Real-Time Implementation Of Optimal Energy Management In .

contributions that this paper makes to the field of optimal EMS.These include:The control strategy described in this paper is not suboptimal orheuristic; instead, it is the globally optimal control solutionapplied in a way that takes advantage of its natural robustness(again this is a surprising conclusion from a previous study [40]).If the actual driving segment is different than what was predicted,the result will be suboptimal; otherwise, the result will be globallyoptimal. This is a new technique that other researchers missed intheir rush to investigate stochastic and fast-computation optimalEMS that followed the original discrete DP results from 2001.This paper continues to demonstrate that there is indeed a naturalrobustness of discrete DP for the hybrid electric vehicle (HEV)optimal EMS problem, which may be the key to commercialrealization.2Fig. 1 One of the drive cycles in the real-world drive cycledatasetFig. 2 Example of the results from the AE extraction algorithm.Note that one AE is filtered out for having a velocity increaseless than 5 mph.MethodsTo understand the FE improvement potential of AE optimalcontrol, first a large database of real world AEs is extracted fromreal-world drive cycles. These AEs are then organized intovarious categorization schemes. Next, two control methods aredeveloped using a validated 2010 Toyota Prius model: a baselineenergy management strategy (baseline EMS) and a globally optimal EMS. A custom battery state-of-charge (SOC) adjusted FEcalculation technique is developed for AEs to ensure unbiased FEcomparison.Then, to determine the impact of AE category prediction indrive cycles, several steps are required. The first is to develop aset of drive cycles representing various styles of driving. Next,four control strategies are compared: (1) a baseline energy management strategy (baseline EMS), (2) a full drive cycle predictionoptimal EMS, (3) an exact AE prediction optimal EMS, and (4) acategory AE prediction optimal EMS. By comparing the AE category prediction (which is real-time implementable and uses verylimited future information) with the baseline EMS as well as perfect prediction optimal EMS, we will have determined the FEimprovement for modern vehicles and we will have determinedhow much of the maximum possible FE improvement is achieved.2.1 Acceleration Event Dataset Development. Initialresearch on AEs suggests that velocity and fuel consumption canbe accurately modeled with sinusoidal and polynomial modelsthat satisfy a zero jerk condition consistent with real-world driving[45] but it is difficult to capture an inclusive set of AEs due to thevariability introduced by obstacles such as roundabouts, intersections, and crossings for different vehicles’ traffic conditions androad types [46,47]. Additionally, substantial variations in driverbehavior in regard to AEs results in significantly different fuelconsumption rates [48] and many studies of AEs have becomeexperimental and data-driven [49].In this research, data were recorded from several 2010 ToyotaPrius drivers in the California area. The data are composed of 384drive cycles measured at 10 Hz (0.1 s time-steps) with an averagetime length of 1086 s and an average velocity of 28.05 mph. Anexample drive cycle from the dataset is shown in Fig. 1. AEs canbe extracted from these drive cycles by identifying sections ofspeed data where the velocity increases in the next time-step, i.e.,vkþ1 vk 0 where k is a discrete time-step. But, for real-world081002-2 / Vol. 142, AUGUST 2020accelerations, there are short moments of steady or even decreasing speed within an AE and a two time-step evaluation will yielderroneous results. Additionally, the real-world drive data have ahigh resolution and a strict equality evaluation for steady sections(i.e., vk vk 1 ¼ 0) is insufficient. To address these issues, AEswere extracted by searching for sections satisfying the followinglogic statement where Ù represents logical conjunction (i.e., an“and” statement)”ðvkþ1 vk Þ 0:05 mphÙðvkþ2 vkþ1 Þ 0:05 mphÙðvkþ3 vkþ2 Þ 0:05 mphÙðvkþ4 vkþ3 Þ 0:05 mph(1)If Eq. (1) is true, then this section of the drive cycle is labeled asan AE. From these extracted AEs, if they either start from a negative speed, last for one second or less, or only increase speed by5 mph or less then they are filtered out. A conceptual plot of theidentification of AEs in an example drive cycle is shown in Fig. 2.Using this process, 7708 AEs are extracted from the 384 drivecycles for analysis. Since these AEs will be used to compare abaseline EMS and optimal EMS, we must ensure that the vehicleis at steady-state before and after each AE. To accomplish this,each of these AEs is prepended with 8 s of the initial velocity toensure the vehicle is at steady-state at the beginning of each AEand appended with 12 s of the final velocity to ensure the vehicleis at steady-state at the end of each AE. An example of the resulting AE cycle is shown in Fig. 3. The 7708 AEs with the prepended and appended velocity states range from 22 s long to 76 slong and include speeds from 0 mph to 50 mph. To derive generalized improved control strategies, this dataset of AEs must now becategorized.2.2 Acceleration Event Categorization. Three different AEcategorization schemes were chosen for this dataset based on principle component analysis:(1) Starting velocity and ending velocity categorizationvi ; vfTransactions of the ASMEDownloaded from ems/article-pdf/142/8/081002/6516718/ds 142 08 081002.pdf by Western Michigan University user on 15 April 2020(1) Rigorous analysis of optimal EMS implementation and theeffect of prediction error using 384 real-world drive cycles.(2) Quantification of prediction accuracy required for optimalEMS using a rigorous study of driving segment categorization.(3) Direct implementation of discrete dynamic programmingusing a precomputed look-up table.(4) Implementation of optimal EMS in discrete accelerationevents.(5) Use of optimal control matrix solutions that are a function ofvelocity, which only works for monotonic drive segments.

Fig. 3 Example of prepending and appending constant velocity of each AE to ensure steady-statet; vf(3) Average acceleration and ending velocityvf vi; vftwhere the variables vi, vf, and t are shown in Fig. 3.An example of the first categorization scheme, starting velocityand ending velocity, that uses a new category every 3 mph isshown in Fig. 4. The x-axis shows the assigned AE category number, e.g., category 1, 2, 3, etc. The left y-axis shows the velocityrange. For example category 1 captures all AEs that start at 0 mphand end at 7.8 6 1.5 mph. The right y-axis shows the number ofAEs in the AE category, for example, there are about 321 AEs incategory 1 (starting around 0 mph and end around 7.8 6 1.5 mph).Overall, Fig. 4 shows there are a high number of low velocity AEsand a small number of high velocity AEs in the dataset.2.3 Baseline Energy Management Strategy Development.The vehicle model chosen for analysis is a 2010 Toyota Priusbecause it is a popular and well documented vehicle. It also hasthe highest FE of any vehicle in its class (excluding electricvehicles) [50], implying that FE improvements would beFig. 4 Plot showing the velocity range and the number of AEs in each category for the starting velocity and ending velocitycategorization schemeFig. 5 Plot showing total duration, end velocity, and the number of AEs in each category for the time duration and endingvelocity categorization schemeJournal of Dynamic Systems, Measurement, and ControlAUGUST 2020, Vol. 142 / 081002-3Downloaded from ems/article-pdf/142/8/081002/6516718/ds 142 08 081002.pdf by Western Michigan University user on 15 April 2020(2) Time duration and ending velocityAn example of the second categorization scheme, time duration, and ending velocity, which uses a new category every 2.8 sand 4.4 mph, is shown in Fig. 5. The x-axis and right y-axis areconsistent with first categorization scheme plot, Fig. 4. But nowthe left y-axis shows the ending velocity (as red Xs) and the totaltime duration (as blue dots) of each category. For example,category 1 has a total time duration of 6.2 6 1.4 s and an endingvelocity of 12.2 6 2.2 mph for which there are 274 AEs. Note thatthe total time duration is shown without prepended and appendedvelocity (Fig. 3), which is used to ensure steady-state. Overall,Fig. 5 shows that, in general, there is a high number of shortduration AEs and a low number of long-duration AEs in thisdataset.An example of the third categorization scheme, average acceleration, and ending velocity, which uses a new category every0.02 g’s and 4.4 mph, is shown in Fig. 6. The x-axis and righty-axis are consistent with the other two categorization schemeplots, Figs. 4 and 5. The left y-axis shows the ending velocity (asred Xs) and the average acceleration (as blue dots) of each AE category. For example, AE category 1 has an average acceleration ofabout 0.11 6 0.01 g’s (g-force) and an ending velocity of approximately 34.2 6 2.2 mph. Overall, Fig. 6 shows that the majority ofAEs in this dataset do not go above 1.13 g’s.Note that there were very few AEs, which had an ending velocity above 50 mph in this dataset. AEs that ended at a high velocitywere lumped into AEs with an ending velocity around 50 mph.

Table 1 A comparison of simulated and measured fuel economy for standard EPA drive cyclesEPA drive cycleSimulated fuel economyMeasured fuel economy [52]Percent difference76.6 mpg69.0 mpg44.9 mpg75.6 mpg69.9 mpg45.3 mpg1.3%–1.4%–1.0%UDDSHWFETUS06challenging to demonstrate. Additionally, there is physicallymeasured validation data publicly available for this vehicle.The baseline EMS must be a validated and high accuracy simulation of current real-world vehicle FE performance. Additionally,to compare alternate control strategies over thousands of shortsegments of driving, such as AEs, the vehicle model must havehigh enough fidelity to model FE changes from different controlswhile also having a relatively low computational cost. This typeof model is commonly known as a controls-oriented model sinceit must sacrifice some fidelity in order to lower computational costfor controls development.To satisfy these requirements, a combination of a high fidelityvehicle model developed in the AUTONOMIE modeling software iscombined with an equation-based power-split vehicle model.The AUTONOMIE modeling software has shown strong correlationwith the current 2010 Toyota Prius physical vehicle operation[51] so it was used to derive the engine torque, engine speed,and engine power, which was then implemented in the equationbased power-split model. FE and SOC with respect to time arethen recorded.To ensure that this model does not sacrifice FE predictionaccuracy, a thorough model validation study was conducted.The simulated FE from this model is validated against 2010Toyota Prius FE data physically measured by Argonne NationalLaboratory using all available drive cycles [52]. The publiclyavailable data are measured for the three standard U.S. Environmental Protection Agency (EPA) drive cycles: the city drivingfocused urban dynamometer drive schedule (UDDS), the highway driving focused Highway Fuel Economy Test (HWFET),and the aggressive driving focused US06 cycle. All simulatedFE was within 1.5% of the physically measured data as shownin Table 1. A controls-oriented model is needed for this researchand the focus is not on model development; therefore, this issufficient validation for controls development. The equationbased power-split model was developed according to the literature [53–56]. Each of the 7708 AEs is input into the 2010Toyota Prius Autonomie model and the engine torque, speed,and power output is recorded. For a given engine power, therequired electric power can be determined by subtracting thetotal propulsive power requirement asPelec ¼ Fprop v PICE081002-4 / Vol. 142, AUGUST 2020(2)where Fprop is determined from a force balance on the vehicle as1Fprop ¼ mv þ Crr mg þ Cd qair v2 Afront2(3)and Crr is the coefficient of rolling resistance, m is the mass of thevehicle, g is the acceleration due to gravity, Cd is the coefficientof drag, qair is the density of air, v is the vehicle velocity, Afront isthe frontal area, and v is the vehicle acceleration (calculated usinga numerical derivative). Note that the additional force componentdue to an elevation angle is not a part of this study.The resulting battery SOC at the next time-step is then calculated via a difference quotient asSOCðk þ 1Þ ¼ SOCðkÞ Voc ��ffiffiffiffiffiffiffiffiffiffiffiffiffi2 4PVocbatt RintDt2Rint Qbatt;o(4)where Voc is the open-circuit voltage of 201.6 V, Rint is the batteryinternal resistance of 0.373 X, and Qbatt;o is the battery capacity of6.5 A h.The overall efficiency of the electrical components can then becaptured using response surface fits [57] of data available in theliterature [56]. Using the speed and torque, the electrical systemefficiency is determined and applied asPbatt ¼1gelecPelec(5)where gelec is a function of electric motor speed xEM , electricmotor torque TEM , generator speed xgen , and generator torqueTgen . The electric motor and generator efficiency maps areextracted from the AUTONOMIE modeling software, which are usedto compute gelec as a function of the torques and speeds of theelectric components.The fuel consumption is then obtained using a brake-specificfuel consumption (BSFC) map. This map has to be derived sinceonly its general structure is available in the public domain [55].For the case of a 2010 Toyota Prius, a quadratic response surfacedoes not adequately match the BSFC structure; therefore, a cubicresponse surface is used, which shows strong correlati

Real-Time Implementation of Optimal Energy Management in Hybrid Electric Vehicles: Globally Optimal Control of Acceleration Events Widely published research shows that significant fuel economy improvements through optimal control of a vehicle powertrain are possible if the future vehicle velocity is known