Comparison of Battery Management Approaches forEnergy Flow Optimization in Microgrids

Mario VasakUniversity of Zagreb, Faculty of Electrical

Engineering and ComputingLaboratory for Renewable Energy Systems

Unska 3, 10000 Zagreb, CroatiaEmail: mario.vasak@fer.hr

Goran KujundzicPublic Enterprise Croatian Telecom JSC

Kneza Branimira bb, 88000 Mostar,Bosnia and Herzegovina

Email: goran.kujundzic@hteronet.ba

Abstract—The recently emerged approaches to energy flowoptimization in microgrids focus on planning how much energyneeds to be inserted or exerted from a microgrid energy storageunit in a given fixed time to achieve maximum benefit forthe microgrid operation (economical, environmental, etc.). Asa result of this planning there is an energy flow commandissued from the level of microgrid energy flows optimizationtowards the management systems of individual energy storagesin the microgrid. As the energy flow command can be achievedby different control sequences on the management level of thestorage unit, there is a need to assess the optimal controlsequence for the energy storage as well as to see how thealternative, simplified approaches to realize the energy flowcommand perform in comparison. In this work we focus on thebattery management system that is subordinated to the microgridenergy flow optimization and compare the approaches of theoptimal battery current, constant current and constant power,whereas the optimality is formulated with respect to residual stateof charge available after the energy flow command is realizedon the battery. On a selected example of valve-regulated lead-acid (VRLA) battery we show that these approaches to batterymanagement yield comparable results which suggests that thementioned simplified approaches are quite near to the optimalones with respect to the amount of residual state of charge. Wefurther show how the dynamical model of the optimally managedbattery looks like for the case of battery representation via ahybrid electrical model.

Index Terms—microgrid, hybrid electrical model, energy flowoptimization, battery management system, state of charge

I. INTRODUCTION

A microgrid is the integration of loads, energy resources,and storage devices. From the operation point of view, a mi-crogrid is counted as an independent entity that can work eitherin grid-tied or islanded mode. Microgrids energy resources caninclude utility connection, micro gas turbines, and renewablegenerations such as wind turbines and photovoltaic systems.It is expected and desirable that a considerable amount ofdemand for each microgrid is supplied by its local generation.A battery as a microgrid part can provide a substantial supportfor the operation of the corresponding microgrid system [1],[2], [3]. Battery is a component that converts chemical energycontained in its active materials into electricity using a singleelectrochemical oxidation-reduction reaction, and vice versa.Valve-regulated lead-acid (VRLA) batteries are still the op-

timal choice for telecommunication base stations consideringprice and service life for telecommunications and microgrids[4].

Energy flow optimization in microgrids focusses on plan-ning how much energy needs to be inserted or exerted froma microgrid energy storage unit in a fixed amount of timeto achieve maximum benefit for the microgrid operation [5],[6], [7]. In this respect, a considerable attention is directedto development of better optimization algorithms and suitablemodelling frameworks [8], [9]. Several metaheuristic andheuristic algorithms are developed to solve the power dispatchproblem for microgrids, such as genetic algorithms [10], [11],[12]. These methods implement more complex models but theyare not able to guarantee the optimality of the found solution.

Battery management system (BMS) is a key element tomake utilization of the battery in the telecommunicationpower systems, uninterruptible power supplies (UPS), renew-able energy systems, electric vehicles (EVs) and microgridssafe, reliable, and efficient. The BMS not only manages theoperational conditions of the battery to prolong its lifetime andguarantees its safety but also provides accurate estimation ofthe state of charge (SOC) and state of health (SOH) for theenergy management modules [1], [13]. The main function ofthe BMS is to protect the battery from operating at conditionsthat are harmful to either the battery or the users or both.

The time and efficiency of VRLA battery charging anddischarging are becoming increasingly important parametersin evaluating battery performance in the microgrids. Batterycharge efficiency cannot be considered a simple inverse ofbattery discharge efficiency. Battery charge efficiency is de-fined as the percent of energy stored by a battery chargedat a given power for a unit of time [14]. So far, charge anddischarge efficiency of VRLA batteries are considered constantdepending on charge and discharge power in the microgrids.Constant efficiency in both cases causes errors in predictionof stored and delivered energy from the batteries during theoptimization of battery operation in the microgrids. In [5],[15] the charge efficiency of a VRLA battery stack is equal tothe discharge efficiency and they are constant for the wholerange of charging and discharging powers. Also, authors in[13] and [16] considered the discharge efficiency is higher

than the charge efficiency, but they are also constant for allcharge and discharge powers.

In addition, all the aforementioned papers disregard or donot exploit the operation of the storage management systemthat is subordinated to the microgrid energy flow optimization.In the storage management system, the operating efficiencyitself can be maximized by maximizing the storage state atthe end of the time interval during which a desired amountof energy needs to be exchanged between the microgridand the storage. We show in the subsequent developmentsthat charging and discharging efficiency is a parameter thatneeds not to be characterized explicitly in the model of the(optimally) managed storage which is actually relevant formicrogrid energy flow optimization.

In this work we focus on the BMS that is subordinatedto the microgrid energy flow optimization and compare theapproaches of the optimal battery current, constant current andconstant power approaches to BMS operation. The optimalityis formulated with respect to residual SOC available afterthe energy flow command is realized within the BMS. Theseapproaches are realized based on simulations using the hy-brid electrical model of a VRLA battery stack. Simulationsare performed with different initial SOC for a predefinedamount of time equal to the sampling time of the energyflows optimization level, with different energy flow commandspresumed to be obtained from that level. The aim of thispaper is twofold: (i) to compare performance of the differentapproaches to battery management with the optimal one, and(ii) to characterize the relevant mathematical model of theBMS for the energy flows optimization level.

The major paper contribution is in introducing battery man-agement that completely adheres to commands of energy flowsfrom/to the battery system, and in a preliminary simulations-based analysis of such an approach to battery management.

This paper is organized as follows: Section II presentsenergy flows optimization in a microgrid set-up. Section IIIpresents the hybrid electrical model of a VRLA battery,while Section IV presents the optimal control problem forVRLA battery management in a microgrid. Section V presentssimulation results and comparison of optimal and alternativeapproaches to battery management in the setup of microgridenergy flows optimization. Section VI concludes the paper.

II. MICROGRID AND BATTERY MANAGEMENT SETUPS

A microgrid effectively integrates (i) distributed generationsources such as photovoltaic panels, small wind turbines, fuelcells, diesel and gas microturbines etc., (ii) distributed energystorage devices such as batteries, supercapacitors, flywheelsetc., and (iii) critical and non-critical loads. Its operationalgoals majorly depend on whether the connection with theutility grid exists or does not exist. Energy storage devicesare employed to compensate for the power shortage or surpluswithin the microgrid [5].

Fig. 1 shows a schematic diagram of energy flows optimiza-tion in a microgrid and its subordinated storage managementsystems, the battery management system being one of them.

There is an energy flow command issued from the level ofmicrogrid energy flows optimization towards the managementsystems of individual energy storages in the microgrid.

For the case of a battery storage, SOC is an indicatorthat represents the available charge stored in the batterycompared to the full capacity charge of the battery [16],[17]. Charging/discharging power of the considered VRLAbattery stack as well as its SOC will be dynamically modelledvia the hybrid electrical model (2)-(4) of the battery, brieflyintroduced in the following section together with the relevantreferences [4]. For ease of exposition of the basic principles,self-consumption (losses) of the power converter between thebattery and the microgrid are neglected.

III. HYBRID ELECTRICAL MODEL

In this paper a hybrid electrical model of a VRLA batteryis used for charging/discharging simulations.

Hybrid electrical model (Fig. 2) can be presented by afull-capacity capacitor (Ccapacity), a self-discharge resistor(Rself ), and an equivalent series resistor (the sum of Rserial ,Rfast and Rslow). It incorporates the best characteristics fromThevenin, Impedance and R-B electrical models [18], [19].

The charge of capacitor Ccapacity represents the wholecharge stored in the battery, i.e. the scaled battery SOC. Itcan be calculated by converting the nominal battery capacityin Ahr to charge in Coulomb units and its value is defined as[20]:

Ccapacity = 3600 ·Kpnom · k1(cycle) · k2(temp), (1)

where Kpnom is the nominal battery capacity in Ahr,k1(cycle) is a correction factor for number of charge-dischargecycles the battery experienced, k2(temp) is a temperature-dependent correction factor. Correction factor that definescapacity dependence on the current value is not expressed in(1). In this paper the capacity degradation due to charging witha high current [21] is neglected since the maximum currentvalue is kept below manufacturer-declared one-hour chargecurrent. By setting the initial voltage across Ccapacity(VSOC)equal to 1 or 0 V, the battery is initialized to its fully charged(i.e., SOC is 100%) or fully discharged (i.e., SOC is 0%)state.

The self-discharge resistor Rself represents leakage whenthe battery is stored over a long period. Rself is a functionof SOC, temperature, and, frequently, of the number ofexperienced charge/discharge cycles [22]. If the self-dischargeis neglected, the hybrid electric model shown in Fig. 2, canbe described with the following continuous-time state-spacemodel: VOC

Vfast

Vslow

=

0 0 00 −1

Rfast·Cfast0

0 0 −1Rslow·Cslow

· VOC

Vfast

Vslow

+

−a

Ccapacity1

Cfast1

Cslow

· Ibatt, (2)

POWERCONVERTER

POWERCONVERTER

POWERCONVERTER

WATER

ELECTROLYSER

POWERCONVERTER

POWERCONVERTER

POWERCONVERTER

Batteries

Supercapacitors

Flywheel

PV panels Wind turbine

Fuel cells stack Hydrogen tank

Utility grid Critical loadsNon-critical loads

Distributedloads

Energy flows optimizationon the microgrid level

Storagemanagement

Storagemanagement

Storagemanagement

Measuredstoragevariables

Powerconvertercommand

Storagestate

Energy flowcommand

Measuredstoragevariables

Powerconvertercommand

Storagestate

Energy flowcommand

Storagestate

Energy flowcommand

Measuredstoragevariables

Powerconvertercommand

POWERCONVERTER

Main switch

Distributedstoragesystems

Fig. 1. A schematic diagram of energy flows optimization in a microgrid

Ubatt = VOC − Vfast − Vslow −Rserial · Ibatt, (3)

where Ubatt is the battery terminal voltage, Ibatt is thebattery current and Vserial, Vfast and Vslow are voltages atserial resistor, fast- and slow-transient RC parallel network,respectively. The open-circuit voltage (VOC) is defined usingthe following expression:

VOC = a · VSOC + b, (4)

where a and b define open-circuit voltage dependence onSOC.

Rself

Ccapacity

VSOC

I batt

Voc(V

SOC)

Rserial

Ibatt

Rfast

Cfast

Rslow

Cslow Ubatt

Fig. 2. Hybrid electrical model of a battery

IV. OPTIMAL CONTROL AND ALTERNATIVE APPROACHESFOR VRLA BATTERY MANAGEMENT IN A MICROGRID

In order to get an accurate SOC model which will con-tain variable charge/discharge efficiency depending on thecharge/discharge energy, optimal battery current (OC), con-stant current (CC) and constant power (CP) approaches areapplied to operation of BMS that fully adheres to providedenergy flow commands. The BMS receives from the microgridenergy flows optimization level the control commands onenergy flows that need to be exchanged between the batteryand the microgrid in the defined time T . After the energy flowcommand is realized within the BMS in the time interval T ,the best battery management approach is the one which attainsthe maximal residual SOC.

The OC profile is obtained by solving the following opti-mization problem:

maxIbatt(0),...,Ibatt(N−1)

J = SOC(k +N)

s.t.E =

∫ T

0

Ubatt Ibatt dt = Ecom.(5)

where Ecom is the energy flow commanded to the BMS, with

x(k), k ∈ Z the value x(k · TBMS) is denoted (x is eitherIbatt, Ubatt or SOC), whereas TBMS = T/N is the samplingtime of the BMS.

The OC profile changes with sampling time of BMS opti-mization TBMS .

V. COMPARISON OF OPTIMAL AND ALTERNATIVEAPPROACHES TO VRLA BATTERY MANAGEMENT IN A

MICROGRID

Simulations of the charging/discharging using thecontinuous-time hybrid electric model (2) implementedin Matlab/Simulink environment are carried out. Simulationsof charging/discharging are preformed in duration of T andthe different initial conditions for charging SOCch0 anddischarging SOCdisch0. It is necessary to store or deliverthe different commanded amount of energy Ecom from thebattery with the sampling time T . All the parameters usedfor simulations are shown in Table I. In all simulations initialvalues of Vfast and Vslow voltages are set to 0.

The CC profile is obtained using Matlab functionfminsearch in order to store or deliver the commandedenergy flow Ecom from the battery.

The CP approach uses the ratio of the commanded energyinterpreted as average power required over time T and batteryterminal voltage for determination of current value in contin-uous time.

The OC control sequence of optimal problem (5) is ob-tained using Matlab function fminsearch with sampling timeTBMS . The CC value is selected as initial OC value andthe value of optimal cost is directly determined using thesimulation scheme of the hybrid electrical model.

The important battery constraints during the charging anddischarging are Ubattmax – the upper threshold voltage limit,Ubattmin – the lower threshold voltage limit, Ibatt−c – themaximal charge current, Ibatt−d – the maximal dischargecurrent and maximal and minimal SOC. These values aregiven by manufacturer data sheet [23] and additionally batteryconstraints can be expressed as follows:

Ubattmin ≤ Ubatt(k) ≤ Ubattmax, k = 0, . . . , N − 1,

−Ibatt−c ≤ Ibatt(k) ≤ Ibatt−d, k = 0, . . . , N − 1,

0 ≤ SOC(k) ≤ 100%, k = 1, . . . , N.

(6)

In order to get new energy flow Ecom values which willretain Ubatt(k), Ibatt(k) and SOC(k) under aforementionedconstraints, simulation analysis of the previously obtainedenergy flow values are applied.

The battery states and parameters of VRLA 48 V batterystack 45 Ah are determined from experimental data [23], usingrapid method and resting periods during the charging anddischarging. The complete procedure is described in [4] andobtained values of the battery states and parameters are givenin Table II. These identified parameters are used in the hybridelectric model (2).

The simulation results of model charging/discharging forthe OC approach are shown in Fig. 3. One may see thecontinuity of optimal next SOC values around the zero

charging/discharging energy, unlike previous studies on theenergy flow optimization in a microgrid [5], [6], [7].

The obtained complete model of BMS operation, being

SOC(k + 1) = f(SOC(k), Ecom(k)) (7)

is crucial for correct posing of the energy flow managementproblem for the microgrid. The function f seems to becontinuous and its domain can be approximated with a convexset without high conservativeness – the exact proof of this is asubject of further research on this topic. These properties canmake the function f very appropriate for usage on the levelof microgrid energy flows optimization.

Fig. 4 shows the simulation differences of residual SOCbetween the OC approach and the CC approach, while Fig.5 shows the same between the OC approach and the CPapproach. These differences can be expressed as follows:

J∗(SOC(k), Ecom(k))− SOCCC(SOC(k), Ecom(k)), (8)

J∗(SOC(k), Ecom(k))− SOCCP (SOC(k), Ecom(k)), (9)

where J∗(SOC(k), Ecom(k)), SOCCC(SOC(k), Ecom(k)),SOCCP (SOC(k), Ecom(k)) are residual SOC values of OC,CC and CP approaches, respectively. SOC(k) is initial SOCvalue for charging or discharging. Ecom is commanded energy

TABLE ITHE SIMULATION PARAMETERS

Symbol Description Value

Ecom Commanded energy flow -1000 – 1000 WhSOCch0 Initial SOC value for

charging0 – 90 %

SOCdisch0 Initial SOC value for dis-charging

10 – 100 %

N Optimization length 60 minT Sampling time of micro-

grid energy flows opti-mization

60 min

TBMS Sampling time of BMSoptimization

1 min

−1000

−500

0

500

1000 020

4060

80100

0

20

40

60

80

100

SOCk(%)

Ecom(Wh)

SOCk+1(%)

Charging/discharging− Optimal current

Fig. 3. Simulation results of charging/discharging - the OC approach

TABLE IITHE HYBRID ELECTRICAL MODEL PARAMETERS

Symbol Description Value

Rserial Serial resistor 0.1395 Ω

Rfast Fast-transient resistor 0.0806 Ω

Rslow Slow-transient resistor 0.0465 Ω

Rself Self-discharge resistor 42.6 kΩ

Cfast Fast-transient capacitor 3400 FCslow Slow-transient capacitor 89145 F

a Open-circuit voltage pa-rameter

7.70

b Open-circuit voltage pa-rameter

44.20 V

−1000

−500

0

500

1000 020

4060

80100

0

0.01

0.02

0.03

0.04

0.05

SOCk(%)E

com(Wh)

dSOCk+1(%)

Optimal current −Constant current

Fig. 4. Simulation differences of residual SOC between the OC approachand the CC approach

−1000

−500

0

500

1000 020

4060

80100

0

0.01

0.02

0.03

0.04

0.05

SOCk(%)

Ecom(Wh)

dSOCk+1(%)

Optimal current −Constant power

Fig. 5. Simulation differences of residual SOC between the OC approachand the CP approach

flow which is considered negative during charging and positiveduring discharging.

The differences are very small in both cases, and slightlybetter results are achieved using the constant current approachfor charging/discharging compared to the constant power case.

It can be concluded that the CC approach for charg-

0 10 20 30 40 50 60−8

−7.5

−7

−6.5

−6

−5.5

−5

−4.5

−4

Time (min)

Chargecurrent(A)

Constant powerConstant currentOptimal current

SOCch0= 50 W

Ecom= −300 Wh

Fig. 6. Comparison of three different current approaches for charging

0 10 20 30 40 50 609

9.5

10

10.5

11

11.5

12

12.5

13

Time (min)

Dischargecurrent(A)

Constant powerConstant currentOptimal current

SOCdisch0= 70 %

Ecom= 500 Wh

Fig. 7. Comparison of three different current approaches for discharging

ing/discharging of a battery is very close to the optimal ap-proach considering the final effect – residual SOC – under thecondition of exactly the same energy exchanged. Figs. 6 and7 show the comparison of three different current approachesfor charging and discharging, respectively. The sampling timeof the energy flows management algorithm on the microgridlevel is T= 60 minutes. The initial SOC value is 50% andcommanded amount of energy Ecom is -300 Wh for chargingwhile for discharging their values are 70% and 500 Wh.

In further research charging/discharging using the constantcurrent approach will be used for determination of the explicitform of the function SOC(k + 1) = f(SOC(k), Ecom(k))with sampling time T . This discrete-time SOC model will beused for more accurate optimization of the microgrid energyflows. The variable efficiency of the charging/dischargingdepending on charge/discharge powers is in this way incor-porated in the BMS model.

VI. CONCLUSION

The article focusses on the Battery Management System(BMS) that is subordinated to microgrid energy flows opti-mization and receives from it energy flows commands thatneed to be realized between the battery and the microgridin a pre-fixed amount of time. A new approach to BMS isintroduced in this paper that completely adheres to issuedcommands of energy flows from/to the battery system, i.e.a sequence of charge/discharge currents is computed on thelevel of BMS such that the commanded energy flow is exactlyrealized in the required time. We use VRLA batteries for a casestudy and consider three different approaches to the introducedbattery management: optimal, constant current and constantpower, whereas the optimality is attained by maximizing theresidual state of charge after implementing the commandedenergy flow. We compare the three approaches and showthat both constant current and constant power approachesare close to the optimal in the entire operational range. Wefurther graphically characterize the explicit model of the entireBMS that should be used on the level of micorgrid energyflows optimization, i.e. the model between the current batterycharge state and energy flow command as inputs, and thenext battery charge state as output. By relying on graphicalrepresentation and without any formal proof, we point on themodel’s potentially very beneficial properties – continuity evenon the border between charging and discharging regime (zeroenergy flow command) as well as convexity of the modeldomain – which should be exploited in future developmentof microgrid energy flow optimization schemes.

ACKNOWLEDGMENT

This work has been supported by Croatian Science Founda-tion under the project No. 6731 (project 3CON – Control-based Hierarchical Consolidation of Large Consumers forIntegration in Smart Grids, http://www.fer.unizg.hr/3con.

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