IEEE INTERNET OF THINGS JOURNAL, VOL. 6, NO. 5, OCTOBER 2019 7395

IoT-Based Proactive Energy Supply Controlfor Connected Electric Vehicles

Yuying Hu, Cailian Chen , Member, IEEE, Jianping He , Member, IEEE,

Bo Yang, Senior Member, IEEE, and Xinping Guan , Fellow, IEEE

Abstract—The frequent stop-and-go operations require highand fast burst driving power, which accelerates the electric vehi-cle batteries degradation. Hybrid electric storage system (HESS)is a promising solution, which supplements the battery withsupercapacitor for rapid charging/discharging. If future powerdemand is available, effective power management can be doneby fully exploiting the HESS benefits. Recent advances in theInternet of Things (IoT) have made the future informationprediction practical, since surroundings information is obtain-able. In this paper, a proactive energy management strategy isdeveloped for the HESS with the IoT support. By analyzing thetraffic data, a probabilistic graphical model, i.e., the conditionallinear Gaussian (CLG), is designed for future driving informationprediction. Since, the CLG prediction results are probability dis-tributions, a scenario-tree method is developed to approximatethe future power demand by sampling the possible future velocityprofiles from the results. A stochastic model predictive controlproblem is established by incorporating the sampled trajecto-ries. A fast dual proximal gradient method is proposed to solvethe problem and facilitate real-time implementation. Simulationresults demonstrate that the magnitude and fluctuation of thebattery discharging power are reduced by 46.4% and 27.7%,respectively, compared with the battery only case.

Index Terms—Conditional linear Gaussian (CLG), energymanagement, hybrid electric storage system (HESS), stochasticmodel predictive control (SMPC).

I. INTRODUCTION

STOP-AND-GO driving affects the service life of batter-ies profoundly and thus raises the maintenance costs of

electric vehicles (EVs). Moreover, oversized battery packs areassembled to meet the peak power demand during driving,which increases the production costs of EVs [1]. Thus, super-capacitor (SC) is utilized in EVs to support rapid discharging.The peak load of the battery can be shifted. This kind ofenergy supply is called the hybrid electric storage system(HESS) [2]. The battery has a high energy density, and SChas high power-density but limited energy storage capacity [3].

Manuscript received September 1, 2018; revised December 22, 2018;accepted February 4, 2019. Date of publication February 18, 2019; date of cur-rent version October 8, 2019. This work was supported by the National NaturalScience Foundation of China under Grant U1405251, Grant 61731012, Grant61828301, and Grant 61573245. (Corresponding author: Cailian Chen.)

The authors are with the Department of Automation, Shanghai JiaoTong University, Shanghai 200240, China, and also with the KeyLaboratory of System Control and Information Processing, Ministry ofEducation of China, Shanghai Jiao Tong University, Shanghai 200240, China(e-mail: hyy0022@sjtu.edu.cn; cailianchen@sjtu.edu.cn; jphe@sjtu.edu.cn;bo.yang@sjtu.edu.cn; xpguan@sjtu.edu.cn).

Digital Object Identifier 10.1109/JIOT.2019.2899928

Thus, the battery should be used to provide long-term energyat low to moderate power level, while SC is used to supportfast burst discharging. To capitalize upon the SC for batterystress relieving, it is crucial to use the complementary betweenbattery and SC fully and split the demand power properly.

The power split optimization has received increasinglyattentions recently [4]–[6]. In [4] and [7], the torque splitwas optimized for buses by predicting the future driving stateswith the Markov chain (MC). The stochastic model predictivecontrol (SMPC) method proposed in [4] shown that the fueleconomy can be significantly enhanced by utilizing the futureinformation. For vehicles in the highway, a traffic data-enabledpredictive energy management was proposed in [5]. With thetraffic and vehicles driving information, the fuel economy iswell improved. The energy management of the HESS in small-sized EVs was investigated in [6]. Results shown that theHESS power is effectively balanced and the batteries’ stress isreduced while considering the future information. These worksdemonstrate the significance of the prediction-based strategieswhich incorporate the future energy demand into the design.However, the existing works usually focus on the buses orvehicles in the highway, whose future power demand is mainlydetermined by vehicles’ states and easy to predict. In thispaper, the complex traffic situations are considered, where thestop-and-go pattern takes places frequently. This is preciselythe type of traffic situation where the HESS is of value.

In complex situations, the vehicle driving is influenced byvarious uncertainties. The future power demand informationis difficult to obtain [8], [9]. The recently developed Internetof Things (IoT) technologies, e.g., the intelligent transporta-tion system (ITS) and vehicular networks, have paved the wayfor connected vehicles [10]. The information shared betweenconnected vehicles/infrastructures can improve the situationalawareness of real-time traffic and facilitate smarter decisionmaking for individual EVs [11], [12]. This motivates us toexploit efficient energy management strategy (EMS) for EVsdrawn the support of the IoT.

There are three main challenges while optimizing the HESSpower split in the complex traffic scenes. First, how to assignthe demand driving power between the battery and SC prop-erly is challenging. The SC is required to support the peakdischarging with limited stored energy as well as guaran-tee the vehicles’ driving performances. Second, future powerprediction is challenging because the driving process becomescomplex to model in this situation. Finally, the timeliness isrequired in the strategy design.

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7396 IEEE INTERNET OF THINGS JOURNAL, VOL. 6, NO. 5, OCTOBER 2019

Taking these challenges into account, a proactive EMSbased on the SMPC is developed. Our main contributions areas follows.

1) A proactive HESS management strategy is designed byutilizing the predicted future information. Consideringthe uncertainties in the driving process, a probabilis-tic model, i.e., conditional linear Gaussian (CLG), isexploited for future driving information prediction.

2) Since the CLG prediction results are distributions,to incorporate the predicted results into the modelpredictive control (MPC) formulation, a scenario-treemethod is designed to approximate the possible futurepower demand by sampling trajectories from theprediction results.

3) To make strategy real-time implementable, a proximalgradient method is proposed to solve the formulated con-vex but nonsmooth constrained optimization problem.

The rest of this paper is organized as follows. Related workis given in Section II. Section III introduces the consideredscenarios and system model. An MPC-based HESS proac-tive energy management problem is formulated. In Section IV,detailed prediction and SMPC-based problem solution aregiven. Simulation and performance evaluation is provided inSection V, and the conclusion is given in Section VI.

II. RELATED WORK

Existing researches on the prediction-based energy manage-ment problem mainly embrace two aspects: 1) power demandprediction and 2) management strategies design.

A. Power Demand Prediction

Many prediction methods which can be classified as deter-ministic and probabilistic, have been studied to obtain thefuture power demand [7], [13]–[17]. The deterministic models,such as the radial basis function neural network in [5], onlyconsider the vehicle’s own historical velocity in the prediction.Therefore, this method is mainly used in the simple trafficsituation (e.g., highway). The commonly used probabilisticmodels are the MC. In [4], a 1-D MC is adopted to character-ize the future power demand of buses. Transition probabilitymatrix is estimated from known cycles and utilized to generatea possible future power request. As doubted by [18], the MCis reliant on the selected original data and not suitable for thegeneral driving routes. An MC model with learning capabilityis proposed in [15]. As more information is considered, thedimension of the MC model increases which brings a heavycomputational burden. Therefore, only few influence factorscan be incorporated into the MC.

B. Power Management Strategy

Targeting power-train system performance optimization,various strategies have been studied [6], [19]–[22]. Theycan be classified into the rule-based and the optimization-based method. The former regulates the battery dis-charging by predefined rules. Though easy to implement,their performances cannot be guaranteed [20]. Therefore,optimization-based methods are proposed. In the global

Fig. 1. Considered car-following scenario in vehicular networks.

optimization methods [e.g., dynamic programming (DP)],the completely driving profile is required which is unavail-able in real-world applications [21]. In [22], the HESSpower allocation is optimized by the equivalent consumptionminimization strategy, which only uses the current mea-sured power demand. Due to the lack of utilizing any futureinformation in optimization, the potential of the HESS isunder-explored. A compromise between the global and instan-taneous optimization is offered by the MPC [6], [15]. MPCcan incorporate the predicted short-term future informationinto problem formulation and be solved effectively. The MPCproblem formulated in [6] assumes the future energy demandis directly available. The difficulty in the future informationprediction is not considered. In [15], a stochastic MPCproblem is formulated by predicting the future power demandwith the MC. Since only the vehicle’s states are used inprediction, this is suitable for the complex traffic scenes.

Compared with the existing works, the problem in a com-plex traffic scene is considered by incorporating the vehicle’sstates and IoT information into a compact prediction model.Since the prediction results are distributions, to incorporatethese into problem formulation, the scenario-tree method isdesigned to approximate the possible future power demand bysampling trajectories from the predicted distributions, and anSMPC problem is established.

III. SYSTEM DESCRIPTION AND PROBLEM FORMULATION

In this section, the system architecture is first describedfollowed by the battery and SC models, and the power bal-ance model. Then, an MPC-based HESS energy managementproblem is given.

A. Scenario and Assumptions

We consider a car-following scenario with the IoT supportas illustrated in Fig. 1. Suppose two vehicles are traveling in arow where the Vehicle A is the controlled one with the HESSas energy supply. Vehicle B is the preceding vehicle which isassumed to be able to exchange information with Vehicle Athrough the vehicle-to-vehicle (V2V) technology. Vehicle Ais assumed to be equipped with communication devicesand some embedded sensors, e.g., radar, gyroscope, andaccelerometer. They can measure their states, i.e., speed, accel-eration, and spacing (the distance to the vehicle in front), andupload these data to the cloud (e.g., the traffic monitoringcenter) periodically through the roadside units (RSUs) byvehicle-to-infrastructure (V2I) communication. These data areused for real-time traffic condition evaluation, and results are

HU et al.: IoT-BASED PROACTIVE ENERGY SUPPLY CONTROL FOR CONNECTED EVs 7397

sent back to support vehicle driving. Data can be stored andprocessed in the electronic control units (ECUs) which is anin-vehicle embedded system capable of performing complexcalculation and making control decisions.

For the HESS, the fully active topology is chosen dueto its control flexibility and simple dc link voltage match-ing [23]. Uni-directional dc/dc converter is used to regulatethe discharging power of battery packs, and the bi-directionalconverter allows the SC to charge or discharge frequentlyaccording to the control decisions made by the ECUs. TheECUs communicate with these devices through the CANbus upon which the majority of intravehicular communicationtakes place. The state of the battery and SC packs are avail-able because many accurate state of charge (SoC) estimationmethods have been developed [24], [25]. A motor driver isutilized to interface the dc bus and vehicle motor.

B. Basic System Dynamic Models

To avoid impairing vehicle driving performances whilesplitting the load power, the primary requirement is keepingbalance between the energy supply and driving demand. Thepower balance equation is derived as follows:

ηb(k)Pb(k) + ηsc(k)Psc(k) = Pd(k) (1)

where Pb(k), Psc(k), and Pd(k) are the battery power, SCpower, and demand power at current instant k, respectively.ηi(k) ∈ [0, 1](i ∈ {b, sc}) is the efficiency coefficients of theconverters which depend on the power and current. By refer-ring to [6], the ηi is modeled as constant (i.e., an average value0.92) to facilitate calculation.

Battery and SC are two essential elements in the HESS.Their control-oriented and high-fidelity models are necessaryin the EMS design and performance evaluations.

1) Battery and SC High-Fidelity Models: For battery, SoCis a critical state which is defined as

SoCb(t) = 1 −∫ t

0

k1(t)Pb(t)dt

ub(t)Qn(2)

where k1(t) is the gain determined by charging/dischargingrate at time t, ub(t) is the battery voltage source, and Qn is thenominal capacity of battery. By referring to [26], the capacityloss can be modeled by

Qloss = l1e−l2/(RTb)il3b (3)

where li, i ∈ {1, 2, 3}, are the coefficients of the empiricalmodel of battery degradation. R is the ideal gas constant, Tb

is battery temperature.For SC, its capacity is defined as [27]

Qsc(t) = Q0 −∫ t

0

Psc(t)

usc(t)dt (4)

where Q0 is the SC full capacity and usc(t) the voltage source.The SoC of SC is defined as SoCsc = (Qsc(t)/Q0).

2) Control-Oriented Model: High-fidelity models are com-plicated in mathematical expressions due to their intrinsicallynonlinearity which are not suitable for control implemen-tation. Thus, the T–S fuzzy model is adopted here as thecontrol-oriented model, which is an empirical model and uses

experimental data to identify several linear models and fuzzyinference rules [28]. According to (2) and (4), the SoC vari-ation, which is the most vital dynamic of battery and SC,can be modeled as below. The T–S model consists of L fuzzyinference rules where each one is related to a local state-spacemodel. The ith rule

Ri : IF SoC(k) is Ai AND P(k) is Ui THEN

SoC (k + 1) = Ai · SoC(k) + Bi · P(k) + Ei

where SoC(k) = [SoCb(k); SoCsc(k)], P(k) = [Pb(k); Psc(k)].Ai and Ui are the fuzzy sets which are represented by Gaussianmembership functions. Ai, Bi, and Ei are the consequentparameters of the T–S model which describe the ith local state-space model. According to the current state SoC(k) and inputP(k), combining all these local models together, a generalrepresentation is obtained

SoC(k + 1) = Ak · SoC(k) + Bk · P(k) + Ek (5)

where (Ak, Bk, Ek) = ∑Li=1 ωi(Ai, Bi, Ei), the ωi denotes

the normalized degree of satisfaction of the ith rule. For moredetails about the T–S fuzzy model inference, we refer thereader to [28].

According to (3), battery degradation is highly affected bythe magnitude of charging/discharging rate [22]. We model thecost of battery fast discharging as

J1(Pb(k)) � α1Pb(k) (6)

where α1 is a positive scaling factor.Frequent power variation also causes battery lifetime reduc-

tion [6], [20]. The penalty is modeled by

J2(�P(k)) � α21(�Pb(k))2 + α22(�Psc(k))

2 (7)

where �P(k) = P(k)−P(k−1), α21 and α21 are both positivescaling factors.

To guarantee the safety operation of the HESS, the powerand SoC of battery and SC are bounded by

Pi ≤ Pi(k) ≤ Pi, and SoCk ≤ SoCi(k) ≤ SoCi (8)

where i ∈ {b, sc}. Pi denotes the maximum available dis-charging power of batteries and SCs, and Pi the maximumallowable charging power. While vehicle driving, the SCs canbe recharged by batteries or capture energy from regenera-tive braking which means Psc < 0. Meanwhile, to eliminatecapacity degradation, battery recharging is prohibited by set-ting Pb = 0. SoCi and SoCi are the minimum and maximumallowable SoC levels.

C. Problem Formulation

The fundamental objective of the HESS EMS in EVs is tooptimize the discharging behaviors of battery without sacrific-ing the vehicles’ driving performance. Considering the limitedcapacity of SCs, the SoC of SCs should be well regulated toassist battery discharging while meeting high driving powerdemand, and absorb regenerative braking energy while vehi-cle decelerating. Therefore, a desirable SoC range is set forSCs to keep it working efficiently. We model this by

J3(SoCsc(k)) � α3dist(SoCsc(k)|S) (9)

7398 IEEE INTERNET OF THINGS JOURNAL, VOL. 6, NO. 5, OCTOBER 2019

where dist(x|S) = infxd∈S(1/2)‖x − xd‖22 represents the

squared distance between x and the set S = {xd|xl ≤ xd ≤ xu}.xl and xu are the lower and upper bound of the set S whichdenotes the desirable range, and α3 is a positive scaling factor.The desirable SoC range of SCs is determined experimentally.While SoC in this range, sufficient energy can be guaranteedto support unexpected high power demand. Also, adequatereserved energy storage is left for braking power recycling.

Therefore, if future power demand information is availablein advance, the performances of the HESS can be enhancedby splitting power proactively. With the above mentioned costfunction (6), (7), and (9), an MPC-based proactive power splitoptimization problem is proposed by taking the future N stepspower demand Pd{k + i|k}N

i=0 into account. We use (k + i − k)to represent

P0: minU

J(xk, uk−1) =N−1∑i=0

3∑j=1

Ji(k + i|k)

s.t. xk|k = xk, uk−1|k = uk−1

xk+i+1|k = Ak · xk+i|k + Bk · uk+i|k + Ek

(1), (8)

∀i ∈ {0, . . . , N − 1} (10)

where xk+i|k = [SoCb(k + i|k); SoCsc(k + i|k)], uk+i|k =[Pb(k + i|k); Psc(k + i|k)], and U � u{k + i|k}N−1

i=0 . xk|k isthe current measured state, uk−1|k the control decision imple-mented at previous time step. In P0, the future power demandPd{k+i|k}N

i=0 is required in the equality constraint. However, itis unknown before finishing the trip which makes this problemdifficult. To solve the problem, future power demand need tobe predicted. Detailed prediction and utilization method willbe provided in the following section.

IV. SMPC-BASED PROACTIVE ENERGY MANAGEMENT

In this section, to control the battery and SC dischargingproperly, we start by introducing a probabilistic method topredict the short-term power demand. Then, the results areincorporated into the P0 so that an SMPC strategy is obtained.

A. Power Demand Prediction

The driving power composes the inertial, aerodynamic,friction, and road slope parts [29], which is given by

Pd =(

1

2mρairCdAv2 + a + gv sin θ + gKr

)· mv (11)

where v and a are the vehicle velocity and accelerationwhich expose a highly dynamic nature. From this equation,we can see that though future power demand information ishelpful for the HESS performances enhancement, its accu-rate prediction up to a desirable horizon is barely possible.Therefore, compared with putting much effort in improvingprediction accuracy, capturing abrupt peak power demand,and braking energy recovery are more important. To obtainthis power demand variation trend, we need to predict theshort-term future velocity trajectories and calculate the powerdemand.

Fig. 2. Structure of the CLG network.

1) Velocity Trajectory Prediction: While a vehicle is driv-ing in complex traffic situations, the velocity is affected bymany factors, e.g., the driving habit, traffic condition, and ter-rain. According to the vehicle dynamics, the first few secondsof future velocity is dominated by the vehicle’s current states.For one-step velocity prediction, the commonly used modelsas mentioned in Section II-A are practical. However, as theprediction horizon gets longer, the possible future velocity ismore determined by the driver’s reactions on the surroundingtraffic environments. Therefore, to make a better prediction onthe future velocity, in addition to the vehicle’s driving data,the information provided by the ITS and vehicular networksalso need to be incorporated into the prediction model.

Since the scenario we considered is in car-following contextas presented in Section III-A, the influence issues consid-ered here include the current and previous velocity of theVehicles A and B (denote as VA, VB), the current accelera-tion of the two vehicles (aA, aB), the spacing between twovehicles (h) and the current traffic conditions (Z). The trafficcondition information is provided by the RSUs and denotedby discrete values (i.e., Z = {1, 2, 3, . . . , }).

However, the driver’s reactions on the surrounding envi-ronment are nondeterministic, and there are still many otherunmeasured issues that influence the driver’s operations. Sinceit is impossible to take all factors into account, using a prob-abilistic method to model the future velocity is a conceivablesolution to provide sufficient flexibility to reflect the relation-ships between the future velocity and the issues we used inmodeling. As the velocity profile is time series, the probabilis-tic graphical models, which can be extended to time series byconsidering the probabilistic dependencies between the timeseries elements, are considered. Meanwhile, since the influenceissues contain both the continuous and discrete variables, theCLG method is adopted. It is a hybrid probabilistic graphicalmodel which can combine the discrete and continuous nodesand represent their relationship in a compact form.

To represent the relationships between the consideredinformation and the future velocity, the graph structure is spec-ified as shown in Fig. 2. The CLG model is denoted by graphG = (V, E) that contains a set of nodes V = {1, . . . , v} andedges E = {(s, t) : s, t ∈ V}. The G is defined by the adjacencymatrix, i.e., using G(s, t) = 1 representing the edge s → t.The shaded means observed nodes whose value are available,and the un-shaded nodes value are not known. Meanwhile,the squares represent discrete nodes and the round nodes arecontinuous-valued. The N-steps future velocity are modeledby the round and un-shaded nodes that can be presented as

HU et al.: IoT-BASED PROACTIVE ENERGY SUPPLY CONTROL FOR CONNECTED EVs 7399

Fig. 3. Sampled velocity trajectories.

the joint Gauss distribution of the relevant random variables

p(x|pac(x), Z = i

) = N (x|WT

i · pac(x) + μi, �i)

(12)

where pac(x) is the measured continuous parents value, andZ = i means the ith type of traffic conditions. Wi, μi, and �i

are the parameters of this CLG network which can be trainedfrom measured data. In real application, these learned param-eters must be update by using new data actively, in order tobest reflect current driving behavior. For detailed mathematicaland training information, interested readers can refer to [30].At each time instant, using the measured real-time data asinput, the predicted future velocity is obtained as a Gaussiandistribution in each step.

2) Tree Structure-Based Power Demand Representation: Topredict the future power demand trend, considering all possiblevalues of velocity in each prediction step is computationallyintractable due to its infinite dimensional characteristic. Anapproximation approach can be adopted by sampling severalscenarios to represent the possible future velocity evolution.A few points are sampled in the first few steps because theprediction results have a good degree of accuracy in this range.As step increasing, more points need to be sampled due tothe increased uncertainty in prediction results. Therefore, tra-jectories vj = [vj(k), vj(k + 1), . . . , vj(k + N)] for j ∈ N[1,n]are sampled from the predicted distribution result of the CLGnetwork as shown in Fig. 3. Here, N is the total predictionsteps, and n is the number of sampled trajectories.

According to the sampled velocity trajectories, the corre-sponding power demand can be calculated from (11) andsatisfies

Pd

(k + i|εj

k+i

)= Pd(k + i) + ε

jk+i (13)

where Pd(k + i) denotes the mean value of power demand inthe ith prediction step. ε

jk+i means the difference of the jth cal-

culated power demand from the mean Pd(k+i). Thus, multiplescenarios in (13) need to be incorporated in the P0 in (10).This is accomplished by adopting a scenario-tree structure torearrange these multiple Pd(k + i|εj

k+i) and therefore facilitateproblem description. As shown in Fig. 4, the scenario-treedepicts the interconnection of a finite number of nodes. Thepossible appeared ε

jk+i is represented by these nodes. At the

current stage k, the node is called the root node and withoutuncertainty due to the available observation (i.e., εk = 0). Atstage k+1, only one point is sampled, we denote ε2:n

k+1 = ε1k+1.

Fig. 4. Scenario-tree structure.

Fig. 5. Problem formulation and solution scheme.

At the last stage k + N, these nodes are called leave node ofwhich the amount equals to the sampled trajectory scenarios.Moreover, the predecessor of a node (k + i, j) is denoted byp(k + i, j) and the successor is s(k + i, j).

B. Decision-Making Based on SMPC Method

The main idea in this section is using the sampled scenariosto approximate the future power demand and then optimizingthe power split decisions. The scheme used in the problemformulation and solution is summarized in Fig. 5.

We incorporate the predicted power demand (13) intothe power balance equation (1) and propagate each samplePd(k + i|εj

k+i) through the state xjk+i|k. This results in different

scenarios and P0 is reformulated as stochastic form P1 as givenbelow. For the sake of convenience, we denote xj

k+i|k, ujk+i|k

as xji, uj

i

P1: minU

J(x0, uc−1) =N−1∑i=0

3∑l=1

n∑j=1

Jl

(xj

i+1, uji,�uj

i

)(14a)

s.t. x0 = xk, u−1 = uk−1 (14b)

12 · uji − Pd

(k + i|εj

k+i

)= 0 (14c)

xji+1 = Ak · xp(i+1,j)

i + Bk · uji + Ek (14d)

xji ∈ X , uj

i ∈ U (14e)

where 12 = [1 1

]. X and U defined the feasible set of

decision variables. For P1, as multiple scenarios are consid-ered, the size of optimization variables are become larger thanP0. Meanwhile, the existence of the nonsmooth cost termJ3 in objective function and the hard constraints on deci-sion variables makes the solution of the P1 more complex.Considering the above characteristics, we exploit a proximalgradient method to solve this problem. This kind of methodis suitable for solving nonsmooth, constrained, or large-scaleconvex optimization problems [31].

7400 IEEE INTERNET OF THINGS JOURNAL, VOL. 6, NO. 5, OCTOBER 2019

While solving P1, to guarantee the recursive feasibility, wereplace the hard state constraint by a penalty term

J4(x) � α4dist(x|X ) (15)

where α4 is a positive scaling factor. Considering the nons-mooth term and hard constraints, we separate the P1 into twoparts: 1) the smooth part f (·) and 2) nonsmooth part g(·)

minz

J(z) = f (z) + g(x) (16)

where z � [xji+1; uj

i]i∈N[0,N−1],j∈N[1,n] is the decision variables

and x = [xji+1]i∈N[0,N−1],j∈N[1,n] . f and g are defined as

f (z) =2∑

l=1

N−1∑i=0

n∑j=1

Jl

(zj

i

)+ (z|(14c), (14d)) (17a)

g(x) =N−1∑i=0

n∑j=1

J3

(xj

i

)+ J4

(xj

i

)+ J5

(uj

i

)(17b)

where J5 = δ(u|U) denotes the hard constraints on con-trol variables. (z|Z) represents the equality constraints.The f -part is a closed proper convex, smooth, and differen-tiable function. The g-part is convex and nonsmooth whichencodes the soft and hard constraints. For the g(x) in (17b),we introduce a new variable x to replace J3(x

ji) with J3(x

ji)

and the reason will be explained later. Therefore, the primalproblem (16) can be written as the following form:

P′1 : min

z,s{f (z) + g(s) : Gz − s = 0} (18)

where the variable s � [x; x; u] and the parameter matrix

G =[

[0 1]T ⊗ 1Tn×N I2n×N 02n×N

[0 0]T ⊗ 1Tn×N 02n×N I2n×N

]T

.

Meanwhile, the Lagrange duality problem of (18) is

D : miny

f ∗(−GTy) + g∗(y) (19)

where f ∗(y) = supz{yTz − f (z)} and g∗(y) = supz{yTz − g(z)}are the Fenchel conjugate functions of f and g. According tothe strong duality theorem [32], [33], if the primal problem isconvex and there exists z ∈ ri(domf ), s ∈ ri(domg) such thatGz − s = 0, the duality gap is zero which means val(P′

1∗) =

val(D∗), i.e., the dual problem is feasible.Observing the objective function in primal P′

1 and dualproblem D : f is continuous and differentiable; g is prox-friendly which means its proximal operator is easy to evaluate.Taking advantages of this structure, a specific proximal gra-dient method, i.e., the fast dual proximal gradient (FDPG),is utilized to solve this problem [34]–[36]. Note that evalu-ating the proximal operator of a function proxf (v) is a baseoperation in the proximal gradient method, which is defined as

proxλf (v) = arg minx

(f (x) + 1

2λ‖x − v‖2

2

)(20)

where λ is a scale parameter. This definition indicates thatthe proximal operator is a point which compromises between

minimizing f and being near to v. The FDPG algorithm isgiven as below [33]

wτ = yτ + θτ

(θ−1τ−1 − 1

)(yτ − yτ−1

)(21)

zτ = arg minz

{f (z) + (

wτ)T

Gz}

(22)

yτ+1 = proxλg∗(wτ + λGTzτ

)(23)

θτ+1 = 1

2

(√θ4τ + 4θ2

τ − θ2τ

)(24)

where (21) is an extrapolation step to accelerate conver-gence rate. For rapid convergence, the θ should decrease fastand (24) is the best choice. The calculation of primal vari-ables in (22) is also meant to calculate the proximal gradientz = ∇f ∗(−w) to update the dual variables in (23). Equations(22) and (23) are the two most essential steps that requireattentions.

To calculate the dual variables in (23), considering theMoreau decomposition property [31], the proximal operator ofg∗(·) can be deduced from the proximal with g(·). Accordingto [36], prox-operation has separable sum property. The intro-duced variable x makes g(s) separable and the evaluation ofproxg is reduced to proximal each composite function. Theprox-operator of J5 [i.e., the delta function δ(·)] is given

proxJ5(v) = arg min

u∈U‖u − v‖2 (25)

and the proximal operator of the distance function whichdefined the cost terms J3 and J4

proxλ·dist(x|C)(v) = v

1 + λ+ λ

1 + λPC(x) (26)

where PC is the projection on a rectangle set C = [l, u] ={xd|l ≤ xd ≤ u} defined as

PC(x) =⎧⎨⎩

l, x ≤ lx, l < x < uu, x ≥ u.

Thus, the prox-operator of g∗ is given

proxλg∗(v) = v − λ · proxλ−1g

(λ−1v

)

= v − λ ·(∑5

l=3proxλ−1Jl

(λ−1v

)). (27)

This indicates that (23) can be solved easily and efficiently.To solve the optimization problem in (22), we introduce

particular and homogeneous solutions u and ϑ to represent u.Thus, the power balance equation (14c) is rewritten as

1 · ([1 −1]T · ϑ + u

) − Pd

(k + i|εj

k+i

)= 0 (28)

where u = [u1, u2]T and it can be determined once thepower demand prediction results Pd is known. The systemstate equation (14d) becomes

xji+1 = Akxp(i+1,j)

i + Bk[1 −1]Tϑji + Bkuj

i + Ek

= Akxp(i+1,j)i + Bkϑ

ji + Ek (29)

HU et al.: IoT-BASED PROACTIVE ENERGY SUPPLY CONTROL FOR CONNECTED EVs 7401

where Bk = Bk[1 −1]T and Ek = Bkuji + Ek. Replacing u

by ϑ in f (z) and denoting w = [w1, w2, w3], the optimizationproblem in (22) becomes the following form:

minx,ϑ

f (x, ϑ) + wTGz

= minx,ϑ

N−1∑i=0

n∑j=1

[W2

(ϑ

ji

)2 − 2[W2ϑ

p(i,j)i−1 − WT

2 �uji

]ϑ

ji

+ W2

(ϑ

p(i,j)i−1

)2 − 2(�uj

i

)TW2ϑ

p(i,j)i−1

+ (x, ϑ |(29))

+ W1ϑji +

[(w j

1i

)T[0 1] +

(w j

2i

)T]

xji+1

+ [1 −1]w j3iv

ji

](30)

where W1 = [α1 0], W2 = α21 + α22, W1 = α1, W2 =[α21 α22]T , and �uj

i = uji − up(i,j)

i−1 . From this equation, wecan see that f (z) is strongly convex which implies a Lipschitzgradient property of the function f ∗(y) [33]. The Lipschitz con-stant of the dual gradient �f ∗(−GTz) determines the optimaliteration step size λ. Meanwhile, this is an unconstrainedminimization problem and can be solved via the DP method.The calculation result is given

(ϑ

ji

)∗ = ϑp(i,j)i−1 − ν

ji

2(α21 + α22)(31)

νji = Fj

i + [1 −1]w j3i + γ

ji · Bk + ν

s(i,j)i+1 (32)

γji = wj

i + γs(i,j)i+1 · Ak (33)

where wji = (w j

1i)T [0 1] + (w j

2i)T , ν

s(i,j)i+1 represents all the suc-

cessors of νji . Fj

i is corresponding to the particular solution uwhich is defined as

Fji = α1 − 2WT

2

[up(i,j)

i−1 − (1 + ‖s(i, j)‖)uji + us(i,j)

i+1

](34)

where ‖s(i, j)‖ is the successor amount of node j in stage i.Once the initial values xk and uk−1 are given, the originalvariables x and u can be derived.

According to all above in this section, the complicated non-differentiable convex optimization problems P1 is solved bythe FDPG method effectively. zτ in (22) and yτ+1 in (23) canbe easily calculated since the closed-form solution is givenin (27) and (31)–(33). Therefore, the FDPG method is fastand suitable for real-time applications.

C. Proactive Energy Management Strategy

The HESS power split control decisions are determined bythe SMPC method and then used as reference signals to controlthe dc/dc converters (as shown in Fig. 1) to regulate batteryand SC discharging. The overall control procedures of theproposed smart proactive EMS (SPEMS) are summarized inAlgorithm 1.

V. SIMULATION AND PERFORMANCE EVALUATION

The performances of the proposed proactive EMS and thecomparison with the state-of-the-art are given in this section.

Algorithm 1 SPEMSInput: v, a, h, Z, x0, u−1, Pd(k).

1: Predict velocity information using the CLG method andcalculate power demand Pd(k + i|εj

k+i).2: Determine the particular solution u from Pd (28) and infer

the parameters Ak, Bk, Ek according to the working pointx0, u−1 and u.

3: Solve the P1 in (14)3.1: Set θ0 = θ−1 = 0, y0 = y−1 = 0 and solve itsLagrangian duality problem (21)-(24) and get (ϑ

ji )

∗.3.2: Given x0, u−1, compute primal solution (x, u)∗

for i = 0, ..., N − 1 dofor j = 1, ..., n do

(uji)

∗ = [1 −1]T · ϑji + uj

i;(xj

i+1)∗ = Akxp(i+1,j)

i + Bkϑji + Ek;

end forend for

4: Apply the first control action uk to converters to controlthe charging/discharging behavior of battery and SC.

5: Update u−1 = uk and current states x0. Then, return toStep 1.

Output: (x, u)∗

A. Data Preparation and Simulation Setup

To demonstrate the performances of the proposed proactiveEMS, fine-grained and detailed driving trajectory and trafficdataset are vital. However, in real traffic environment, V2Vand V2I technologies are not widely used yet which meansthis kind of data is difficult to obtain in field experiments.Therefore, the data we adopted in this section is prepro-cessed and reconstructed from the NGSIM traffic dataset [37].Comprehensive vehicle trajectory data is sampled every one-tenth of a second. During the data collection period, the trafficsituation changes from free flow to the congested state.

To train the CLG model, leader–follower paired trajectorydata is extracted which contains the velocity and accelerationof these two vehicles and their relative distance. Meanwhile,traffic conditions are classified into different types accordingto the traffic density and mean velocity which can be obtainedfrom raw data. In the perspective of this paper, the followerdata is representing the data of Vehicle A in Fig. 1. The leaderand traffic condition data serve as the received information ofVehicle A under vehicular networks.

For the CLG network, model learning, inference, and sam-pling procedure is conducted by utilizing the Bayes NetToolbox which is a MATLAB package developed for graphi-cal models [38]. To calculate power demand, the parametersin (11) is set according to the default EV model in ADVISOR2002 [39], [40]. The vehicle mass m is 1140 kg, air den-sity ρair = 1.2 kg/m3, the frontal area A = 2.0 m2, anddrag coefficients Cd = 0.335. Meanwhile, the road slope isassumed to be 0. The high-fidelity HESS model with the struc-ture shown in Fig. 1 is constructed in MATLAB/Simulink. Asmentioned in Section III-B1, the battery pack consists severalseries connected LiFePO4 cells and the SC pack is based onthe Maxwell cells. Detailed explanation is presented in Table I.

7402 IEEE INTERNET OF THINGS JOURNAL, VOL. 6, NO. 5, OCTOBER 2019

TABLE IPARAMETERS OF THE HESS MODEL

Fig. 6. Predicted velocity distribution in three prediction steps. From top tobottom plot, different confidence intervals 95%, 80%, and 50% are used inthese three different steps separately.

B. Performance Evaluation

In this section, the validation results of the velocityprediction and power split are presented.

1) Velocity Prediction: Since the velocity prediction resultsof the CLG model is a Gaussian distribution in each predictionstep, the mean values of these distributions are plotted in Fig. 6by blue dashed line, and the gray shadow is used to presentthe prediction confidence intervals. The solid red line denotesthe record real velocity values. The time interval in each stepis 1 s and the entire prediction horizon N = 10 s which isthe typical values used in [4] and [5]. The predicted resultsof future velocity in steps 2, 5, and 10 (i.e., the velocity after2 s, 5 s, and 10 s which is predicted at the current instant), areshown in Fig. 6. According to Fig. 6, the predicted mean val-ues of the first few steps (e.g., in step 2) are almost the sameas the real values, and the confidence interval is narrow. Thisindicates that the prediction is accurate and fewer scenariosneed to be sampled. However, as the prediction step increases(e.g., in steps 5 and 10), the confidence interval becomes widewhich means the true value lies in a large interval. Therefore,more scenarios need to be sampled to approximate futurevelocity evolution which is consistent with the description inSection IV-A2.

2) Power Splitting: The simulation results of the proposedEMS for the evaluation velocity profile are depicted in Fig. 7.The velocity profile in Fig. 7(a) represents the real drivingcycle of the controlled vehicle. Fig. 7(b) shows the optimizedbattery and SC discharging power profiles. From this figure, itis o that SC supports battery to provide fast burst power whilethe vehicle is accelerating and recycles the regenerative energywhile braking. Compared with the demand power, the mag-nitude and fluctuation of the batteries discharging power areboth reduced. In Fig. 7(c), the discharging current is describedby C-rate, which is defined in units of C. The C-rate plottedin Fig. 7(c) shows that the battery is working at a low to mod-erate discharging level (i.e., below 1 C). Fig. 7(d) shows thatthe SoC of SC is kept in the desired range so that SC works inan efficient condition. The simulation results can demonstratethat the claims on the performance described in Section III-Care validated.

3) Computational Effort: As the proposed method is work-ing at the decision layer where a basic BMS is superimposed,the control frequency is chosen as 1 Hz. Thus, for real-timeimplementation, the calculation time of this method must beassessed. The time-consuming includes three parts: 1)HESSmodel parameter extraction from the fuzzy model Te; 2) veloc-ity prediction and power demand calculation Tp; and 3) theSMPC solving process Ts. The simulation is performed on adesktop PC with 3.3 GHz Intel Core i5. From the results,we know that Te ≈ 0.011 s. While we sample eight tra-jectories as shown in Fig. 4, Tp ≈ 0.01 s and most of thetime is cost in solving the optimization problem. We imple-ment the FDPG method in MATLAB and compare it withthe solving process which is modeled with Yalmip and solvedusing Gurobi [41], [42]. The Gurobi solver takes an average of4.291 s to solve this problem, whereas the FDPG solves it in0.6765 s. In the real application, optimized C implementationcan further improve the calculation speed.

C. Comparison Study

The comparison of several energy management strategieshas been carried out in this section.

1) Performance Criteria: To assess the performanceimprovements of different strategies, three indicators are con-sidered to characterize the discharging behavior of battery. Dueto the mean power is corresponding to energy consumptionand reflects the long-term stress level, it is chosen as the firstindicator

Pb = 1

N

N∑k=1

Pb(k).

The second indicator is the peak discharging power whichhighly affects the lifetime of battery. Power variation is anotherindicator which is defined by the standard variance of thedischarging profile

σ =√√√√ 1

N

N∑k=1

(Pb(k) − Pb

)2.

HU et al.: IoT-BASED PROACTIVE ENERGY SUPPLY CONTROL FOR CONNECTED EVs 7403

(a)

(b)

(c)

(d)

Fig. 7. Power split results of the test driving cycle. (a) Velocity profile.(b) Power splitting. (c) Battery discharging current. (d) SoC profile of SC.

2) Comparison Results: Another three management strate-gies are implemented and compared with the same drivingcycle. The battery-only strategy refers to the basic BMS whichworks only with battery packs and thus without power splitoptimization. Instantaneous management method optimizes thepower split process with the same objective terms and con-straints given in (6)–(9). The deterministic MPC method usesaccurate future power demand which is not available in thereal-time application. It serves as a benchmark to show theperformances upper bound with the short-term power demandprediction. The results of the performance analysis of these

TABLE IIPERFORMANCES OF DIFFERENT EMS

(a)

(b)

Fig. 8. Power splitting results under different control strategies. (a) Batterydischarging power comparison. (b) SoC trajectories of SC comparison.

Fig. 9. Discharging rate of battery comparison.

four compared strategies are summarized in Table II. Theoptimized battery discharging profiles, SoC variation of SCand battery discharging rate are given in Figs. 8 and 9 todemonstrate their performances.

The power split results in Fig. 8 indicate that all thethree energy management strategies reduced the peak dis-charging power of battery compared with the battery-onlycase. Since future power demand is not considered in the

7404 IEEE INTERNET OF THINGS JOURNAL, VOL. 6, NO. 5, OCTOBER 2019

instantaneous method, it provides limited enhancement in peakpower shaving and discharge smoothing. Meanwhile, the SCworks out of the desirable range sometimes due to superflu-ous power is generated by the battery and absorbed by theSC. By taking the predicted future power demand trend intoaccount, the proposed SMPC method achieves satisfying per-formances even compared with the DMPC which providesthe best achievable effect. The peak power is reduced by46.4%, and power variation is reduced by 27.7% comparedwith the battery-only strategy. The mean power is also reducedby properly using SC for energy recovery. Fig. 9 shows thatthe battery discharging rate of the proposed method is almostwithin 1 C whereas the discharging rate under battery-onlyand instantaneous cases has a span of 1.6 C.

VI. CONCLUSION

In this paper, the power split optimization problem of theHESS in connected EVs has been investigated. An SMPC-based proactive EMS was proposed to reduce the peak dis-charging power of batteries and eliminate power vibration.We utilized a probabilistic learning model to predict futuredriving velocity with the assumptions that ITS and vehicu-lar networks are deployed. Then, trajectories were sampledfrom the CLG prediction results to represent the possiblefuture driving conditions and calculate the power demand. Wereconstructed the predicted power information with a scenario-tree structure and incorporated it into the MPC to formulatean SMPC problem. Considering the computational complex-ity, FDPG algorithm was utilized to solve this problem. Asa result, the magnitude of batteries discharging power waswell reduced, and the power was smoothed compared with thebattery-only and instantaneous cases. Meanwhile, the SoC ofSC was maintained in an ideal range. Moreover, the proposedSMPC method performed satisfactorily even compared withthe DMPC case.

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Yuying Hu received the B.Eng. degree fromthe College of Automation, Harbin EngineeringUniversity, Harbin, China, in 2015. She is cur-rently pursuing the Ph.D. degree at the Departmentof Automation, Shanghai Jiao Tong University,Shanghai, China.

Her current research interest includes energy man-agement and power-split optimization of the hybridenergy storage systems.

Cailian Chen (S’03–M’06) received the B.Eng. andM.Eng. degrees in automatic control from YanshanUniversity, Qinhuangdao, China, in 2000 and 2002,respectively, and the Ph.D. degree in control andsystems from the City University of Hong Kong,Hong Kong, in 2006.

She joined the Department of Automation,Shanghai Jiao Tong University, Shanghai, China,in 2008, as an Associate Professor, where she is cur-rently a Full Professor. She was a Senior ResearchAssociate with the City University of Hong Kong,

in 2006, and a Post-Doctoral Research Associate with the University ofManchester, Manchester, U.K., from 2006 to 2008. She was a VisitingProfessor with the University of Waterloo, Waterloo, ON, Canada, from 2013to 2014. She has actively been involved with research on various topics suchas wireless sensor networks and industrial applications and computationalintelligence and distributed situation awareness.

Prof. Chen was a recipient of the Changjiang Young Scholar by the Ministryof Education of China in 2015 and the Excellent Young Researcher by theNSF of China in 2016.

Jianping He (M’15) received the Ph.D. degreein control science and engineering from ZhejiangUniversity, Hangzhou, China, in 2013.

He is currently an Associate Professor withthe Department of Automation, Shanghai JiaoTong University, Shanghai, China. He was aResearch Fellow with the Department of Electricaland Computer Engineering, University of Victoria,Victoria, BC, Canada, from 2013 to 2017. His cur-rent research interests include smart sensing andcontrol, security and privacy theory and its appli-

cations, distributed learning, and big data.Dr. He was a recipient of the Outstanding Thesis Award, Chinese

Association of Automation in 2015, the Best Paper Award of IEEEWCSP17, the Finalist Best Student Paper Award of IEEE ICCA17, and theChina National Recruitment Program of 1000 Talented Young Scholars. Heserves as an Associate Editor for the KSII Transactions on Internet andInformation Systems. He was also a Guest Editor for the International Journalof Robust and Nonlinear Control and Neurocomputing.

Bo Yang (SM’16) received the Ph.D. degree inelectrical engineering from the City University ofHong Kong, Hong Kong, in 2009.

He was a Post-Doctoral Researcher with the KTHRoyal Institute of Technology, Stockholm, Sweden,from 2009 to 2010, and a Visiting Scholar withthe Polytechnic Institute of New York University,New York, NY, USA, in 2007. He is currently aFull Professor with Shanghai Jiao Tong University,Shanghai, China. His research interests includeenergy internet, mobile computing, and industrial

IoT. He has authored or coauthored more than 110 papers. He has beenthe Principle Investigator of several research projects funded by NSFC, andMinistry of Science and Technology of China, including Key project of NSFCand National Key R&D Program of China.

Dr. Yang was a recipient of the National Young Top-Notch Talent program.He is on the Editorial Board of Digital Signal Processing (Elsevier) and onthe TPC of several international conferences. He is a member of the ACM.

Xinping Guan (M’02–SM’04–F’18) received theB.Sc. degree in mathematics from Harbin NormalUniversity, Harbin, China, in 1986, and the Ph.D.degree in control and systems from the HarbinInstitute of Technology, Harbin, in 1999.

He is currently a Chair Professor with ShanghaiJiao Tong University, Shanghai, China, where heis the Deputy Director of the University ResearchManagement Office and the Director of the KeyLaboratory of Systems Control and InformationProcessing, Ministry of Education of China. He is

the Leader of the prestigious Innovative Research Team, National NaturalScience Foundation of China (NSFC). His current research interests includeindustrial cyber-physical systems and wireless networking and applications insmart factories.

Dr. Guan was a recipient of the First Prize of the Natural Science Awardfrom the Ministry of Education of China in 2006 and 2016, the SecondPrize of the National Natural Science Award of China in 2008, the NationalOutstanding Youth Honored by the NSFC, and the Changjiang Scholar bythe Ministry of Education of China. He is an Executive Committee memberof the Chinese Automation Association Council and the Chinese ArtificialIntelligence Association Council.