Digital twin for battery systems: cloud battery management

system with online state-of-charge and state-of-health estimation

Weihan Lia,b,∗, Monika Rentemeistera,b, Julia Badedae, Dominik Josta,b, Dominik Schultef,Dirk Uwe Sauera,b,c,d

aChair for Electrochemical Energy Conversion and Storage Systems, Institute for Power Electronics andElectrical Drives (ISEA), RWTH Aachen University, Jaegerstrasse 17/19, 52066, Aachen, Germany

bJuelich Aachen Research Alliance, JARA-Energy, GermanycInstitute for Power Generation and Storage Systems (PGS), E.ON ERC, RWTH Aachen University,

GermanydHelmholtz Institute Munster (HI MS), IEK-12, Forschungszentrum Julich, Germany

eABO Wind AG, GermanyfBatterieIngenieure GmbH, Germany

Abstract

Battery management is critical to enhancing the safety, reliability, and performance of thebattery systems. This paper presents a cloud battery management system for stationary andmobile battery systems to improve the computational power and data storage capability bycloud computing. With the proposed Internet of Things component, all battery relevant datacan be measured and transmitted in real-time to the cloud platform to build up the digitaltwin for the battery system, where advanced battery diagnostic algorithms evaluate thedata and open the window into the battery’s remaining capacity and aging level. Notably,an adaptive extended H-infinity filter is proposed to estimate the state of charge of thebattery robustly and shows a strong self-regulation ability even with a large initializationerror. Furthermore, a particle swarm optimization-based state-of-health estimation approachis innovatively exploited to estimate both capacity and ohmic resistance of the battery,indicating the capacity fade and power fade during battery aging. The functionalities andstability of both hardware and software of the proposed cloud battery management systemand battery diagnostic algorithms are validated with prototypes under field operation andexperimental validation on both lithium-ion and lead-acid batteries.

Keywords: digital twin, cloud computing, internet of things, battery management system,state of charge, state of health

∗Corresponding author. Chair for Electrochemical Energy Conversion and Storage Systems, Institutefor Power Electronics and Electrical Drives (ISEA), RWTH Aachen University, Jaegerstrasse 17/19, 52066,Aachen, Germany

Email address: batteries@isea.rwth-aachen.de (Weihan Li)

Preprint submitted to Elsevier April 3, 2020

1. Introduction1

With the rapid advances in energy storage technologies, the battery system has emerged2

as one of the most popular energy storage systems in stationary and mobile applications to3

reduce global carbon emissions [1]. However, without proper monitoring and controlling of4

the batteries by a battery management system (BMS), problems concerning safety, reliabil-5

ity, durability, and cost will appear. The state-of-the-art BMS includes two main modules:6

BMS-Master and BMS-Slave, which can be combined in one embedded system or designed7

as two separate systems with wiring communication [2]. While the BMS-Slave is respon-8

sible for monitoring the battery cells with signal acquisition and filtering, more advanced9

functions, such as battery diagnostic algorithms, which require high computation power, are10

implemented in the BMS-Master. However, with the increase in the number of battery cells11

and the scale of the battery systems, the reliability and cost of the wiring communication12

are becoming challenging.13

As the most important functions of the BMS, accurate estimation of the state of charge14

(SOC) and the state of health (SOH) deliver essential information about the battery’s re-15

maining capacity and aging level, which can be used to perform maintenance or adapt16

operational strategies to extend its service life. Due to the easy implementation and small17

computation power requirement, open-loop algorithms, e.g., Coulomb counting [3] and open-18

circuit voltage method [4], are widely used to estimate the battery’s SOC. Considering the19

high dynamic operation load in mobile battery systems and the tendency of multi-use appli-20

cation of stationary battery systems [5], the significant accumulated error due to current sen-21

sor uncertainties and the rare appearance of relaxation status reduce the reliability of these22

open-loop algorithms. Compared with SOC estimation, SOH estimation is more challenging23

due to the complex nonlinear aging mechanisms of the batteries. Although Electrochemi-24

cal Impedance Spectroscopy [6–8] is commonly applied offline to detect the aging levels of25

the batteries, the strict input-signal requirements are obstacles for their online application26

in a BMS. To achieve accurate battery state monitoring, different model-based approaches27

were developed for SOC [9–13] and SOH [14–16] estimation. However, with the increase28

of battery cell number and algorithm complexity, on-board BMS is faced with problems in29

computation power and data storage for precise estimation and prediction of the battery’s30

states with model-based algorithms.31

To overcome these obstacles, BMS can be revolutionized by applying cloud computing32

[17] and the Internet of Things (IoT) [18] technologies. The computation and data storage33

capabilities increase exponentially, and all battery relevant data can be measured and trans-34

mitted in real-time to the cloud platform to build up the digital twin [19] for battery systems,35

where advanced battery diagnostic algorithms are implemented. With the collection of big36

data in one base, system prognostics and optimizations can be achieved by machine learning37

algorithms, which will revolutionize our understanding of battery aging. Furthermore, the38

system reliability increases by replacing wiring communication with wireless IoT communi-39

cation. The pioneering work has shown several concepts to apply cloud computing and IoT40

in BMS for both stationary and mobile battery systems [20–22]. Tanizawa et al. [20] pro-41

posed a cloud system for electric vehicles to manage the battery information in the battery42

2

replacement system. Harish et al. [21] proposed a battery monitoring system based on IoT43

for batteries in a microgrid system. Most recently, Kim et al. [22] proposed a cloud-based44

battery condition monitoring and fault diagnosis platform for large-scale stationary battery45

systems. However, the aforementioned works suffer from two major drawbacks awaiting46

further improvements. Firstly, the technical details of both software and hardware design of47

the cloud BMS are rarely introduced, and the functionalities of the system are not validated48

with field operation. Secondly, cloud suitable battery diagnostic algorithms are missing,49

which can improve the diagnostic accuracy and benefit from the high computation power50

and data storage capability of the cloud BMS.51

This paper aims to bridge the aforementioned research gap and proposes a cloud BMS52

for stationary and mobile battery systems, releasing the computation and data storage53

limitations of the on-board BMS. The information of the batteries connected with the cloud54

can be shared by the proposed IoT component, enabling the data communication among55

individual battery systems and the cloud platform. Moreover, the proposed model-based56

battery diagnostic algorithms with adaptive extended H-infinity filter (AEHF) and particle57

swarm optimization (PSO) for SOC and SOH estimation, are implemented in the cloud58

BMS in real-time, ensuring continuous and accurate monitoring of the battery’s status with59

the digital twin and intelligent controlling of the battery’s behavior. The AEHF algorithm60

based on the extended Thevenin model provides a robust approach for SOC estimation.61

The PSO-based algorithm estimates all the parameters of the extended Thevenin model,62

providing both information of the battery’s capacity fade and power fade synchronously.63

Furthermore, two prototypes of the cloud BMS are designed and produced for both the field64

test of the system’s functionalities and experimental test of the proposed battery diagnostic65

algorithms with two different battery technologies, i.e., lithium-ion and lead-acid batteries.66

We begin in Section 2 by introducing the operation principles of the cloud BMS and67

the technical details of the subsystems. Battery modeling is presented in Section 3. In68

Section 4 and 5, the model-based SOC estimation approach with the AEHF algorithm and69

SOH estimation approach with the PSO algorithm are introduced, respectively. In Section70

6 and 7, the experimental set-up and validation results of both cloud BMS functionalities71

and battery diagnostic algorithms are discussed. Section 8 draws the conclusions and points72

towards future work.73

2. Cloud battery management system74

In this section, operation principles of the cloud BMS and the functionalities of the75

subsystems are introduced, as depicted in Figure. 1.76

2.1. Stationary and mobile battery systems77

In electricity systems with a high penetration of renewable energy generation, such as78

solar and wind energy, stationary battery systems can be used to balance the power supply.79

High costs and single applications make the stationary battery systems operating under80

inefficient scenarios. To use the energy of the UPS systems efficiently, Badeda et al. [5]81

investigated multi-use applications by delivering additional services, e.g., peak shaving and82

3

Data Generation Data Sensing

Battery Systems BMS-Slave IoT Component Cloud API UI

Data VisualizationData Collection Data Storage Data Analytics

Figure 1: Schematic of the cloud BMS, which consists of six subsystems: the battery systems for datageneration, the BMS-Slave for data sensing, IoT component for data collection, cloud for data storage,application programming interface (API) for data analytics and user interface (UI) for data visualization.

primary containment reserve. Compared with the batteries in single applications, multi-use83

battery systems need continuous real-time state monitoring and diagnostics to ensure the84

availability of power for different use cases, highlighting the benefits of the cloud BMS.85

With the electrification of vehicles, battery systems are playing an essential role in the86

energy storage of electric vehicles. Compared with the stationary battery systems, the87

batteries in mobile applications are usually working with larger depth of discharge (DOD)88

and under more dynamic conditions, which in turn require more advanced algorithms for89

battery diagnostic, prognostic, and optimization. With the emerging new communication90

technologies, e.g., 5G technology, the mobile battery systems can be connected with the91

cloud by the proposed cloud BMS, reducing battery aging and improving the battery’s92

safety, reliability and performance. The data generated by stationary and mobile battery93

systems contain a wealth of information about the operation history, which can be analyzed94

to adapt the operation strategy to extend service life.95

2.2. BMS-Slave96

The main components in the developed BMS-Slave for data sensing are multi-cell battery97

monitors LTC 6804G-2 and LPC 11C14F/301. The LTC measures up to 12 battery cells98

connected in series with a total measurement error of less than 1.2 mV, which can also99

be connected in series to monitor high-voltage battery strings. The LPC is a 32-bit ARM100

Cortex-M0 based microcontroller, which sends the measurement commands to the LTC and101

receives the measured data in hexadecimal values from the LTC. The BMS-Slave performs102

data acquisition by measuring the voltage, current, and temperature of the batteries with103

sensors at different sampling rates.104

4

2.3. IoT component105

The basic idea behind IoT is to make the devices, i.e., the stationary and mobile battery106

systems embedded with electronics and connected with the internet, communicate and in-107

teract with others to be monitored and controlled remotely. Considering the advantages of108

Raspberry Pi as a single-board computer with relatively low price and weight, it is respon-109

sible for collecting data from the batteries and communicating with the cloud platform and110

other battery systems. The measured data of the batteries are sent to the IoT component111

by the BMS-Slave based on the Controller Area Network (CAN) protocol. The software112

programs were developed and implemented with Python in the IoT component to translate113

the CAN signals into physical values. Furthermore, the IoT component is also responsible114

for sending the generated data to the cloud under TCP/IP and Message Queuing Telemetry115

Transport (MQTT) protocol with the assured security and privacy.116

2.4. Cloud117

As IoT devices usually have limited storage and computation capabilities and do not118

allow complex data processing onboard, cloud computing with virtually unlimited storage119

capability and processing power enables the scalable and real-time data analysis of the120

IoT devices. The proposed cloud platform in cloud BMS consists of a data logger and a121

database hosted in Germany. The data logger captures a massive amount of non-structured122

or semi-structured data produced by the battery systems and enables a secure gateway and123

data transfer into the cloud database, which was extensively certified and has distributed124

denial-of-service (DDoS) protection and multi-redundant connections. Only the owners and125

operators of the battery systems have access to the data, and the data privacy and security126

are guaranteed.127

2.5. Application programming interface128

As a part of the cloud BMS, Application Programming Interface (API) is the bridge129

between the cloud database and the data-analytic algorithms, which offers several popular130

programming languages. With the proposed API, the battery diagnostic algorithms, e.g.,131

SOC and SOH estimation algorithms, which will be introduced in Section 4 and 5, run in132

real-time in the cloud. Furthermore, the field data collected from different battery systems133

can be used for precise predictions and system optimization and reducing the wear and tear134

on the batteries through the adaption of battery management.135

2.6. User interface136

User Interface (UI), which is the belt between the cloud platform and the battery system137

operators, is responsible for inspecting and visualizing the data analytic results. Compared138

with the onboard BMS with little data visualization opportunities, the browser-based UI in139

our cloud BMS can provide not only the real-time status of the batteries but also histori-140

cal operation data with numerous display types and options, which helps the operators in141

scheduling maintenance and repair. With different kinds of alarm functions, which can be142

set up for the original and virtual data points, the operators can be informed by the UI as143

soon as the fault of the systems is identified, increasing the chances of preventing damaging144

5

Uoc Ut

C2C1

R1 R2

R0

Figure 2: Schematic of the extended Thevenin model.

effects and thus improving the system reliability and reducing the maintenance cost. In145

order to protect the data, the UI endpoints are accessible only via HTTPS and require user146

authentication.147

3. Battery modeling148

The numerous equivalent circuit models (ECMs), such as Rint model, Thevenin model,149

and nth RC networks model, have attracted a lot of interest in past years for real-time150

battery state estimation. These models use electrical circuit components, such as resistances,151

capacitances, and voltage sources, to mimic the dynamic response of a battery. Considering152

the balance between model accuracy and computation time, an extended Thevenin model,153

as shown in Fig. 2, is proposed in this paper to model the battery dynamics, which can be154

expressed as follows:155

U1 = − U1

R1C1

+I

C1

(1)

156

U2 = − U2

R2C2

+I

C2

(2)

157

Ut = Uoc − U1 − U2 − IR0 (3)

where I denotes the input current, Ut denotes the terminal voltage, Uoc denotes the open-158

circuit voltage which has a measurable nonlinear relationship with battery SOC, R0 is the159

ohmic resistance, R1,2 are polarization resistances, C1,2 are polarization capacitances, and160

U1,2 are voltage drops over R1,2. Based on the extended Thevenin model, state estima-161

tion and parameter identification algorithms will be introduced in the following sections to162

estimate the SOC and SOH of the battery.163

4. State-of-charge estimation with adaptive extended H-infinity filter164

4.1. Adaptive extended H-infinity filter165

H-infinity filters have shown high robustness and are widely studied in battery state166

estimation [12]. The adaptive extended H-infinity filter (AEHF) is an optimal estimator,167

which can be computed recursively using noisy input data in real-time to analyze and solve168

a wide class of state estimation problems. Zhang et al. [12] applied AEHF to estimate the169

SOC of the lithium-ion battery and the AEHF has shown its advantage compared with the170

6

Estim

atio

n P

roce

ss

Pre

dic

tio

n P

roce

ss

Ad

ap

tive

La

w

Linearization matrix

Error covariance

propagation

Stability check

Gain matrix

Output estimation

State estimation

update

Error covariance

update

Process noise

covariance matrix

Measurement noise

covariance matrix

Figure 3: Implementation flowchart of the adaptive extended H-infinity filter.

Kalman filters considering the uncertainty in battery dynamic models and noise statistics.171

Considering the discrete-time model of a general nonlinear system in a state-space form, we172

have173

xk+1 = Axk +Buk + wk (4)

174

yk = Cxk +Duk + vk (5)

where uk and yk represent the system inputs and outputs, xk denotes the system states, wk175

and vk are the system process noise and measurement noise, the matrices Ak, Bk, Ck, and176

Dk describe the system dynamics.177

The aim of H-infinity filters is to estimate the states zk = Lkxk by applying the game178

theory and to improve the algorithm robustness by estimating the covariance values using179

the covariance matching technique [11]. If xk are states to be estimated, then Lk is an180

identity matrix. The implementation flowchart of AEHF for processing state estimation is181

depicted in Figure. 3. The realization of the AEHF is divided into three sub-processes and182

is detailed as below.183

4.1.1. Estimation process184

In this process, the estimation of the states and outputs of the system are updated. The185

prior state estimation x−k and error covariance P−k are calculated by186

x−k = Ak−1x+k−1Bk−1 (6)

187

P−k = Ak−1Pk−1A>k−1 +Qk−1 (7)

where Qk−1 is the weighting matrix. Afterward, the observer stability criteria are checked188

by189 (P−k)−1 − θ−2

k L>k Lk > 0 (8)

where θk is the tuning parameter. Furthermore, the gain matrices are updated as follows:190

Re,k =

[Rk−1 0

0 −θ2kI

]+

[CkLk

]P−k[C>k L>k

](9)

7

191

Hk = P−k[C>k L>k

]R−1e,k (10)

192

Hs,k = P−k C>k

(Rk−1 + CkP

−k C

>k

)−1(11)

where Re,k and Hs,k are transition matrices and Hk is the H-infinity matrix. The estimation193

of the system output yk is provided by194

yk = Cx−k +Duk + vk. (12)

4.1.2. Prediction process195

In the prediction process, the state and error covariance matrix for the next time step is196

calculated by197

xk+1 = Axk +Buk +Hkek (13)

198

Pk =

(I −Hk

[CkLk

])P−k (14)

where ek represents the output estimation error as follows:199

ek = yk − yk. (15)

4.1.3. Adaptive process200

The tuning parameter θk and the weighting matrices Qk and Rk play important roles in201

H infinity filters and are adjusted in each time step as follows:202

θk = α√

max(eig(P−k))

(16)

203

Rk =1

N

k∑j=k−N+1

(eje>j − CjPjC>j

)(17)

204

Qk =1

N

k∑j=k−N+1

(Hs,keke

>j H

>s,j − Aj−1Pj−1A

>j−1

). (18)

4.2. SOC estimation with AEHF205

The SOC of the battery is defined as the ratio of the present remaining capacity to the206

nominal battery capacity CN , given by207

SOCt = SOC0 −1

CN

∫ t

t0

ηIdt (19)

where SOCt and SOC0 are the SOC of the battery at initial time t0 and current time t,208

respectively, η is the Coulomb efficiency, and I denotes the current flowing through the209

8

voltage source. With the transformation of (1) - (3) and (19) into a discrete-time system,210

the input matrix uk, output matrix yk and the state matrix xk as shown in (4) and (5), are211

defined as follows:212

uk = Ik (20)

213

yk = Ut,k (21)

214

uxk =[SoCk U1,k U2,k

]>. (22)

The parameter matrices Ak, Bk, Ck and Dk are defined by215

Ak =

1 0 0

0 exp(−∆tR1C1

)0

0 0 exp(−∆tR1C1

) (23)

216

Bk =

η∆tCN

R1

(1− exp

(− −∆tR1C1

))R2

(1− exp

(− −∆tR2C2

)) (24)

217

Ck =[dUoc,k(SoC)

dSoC| ˆSoCk

−1 −1]

(25)

218

Dk =[−R0

](26)

where Uoc,k (SOC) represents the nonlinearity between SOC and Uoc, which can be measured219

with experiments. The measurement and identification of the parameters in the parameter220

matrices will be introduced in the next sections.221

With the definitions of the system states and parameter matrices in (20) - (26), AEHF222

described with (6)−(18) can be applied to estimate the SOC of the battery.223

5. State-of-health estimation with particle swarm optimization224

5.1. Particle swarm optimization225

As a branch of Artificial Intelligence (AI), PSO is a meta-heuristic algorithm initially226

inspired by the choreography of a bird flock [23]. It can optimize a numeric problem by227

simulating the behaviors of swarms. PSO and its variants are becoming quite popular due228

to their high convergence rate and robustness. They are widely researched and utilized to229

optimize the nonlinear system parameters [16]. The main steps of PSO are summarized as230

follows.231

5.1.1. Random initialization232

The positions xi and velocities vi of all the particles are generated and initialized ran-233

domly, the dimensions of which are depending on the number of the parameters to be234

optimized.235

9

Sw

arm

evalu

atio

nR

andom

initia

lization

Evaluate fitness

function

Update

Pbest particle

Update

Position and velocity

Algorithm

parameters

Stopping criterion

Particle position

and velocity

Update

Gbest particle

Optim

ization

End

Figure 4: Implementation flowchart of the particle swarm optimization.

5.1.2. Swarm evolution236

At each iteration, each particle in the swarm is improved by two values, namely Pbest,237

and Gbest. Pbest represents the best solution in all previous generations of each particle and238

Gbest represents the best solution of all the particles in previous generations, also called the239

best global solution. Each particle updates its location xi and velocity vi by240

xi+1 = vi+1 + xi (27)

241

vi+1 = wvi + c1r1 (Pbest − xi) + c2r2 (Gbest − xi) (28)

where c1,2 are learning rates influencing the algorithm convergence performance, w is the242

inertia weighting factor, r1,2 are random values between 0 and 1. After updating the positions243

and velocities, the fitness function is evaluated for each particle to update the Pbest and244

Gbest. The iterated optimization process will stop when the predefined fitness value or the245

maximum iteration number is reached. The implementation flowchart of applying PSO for246

parameter identification is depicted in Figure. 4.247

5.2. SOH estimation with PSO248

The SOH of the battery is a metric to indicate the battery’s aging level. The commonly249

used SOH indices can be divided into two groups: capacity fade indices and power fade250

indices [24]. With battery aging, the value of the nominal capacity of the battery will de-251

crease because of the capacity loss mechanisms, resulting in the capacity fade of the battery.252

Meanwhile, the value of ohmic resistance and polarization resistances will increase, resulting253

in the power fade of the battery. In this work, the SOH indicating the battery’s capacity254

fade, SOHC , and the SOH indicating the battery’s power fade, SOHR, are determined by255

PSO synchronously.256

The SOHC of the battery is usually defined as follows:257

SOHC,t =CN,tCN,0

(29)

10

SOC

SOHSOH SOH

TT T

Figure 5: Implementation strategy of AEHF-based SOC estimation and PSO-based SOH estimation. TheAEHF will run continuously for all time. The battery parameters and SOH are updated after each periodof T by running the PSO based on the field data in the previous period. This process is repeated for theduration of use.

where CN,0 and CN,t are the nominal capacity of the battery at battery’s Begin of Life (BoL)258

and current time t. The SOHR of the battery is investigated from the ohmic resistance259

increasing, namely260

SOHR,t =R0,t

R0,0

(30)

where R0,0 and R0,t are the ohmic resistance at battery’s BoL and current time t. It is worthy261

of notifying that the identification of the aging level of the battery based on the increase262

of the polarization resistances R1 and R2 can also be implemented, which is not introduced263

in detail in this work. The End of Life (EoL) of the battery regarding the capacity fade is264

reached when the value of SOHC,t reaches 80%, as shown in (29). However, the EoL can also265

be defined as the time that the value of the ohmic resistance increases 30%, i.e., the value of266

SOHR,t reaches 1.3, considering the battery’s power fade, as shown in (30). Therefore, it is267

important to estimate both SOHC,t and SOHR,t at the same time, which were not provided268

by most of the literature.269

The ECM parameters, such as nominal capacity CN , resistances R0,1,2, and capacitances270

C1,2, can be identified based on the measurement data of current and voltage with PSO271

according to the fitness function F as follows:272

F =1

N

N∑i=1

(Ut,i − Ut,i

)2

(31)

where N is the total number of the data points, Ut,i is the measured battery terminal voltage,273

Ut,i is the estimated battery terminal voltage with the identified parameters. The PSO will274

stop the optimization process when the values of the estimated parameters converge. The275

identified CN and R0 in the final Gbest are then used to calculate the SOHC and SOHR of276

the battery in (29) and (30).277

Considering that the aging mechanism is slower compared to the capacity change, the278

parameter identification with PSO was designed to run based on a period of field data. The279

identified parameters CN , R0,1,2, and C1,2 can not only be used to estimate the battery’s280

SOH but can also be injected back into SOC algorithms to improve the estimation accuracy281

with accurate model parameters. Figure. 5 presents a strategy in which the SOC and SOH282

estimation can be implemented together online.283

11

Voltage measurement Temperature measurement

Current measurement BMS-Slave

(a)

(b)

Figure 6: (a) UPS system connected with the cloud BMS prototype A. (b) Battery test bench for lithium-ionand lead-acid batteries connected with the cloud BMS prototype B to validate the proposed SOC and SOHalgorithms.

6. Experimental set-up284

To validate the functionalities and stability of both hardware and software, we designed285

and produced two prototypes of the proposed cloud BMS. As the dominating battery tech-286

nology nowadays for the UPS market is the lead-acid battery, a UPS system consisting of287

lead-acid batteries was chosen to validate the monitoring functionalities of the cloud BMS.288

Furthermore, the proposed battery diagnostic algorithms were validated with different bat-289

tery technologies, i.e., lithium-ion battery and lead-acid battery, considering the increasing290

market share of lithium-ion batteries and application potential of the cloud BMS in mobile291

battery systems, e.g., electric vehicles.292

6.1. Field validation of the cloud BMS functionalities293

The prototype A of the cloud BMS was connected with a UPS system in Denmark, as294

shown in Figure. 6 (a). The battery system consists of four 12 V, 92 Ah Hawker Enersys295

AGM lead-acid batteries connected in series, as summarized in Table. 1. The UPS system296

was under operation and kept at float charge. The voltage and temperature of four batteries297

were monitored in Germany remotely with the developed UI in real-time to validate the298

performance of the system’s functionalities.299

12

Hawker Enersys Yuasa NP7-12 Samsung INR18650-35e

Chemistry Lead-acid Lead-acid Lithium-ionCapacity [Ah] 92 7 3.40Norminal voltage [V] 12 12 3.60Cell dimension [mm] 395 x 105 x 264 151 x 65 x 94 65.25 x 18.55Weight [kg] 27.60 2.20 0.05

Table 1: Specifications of the batteries for experimental validations of the cloud BMS.

0 20 40 60 80 100 120Time in min

−4

−2

0

2

4

Curre

nt in

A

(a)

0 20 40 60 80 100Time in min

−10

−8

−6

−4

−2

0

2

Curre

nt in

A

(b)

Figure 7: Current profile for experimental validation of the AEHF-based SOC estimation algorithm. (a)Dynamic pulse profile for a multi-use stationary battery system. (b) Real-world driving data-based currentprofile for the mobile battery system.

6.2. Experimental validation of the AEHF-based SOC estimation algorithm300

To validate the proposed AEHF-based SOC estimation algorithm experimentally, we301

installed prototype B of the cloud BMS on batteries with different chemistries in our labora-302

tory in Germany. The lead-acid batteries and lithium-ion batteries were applied to verify the303

accuracy and stability of the algorithm in multi-use stationary battery systems and mobile304

battery systems, respectively.305

The stationary battery system is composed of four 12 V, 7 Ah Yuasa AGM lead-acid306

batteries, as summarized in Table. 1, connected in series. This 48 V battery system was con-307

13

0 50 100 150 200 250 300 350Time in min

−10.0

−7.5

−5.0

−2.5

0.0

2.5

5.0

7.5

10.0

Curre

nt in

V

Current

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

Volta

ge in

V

Voltage

(a)

0 100 200 300 400 500 600 700Time in min

−10.0

−7.5

−5.0

−2.5

0.0

2.5

5.0

7.5

10.0

Curre

nt in

V

Current

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

Volta

ge in

V

Voltage

(b)

Figure 8: Characterization test in the cyclic aging test. (a) Pulse test with 0.5 C, 1 C, and 2 C at 80% SOC,50% SOC, and 20% SOC. (b) Capacity test with 0.33 C.

nected with a Digatron battery tester with 100 V, 50 A test circuits, as shown in Figure. 6 (b).308

To validate the proposed AEHF-based SOC estimation algorithm for the mobile application,309

a lithium-ion battery, Samsung INR18650-35e, was connected with a Digatron battery tester310

with 5 V, 20 A test circuit and tested in a temperature chamber. The cathode and anode311

material of the lithium-ion battery is Lithium-Nickel-Cobalt-Aluminium-Oxide (NCA) and312

graphite, respectively. The specifications of the battery are summarized in Table. 1. Before313

the validation test of the cloud BMS diagnostic algorithms, battery characterization tests,314

e.g., capacity tests and OCV tests were conducted for both batteries.315

Considering the multi-use tendency of the stationary battery systems, we applied a316

dynamic current profile consisting of charging and discharging current pulses with amplitudes317

from 1 A to 5 A to validate the proposed SOC estimation algorithm with the lead-acid318

battery, as shown in Figure. 7 (a). In contrast, a real-world driving data-based test profile319

was applied to the lithium-ion battery considering its high demand in automotive battery320

systems. As shown in Figure. 7 (b), the maximum discharging and charging current of the321

test profile is 2 A and 9.6 A, respectively.322

14

6.3. Experimental validation of the PSO-based SOH estimation algorithm323

To validate the PSO-based SOH estimation algorithm, we carried out aging tests to324

age the same lithium-ion battery as introduced in Section 6.2. Cycling of the battery was325

conducted at a constant temperature of 25C. In each aging cycle, the battery was discharged326

with the real-world driving data-based test profile, as depicted in Figure. 7 (b), from 90% to327

10% SOC. Then the battery was charged with 0.33 C constant current from 10% SOC back328

to 90% SOC. After every 30 aging cycles, a characterization test consisting of a pulse test and329

a capacity test was conducted at 25C, as shown in Figure. 8. Within the multi-pulse test,330

a dynamic profile consisting of multi 10s charging and discharging pulses at three different331

SoC levels, i.e., 80%, 50%, and 20%, with 0.5C, 1C, and 2C was conducted. After that,332

the battery cell was discharged and charged under a capacity test with a constant current333

of 0.33 C between its cut-off voltages. The variance of the temperature does influence the334

value of the battery parameters, e.g., CN , R0,1,2, and C1,2. This temperature relationship can335

be modeled by parameterizing the battery model under the same aging level with different336

temperatures, which is out of the scope of this work.337

7. Results and discussions338

7.1. Field validation of the cloud BMS functionalities339

The validation results of the cloud BMS functionalities, as proposed in Section 2, are340

depicted in Figure. 9, where about 160 hours of the voltage and temperature measurement341

data with the cloud BMS are visualized with the UI. It is clear that the data were collected342

continuously, and the sensors have caught the variation of voltage and temperature of each343

battery in the system. The real-time remote monitoring of the battery system with the344

cloud BMS prototype A was verified.345

Within the field validation of the cloud BMS, the hardware of the system, consisting of346

the BMS-Slave, the IoT component and the data logger in the cloud were working together347

with the proposed system’s software, successfully verifying the functionalities of the cloud348

BMS, e.g., data sensing, data collection, data storage, and data visualization. The cloud349

BMS enables direct and real-time visualization and monitoring capability of large scale350

battery systems for the users and battery experts, which can also be adapted with new351

communication technologies, e.g., 5G technology, for the mobile battery systems, reducing352

the battery aging and improving the battery’s safety, reliability and performance.353

7.2. Experimental validation of the AEHF-based SOC estimation algorithm354

The validation results of the AEHF-based SOC estimation algorithm, as proposed in355

Section 4, are depicted in Figure. 10. While the real voltage value was measured directly,356

the reference value of SOC was calculated by Coulomb counting with high-accuracy current357

sensors of battery tester with accurate SOC initial value.358

The validation results for the lead-acid battery are shown in Figure. 10 (a), (b), and359

(c). To check the self-regulation ability and the stability of the SOC algorithm, we applied360

an erroneous initial value of SOC to the cloud BMS. Both voltage estimation and SOC361

estimation can converge to the real value very fast. With a relatively long operation period,362

15

0 20 40 60 80 100 120 140 160Time in h

12.0

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Ut, 1

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rature in

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0 20 40 60 80 100 120 140 160Time in h

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rature in

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(b)

0 20 40 60 80 100 120 140 160Time in h

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mpe

rature in

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(c)

0 20 40 60 80 100 120 140 160Time in h

12.0

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Ut, 4

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rature in

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T4

(d)

Figure 9: Voltage and temperature measurement of the stationary battery system with the cloud BMSprototype A. (a) Field data collected from battery 1. (b) Field data collected from battery 2. (c) Field datacollected from battery 3. (d) Field data collected from battery 4.

the voltage and SOC estimation can always follow the reference value of the battery with363

mean absolute error (MAE) of 0.01 V and 0.06%. The validation results for the lithium-364

ion battery under a real-world driving cycle are depicted in Figure. 10 (d), (e), and (f).365

Similarly, an erroneous initial value of SOC was applied to check the self-regulation ability366

and stability of the algorithm for the lithium-ion battery. Both the estimation of voltage and367

SOC converged fast to the reference value. Within 90% DOD range, the voltage and SOC368

estimation of the lithium-ion battery can always match with the reference values with MAE369

of 0.01 V and 0.49%, respectively. The validation results show that the proposed AEHF-370

based SOC estimation algorithm is accurate and stable for both lead-acid and lithium-ion371

batteries in stationary and mobile application scenarios.372

7.3. Experimental validation of the PSO-based SOH estimation algorithm373

The validation results of the PSO-based SOH estimation algorithm, as proposed in Sec-374

tion 5, are presented in Figure. 11. The results of the parameter identification for the battery375

at Begin of Life (BoL) are visualized as an example in Figure. 11 (a), (b), (c), and (d).376

With the identified battery parameters, e.g., CN , R0,1,2, and C1,2, identified by the pro-377

posed PSO approach, the extended Thevenin model is able to estimate the voltage of the378

16

0 20 40 60 80 100 120Time in min

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ReferenceEstimation

50.0 52.5 55.0 57.5 60.0 62.5 65.05152535455

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0.0

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C in %

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38 40 42 4455.057.560.062.565.0

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(f)

Figure 10: Validation results of the AEHF-based SOC estimation algorithm with a lead-acid battery and alithium-ion battery. (a) Validation results of the voltage estimation for the lead-acid battery. (b) Validationresults of the SOC estimation for the lead-acid battery. (c) The absolute error of voltage and SOC estimationfor the lead-acid battery. (d) Validation results of the voltage estimation for the lithium-ion battery. (e)Validation results of the SOC estimation for the lithium-ion battery. (f) The absolute error of voltage andSOC estimation for the lithium-ion battery.

battery accurately with the maximum absolute error of 0.11 V as shown in Figure. 11 (a)379

and (b), indicating the accuracy of the parameter identification. As shown in Figure. 11380

(c), the fitness value, as described in (31), decreased very fast with the increase of the itera-381

17

0 20 40 60 80 100Time in min

2.6

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ge abs

olute error in V

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alue

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4 V2

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3.300

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3.475C N

in Ah

CN

20

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mΩ

R0

(d)

0 100 200 300 400 500N

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MeasurementEstimation

(e)

0 100 200 300 400 500N

1.00

1.05

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SOHR

MeasurementEstimation

(f)

Figure 11: Validation results of the PSO-based SOH estimation algorithm. (a) Validation results of thebattery voltage estimation with the parameters estimated by PSO at BoL. (b) The absolute error of voltageestimation with the parameters estimated by PSO at BoL. (c) Convergence performance of the fitness valuefor the battery at BoL. (d) Convergence performance of the capacity and ohmic resistance for the batteryat BoL. (e) Comparison between the measured and estimated SOHC of the battery during aging test. (f)Comparison between the measured and estimated SOHR of the battery during aging test.

tion number and converged to the minimum value within 600 iterations. This phenomenon382

indicates that the PSO-based algorithm is working to adapt the parameter values within383

the parameter boundaries to reduce the error between the measured and modeled voltage384

18

Cycle number 0 10 40 70 100 130 160 190 220 250 280 310 340 370 400 430 460 490 520

CC [Ah] 3.39 3.34 3.31 3.27 3.25 3.23 3.20 3.19 3.19 3.11 3.11 3.10 3.09 3.08 3.07 3.07 3.06 3.05 3.03CN [Ah] 3.43 3.38 3.35 3.29 3.27 3.25 3.24 3.19 3.16 3.14 3.11 3.10 3.07 3.07 3.08 3.05 3.00 3.00 3.01

Table 2: List of cell capacity degradation index CC and CN during cell aging, where CC is the measuredcell capacity with 0.33 C discharging in characterization test and CN is the output of the PSO-based SOHestimation algorithm.

Cycle number 0 10 40 70 100 130 160 190 220 250 280 310 340 370 400 430 460 490 520

RC [mΩ] 26.7 27.8 28.0 28.2 28.5 27.7 29.2 29.6 29.7 30.8 30.9 29.9 31.5 31.8 32.2 31.3 32.7 32.9 33.3R0 [mΩ] 27.2 27.8 27.9 28.5 28.8 29.3 29.8 30.3 29.9 30.1 30.6 30.7 31.1 31.2 32.1 31.0 32.7 32.7 32.6

Table 3: List of cell impedance degradation index RC and R0 during cell aging, where RC is the measuredcell ohmic resistance with 2 C current pulse at 80% SOC in characterization test and R0 is the output ofthe PSO-based SOH estimation algorithm.

of the cell. The capacity of the battery CN,t also converged fast to a stable value within385

600 iterations, as shown in Figure. 11 (d). Meanwhile, the ohmic resistance R0,t of the386

battery, which is used in this work as an index for the power fade, also showed a fast con-387

vergence performance. The final estimated values of CN and R0 are 3.43 Ah and 27.2 mΩ,388

respectively.389

Based on the real-world driving data, as shown in Fig. 7, the cell parameters, i.e., CN390

and R0, are identified with the proposed PSO-based algorithm at 19 different aging status391

within 540 aging cycles. As a benchmarking for the capacity estimation, the measured392

capacity of the battery with Coulomb counting under C/3 discharging was calculated as CC393

from the characterization tests. The measured capacity CC and estimated capacity CN at394

19 different aging status are summarized in Table 2. According to (29), the measured and395

estimated SOHC are depicted in Figure. 11 (e). It is clear that the SOHC of the battery396

decreased continuously from 1 to 0.89 within 520 aging cycles, indicating the capacity fade397

of the battery. The estimated SOHC matches with the measured SOHC with MAE of 0.74%.398

Similarly, the ohmic resistance of the battery under 2 C current pulse at 80% SOC was399

calculated as RC from the characterization tests for benchmarking. The measured ohmic400

resistance RC and estimated ohmic resistance R0 at 19 different aging status are summarized401

in Table 3. Both RC and R0 show the same increasing trend during cell aging. According402

to (30), the measured and estimated SOHR are depicted in Figure. 11 (f). The SOHR of403

the battery increased from 1 to 1.25 within 520 aging cycles, showing the power fade of the404

battery during aging. The estimated SOHR matches with the measured SOHR with MAE405

of 1.70%.406

With the experimental validation, it is clear that the proposed PSO-based SOH estima-407

tion algorithm can provide clear information of both capacity fade and power fade of the408

battery, highlighting its application potential. The limitation of the proposed approach is409

the relatively high computation burden because of the iterated simulation of the battery410

model. However, the ultra-high computation and data storage capabilities of the proposed411

cloud BMS is able to implement this advanced SOH algorithm and open the window into412

19

the battery’s capacity and power fade synchronously, which can be further used to take413

actions to optimize the operation scenarios, enhance the battery’s performance and extend414

their service lives.415

8. Conclusions416

A cloud battery management system was developed based on the concept of the Internet417

of Things and cloud computing in this work to build up the digital twin for battery systems418

in the cloud and improve the computation power, data storage capability and reliability of419

the BMS. We believe that this is the first work that shows both the technical details of a420

cloud BMS and the operation results of the cloud-suited advanced battery diagnostic algo-421

rithms in this platform, which is a big step to bring digital twin from theory to real industrial422

application, ensuring intelligent monitoring and utilizing the stationary and mobile battery423

systems. Furthermore, SOC and SOH estimation algorithms were developed based on an424

extended Thevenin model with AEHF and PSO, respectively, and were validated experi-425

mentally with the cloud BMS prototypes for both lithium-ion and lead-acid batteries. It is426

also the first work providing both capacity fade and power fade of the battery synchronously427

with the PSO. In future work, machine learning algorithms will be developed based on the428

collected data from the battery systems in the cloud for precise lifetime prediction and429

system optimization purposes.430

Acknowledgment431

This work was supported within the project BSMS by the European EFRE program432

(grant number EU-1-1-081) and within the project EVERLASTING from the Horizon433

2020 program by the European Union (grant number EVERLASTING-713771).The authors434

would like to thank Voltia Automotive for the real-world driving profile, Patrick Borycka435

from BatterieIngenieure GmbH for his contributing work and support at hardware design,436

and Erik Brummendorf from aedifion GmbH for his support at the cloud platform. Thanks437

are also given to Decheng Cao and Ruilin Li for their support at simulation works.438

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