thresh-405 old. In contrast, the turning points D, E, and F show that 406 when TOU charging price switches from the peak price to 407 the off-peak price, or from off-peak price to valley price, 408 the WCEB starts to increase charging until the charging 409 amount reaches to the battery capacity. However, the instant 410 charging strategy can not guide to charge in off-peak price 411 periods. Tables 6 and Table 7 illustrate the energy cost of 413 the two charging strategies. In the off-peak hours, i.e., 414 0.369 RMB/kWh, the delayed charging strategy guides to 415 charge 141.61kWh, while the instant charging strategy guides 416 to charge 118.49 kWh. It indicates that the bus can charge 417 VOLUME 10, 2022    Table 7, the daily charging cost is

431
Because the unit battery cost varies widely in the market, 432 it is vital to investigate the effect of battery capacity and 433 unit battery cost on the energy cost [52]. The charging costs 434 with various battery capacity specifications are tested by the 435 delayed charge strategy as shown in Figure 7. It is found that 436 as the battery capacity increases (indicating the battery cost 437 increases), the charging cost gradually decreases. Since the 438 unit battery cost is a constant value, the growth rate of the 439 battery cost is also constant. When the battery capacity is 440 larger than 40kWh, the decreasing rate of the charging cost is 441 less than the increasing rate of the battery cost, which results 442 in the minimum total cost. 443 Figure 8 illustrates the marginal diminishing effect of the 444 daily charging cost. Though the battery with larger capacity 445 can lengthen the driving time, the unit charging cost can not 446 reduce in proportion because the high-capacity battery cost 447 more. It means that the total cost will increase by using the 448 battery with larger capacity.

449
Because the delayed charging strategy can adapt to the 450 TOU electricity price, the charging behavior is often intermit-451 tent. That means the high-capacity batteries cannot be fully 452 utilized. To illustrate this phenomenon, the delayed charging 453 strategies with 40 kWh and 80 kWh battery tested to investi-454 gate the energy consumption for the high-capacity battery and 455 low-capacity battery. As shown in Figure 9, when the charg-456 ing price was rising from off-peak to peak, the high-capacity 457 battery was not fully charged. In the same condition, the 458 low-capacity battery can be fully charged. It means that the 459 delayed charging strategy using low-capacity batteries can 460 respond to TOU energy prices more efficiently, because the 461 battery capacity can be fully utilized.  The simulation results demonstrate the effectiveness and 503 efficiency of the proposed model in a real-world bus line. 504 Compared with the instant charging strategy, the total energy 505 cost of a single WCEB can be saved by 13331.26 RMB 506 per year under the charging strategy proposed in this paper. 507 It greatly improves the economic efficiency, which indicates 508 that it is promising to encourage governments or enterprises 509 to promote the WCEB system. Besides, the simulation result 510 shows that the optimal battery capacity is 40kWh, instead of 511 150kWh with the current unit battery cost. It indicates that it 512 is possible to reduce the operation cost by reducing the battery 513 capacity at the current market price. The solver performance 514 analysis indicates that the proposed GWO can find the best 515 solution within an acceptable time more effectively compared 516 with other solvers.

517
A sensitive analysis is conducted to investigate the 518 marginal effect of unit battery cost or battery capacity on 519 the charging strategy. It shows that blindly increasing the 520 battery capacity is not a good choice. It is necessary to fully 521 consider the detailed parameters of the road and customize 522 the configuration. In future research, we will apply the pro-523 posed charging strategy in a large-scale scenario and further 524 improve the capability of vehicle-to-grid.