3882 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, …ot/publications/papers/j7_laldin... · 2019. 12. 26. · 3882 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 8, AUGUST

3882 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 8, AUGUST 2013

Predictive Algorithm for Optimizing Power Flowin Hybrid Ultracapacitor/Battery Storage Systems

for Light Electric VehiclesOmar Laldin, Student Member, IEEE, Mazhar Moshirvaziri, Student Member, IEEE,

and Olivier Trescases, Member, IEEE

Abstract—This study deals with the optimal control of hybridenergy storage systems for electric vehicle applications. Thesestorage systems can capitalize on the high specific energy ofLithium-Ion batteries and the high specific power of modern ul-tracapacitors. The new predictive algorithm uses a state-based ap-proach inspired by power systems optimization, organized as aprobability-weighted Markov process to predict future load de-mands. Decisions on power sharing are made in real time, basedon the predictions and probabilities of state trajectories along withassociated system losses. Detailed simulations comparing variouspower sharing algorithms are presented, along with converter-levelsimulations presenting the response characteristics of power shar-ing scenarios. The full hybrid storage system along with the me-chanical drivetrain is implemented and validated experimentallyon a 500 W, 50 V system with a programmable drive cycle havinga strong regenerative component. It is experimentally shown thatthe hybrid energy storage system runs more efficiently and cap-tures the excess regenerative energy that is otherwise dissipated inthe mechanical brakes due to the battery’s limited charge currentcapability.

Index Terms—Battery management, dc–dc converters, digitalcontrol, electric vehicles (EVs), energy management, hybrid energystorage, ultracapacitors (u-caps).

I. INTRODUCTION

IMPLEMENTING low-cost, high-density, and power-efficient energy storage is one of the key technological hur-

dles for enabling mass-adoption of electric vehicles (EVs) in thefuture. Electrochemical double-layer Capacitors, also known asultracapacitors (u-caps), have been developed as a complimen-tary energy storage technology to batteries. Today’s u-caps havesymmetric input and output specific power in the range of 0.5–25 kW/kg [1], which is at least one order of magnitude higher

Manuscript received January 6, 2012; revised September 30, 2012; acceptedOctober 8, 2012. Date of current version January 18, 2013. This work wassupported in part by the Natural Sciences and Engineering Research Councilof Canada, in part by the Canadian Foundation for Innovation, and in part bythe Ontario Research Fund. Recommended for publication by Associate EditorM. Ferdowsi.

O. Laldin is with Purdue University, West Lafayette, IN 47904 USA (e-mail:[email protected]).

M. Moshirvaziri is with Motive, York, ON M6B 4C6 Canada (e-mail:[email protected]).

O. Trescases is with the Department of Electrical and Computer En-gineering, University of Toronto, Toronto, ON M5S 3G4 Canada (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2012.2226474

than typical lithium-ion (Li-Ion) based batteries [2]. U-caps of-fer improved cycling lifetime and do not suffer as severely fromhigh depth of discharge effects as Li-Ion batteries [3].

The high specific power and low-equivalent series resistance(ESR) of modern u-caps allow their integration into smart, elec-tronically controlled hybrid energy storage systems (HESS) forlight electric vehicles (LEVs). LEVs may include electric scoot-ers, bicycles, wheelchairs, forklifts, riding lawnmowers, andother emerging utility/maintenance vehicles.

Effectively combining the high specific power of u-caps andthe high specific energy of Li-Ion batteries is a major challenge.In conventional LEVs, the excess regenerative power (regen)that cannot be safely absorbed by the battery must be dissi-pated in the mechanical brakes. The u-cap/battery HESS solu-tion maximizes the reuse of regen energy, reduces the wear onthe mechanical brakes and minimizes the strain on the batteryduring rapid acceleration. The HESS concept has been pre-viously studied through system-level simulations [3]–[7] withreported driving-range improvements of up to 46% [4].

The HESS with two energy storage elements and one load hasseven possible configurations, as shown in Fig. 1. The motor-drive load and all dc–dc converters have bidirectional power ca-pability. Choosing the most appropriate configuration dependson the application and power level. The simplest choice is shownin Fig. 1(a), where the u-cap, battery, and load are directly con-nected in parallel. The simplicity of this system is attractive,however, it has several limitations; the power sharing betweenthe battery and u-cap is uncontrolled and dictated only by theparasitic elements [8], which are not well known and vary withaging, there is no flexibility in the choice of nominal battery andu-cap voltage, the bus voltage Vbus is unregulated and varies de-pending on the battery voltage range, which impacts the inverterdesign in LEV applications.

In Fig. 1(b) a dc–dc converter rated to handle the total loadpower regulates Vbus . The configurations shown in Fig. 1 (c)–(g)have one or more controlled power sources. More importantly,the battery and the u-cap can operate at different voltages, whichallows the specific power and specific energy to be optimizedusing the best available technology. The power sharing betweenthe u-cap and battery, arranged as in Fig. 1(c), is not alwaysfully controlled due to the unknown load current profile [3], [9].In [3], a model predictive control of this HESS configurationwas demonstrated to reduce the discharge intensity of the bat-tery to maximize its lifetime. In another study, the main controlobjectives for HESS were stated as: 1) setting the power mix

0885-8993/$31.00 © 2012 IEEE

LALDIN et al.: PREDICTIVE ALGORITHM FOR OPTIMIZING POWER FLOW IN HYBRID ULTRACAPACITOR/BATTERY STORAGE SYSTEMS 3883

(a) (b)

(c) (d)

(e) (f)

(g)

Fig. 1. Seven possible configurations for a two-source, single-load HESS.

based on the optimal operating point of each source; 2) mini-mizing the losses of the overall system; and 3) optimizing theu-cap SOC [9].

In Fig. 1(d), the u-cap phase may be more efficient [10], [11],but it is underutilized and introduces weight and balancing issuesgiveing higher bus voltages. Hysteretic control schemes havebeen applied to control Vuc for this configuration [10]. It wasshown that despite the improvement of battery current profile, itcan experience high discharge currents if Vuc drops below Vbt .The specific power improvement of this configuration has alsobeen studied for pulsed power applications in [11].

The configuration shown in Fig. 1(e) has flexible operatingvoltages and provides explicit power sharing control [12]–[15].A comparison of different control strategies is presented in [12].These include minimizing the overall system losses, usingu-cap in acceleration and braking instances, servicing the low-frequency component of the load power from the battery, andlimiting the battery current to predefined values based on elec-trical consumption. For the same configuration, [13] uses the

u-cap during transients to provide a smooth battery currentprofile, thereafter restoring the u-cap SOC to a desired level.However, it does not describe the HESS system under regenconditions as we have considered in this study. The configura-tion is also used in [15] to control the power-flow and avoidoverstressing the storage elements in a system containing a fuelcell, battery, and u-cap used in a hybrid vehicle.

A self-optimizing, multiobjective technique is proposed in[14] used to control a NiMH-based HESS. The algorithm usestwo objectives minimization of energy loss and maximizationof the power reserve (i.e. the deviation of the u-cap SOC fromits midpoint). A RailCab application is considered, containingpredefined sets of short-range load profiles (approx. 2 min) fromknown turns and paths. APareto-front for these sets is generatedoff-line based on a sequence of power mixes. A specific mem-ber is chosen based on a real-time decision tree consideringthe competing objectives. Variable profiles are accounted forthrough discretized search tree optimization, albeit producinglower quality results. For the application in this study, the drivecycle contains significant variability is considered unknown,making off-line methods of limited use. Furthermore, loss min-imization over multiple hours is required.

The configurations shown in Fig. 1(f) and (g) offer the samecontrol flexibility as Fig. 1(d) and (c), but the extra dc–dc con-verter must handle the total load power, increasing the cost. Therated and peak power capability of the converters in Fig. 1(c)–(e)can be lower than those of the load due to power sharing.

The salient features of the seven HESS configurations aresummarized in Table I. In this study, Fig. 1(e) is selected, sinceit offers the most flexibility in operating voltages, while mini-mizing the number of conversion stages from battery to load.The configuration in Fig. 1(c) is recommended for high-powerEV applications, where the additional cost of the second dc–dcconverter is prohibitive.

The main focus of this study is a novel real-time predic-tive power optimization (PPO) (PPO) algorithm to control thepower flow in the HESS of Fig. 1(e) based on loss minimization.We first reported the basic PPO operation in [16]. This paperprovides an extended discussion of HESS systems, importantdesign guidelines, extensive simulations comparing a variety ofpower sharing algorithms, as well as additional results.

The capacitance and ESR versus mass for a wide range ofcommercially available 2.7 V u-cap cells are shown in Fig. 2(a)and (b), respectively. The basic trend between the u-cap massMuc and the ESR Rucs versus the capacitance Cuc can be ap-proximated by

Muc = 0.5873 C0.8491uc (1)

Rucs = 0.4667 C−0.914uc (2)

The specific energy and specific power for the same u-caps asFig. 2 are shown in Fig. 3. The best 2.7 V u-caps have a superiorspecific power and specific energy compared to the older 2.5 Vtechnology. The data for both u-caps and batteries in this sectionis presented for a single packaged cell from which high-capacitymodules can be constructed, as was done in this study. Theaddition of monitoring, protection, and balancing circuits in


TABLE ICOMPARISON OF HESS ARCHITECTURES

Fig. 1(a) Fig. 1(b) Fig. 1(c) Fig. 1(d) Fig. 1(e) Fig. 1(f) Fig. 1(g)[8] [3], [9], [13] [10], [11] [12]–[14], this work

DC-DC Converters 0 1 1 1 2 2 2Constant Vbus N Y N N Y Y YVoltage Swing on Vuc Low Low High Low High High HighControlled Iuc N N Y N Y Y YControlled Ibt N N N Y Y Y Y

(a)

(b)

Fig. 2. (a) Mass versus capacitance for commercially available 2.7 V u-caps.(b) ESR versus capacitance for commercially available 2.7 V u-caps.

these modules can increase the mass and the ESR by up to 50%.Based on Fig. 3, the best available u-cap technology as of thiswriting offers up to 5.95 Wh/kg [17] and 23.6 kW/kg [18] inseparate devices. The specific power is calculated based on themaximum extractable power when the u-cap is fully chargedand is given by

Puc,max =V 2

uci

4Rucs(3)

where Vuci is the internal capacitor voltage. This maximumextractable power, which is limited by Rucs , is seldom used inpractice due to the high power losses. If we consider a short timeinterval such that Vuci remains constant then the u-cap efficiency

Fig. 3. Specific power versus specific energy for commercially available u-caps and Lithium-based rechargeable batteries.

Fig. 4. U-cap efficiency versus normalized extracted power.

ηuc can be calculated as a function of the normalized extractedpower Puc0 = Puc/Puc,max

ηuc =1 +

√1 − Puc0

2. (4)

It is interesting to note that ηuc is independent of the ESR whenplotted against the normalized extracted power, as shown inFig. 4. For example, the extracted power must be limited to37% of Puc,max in order to achieve ηuc > 90%. Operating atthe maximum power, Puc = Puc,max , gives ηuc = 50%.

The specific power and energy of commercially available3.6-V Lithium-based battery cells are also included in Fig. 3.Unfortunately the ESR of cells is seldom provided in datasheets.


Furthermore, unlike u-caps, the maximum charge and dischargepowers are not equal and are significantly lower than the pre-dicted values when one considers the battery ESR, as in (3). Itis apparent from Fig. 3 that there is a tradeoff between batterieshaving a high specific power and specific energy, dependingon the cell chemistry. Today’s high-power batteries have a dis-charge specific power approaching that of the best u-caps. Atfirst glance, it would appear from Fig. 3 that the benefit of in-troducing u-caps into a HESS is mainly to achieve a more sym-metric charge/discharge power capability. In fact, the additionaldesign considerations are somewhat more subtle.

1) The long-term health of the battery is heavily dependenton the cumulative number of charge/discharge cycles, aswell as the power profile. Even if the battery can handle thepeak power requirements in the application, offloading thepower transients to the u-cap extends the battery lifetime.

2) The battery data in Fig. 3 is provided at nominal condi-tions. In practice, the energy capacity and ESR are strongfunctions of temperature. The benefits of a HESS may be-come significantly more attractive when considering thevehicle temperature range.

3) Fig. 3 does not include economic considerations, whichare rapidly evolving. In general, the cost of using a high-power Li-Ion battery technology has to be weighed againstusing a u-cap-based HESS with a low-cost, high-energy-density battery.

The following simplified analysis helps to clarify the HESSdesign constraints, with respect to the ESR and dc–dc converterlosses. Based on the model shown in Fig. 14, if we consider thelosses inside the battery and the u-cap to be dominated by theirrespective ESRs, Rbti and Ruci , then we can define the loss ratioKp by

Kp ≈ Rbti

Ruci·(

Vuci

Vbti

)2

(5)

where the dc–dc converters are assumed to be ideal. Kp > 1implies that extracting power at Vbus from the u-cap is moreefficient then from the battery. In Fig. 5(a), Kp is plotted overthe battery operating range for different values of Vuci , basedon the system parameters of Table IV. Kp captures the fact thatsince both energy sources must supply power to the commonVbus , the ESRs must be referred to Vbus by the conversion ratioof the dc–dc converters. Kp drops as the u-cap gets dischargedand the bus-referred ESR increases by (Vbus/Vuci)2 . A moreaccurate loss ratio is obtained by considering the efficiencymodel of the dc–dc converters

Kp ≈Rbti ·

(P l o a d

ηd c , b t ·Vb t i

)2+ (1 − ηdc,bt) · Pload

Ruci ·(

P l o a dηd c , u c ·Vu c i

)2+ (1 − ηdc,uc) · Pload

(6)

where ηdc,bt and ηdc,uc are the efficiencies of the dc–dc con-verter phases connected to the Vbt and Vuc , respectively. Inthis case, Kp is a function of the load power and is plotted inFig. 5(b) at Pload = 500 W. The converter losses further reduceKp ; Fig. 5(b) shows the importance of maintaining a high u-capSOC to avoid high losses. Note that Kp is only valid over the

(a)

(b)

Fig. 5. Power loss ratio versus the battery operating range for (a) ideal dc–dcconverters and (b) nonideal dc–dc converters used in this study operating at500 W.

permitted power range of the battery; additional power demandsmust be satisfied by the u-cap.

This paper is organized as follows. Section II outlines theelectrical system operation. The predictive power optimizeris described in Section III. The system models used by thepredictive algorithm are covered in Section IV. Simulationand experimental results are reported in Sections V and VI,respectively.

II. ELECTRICAL SYSTEM

Several isolated and nonisolated dc–dc converter topologieshave been considered for HESS implementations, including res-onant, boost, Cuk, and SEPIC/Luo. A soft-switching isolatedconverter was used in [19]. Nonisolated converters offer low-cost and high power density [20], especially for the low-powerLEV applications targeted in this study. The nonisolated syn-chronous half-bridge converter HESS [21] is selected for thisapplication.

The electrical LEV system used in this study, is shown inFig. 6. The u-cap and battery modules are interfaced with Vbus


Fig. 6. HESS architecture used in this study.

using a two input, single output, digitally-controlled, and bidi-rectional dc–dc converter. Both phases operate in average cur-rent mode control (ACMC). Vbus is regulated to Vref/Ksenseby a high-bandwidth linear compensator Gv2 . The battery cur-rent reference, I∗bt is set by the PPO based on the algorithmdescribed in Section III. The PPO operates with a much lowerbandwidth than Gv2 . Using this scheme, Iuc is automaticallyadjusted by Gv2 to account for the changes in Ibt and Iload ,such that Iload = I ′uc + I ′bt , where I ′uc and I ′bt refer to the boostconverter output currents.

III. PREDICTIVE POWER OPTIMIZER

A. Algorithm Overview

The aims and operating conditions of the algorithm are:1) it must operate without specific, detailed information re-garding the approaching drive cycle, 2) it must determine anappropriate power mix in real-time, based on the current systemSOCs and load so as to minimize the losses over the course ofthe entire drive cycle and 3) it must obtain a solution as eachtime step within a reasonable amount of time and computationaleffort.

To these ends, the proposed algorithm estimates future loaddemands by determining the probabilities of state transitions,whereby states are defined by EV speed and acceleration. Thestates are characterized by predicted load torques and currents.The probabilities are determined by a training set, and the meth-ods involved in obtaining these are explained.

0 500 1000 1500 2000 2500 3000 3500 4000−6

−4

−2

0

2

4

6

Time, s

Tor

que,

Nm

(a)

0 1000 2000 3000 40000

0.2

0.4

0.6

0.8

1

Time, s

Spe

ed, k

RP

M

(b)

Fig. 7. (a) Torque and (b) motor speed data for drive cycle.

B. Drive-Cycle Data

An experimental drive cycle for an electric bicycle LEV ispresented in [22]. By appropriately scaling the data, the ex-pected drive cycle of any LEV containing high variability intorque and speed can be approximated. The scaled speed data isdifferentiated to obtain acceleration, which is then used to ob-tain the applied torque based on a simplified mechanical modelof an LEV. The resulting torque and speed data are shown inFig. 7(a) and (b), respectively. The associated torque and speedhistograms are shown in Fig. 8(a) and (b), respectively.

C. Operating States and Transitions

The drive cycle is divided into time segments and representedby a statistical Markov process using a finite number of states,characterized by speed and acceleration, with conditional prob-abilities assigned to the transitions. The process is shown inFig. 9. Using a qd-axis machine/inverter model, a bus current ispredicted at each state. Although a nine state process is shownfor clarity in Fig. 9, a 5×5 transition matrix was used based ona reasonable tradeoff between prediction accuracy and compu-tational cost, determined during system-level simulations. Thetransition probabilities can be adaptively adjusted based on end-user behavior and regional terrain.

To allow for short-term predictability, a state tree was gen-erated from the current state to three future states, as shown inFig. 10 for a starting state of S1. The probability of travers-ing a given path is determined from the product of the branchtransition probabilities.


(a)

(b)

Fig. 8. Drive-cycle histograms for motor (a) torque and (b) speed.

Fig. 9. Drive cycle is represented as a Markov process with nine states.P {Sn |Sm } represents the probability of entering state n from state m.

For each state, the midpoint speed and acceleration values areused to predict applied torques, and subsequently, load currents.However, if torque sensors are available, the state matrix can bebased directly on torque and speed.

D. Cost Function and Constraints

Using the predicted currents and a test power mix I ′uc and I ′bt ,and subsequently, Iuc and Ibt are determined at the predictedstates. To allow the algorithm to predict meaningful u-cap SOCtrajectories, an expression has to be developed to determine apower mix that approximately minimizes the cost function atfuture loads, albeit based on the current system state. Such anexpression can be determined by a simplified loss model of thedevice and converters. Considering a power mix α the converterconduction and switching losses and the device ESR losses, in

Fig. 10. Path tree of future current loads and probabilities.

2000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500

−5

0

5

10

15

Time, s

Cur

rent

, A

IloadIlx,k

Fig. 11. Actual and expected value of load current.

Section IV, the loss at a given operating point is

PL (α, Iload) = (αmbtIload)2Rbt + ((1 − α)mucIload)2Ruc

+ VbusK|Iload |(mbt |α| + muc |1 − α|) (7)

where

K = fsw (tr + tf ) (8)

mbt =Vbus

Vbt, Rbt = Rbte + Rbti + RL + Ron (9)

muc =Vbus

Vuc, Ruc = Ruce + Ruci + RL + Ron (10)

where tr and tf are the transistor rise and fall times, respec-tively, and fsw is the switching frequency. The expression canbe differentiated and solved for the minimizing power mix αminfor the present operating point. To find a power mix approx-imately minimizing the loss at future loads, one can considerthe expected value of the load current over the next three states,(Ilx,k ) based on the current state. The value of this current isobtained as follows:

Ilx,k = E[Il,k ] =M∑m

⎛⎝ 1

J

J∑j

(Il,mj,k · Pmj,k )

⎞⎠ (11)

where M is the total number of paths, J is the number of futuretime segments considered, and Il,mj,k is the predicted current inpath m, j states ahead, while in state k. Pmj,k is the probabilityof traversing from Il,m (j−1),k to Il,mj,k (i.e. to the next state inthe branch) in path m. A comparison between the actual andexpected load current value is presented in Fig. 11.

The rms of the error between the expected and actual valuesof the load current, as a percentage of maximum, ranges from


8.27% to 14.2%, based on the length of prediction interval cho-sen. If it is assumed that the SOCs do not change significantlyover the next three states, it is sufficient to use (Ilx,k ) in (7). Theexpected power mix, from state k, is

αmin,k =m2

ucRuc − 1|Il x , k |VbusK(mbtA + mucB)

m2btRbt + m2

ucRuc. (12)

Note that the switching losses introduce a discontinuity inthe solution. Accordingly, three different expressions must besolved, depending on the factors A and B. These factors, in turn,depend on the value of αmin,k and are

(A,B) =

⎧⎨⎩

(−1,−1) αmin,k < 0(−1, 1) 0 < αmin,k < 1(1, 1) 1 < αmin,k .

(13)

Only one, if any, of the three cases can yield a valid minimizer.A valid minimizer will satisfy the aforementioned range con-straints, depending on the values of A and B used to calculateit. If none of the cases yield such a minimizer, then it exists ateither αmin,k = 0 or αmin,k = 1, and its value is determined bysolving (7) in both cases.

The prediction algorithm accounts for the changing SOCsbased on the inductor currents (obtained using αmin,k ). Thecost function is the average of the probability-weighted loss andis minimized using MATLAB’s fmincon function. The batterySOC is tracked by coulomb-counting from the device terminals.A meaningful prediction requires a segment time large enoughto recognize upcoming changes in load, but small enough toreduce the filtering effect. Therefore, although the power mixis optimized every 500 ms, a segment time of 5 s, allowing thealgorithm to optimize over 20 s, was found to be reasonablethrough extensive simulations.

When Vuc is high, the energy transactions from the u-capare cheaper than the high-ESR battery in terms of losses, asdescribed by the loss ratio Kp in Section I. Consequently, inthe long term, the algorithm may eventually tend to disregardthe u-cap. A similar situation arises for a drive cycle with highregen, whereby the u-cap tends to be overcharged. To avoid thistrivial SOC trajectory, a multiplier, fm u c was introduced andapplied to the u-cap converter losses

fm u c (SOC, I ′uc) = 1 + sgn(I ′uc) · (1 − e−|I ′u c |)

·(

SOCmid − SOCSOCmid − SOCmin

)(14)

where SOCmid is the preferred midpoint SOC, SOCmin is theminimum allowable SOC and I ′uc is the u-cap phase output cur-rent. The multiplier, fm u c , allows the PPO to accept transactionswith marginally higher costs in an effort to provide long-termbenefits. Its effect is eliminated at the midpoint and maximizedat the SOC endpoints. A plot of the multiplier function valueswith respect to the u-cap output current is provided in Fig. 12 atvarious SOCs.

It is clear that at SOCmid , fm u c is 1 across the current range. AtSOCmin , as I ′uc → −∞, fm u c → 0 and as I ′uc → ∞, fm u c → 2.As a result, the cost of using the u-cap to service a positive

−5 0 50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Mul

tiplie

r

Output Current [A]

SOC = 0.7

SOC = 0.8

SOC = 0.9

SOC = 1SOC = 0.3

SOC = 0.4

SOC = 0.5

SOC = 0.6

Fig. 12. U-cap SOC cost multiplier function.

load may at most double, while servicing a regenerative loaddecreases the cost logarithmically.

The cost at a given state, due to a power mix α, is thenobtained by

fcost(α) =1M

(M∑

m=1

fP l,pm (α) · Pm

)(15)

fP l,pm (α) = fP l,s1(α) +J∑

j=2

fP l,sj (αmin,j ) (16)

fP l,sj (α) = Pl,bt(α)

+ Pl,uc(α) · fm u c (SOC, αIload) (17)

where fP l,pm is the adjusted loss along path m, fP l,sj is theadjusted loss in time segment j within path m, Pl,bt(α) is theloss in the battery phase, Pl,uc(α) is the loss in the u-cap phase,and αmin,j is the approximate minimizing mix for state j, de-termined in (12).

IV. HESS MODELS

The models presented in this section are used to implementa detailed system simulation, as described in Section V. Fur-thermore, with the exception of the models in Section IV-Cand IV-D, the models presented here are used by the PPO inreal-time to minimize losses, as described in Section III.

A. Li-ion Battery and Ultracapacitor Loss Models

The Li-ion battery is used as the primary energy storageelement in the system. The chosen Li-ion battery has a nominalvoltage of 43.3 V and a 5.3 Ah capacity. The maximum chargeand discharge currents are limited to 2 and 12 A, respectively.The measured discharge and charge curves at 1, 3, and 5 A areshown in Fig. 13(a) and (b), respectively.

The internal cell voltage is modeled as in [23]

Vbti = E0 − K

(Qbt0

Qbt0 − Qit

)· Qit + Ae−B

∫i·dt − Vdir


(a)

(b)

Fig. 13. Measured Li-ion battery (a) charge and (b) discharge curves.

(a)

(b)

Fig. 14. Energy storage device models for a) battery and b) u-cap.

where

Vdir =K

(Qb t 0

Qb t 0 −Qi t

)· i, if i ≥ 0

K(

Qb t 0kc ·Qb t 0 +Qi t

)· i, otherwise

Qit =∫

i · dt

Vbt0 = E0 + A (18)

A resistor circuit is added in the model to account for the limitedcoulometric efficiency in both the battery and the u-cap, asdescribed as follows:

In the case of the u-cap, the internal source voltage Vuciis modeled by an ideal capacitor. The energy storage devicesare modeled by the circuits shown in Fig. 14. The three resistorsrepresent the power loss in the circuit for the given state voltagesand currents.

In the loss derivation, it is assumed that Ibt behaves as a loadin the positive direction and a source in the negative direction.That is, Ibt is divided between the parallel and internal branches.Superposition is then used to determine the contributions of Ibtand Vbti to the total power loss. Doing so ensures that duringboth charge and discharge, the contribution from both sourcesto Ibtp (modeling leakage and coulometric loss) is positive [16].

The power losses for the storage device are obtained by sum-ming the respective I2R losses. A relatively simple batterymodel has been used in this study to reduce the computationaloverhead; it may be augmented by more advanced models [24]for improved accuracy.

B. Converter Loss Model

Both phases of the dc–dc converters are identical and mod-eled by a time-averaged model [25]. The on-resistances of bothswitches Ron are symmetric.

Assuming the converter is loaded by an ideal current sourceIload at a given time-step, the output voltage can be calculatedas follows:

Vbus =(

Vin − (RL + Ron)Iload

D′

)1D′ (19)

where D′ is the duty-cycle of the high side switch, and is givenby

D′ =Vin +

√V 2

in − 4VbusIload(RL + Ron)2Vbus

. (20)

The input current is then Iin = Iout/D′. The power loss in theconverter includes the I2R conduction loss and the switchinglosses. The switching losses are approximated as

Psw = Vbus · |Iin | · fsw (tr + tf ) (21)

where fsw , tr , and tf are as defined in Section III, Iin is the phaseinput current and Vbus is the bus voltage. The aforementionedmodel, although simplified, suffices for system level simulationsand is critical to the run-time of the real-time optimization.Improving the model accuracy by including higher order effectssuch as body-diode and very accurate switching losses as in [26]is useful for off-line efficiency prediction and converter design.Furthermore, the dead-times of the MOSFETs were specificallyoptimized to reduce body-diode conduction intervals and wehave chosen devices with very low-reverse recovery charge.

C. LEV Mechanical Model

A simplified LEV mechanical model, employed in the system,is described by

Tf = mgμRw + Kw ω2rm (22)

Tnet = Jωrm (23)

J = mR2w (24)

TL = Tnet + Tf (25)

where TL is the load torque, Tnet is the net (accelerating) torqueexperienced by the vehicle and Tf is the excess torque requiredto overcome friction, g is the acceleration due to gravity, m is


the vehicle mass, μ is the coefficient of friction, Rw is the wheelradius, Kw is the rotational load constant of the motor, ωrm isthe mechanical rotation speed of the motor, and J is the inertia.In practice μ will vary over the course of the drive cycle, alongwith the terrain. Simplifications abound, the model serves toprovide workable torque data for algorithm development.

D. PMSM Machine and Inverter Model

Given the load torque and speed, PMSM machine and invertermodels are used to obtain the load current on Vbus . Note thatthese models are only used for system simulation and not aspart of the loss calculation in the PPO. Both components aremodeled in the rotor reference frame [27]. The inverter usessine-triangle modulation, without third harmonic injection. Theqd voltage equations are

Te =32

P

2(Irqsλm + (Ld − Lq ) Ir

qsIrds

)(26)

V rqs = rsI

rqs + ωrLdI

rds + ωrλm (27)

=12d · Vdc cos(φv )

V rds = rsI

rds − ωrLqI

rqs = −1

2d · Vdc sin(φv ). (28)

where Te is the electromagnetic torque, set equal to the steady-state load torque obtained in (25), P is the number of rotor poles,λm is the flux linkage due to the PMs, V r

xs and Irxs represent

the qd-axis stator voltages and currents in the rotor referenceframe, the speed of which is denoted ωr . The qd inductancesare labeled Lq and Ld , respectively. Finally, d is the converterduty cycle, Vdc is the dc-bus voltage and φv is the voltage angle.

The inverter can provide a maximum voltage of 12 Vdc . The

motor is controlled for maximum efficiency with the d-axis cur-rent set to 0. The q-axis current command is therefore obtainedfrom the torque in (26). The converter operating angle is ob-tained from the calculated q- and d- axis voltages. Finally, therequired duty cycle is obtained from (27).

To obtain the load current on Vbus , the inverter current Iciq

must be obtained in its own reference frame. The magnitude isobtained from the values in the rotor reference frame. SettingIrds = 0 is equivalent to setting the angle of the current reference

frame, φi , to be 0 (π) for positive (negative) torque commands.The power factor angle, φ, is then φv − φi . The load current isgiven by [27]:

Iload =34d · Ici

q cos(φ). (29)

V. SIMULATION RESULTS

A. System Level Simulations

System-level simulations were performed to investigate thebenefit of the proposed algorithm. Four power-mix selectionalgorithms were considered, as well as a system containing justthe battery without the u-cap. The mechanical braking losses foreach power-mix are obtained based on excessive regen currents.The simulated algorithms are described as follows:

TABLE IIBATTERY POWER-MIX, α, USED FOR HEURISTIC ALGORITHM

U-cap SOC Range Battery Power-Mix αLower Upper Iload ≥ 0 Iload < 00 0.3 1 -10.3 0.434 0.6667 -0.66670.434 0.568 0.3333 -0.33330.568 0.702 0 00.702 0.836 -0.3333 0.33330.836 0.97 -0.6667 0.66670.97 1 -1 1

TABLE IIISIMULATED LOSS COMPARISON

Elec Loss(Wh)

Mech Loss(Wh)

Unserviced(Wh)

Total(Wh)

No-U-cap 2.2543 6.5519 0 8.8062Heuristic 6.558 0 0 6.558CPL 3.7743 1.8121 0 5.5864PPL 3.7533 0.8267 0 4.5799PPO 3.7485 0 0 3.7485

Elec Loss(Wh)

Mech Loss(Wh)

Unserviced(Wh)

Total(Wh)

No-U-cap 7.0424 16.5027 3.0544 26.5995Heuristic 17.4301 0 0.8722 18.3023CPL 9.8567 0 0.7586 10.6153PPL 9.33 0 0.1875 9.5176PPO 8.8352 0 0.1002 8.9354

Regen Energy: 22.6 WhSink Energy: 47.14 Wh

Light Drive Cycle-6.33<Iload<5.41

Heavy Drive Cycle-7.28<Iload<20.59

Sink Energy: 103.35 WhRegen Energy: 41.95 Wh

Net Energy: 61.40 Wh

Net Energy: 24.54 Wh

1) No-Ucap: This simulation is used to establish a bench-mark, with the load current entirely serviced by the bat-tery and excess regenerative components directed to themechanical brakes.

2) Heuristic Algorithm: The power-mix is determinedthrough a lookup table, as given in Table II, based onthe allowable range.

3) CPL Algorithm: The current power loss (CPL) methodminimizes system losses at the present operating point,without prediction.

4) PPL Algorithm: Similar to the proposed PPO, the predic-tive power loss (PPL) method makes use of the short-termload prediction for the next three time segments. The prob-ability weighted losses for each branch of the state tree aresummed to provide the expected losses over the next 20 s.The mix minimizing the losses is used.

5) PPO Method: The proposed PPO is an adjustment to thePPL, whereby the losses obtained for the u-cap phase areadjusted by the multiplier function (14), as described inSection III.

The drive cycle obtained through measurements was parame-terized to simulate various types of EVs, while maintaining the


(a)

(b)

0 500 1000 1500 2000 2500 3000 3500 4000 45000.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Uca

p S

OC

HeuristicCPLPPLPPO

0 500 1000 1500 2000 2500 3000 3500 4000 45000.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Uca

p S

OC

HeuristicCPLPPLPPO

Fig. 15. Simulated u-cap SOC for (a) light drive cycle and (b) heavy drivecycle.

variable characteristics of the original. For instance, by chang-ing the total mass, a slightly heavier vehicle or rider with higherinertia may be simulated. Accordingly, two different drive cy-cles with the parameters listed in Table III were used to evaluatethe algorithms. The dynamic u-cap SOCs for the four algorithmsand two drive-cycle simulations are shown in Fig. 15. The sim-ulation results are presented in Table III, based on the sameparameters as the experimental system described in Section VI.

In Table 3, “Mech Loss” represents the regen energy directedto the mechanical brakes, “Unserviced” represents the sink en-ergy that cannot be provided resulting in lower output torque,and “Total” represents the sum of the losses and unservicedloads, or the difference between the input and requested en-ergies. Comparing the results from the No-U-cap case to theHeuristic algorithm, it is clear that including a u-cap in the sys-tem offers obvious benefits due to high current handling capa-bility. Including losses in the decision, as in the CPL algorithm,offers another significant improvement.

Compared to the CPL, the PPL reduces the energy differencefor a lighter and heavier drive-cycle, by 18% and 10%, respec-tively. However, for a heavier drive cycle (with comparativelylow source currents), the CPL algorithm tends to lead the u-capSOC to an undercharged trajectory. Although not presented heredue to space constraints, a similar situation results if a drive cy-cle contains numerous large source bursts (whereby the u-cap

TABLE IVSYSTEM PARAMETERS

System Parameters Value UnitsBus Voltage, Vbus 50 VMax. Power, Pmax 500 WMax. Current, Imax 10 AMax. Torque, τmax 6 NmMax. Speed, nmax 1000 RPMUltracapacitor ModuleRated Capacity, Quc0 0.263 AhRated Voltage, Vuc0 27 VCapacitance, Cuc 34.24 FESR, Ruc,esr 48 mΩ

Max. Dis/charge Current, Iucm +/-30 AMass 0.63 kgBatteryRated Capacity, Qbt0 5.3 AhO. C. Voltage, Vbt0 43.3 VMeasured ESR, Rbt,esr 268 mΩ

Max. Discharge Current, Ibtmp 12 AMax. Charge Current, Ibtmn 2 AMass 4 kgDC-DC ConverterInput Capacitors, Cin 220 μFBus Capacitor, Cbus 5.02 mFSwitching Frequency, fs 250 kHzInductors, L 10 μHInductor ESR, RL 2.7 mΩ

Switch on-resistance, Ron 5 mΩ

(a)

(b)

(c)

(d)

Fig. 16. Simulated (a) load current, Iload , (b) battery current, Ibt , (c) busvoltage, Vbus and (d) u-cap current, Iuc .


Fig. 17. Experimental system used to demonstrate the PPO algorithm.

SOC tends to stay at its upper limit). By introducing a predictiveaspect for the short term, the algorithm is able to compensatefor both large and small regenerative components.

Finally, adding the u-cap SOC multiplier in the PPO allowsthe algorithm to address the limitations in predicting load cur-rents in the long term. As shown in Fig. 15(a), this limitationleads the PPL to keep the u-cap near its upper SOC limit (similarto the CPL algorithm). In Fig. 15(b), the PPL eventually leadsto a lower u-cap SOC limit. In both cases, the PPO is able toreduce the energy difference compared to the PPL by 18% and6.1%, respectively. To allow the PPO to further utilize the u-capSOC range, it is possible to tune parameters in the u-cap costmultiplier function.

B. Dc–Dc Converter Simulations

Simulations were performed with a full switching model ofthe HESS shown in Fig. 6 using the PLECS blockset for MAT-LAB Simulink. The parasitic resistances of all components wereadded to the simulator. The accuracy of the switching losses inPLECS is limited, however, it is sufficient for the purpose of thetransient simulations. The main objective of these simulationsis to demonstrate stable dynamic response with bidirectionalpower flow, under a wide range of load conditions.

The simulated system parameters are listed in Table IV. Thetwo converters operate in ACMC, while I∗bt is issued by thePPO and I∗uc is updated by the voltage loop compensator. Thebandwidth of the voltage loop is set around 10× lower than thatof the current loops, as is common practice to avoid interference.The detailed second order compensator design procedure forACMC is well covered in the literature [25].

The simulation results of the converter operating at Vbt =43.3 V and Vuc = 15 V are shown in Fig. 16, where the load ismodeled by a current source. In order to reduce the simulationtime, the current steps are applied every 25 ms. The simulated

step-response under a wide range of conditions is shown inFig. 16. The response is well behaved, and the Vuc stays regu-lated within ±3%.

VI. EXPERIMENTAL RESULTS

The full system shown in Fig. 17 was implemented usinga flexible dynamometer experimental platform to evaluate theperformance of the PPO under repeatable test conditions. Theexperimental results were originally published in [16] and arereproduced here. It is to be noted that at the time of testing,the simplified optimization algorithm in [16] assumes that eachtest power mix is also used for the future states when evaluat-ing the cost function, hence (11)–(13) were not implemented.Simulations in this work have shown the use of (11)–(13) toresult in significant improvement. The system parameters areprovided in Table IV. The system consists of a 43.3 V batterywith an ESR of 268 mΩ, a 35 F u-cap module with rated voltageof 27 V and an ESR of 48 mΩ and a load with a maximumpower of 500 W at the regulated Vbus= 50 V. The dynamometerplatform consists of a permanent magnet synchronous machine(PMSM) loaded by a dc machine (DCM). The PMSM operatesin torque-control mode, where τm is regulated using a three-phase inverter fed from Vbus . A two-quadrant chopper is usedto control the speed ωm in the DCM . The electrical load onVbus , Pload , is therefore precisely emulated using the combi-nation of the speed-controlled DCM and the torque-controlledPMSM, based on the drive cycle of Fig. 7. The motor controlis implemented in two real-time Linux (RTL) PCs. The PPOis implemented in real-time software and calculates I∗bt every500 ms. Two different tests were run in Test #1 the u-cap isremoved and the battery acts as the sole energy source. Test #2was performed using the complete HESS system with the PPOenabled. In both tests, the ACMC dc–dc converter imposes a lim-itation on the maximum battery charge current, of Ibt > −2 A


Fig. 18. Measured efficiency for the dc–dc converters with Vbus = 50.4 V.

to maintain the long-term health of the battery. In Test #1, largeregen currents cause Vbus to increase when Ibt saturates to –2A. To emulate power otherwise dissipated in the mechanicalbrakes in the LEV, an electronic load is connected to Vbus andprogrammed to absorb regen energy if Vbus > 51 V.

The measured efficiency for each of the two dc–dc convertersin Fig. 6 is shown in Fig. 18. The efficiency reaches a peakof 97% but is reduced for lower input voltages, mainly dueto the increased inductor current ripple and associated con-duction losses. This justifies the need to keep Vuc high duringoperation.

Fig. 19 shows the input and output currents from the dc–dcconverters for a 350 s segment of the full 2 h drive cycle. Thecalculated and reference currents generated by the PPO duringoperation are also shown. As previously stated, the u-cap cur-rent reference I∗uc is not used explicitly by the dc–dc converters.However, when compared against the current required to regu-late the bus voltage, the reference and measured u-cap currentsserve to validate the system models.

The dynamic SOC of the battery and u-cap during Test #2is shown in Fig. 20. It is evident that the PPO automaticallymaintains a reasonably high SOC on the u-cap in an effort tomaximize efficiency.

The histogram of the load output power, the battery outputpower, and the u-cap output power (after the dc–dc converter),as measured from Test #2, are provided in Fig. 21. It is clearfrom the histograms that the battery tends to stay in the low-output power region, satisfying a large extent of the positivesystem load. Indeed, it is saturated at large regenerative loads,resulting in the peak near 80 W. On the other hand, the u-cap,although moderately used in the sink region, is used extensivelyin the high regenerative region. The response observed here isappropriate, considering the nature of the drive cycle used, char-acterized by low constant acceleration, and sharp decelerationbursts.

An important consideration in evaluating the algorithm is itsuse of the u-cap during various operating states. To that end, it isbeneficial to observe the output currents from the u-cap phase,with respect to its SOC. The plot, over the course of the drivecycle, is given in Fig. 22.

From Fig. 22, it is clear that as the u-cap SOC increases,the algorithm tends favor the u-cap phase to a greater extent.

4750 4800 4850 4900 4950 5000 5050 5100

−5

0

5

Cur

rent

, A

Time, s

Iload

(a)

4750 4800 4850 4900 4950 5000 5050 5100−3

−2

−1

0

1

2

3

4

Cur

rent

, ATime, s

Ibt*Ibt

(b)

4750 4800 4850 4900 4950 5000 5050 5100

−6

−4

−2

0

2

4

Cur

rent

, A

Time, s

Iucp

(c)

4750 4800 4850 4900 4950 5000 5050 5100

−6

−4

−2

0

2

4

Cur

rent

, A

Time, s

Iuc

(d)

Fig. 19. Output currents during the drive cycle for Test #2. a) Load current(measured), Iload . b) Battery current (commanded and measured), Ibt . c) U-capcurrent (predicted), Iucp . d) U-cap current (measured), Iuc .In addition, although the u-cap reaches a minimum SOC of0.47 during extreme conditions, the algorithm tends to preventit from staying in the low region for extended periods of time.The figure also provides qualitative data to aid in the issue ofadequately sizing the device.


0 1000 2000 3000 4000 5000 6000 7000 80000.6

0.7

0.8

0.9

1

Sta

te o

f Cha

rge

Time, s

BatteryU−cap

Fig. 20. Experimental battery and u-cap SOC.

Fig. 21. Experimental power histogram of the load, Pload , u-cap connecteddc–dc converter, P ′

uc , and the battery-connected dc–dc converter, P ′bt .

0.4 0.5 0.6 0.7 0.8 0.9 1−10

−8

−6

−4

−2

0

2

4

State of Charge

Out

put C

urre

nt (

A)

Fig. 22. Measured I ′uc versus u-cap SOC.

The measured results of the two tests are given in Table V.Despite attempts to make the tests as repeatable as possible, themeasured drive-cycle energy from the electrical data is slightlydifferent in the two tests due to inevitable inaccuracies in themotor controllers. Due to this effect, Test #2 has an increaseof 5.7 Wh in net energy demand (sink) from the drive cyclecompared to Test #1. Despite this increased demand, the totalenergy drawn from the battery in Test #2 is actually reducedby 7.2 Wh, mainly due to energy that is captured by the u-capinstead of being dissipated as braking losses. The HESS systemtherefore results in a net savings of 13 Wh. The average powerloss was reduced from 10.5 to 3.8 W from Test #1 to Test #2,primarily due to the low ESR in the u-cap.

Based on the resultsof this study, the following basic guide-lines for sizing the HESS of Fig. 1(c) are obtained:

TABLE VBATTERY AND HYBRID SYSTEM RESULTS

Energy Quantity Test #1 Test #2 UnitsBattery Only HESS

Total Battery Energy Used 69.1 61.9 WhDrive-Cycle Energy (Sink) 98.0 103.3 WhDrive-Cycle Energy (Sourced) -42.8 -42.4 WhBattery /and U-cap Loss 2.30 4.47 WhDC-DC Converter Loss 2.67 4.60 WhBraking Loss 18.7 2.3 WhAverage Power Loss 10.5 3.8 W

1) Select the automotive-grade battery cell technology hav-ing the highest specific energy from Fig. 3 based on thethe maximum allowable mass and volume in the vehicle,as well as the economic constraints. Vbus is set by themotor-drive requirements.

2) Calculate the power demand from the u-cap Puc basedon the drive cycle and the maximum power supplied bythe battery, based on aging considerations and supplierguidelines. We recommend to operate at Puc0 > 0.5 forthe u-cap, based on Fig. 4. The 2.7 V u-cap cells shouldbe stacked to achieve Vuc > 0.5 Vbus when charged. Thisin turn dictates the ESR, Rucs , from (3) and subsequentlythe capacitance and u-cap technology from Fig. 2(b).

3) The loss ratio Kp should be verified over the battery oper-ating range based on the battery pack ESR and the dc–dcconverter efficiency models. The u-cap SOC range canthen be optimized to achieve higher efficiency by operat-ing at higher Kp .

VII. CONCLUSION

A new HESS predictive control algorithm and design proce-dure was demonstrated in this study. The PPO was shown tosuccessfully determine a power-mix in real time, based on theexpected load demand and loss models for all system compo-nents. It can effectively utilize the u-cap to buffer large negativecurrents on the dc bus and share power between the storagedevices in the sink region. A significant benefit of the PPO isits ability to recognize tradeoffs in setting the u-cap voltageswing. The PPO algorithm was found to be relatively sensitiveto system parameters, such as the mid-point of the SOC chosenin the u-cap cost multiplier function and the length of the timesegment chosen over which to optimize. Self-optimization ofthe PPO parameters may be considered as future work.

Additional benefits of this study include basic guidelines forsizing the u-cap module. Given the tendency of the system toreadily utilize the device at a certain SOC range, a minimumoperating SOC limit can be imposed. From the worst case ac-celeration burst, a minimum energy requirement can thus beascertained. Optimally sizing the u-cap depends not only on thedynamic load profile and the parasitic elements but also on thealgorithm itself.

ACKNOWLEDGMENT

The authors would like to thank Prof. J. Tate and G. Kishfrom the University of Toronto for useful discussions related topower flow optimization.


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[14] C. Romaus, J. Bocker, K. Witting, A. Seifried, and O. Znamenshchykov,“Optimal energy management for a hybrid energy storage system combin-ing batteries and double layer capacitors,” in Proc. IEEE Energy Convers.Congr. Expo., Sep. 2009, pp. 1640–1647.

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Omar Laldin (S’02) received the Bachelor’s degreefrom McMaster University, Hamilton, ON, Canada,and the Master’s degree at the Helsinki University ofTechnology, Helsinki, Finland, where he studied ironlosses in induction machines, in 2006 and 2009, re-spectively. He is currently working toward the Ph.D.degree at Purdue University, West Lafayette, IN, inthe design of novel machines for ship-service andpower-plant applications.

From 2004 to 2005, he was an intern at GE LargeMotors and Generators, Peterborough, ON, where he

developed models for large solid pole synchronous motors. He attended Univer-sity of Toronto from 2009 to 2010 to work on electric vehicle projects. His otherinternship experiences have included working at the ABB Corporate ResearchCenter in Raleigh, NC, Infineon Technologies in Villach, Austria, and the Ca-nary Islands institute of Technology in Gran Canaria, Spain. During 2006, heworked on robotics for neurosurgical applications in a joint venture betweenthe McMaster Telerobotics Laboratory and Quanser, Inc. From 2007 to 2008,he worked as an external at Nokia in Helsinki, Finland on WiMAX Basestationprojects. From 2008 to 2009, he was a Maths Lecturer at the HAMK Universityof Applied Sciences, Hameenlinna, Finland.

Mr. Laldin has received the Academy of Finland Research Grant (2008–2009), the National Science and Engineering Research Council [of Canada]Internationaal Award (2009–2010) and the International ABB Fellowship(2011–2014).

Mazhar Moshirvaziri (S’11) received the B.Sc. de-gree in electrical engineering from the Sharif Univer-sity of Technology, Tehran, Iran, in 2010. He receivedthe Masters degree in the electrical and computer en-gineering from the University of Toronto, Toronto,ON, Canada, in 2012. His M.A.Sc. dissertation dealtwith Ultracapacitor battery based hybrid energy stor-age systems for electric vehicles.

In October 2012, he joined in Motive, Toronto,ON, Canada, where he is currently responsible fordeveloping dc–dc and ac–dc converters for mecha-

tronic drives. His research interests include electric vehicles, battery manage-ment systems in electric vehicles, and high-efficiency switching-mode powersupply designs.

Olivier Trescases (M’01) received the Masters andDoctoral degrees from the University of Toronto, ON,Canada, in 2004 and 2007, respectively. His Ph.D.dissertation dealt with high-efficiency and digitally-controlled integrated switched-mode power suppliesfor portable applications.

From 2007 to 2009, he worked as a ConceptEngineer and mixed-signal circuit designer at Infi-neon Technologies AG in Villach, Austria. Whileat Infineon, he designed application-specific ICsin BCD (Bipolar/CMOS/DMOS) technologies for

safety-critical automotive applications, such as electronic control units forairbag modules. He is currently an Assistant Professor with the Departmentof Electrical and Computer Engineering, University of Toronto since January2009. His group conducts research on power electronics for automotive, indus-trial, aerospace, and photovoltaic applications. His research interests includea number of research projects dealing with distributed maximum power pointtracking for PV applications, power converters for high-brightness LEDs, bat-tery management circuits for electric vehicles, integrated dc–dc converters, andhigh-frequency digital control schemes.

Dr. Trescases received the Charitat Award from IEEE ISPSD in 2006 andthe IEEE Hackbush Award in 2002. In 2010, he was co-recipient of the GreenInnovation Award from the City of Toronto. He is a Member of the executivecommittee for the IEEE Toronto Section.

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