Multi-objective component sizing for a battery-supercapacitor power supply considering the use of a power converter

Accepted Manuscript Multi-objective component sizing for a battery-supercapacitor power supply considering the use of a power converter Li Sun, Paul Walker, Kaiwu Feng, Nong Zhang PII:

S0360-5442(17)31756-5

DOI:

10.1016/j.energy.2017.10.051

Reference:

EGY 11695

To appear in:

Energy

Received Date: 10 January 2017 Revised Date:

2 October 2017

Accepted Date: 13 October 2017

Please cite this article as: Sun L, Walker P, Feng K, Zhang N, Multi-objective component sizing for a battery-supercapacitor power supply considering the use of a power converter, Energy (2017), doi: 10.1016/j.energy.2017.10.051. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Multi-Objective Component Sizing for a BatterySupercapacitor Power Supply Considering the Use of a Power Converter

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Li Sun, Paul Walker, Kaiwu Feng, and Nong Zhang

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Abstract-- Owing to a lack of power density of conventional batteries, the onboard energy storage systems of an electric vehicle has

2 to be oversized to compensate worst-case load condition, which is sub-optimal as it induces a heavy penalty on overall system weight

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3 and cost. One solution to overcome this limitation is to hybridize it with supercapacitors in order to boost its power performance via a 4 power converter. This paper presents a multi-objective optimization problem over the parameters of such hybrid energy storage 5 systems, with the aims to solve two conflicting objectives – cost and total stored energy in the hybrid energy storage system, under a set

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6 of pre-defined design constraints. An algorithm is first developed to find all feasible solutions to the problem. Two popular design 7 examples are then tested differentiating Lithium Iron Phosphate based batteries from Lithium Manganese Oxide / Nickel-Cobalt8 Manganese based batteries. A Pareto frontier is recreated for each example and an ξ-constraint method is finally adopted to choose the 9 best member for comparison. This is so far, according to the authors’ knowledge, the first reported multi-objective optimal sizing 10 method for an active hybrid energy storage system considering the effect of the power converter to gain a clearer understanding of its

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11 impact over various design choices.

Keywords—Li-ion batteries; Supercapacitors; DC-DC converters; Load leveling; Multi-objective optimization

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NOMENCLATURE

Battery Pack

15 HCR

Hybridized Cost Ratio

16 HESS

Hybrid Energy Storage System

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14 BP

17 LiFePO4Lithium Iron Phosphate 18 LMO

Lithium Manganese Oxide

19 MOOP Multi-Objective Optimization Problem 20 NCM

Nickel-Cobalt-Manganese

21 P2W

Power-to-Weight (Ratio)

22 PC

Power Converter

This work was supported by the Automotive Australia 2020 Co-operative Research Centre, Commonwealth of Australia under Grant 4-108. L. Sun, N. Zhang and P. Walker are with the Centre for Green Energy and Vehicle Innovations, as well as the School of Electrical, Mechanical and Mechatronic Systems, University of Technology, Sydney, Ultimo, NSW 2007, Australia (e-mail: [email protected]; [email protected]; [email protected]). K. W. Feng is with Qingchi Technology Co., Ltd., Guangdong 518048, Australia, (e-mail: [email protected]).

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23 SP

Supercapacitor Pack

24 ZVC

Zero Voltage Switching

25 26

1.

INTRODUCTION

In this section, background information, literature review and overview of the research outcomes are outlined.

27 1.1. Motivation and Technical Challenges Designs are becoming more complex and have more dedicated components to achieve multiple targets such as cost, size,

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29 performance and a low weight. As a consequence, when solving real world engineering problems, objectives are found to be 30 conflicting and trade-offs occur in order to achieve the best possible overall solution. One such example is in a hybrid electric

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31 vehicle (HEV) where at least one conventional combustion engine is hybridized with one electric motor whose primary job is to 32 shift operation points of the combustion engine into more fuel-economical “sweet spots”. However, this increases the cost and

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33 weight of the vehicle. In addition, the vehicle should still be sufficiently powerful, competitively affordable and practically 34 packagable. In other words, these objectives become in conflict or work against each other. This whole problem thus, can be 35 treated as a multi-objective optimization problem (MOOP). 36

Considering the Toyota Prius as an example, which was ranked at the top of Consumer Reports’ Best-Value New-Car list in

37 2012 and 2013 [1]. Although nothing is said explicitly by Toyota, the MOOP-oriented philosophy can be sensed that if carefully 38 enough, one should be able to find an ideal solution that contains an optimal hybridized ratio as a key parameter between the cost

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39 of the electrical system i.e. battery and motor and cost of engine so that the overall hybrid system delivers its best performance (in 40 the Prius’s example, best fuel economy) at lowest possible price without sacrificing other design requirements such as output peak 41 power, size, and etc.

In the spirit of Prius, the authors realized that the design of a hybrid energy storage system (HESS) for an electric vehicle (EV)

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43 appears to be of a similar nature: an active HESS consisting of three major components, namely battery pack (BP), supercapacitor

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44 pack (SP) and power converter (PC) is analyzed in this paper as shown in Fig. 1, in which, the SP is added in order to lower the 45 over-current and cycling stress that would otherwise be applied to the BP alone. As a consequence, battery aging may occur – a 46 report [2] shows that for lithium-ion batteries, aging effect can be further accelerated and influenced by high temperature under 47 high load and low SOC. To clarify, a statement needs to be made that, the primary focus of this paper is to design and use HESS 48 to reduce the power stress on the BP, the study of its effect on battery lifetime extension is beyond the scope of this paper and is 49 intended to be addressed in future work. 50

Besides, a PC acting as a voltage buffering element coordinates the power split between BP and SP. For examples in [3], DC

51 link is supported by the SP and the PC is used to buffer the voltage gap between the BP and the DC-link; whereas in [4], DC link 52 is supported by the BP and the PC is used to buffer the voltage gap between the SP and the DC-link.

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ACCEPTED MANUSCRIPT Therefore, it is critical to calculate the optimal hybridized ratio, as a key design parameter, for each component (i.e. amongst

54 BP, SP and PC), given a set of system requirements or constraints (e.g. size, power, and energy). 55

Establishing such methodology is challenging since the components to be compared or collaborated are indeed, different in

56 nature, and the objectives or criteria of the overall system can be diverse. e.g. longest driving range, highest acceleration, 57 maximum efficiency, longest lifespan, minimum weight, volume or cost.

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58 1.2. Literature Review 59

Despite the fact that many HESS were designed under ad hoc conditions, such a sizing problem was addressed in past literature.

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Various researchers used a graphical tool called a "ragone plot" to highlight energy and power as functions of weight and time

61 [5]; other scholars size the SP by averaging its performance over various driving cycles [6]. Ravey et al. [7] studied a novel

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62 optimal sizing method based on the statistical description of driving cycles to size the energy source of Fuel Cell Electric Vehicle. 63 Cai et al. [8] have demonstrated a sizing-design methodology for designing hybrid fuel cell power systems for an unmanned

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64 underwater vehicle. Barelli et al. [9] proposed a dynamic model to optimally size a fuel cell electric bus using the SOC control 65 strategy. In addition, C. R. Akli, et al [10] proposed a frequency method in which it sizes the power rating of the SP based on the 66 higher frequency part of the load power whereas the battery takes care of the lower frequency band below a certain cut-off 67 frequency. L. Wang and H. Li [11] proposed a sizing routine to achieve the lightest mass for the HESS compared with BP-only or 68 SP-only solutions at a 95% efficiency basis.

Furthermore, optimal design has been focused on extending the battery lifetime. In [12], L. Wang, et al added another degree of

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70 freedom – "System Joule Loss" – into the objective function to optimize overall life cycle by reducing its total loss. Likewise, E. 71 Schaltz, et al [13] shows battery lifetime extends significantly when BP alone is overdesigned whereas it is rather insensitive if SP

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72 alone is overdesigned while the size of BP remains unchanged. Similarly, a “Loss of Power Supply Probability” (LPSP) 73 optimization method is proposed in [14] to estimate battery size for a required system reliability. Moreover, Gan et al. [15]

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74 developed a model-based sizing tool for a hybrid photovoltaic–wind-diesel–battery system in which, battery life-cycle cost is 75 minimized whilst meeting various performance criteria. 76

It is worth mentioning that R.Sadoun, et al [16] conducted a deeper exploration into different categories of Li-ion batteries from

77 two vendors, where comparison was made between "power batteries" and "energetic batteries" to gain insight into their influence 78 over the HESS design. 79

Various commercial software packages have been developed for modern EV and HEV designs, such as ADVISOR [17] and

80 Autonomie [18]. Four types of couplings over system-level optimization were proposed in [19], including iterative, sequential, 81 simultaneous and bi-level types. 82

Besides, using genetic algorithm is another option to solve this complex nonlinear optimization problem. For example Z.

83 Dimitrova and F. Maréchal [20] proposed an evolutionary genetic algorithm is applied to solve a set of optimal decision variables

ACCEPTED MANUSCRIPT 84 in desigining the powertrain system of a Hybrid Electric Vehicle. Muhsen et al. [21] proposed a differential evolution based 85 multi-criteria optimization method to optimally size a hybrid water pumping system. However, this method is very time 86 consuming and its black-box nature made it impossible for designers to track what exactly is going on during optimization. 87

Moreover, S.Lee and J. Kim [22] proposed using the linear programming (LP) technique to find the optimal power distribution

88 within a hybrid energy storage system considering the driving cycle and the power and energy capacity vatiations. One of the

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89 disadvantages of this method is the approximation formulation of the problem which restricts its applications to uncomplicated 90 hybrid systems. 91

Finally, simultaneous optimal sizing and energy management was carried out using convex programming [23] and PCOA

92 (Parallel Chaos Optimization Algorithm) [24]. Although it appears to be attractive to co-design the component sizing with the

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93 control strategies, there is little sense to calculate one best design option i.e. component sizing ratio, by testing it against every 94 single possible strategy at every single operating condition. On the contrary, the point the authors are trying to make is, as long as

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95 the distilled component sizing candidate can cope with the worst case strategy or load conditions, it itself already is the optimal 96 design solution. 97 1.3. Main Issues and Contributions

Three main issues are found within surveyed literature:

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1) Most of the aforementioned sizing methods adopt a single-objective optimization approach. In addition, for scholars

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considering more than one objective, cost is barely considered. As a consequence, fair comparisons and design trade-offs

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are difficult to make.

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2) Second, a PC is a bulky but key element that is often ignored within the above literature, which is not ideal since its contribution to or influence upon, the final design of an active HESS is not only necessary, but significant.

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98

3) The specific energy (both cost and weight wise) differs substantially between the two types of mainstream Li-ion battery

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technology, namely LiFePO4 (Lithium Iron Phosphate) based battery pack and LMO (Lithium Manganese Oxide) or NCM

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(Nickel-Cobalt-Manganese) based one. Although numerous papers have explored the potential of each electro-chemical

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energy source, the investigation is limited to single chemistry and there is little to compare the relative contributions when

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constructing an HESS for EV or HEV applications.

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109

Having understood the issues, the solutions this paper presents are threefold:

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1) A novel MOOP based problem-solving framework is first derived with the aims to solve two conflicting objectives – cost

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and total stored energy in the HESS. 2) In this study, PC –

a ZVS half bridge DC-DC converter – is considered. Several key parameters of the PC are defined and

imported into the MOOP framework for processing.

114 115 116

MANUSCRIPT 3) In order to differentiate an LiFePO4 ACCEPTED based battery from an LMO/NCM based one, two dedicated design examples are analyzed using proposed MOOP technique. As a result, the most cost-effective design option can be obtained. Although the specific results for HESS applications were shown, the concept of HESS and MOOP can be easily tailored for

117 other types of hybridized systems such as series hybrid electric vehicles, battery assisted fuel cell electric vehicles, and stationery 118 solar-battery power systems or any dual-source power systems that need to perform load-levelling functions.

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119 1.4. Paper Organization The remainder of this paper is structured as follows. In Section 2, before a MOOP problem can be formally presented, a deep-

121 dive into "decision space" [25] is conducted to locate the fundamental design metrics and key parameter for constructing an active 122 HESS, at both component and system levels. The MOOP is then defined in Section 3.1. A Two-step Framework for Pareto

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123 Optimization is introduced in Section 3.2 in order to meet various design requirements whilst reflecting real-world engineering 124 constraints. This method is then tested rigorously in Section 4 by two HESS design examples. As a result, a Pareto frontier is

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125 guaranteed to be recreated for each example. In Section 5, comparison between these two cases is conducted; a prototype HESS is 126 also built based on the analysis. Finally, conclusions and future work is drawn and summarized in section 6. 127 128

2. DESIGN REQUIREMENTS AND COMPONENT SPECIFICATIONS Fundamental design metrics and parameters are studied in this section in order to optimally size an active HESS at both

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129 component and system levels. 130 2.1. Design Requirements and Objective Definition 131

To understand the root causes of the sizing problem and construct an appropriate "decision space" to solve for optimal solutions

132 in "objective space" [25], it is necessary to first resort to final system-level requirements/objectives to ask why the HESS needs to

Four design requirements/objectives are selected at this stage for the overall HESS design in a mobile vehicle traction

135 application:

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134

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133 be designed the way it is and then break them down into component-level sub-requirements so as to explore each contribution.

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1) The HESS must store as much energy as possible, as this will ensure the longest possible drive range.

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2) The HESS must deliver/absorb as much peak power to/from the load as possible, to achieve the best possible performance

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in drivability.

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3) The size (weight) of HESS must be as light as possible for both packaging and drive economy purposes.

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4) The overall cost of HESS including the cost of PC, is expected to be as low as possible.

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By glancing at the requirements one could easily deduce that the most likely energy and power are positively correlated with

142 each other, however, it is also obvious not to oversize BP or SP which induces a penalty on system weight or cost. 143

Note that in this paper, “efficiency” is deliberately excluded, as efficiency is highly dependent on how power distribution is

144 allocated amongst BP, SP, and load via PC. Instead, an assumption is made in which the worst-case power split ratio is fixed as a

ACCEPTED MANUSCRIPT 145 constant between BP and SP at peak load power, and furthermore it will be later introduced into the MOOP specifically as one of 146 the constraints. Such MinMax-type treatment [25] can be understood in the sense that it not only helps reducing the number of 147 objectives to be optimized, but the optimized outcomes should not be jeopardized by this treatment since it already has to cope 148 with a worst-case situation, limited by high-level energy management strategy (EMS) whose other traits and details are outside 149 the scope of this research, and it has been addressed by the authors in [43] to avoid complication.

151

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150 2.2. Component Specifications and Evaluation The system level metrics can be further broken down into component levels i.e for BP, SP, and PC each respectively, Table 1

152 summarizes all relevant metrics at both levels. 153

In this study, another system level metric – power to weight (P2W) ratio [26] – is added as an additional constraint. This is to

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154 realize that during the optimization routine, the weight and power of HESS vary independently as parameter varies. Using power 155 alone is not enough to evaluate vehicle acceleration performance. The weight of targeted vehicle (B or C segment, excluding the

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156 weight of HESS) is set as 1,000kg in this study for simplification. 157

In essence, P2W is introduced, along with power, to ensure minimum vehicle acceleration response is achieved.

158

In order to calculate all metrics listed in Table 1 so as to perform optimization, a set of weight specific variables are further

159 defined and shown in Table 2. 160

In a clearer manner, all variables defined in Table 2 can be also visualized in the form of a matrix, as shown in Table 3 with

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161 corresponding values assigned for BP, SP and PC each respectively. Note in the last two rows of Table 3, BP has been separated 162 into two mainstream categories of Li-ion chemistry, which is assumed to have a significant impact on the final HESS design and 163 these will be compared in later sections with greater details. The values listed in Table 3 are justified as follows.

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First, Φb for each type of BP can be easily found in various datasheet and literatures. For this study, Li-ion battery is only

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166 separated into two main groups because of the similarity of the specific energy within the same group. For example, in [27], Φb of

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167 the LiFePO4 based battery is quoted as 90-110 Wh/kg, the lower bound of this metric is chosen in this case in order to consider 168 other factors constructing the BP such as cooling and BMS system. For NCM or LMO based batteries, direct data is extracted 169 from [32] for the NCM based Li-ion battery produced by Boston Power® upon which its cost model is built. Besides, Φb of NCM 170 or LMO batteries can also be determined at 200 Wh/kg based on [28]. Similarly Φsc is extracted from [29] for SP. 171

Costwise Csc is obtained from a commercial quotes at production volume from Maxwell [30], as well as for LiFePO4 type

172 batteries [31]. 173

For NCM or LMO based Cb, [32] is used to extract the price difference of two variants of the Tesla model S - 40kWh and

174 60kWh – for a price gap of USD $10,000. 175

It’s slightly more complicated to handle power related calculation especially when including that of the PC. This is because

176 indeed there are a myriad of circuit topologies one could adopt to connect SP with BP in a regulated fashion.

177

ACCEPTED A few highly-cited converter topologies are enlisted in Fig. MANUSCRIPT 2: Cao and Emadi [3] proposed a configuration, in which the low

178 voltage side is held by BP and it is interfaced by a power diode with the DC link held by SP. Inversely, in Lu, et al’s design [4], 179 the low voltage side is held by SP and it is interfaced by a bidirectional power switch with the DC link held by BP. Curti, et al [33] 180 further split SP into two groups, with one actively controlled and the other uncontrolled. Furthermore, Jeong, et al [34] proposed 181 an isolated, dual full-bridge topology in order to expand the voltage limitation rooted in the conventional half bridge buck-boost

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182 topology. Finally, a dual half-bridge topology is proposed by Peng, et al [35], claiming to achieve higher power density and lower 183 cost at the same power rating compared with [34]. However, trade-off is made that split DC link capacitors in [34] have to handle 184 the full load current. 185

It is worth mentioning that, after a comprehensive study done by Schupbach and Balda in [36], a conclusion is drawn that a half

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186 bridge buck-boost topology obtains most merits, from both performance and cost aspects, over some of the other topologies. And 187 indeed, topologies (a), (b), (c) and (e) in Fig. 2 can all said to be derived from half bridge buck-boost topology. It is therefore

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188 decided to adopt a commercially available half-bridge DC-DC converter [37] – adopting an interleaving topology [38] as shown 189 in Fig. 3 – into this study and design and apply MOOP framework based on this conventional topology. 190

This topology is free of sudden DC bus voltage commutation between the two power sources, as were exhibited in [3] and [4],

191 both of which would require intricate in-rush current control as well as complex coordination with the motor controller during 192 transient, which may compromise durability and safety. In addition, it has less component counts than that of [34] and [35]. Moreover, the Zero Voltage Switching (ZVS) technique developed in [38] can greatly reduce switching loss of the converter and

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194 thereby boosts its overall efficiency to around 98% under full load conditions. Such evidences have greatly offset the downside of 195 putting the SP at the low voltage side of the converter while reducing overall system heat dissipation and device stress. 196

In Fig. 3, it is clear that the output power of SP is restricted and bundled with PC, this is to say, although the specific current

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197 rating of supercapacitor shown in [29] can tolerate a higher current, the actual current rating of the power converter limits the 198 peak output power or current of SP. In this case, the peak current drawn from the SP alone is limited to no more than 600A so as

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199 to protect the semiconductor switches within PC from being overloaded. Combined with average terminal voltage of SP (cell) and 200 its weight [29], θsc can be calculated. Moreover, it is well documented in [39] that the current power density of automotive 201 electronics is 5kW/kg (θpc) including power electronics, combined with another statement made in [40] – “the power specific cost 202 of power electronic was rated at around $20 USD per kW” – One could deduce Cpc equals to $100 USD/kg. Some buffer is added 203 in order to compensate for the exchange rate between USD and AUD as well as additional cooling effort and control, and Cpc is 204 rounded at $200 AUD/kg for this study. 205

Besides, θb for batteries are limited to the maximum C-rating for discharging from each corresponding battery datasheet

206 [28],[31], in which the LiFePO4 based battery allows peak discharge at 2C in a continuous operation whereas the NCM or LMO 207 based battery allows at 1.5C.

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MANUSCRIPT Lifecycle information can also be found inACCEPTED the corresponding datasheet [28],[29],[31] and a PC is assumed to have relatively

209 much higher longevity than any of the power sources especially under the help of ZVS technology [38]. 210

Table 3 is now completely filled up with relevant data. It is, however, expected that some of these data may vary, especially for

211 the cost related variables due to the so called “learning-curve effect” as more and more EVs are sold in the market as well as the 212 introduction of new break-through technologies and converter circuits. However for the purpose of this study, the latest data

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213 acquired is deemed accurate enough to be processed further for optimization. Let alone, the model itself is fully parametric so one 214 could easily adapt it with any updated data when necessary in the future. 215 216

3. PROBLEM DEFINITION AND A TWO-STEP FRAMEWORK FOR PARETO OPTIMIZATION

In this section, the MOOP is first defined in Section 3.1. A Two-step Framework for Pareto Optimization is then introduced in

219

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218 3.1. Definition over a Multi-objective Optimization Problem with Constraints

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217 Section 3.2 in order to meet various design requirements reflecting real-world engineering constraints.

In general, the multi-objective optimization involves maximizing (or minimizing) multiple objective (or cost) functions while

220 simultaneously subjecting them to a set of constraints [25]. This conceptual method can be explained via two criteria (or objective) 221 example in the JC-JE decision space as shown in Fig 6(b) or Fig 7(b). Here the dotted area represents all possible performance 222 values of the two criteria JC and JE. Assuming to minimize both, then it is clear that only the southwest boundary of this region is 223 of interest. This boundary set is known as the pareto optimal set. It has the property that no points on the boundary dominate other

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224 points on the set, as any movement from one point to another will worsen one of the criteria. On the other hand, any point off the 225 pareto set is dominated by some point on the set [42]. 226

In Section 2, four objectives/design requirements were ascertained and they are: energy, power, weight and cost. For the same

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227 reasoning conducted in Section 1.1, without suffering much from heavy computation time, it is decided to choose only energy and 228 cost as two conflicting objectives to be optimized at the system level, whilst treating power and weight as design requirements or

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229 constraints, at both component and system levels, so as to reduce the dimension of objective functions without distorting inintial 230 intent. A MOOP component sizing problem for an active HESS is defined in (1):

min v J = [J E , J C ] . x v 232 x = {HCR|HCR∈[0,0.05,0.1,0.15,0.2,0.25,0.3,0.35, 231

233 0.4,0.45,0.5,0.55,0.6,0.65,0.7,0.75,0.8,0.85,0.9,0.95,1]} 234 P=Pb+Psc≥P_min. 235 (1) Psc≥Psc_min. s.t. 236 Pb≥Pb_min. 237 Esc≥Esc_min. 238 P2W=(Psc+Pb)/(m+W)≥P2W_min. 239 W=Wb+Wsc+Wpc ≤W_max. 240 where J is the multi-objective optimization function [25], composed of two specific cost functions. In order to frame both cost 241 functions towards a ‘minimum cost’ direction, both JE and JC are defined in (2) so that JE is inversely proportional to the total 242 system energy E whereas JC is the system overall cost X itself.

243 244 245

ACCEPTED MANUSCRIPT (2)

JE= 30-E. JC=X.

v x is the so called decision vector in solving a MOOP [25]. Given the nature of the HESS problem, in this paper, a parameter -

246 Hybridized Cost Ratio (HCR) – is introduced as the only design/decision parameter into

v x . HCR is then used to sweep through

247 the whole decision space for possible solution sets. HCR is defined as the cost ratio of SP and PC to the total HESS cost including

249 250

0 ≤ HCR =

(WscCsc ) + (W pc C pc ) (Wsc Csc ) + (W pc C pc ) + (Wb Cb )

≤ 1 . (3)

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248 BP, SP and PC. It is formulated in (3) and is discretized into a vector to ease downstream operations.

Also in (1), six design metrics are carefully chosen from Table 1 and thresholding is applied to each metric so as to guarantee

251 that these design metrics or requirements are also met during the optimization process. In them, P_min, Psc_min, and Pb_min

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252 correspond with a minimum power total HESS, SP, and BP has to deliver or absorb at worst-case load scenario. Esc_min is the 253 minimum energy stored in SP so as to faciliate load-leveling function without over-stressing BP. P2W_min is to guarantee

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254 minimum accele-ration or gradability performance at vehicular level. Lastly, W_max is to fulfill some degree of the weight 255 reduction target which, can also be accountable for any packaging issues. 256 3.2. A Two-step Framework for Pareto Optimization 257

A two-step framework is adopted in this paper to recreate a Pareto frontier for the given MOOP: As illustrated in Fig. 4, an

258 algorithm is first developed to identify all possible design solutions at every cost and HCR indices within overall design or

260 261

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259 decision space. A Pareto frontier can then be recreated in objective space by calculating (2) using results obtained in step 1.

Note that in order to implement the flowchart in Fig. 4, especially the two highlighted blocks, equation (4)-(13) are derived to

262 solve all relevant variables:

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263 Xsc=X×HCR×Cscθpc/(Cscθpc+Cpcθsc).

(4)

(5)

265 Wsc=Xsc/Csc.

(6)

266 Wpc=Xpc/Cpc. 267 Esc=WscΦsc.

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264 Xpc=X×HCR×Cpcθsc/(Cscθpc+Cpcθsc).

(7) (8)

268 Psc=Ppc=Wscθsc.

(9)

269 Xb=X×(1-HCR).

(10)

270 Wb=Xb/Cb.

(11)

271 Eb=WbΦb.

(12)

272 Pb=Wbθb.

(13)

273

Note equation (4) and (5) can be derived at ease from the portion of HESS power that has to be jointly delivered or absorbed by

274 both PC and SP given the chosen converter topology as shown in Fig. 3.

275

MANUSCRIPT The core function of this algorithm is that, ACCEPTED within a certain price range, it searches throughout all possible design options at any

276 cost-split ratio, filters out results that fail meeting constraints in (1), while keeping and plotting the ones that succeed in meeting 277 those customized constraints. 278 279

4. TWO TYPICAL DESIGN EXAMPLES In this section, the proposed method developed in Section 3 is tested by two HESS design examples in Section 4.2 and 4.3. A

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280 Pareto frontier is guaranteed to be recreated for each example. 281 4.1. Worst-case Load Power Analysis and Assumptions 282

Based on the discussion in Section 2.1, a fixed worst-case power split ratio is introduced as one of the constraints to solve

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283 MOOP. However, the absolute amount of load power under this condition for a passenger EV is unspecified. After comparing 284 various driving cycles, as stipulated on the US-EPA website [41], a conclusion can be drawn that the LA92 driving cycle appears

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285 to possess the worst possible conditions including highest acceleration and power amongst all drving cycles. Combined with the 286 practical EV characteristics listed in Table 4, the time-series load power waveform can be calculated backwards and plotted in 287 Fig. 5. 288

Note that the highest absolute power is observed at approximately 80kW in Fig. 5 during a regenerative braking event at around

289 the 200th second.

291

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290 4.2. Case A: a Lithium Iron Phosphate Battery based Hybrid Energy Storage System The MOOP for Case A can be defined as (14) :

min v J = [J E , J C ] . x v 293 x = {HCR}

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P=Pb+Psc≥P_min=100kW. 294 295 Psc≥Psc_min=75kW. 296 s.t. Pb≥Pb_min=25kW. (14) Esc≥Esc_min=200Wh. 297 P2W=(Psc+Pb)/(m+W)≥P2W_min=0.12. 298 299 W=Wb+Wsc+Wpc ≤W_max=400kg. 300 301 Note P_min is chosen at 100kW considering the effect of fixed vehicle mass. Also the worst-case power split ratio between BP 302 and SP is chosen at 1:3 and this is assumed to be guranteed by the higher level energy management strategy as explained in 303 Section 2.1. 304

A two-step framework is then applied to solve this MOOP.In the first step, all possible design options/solutions are identified

305 and plotted in Fig. 6(a) using the algorithm illustrated in Fig. 4. Note the price range for the whole HESS is chosen to vary from 306 $8,000 AUD up to $38,000 AUD. The purpose of this setup is to match the budget of the HESS application to the cost of an 307 equivalent engine system for any standard B or C segment passenger vehicle.

308

ACCEPTED MANUSCRIPT Moreover, visualization of the Pareto optimal set can be obtained using (2). Also as shown in Fig. 6(b), all possible design

309 options are plotted in circles in the JE-JC objective space. Since minimizing, it is clear that only the southwest boundary of this 310 region is of interest. This boundary, composed of seven green circles (1’~7’), is known as the Pareto optimal set or non-dominated 311 solution set which forms a Pareto frontier for informing the decision maker about the feasible Pareto optimal solutions against 312 given MOOP. Note that all red circles indicate dominated solutions to this MOOP. Amongst 1’-7’, however, a problem still needs to be resolved in choosing one member out of this Pareto set. Considering the

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314 non-convex nature of this southwest boundary in the JE-JC space, the conventional method used in selecting the best member using 315 weighted average sum to minimize the scalarized objective vector would not work here [42]. Therefore, the decision is made to 316 regard one of the objectives as a constraint, i.e. in this case subject to JE ≤ ε for ε=1. Again geometrically in Fig. 6(b), It can be

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317 shown that by using this so-called ε-constraint method [42], only 7’ will satisfy this constraint by intersecting this southwest 318 boundary right across the red cross-hatched area. Therefore, 7’ is chosen as the optimal design solution for Case A. Note that ε is

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319 chosen as 1 for the following reasons:

1) EV designers prefer a maximum driving range in general i.e. minimum JE as long as budget permits.

321

2) Although non-convex in shape, the slope derived from the intepolated segment between 6’ and 7’ is visually the steepest

322

(4kWhr/$1500) across all six segments as shown in Fig. 6(b) (i.e. 1’-2’; 2’-3’; 3’-4’; 4’-5’; 5’-6’; 6’-7’) indicating a

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maximum marginal performance gain against a fixed cost increment.

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324 4.3. Case B: a Lithium Manganese Oxide/Nickel-Cobalt-Manganese Battery based Hybrid Energy Storage System Similar to Case A, The MOOP for Case B is defined as (15):

min v J = [J E , J C ] . x v 327 x = {HCR}

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328 P=Pb+Psc≥P_min=100kW. 329 Psc≥Psc_min=75kW. 330 s.t. Pb≥Pb_min=25kW. (15) Esc≥Esc_min=200Wh. 331 332 P2W=(Psc+Pb)/(m+W)≥P2W_min=0.08. 333 W=Wb+Wsc+Wpc ≤W_max=200kg. 334 Note requirements for weight and P2W are slightly adjusted for Case B to compensate for the non-linearity effect [26] of the 335 P2W ratio so that it is comparable to Case A. 336

Following the same two-step framework, all possible design options/solutions can be first identified and plotted in Fig. 7(a).

337 The price range for HESS design in case B is varying from $5,000 AUD up to $24,000 AUD. 338

The second step of the framework is then executed in order to solve the Pareto optimal set using (2). In a similar fashion to

339 Case A, differentiation between the non-dominated solution set and dominated solution set can be visualized in Fig. 7(b). A 340 Pareto frontier consisting of six green circles (1”~6”) is obtained against given MOOP (15).

341

Again for the same reasoning as depictedACCEPTED in Section 4.2 forMANUSCRIPT Case A, 6” in Fig. 7(b) is chosen as the best member out of this

342 pareto set using ε-constraint method where ε=2. 343

One interesting observation can be made for both cases, namely in Fig. 6(b) and Fig. 7(b), JE ramps down as the system overall

344 cost or Jc increases, however, it reaches a certain point where it rises no matter how much higher Jc increases. 345

This is because the pre-set constraints such as weight or power to weight ratio (P2W), have eliminated it from happening.

347

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346 Moreover in this case, these two salient points (one for each case) coincide with corresponding optimal solutions.

The designers or decision makers should now be able to fully appreciate the results and findings by using this two-step

348 optimization framework without which such unique insights cannot be easily acquired. This is especially true in solving even more

350

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349 complex problems whose dimension of feature, number of constraint, and objective space expands.

In this study, these two design choices (with coordinates located and circled at (2.9K, 0.35) in Fig. 6(a) for Case A and (2.1K,

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351 0.35) in Fig. 7(a) for Case B) are chosen as the absolute optimal solution in each case to be further compared and analyzed in the 352 coming section. 353

5. COMPARISONS AND VALIDATION

354

Fair recommendations can now be given after comparing side by side aforementioned two design choices.

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First, the total stored energy E for both design choices are of close value (approximately 29kWh in Case A and 28kWh in Case

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356 B), making further comparisons at component level meaningful.

Component-level comparisons are split into three aspects as shown from Fig. 8(a)-(c) in terms of cost, weight, and output

358 power. By the way, it is also a good approach to doublecheck should any mistakes occur in the algorithm development process. A few findings are reported below:

360

1) The trend is, in general, consistent between two cases, in terms of the proportion each component is contributing towards overall system objectives.

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2) In Fig. 8(a) and 8(b), BP alone takes up 65% in total cost and 79.9% in total weight for both cases due to the effect of

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sharing a common HCR value at 0.35. This correlates well with human intuition that both HESS are designed more in favor

364

of the longest driving range while retaining some level of power attributes.

365

3) In Fig. 8(c), for both cases, the theoretical maximum power BP delivers and absorbs is calculated as 33.3% of the peak

366

load power. The remainder of this power is diverted via the SP-PC path so that a 1:2 ratio of load leveling feature can be

367

achieved in both designs. This result once again, complies with corresponding setup conditions defined in MOOP (14) and

368

(15).

369

4) Both total cost and total weight are 27.6% lower in Case B than Case A, when comparing between Fig. 8(a) and 8(b).

370

However designers should be aware of the fact that there is also a 27.6% total output power reduction in Case B compared

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to case A (may be alleviated by a lowerACCEPTED overall weight inMANUSCRIPT Case B), due to the effect that both designs adopt a common HCR

372

value. Based on comparison and findings reported above, the optimal solution in Case B is recommended to achieve commensurate

374

driving range, acceleration performance, and being able to cope with worst-case peak load conditions at considerably lower cost

375

and weight. Such optimal solution is then built, as shown in Fig. 9, in order to conduct future work such as developing more

376

advanced control strategies for the HESS.

377 378

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6. CONCLUSIONS

In this paper, a multi-objective optimization approach has been applied to size and design of a battery-supercapacitor power

379 supply, when considering the presence of a power converter. A two-step framework is proposed to first identify all relevant design

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380 requirements and cascaded them into two groups: objectives and constraints, at both component and system levels. Feasible 381 Pareto optimal solutions can then be located and compared between two typical design cases where more insights can be obtained

383

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382 to aid making sensible design decisions. As a result, a prototype HESS is built based on this work. Compared with other methods, this approach is practical, fast, easy to adapt, and most importantly, effective enough to size a

384 hybrid system with multiple sources or components especially including intermediate power converters. 385

The most optimal solution, as a result, is recommended in order for EV designers to achieve meeting pre-defined performance

386 objectives at minimum system cost and size.

Future work of development will be twofold. On the one hand, authors will look into second order factors such as battery

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388 depreciation and learning-curve effect so as to ascertain each contribution; and on the other hand, a more sophisticated power split 389 strategy needs to be developed on the prototype, in order to further enhance its practicality in the field. REFERENCES

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462 463 [39] Miller J, “Propulsion Systems for Hybrid Electric Vehicles”, IEE Power and Energy Series, 2004.

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468 [42] Yu-Chi Ho, "Optimization - A Many-Splendored Thing", IFAC Congress, Plenary Lecture, 1999, Beijing, China 469 [43] L. Sun, K. Feng, C. Chapman, N. Zhang., "An Adaptive Power Split Strategy for Battery-Supercapacitor Powertrain – Design, Simulation and Experiment", in IEEE Transactions on Power Electronics, vol. 12, pp.9364-9378, Dec. 2017. doi: 10.1109/TPEL.2017.2653842

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Fig. 1. The configuration of a general HESS equipped in an EV.

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476 477

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474 Fig. 2. 5 Five attractive converter topologies to construct a HESS for an EV application including: (a) Half-bridge topology I [3]; (b) Half-bridge topology II [4]; (c) Half-bridge topology III [33]; (d) Isolated full bridge topology [34]; (e) Isolated Half-bridge topology [35];

Fig. 3. Circuit diagram of a ZVS three-phase interleaved half bridge converter topology

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Fig. 4 Flowchart of an algorithm to identify feasible design options/solutions

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Fig. 5 Time-series speed waveform (Top) and power waveform (Bottom) of EPA LA92 Driving Cycle for a typical EV passenger car

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482 483 Fig. 6 (a) All possible design solutions for HESS design in Case A; (b) Non-dominated solutions (green circles) and dominated solutions (red circles) for HESS design in Case A

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Fig. 7 (a) All possible design solutions for HESS design in Case B; (b) Non-dominated solutions (green circles) and dominated solutions (red circles) for HESS

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design in Case B

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Fig. 8(a) Component/module cost comparison between two cases; (b) Component/module weight comparison between two cases;

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(c) Component/module power comparison between two cases

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Fig. 9. Overall prototyped HESS using the optimal solution of Case B.

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ACCEPTEDTABLE MANUSCRIPT 1

495

CORE HESS DESIGN METRICS AT SYSTEM & COMPONENT LEVEL Metric Metric Description (units)

Total weight of HESS (kg)

Wb

Weight of battery pack (kg)

Wsc

Weight of supercapacitor pack (kg)

Wpc

Weight of power converter (kg)

E

Total stored energy of HESS (kWh)

Eb

Stored energy of battery pack (kWh)

Esc

Stored energy of supercapacitor pack (kWh)

P

Total power capacity of HESS (kW)

Pb

Power capacity of battery pack (kW)

Psc

Power capacity of supercapacitor pack (kW)

Ppc

Power capacity of power converter (kW)

X

Total cost of HESS (AUD)

Xb

Cost of battery pack (AUD)

Xsc

Cost of supercapacitor pack (AUD)

Xpc

Cost of power converter (AUD)

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W

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Symbol

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Curb weight of the vehicle excluding the weight of HESS (kg) m

(Note to simplify m is set as 1000kg throughout this study.)

P2W

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TABLE 2

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Power to weight ratio of the vehicle (kW/kg)

WEIGHT SPECIFIC VARIABLES AT COMPONENT LEVEL

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Variable

Variable Description (units)

Symbol

499 500

Φb

(Weight) Specific energy of battery pack (Wh/kg)

Φsc

(Weight) Specific energy of supercapacitor pack (Wh/kg)

θb

(Weight) Specific power of battery pack (kW/kg)

θsc

(Weight) Specific power of supercapacitor pack (kW/kg)

θpc

(Weight) Specific power of power converter (kW/kg)

Cb

(Weight) Specific cost of battery pack (AUD/kg)

Csc

(Weight) Specific cost of supercapacitor pack (AUD/kg)

Cpc

(Weight) Specific cost of power converter (AUD/kg)

501

ACCEPTEDTABLE MANUSCRIPT 3

502

SPECIFIC UNIT INFORMATION AT COMPONENT LEVEL Specific

Specific

Specific

Life Cycle

Energy

Power

Cost

at 80% dis

(Wh/kg)

(kW/kg)

($AUD/kg)

-charge

(Φ)

(θ)

(C)

(cycles)

N/A

5 [39]

200 [39,40]

N/A

5[29]

2 [29]

100 [30]

> 10^6 [29]

90 [27]

0.18 [31]

60 [31]

5*10^3[31]

200 [28]

0.3 [28]

100 [32]

Component

Converter Supercapacitor

(LiFePO4

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Li-ion

based)

503 504

TABLE 4

505

KEY CHARACTERISTICS OF A PRACTICAL EV

Vehicle type Vehicle mass (kg)

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Aerodynamic drag coefficient (-),

508 509 510

1460

0.28 1.9

Air density (kg/m3)

1.29

Rolling resistance coefficient (-)

0.016

Wheel radius (m)

0.2794

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507

Passenger car

Frontal area (m2)

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3*10^3[28]

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Power

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Highlights: • A novel multi-objective optimization method is proposed over a hybrid power supply. • Two conflicting objectives – cost and total stored energy – are considered. • A DC-DC power converter is considered in this paper, and its optimal ratio is also obtained. • Two mainstream electrochemical battery types are separately studied in two cases.