Exploring Adaptive Reconfiguration to OptimizeEnergy Efficiency in Large-Scale Battery Systems

Liang He1, Lipeng Gu2, Linghe Kong1, Yu Gu1, Cong Liu3, Tian He41Singapore University of Technology and Design, Singapore

2Shanghai University of Engineering Science, Shanghai, China3The University of Texas at Dallas, Dallas, TX, USA4University of Minnesota, Minneapolis, MN, USA

Abstract—Large-scale battery packs with hundreds/thousandsof battery cells are commonly adopted in many emerging cyber-physical systems such as electric vehicles and smart micro-grids.For many applications, the load requirements on the batterysystems are dynamic and could significantly change over time.How to resolve the discrepancies between the output powersupplied by the battery system and the input power requiredby the loads is key to the development of large-scale batterysystems. Traditionally, voltage regulators are often adopted toconvert the voltage outputs to match loads’ required input power.Unfortunately, the efficiency of utilizing such voltage regulatorsdegrades significantly when the difference between supplied andrequired voltages becomes large or the load becomes light. Inthis paper, we propose to address this problem via an adaptivereconfiguration framework for the battery system. By abstractingthe battery system into a graph representation, we develop twoadaptive reconfiguration algorithms to identify the desired systemconfigurations dynamically in accordance with real-time loadrequirements. We extensively evaluate our design with empiricalexperiments on a prototype battery system, electric vehicledriving trace-based emulation, and battery discharge trace-basedsimulations. The evaluation results demonstrate that, dependingon the system states, our proposed adaptive reconfigurationalgo-rithms are able to achieve1× to 5× performance improvementwith regard to the system operation time.

I. I NTRODUCTION

Large-scale battery systems with hundreds or thousands ofbatteries are now widely used in electric vehicles [33], [36],energy storage in both macro [9] and micro [35], [42] smartgrids. For many of these applications, the load requirementonthe battery system is dynamic and could significantly changeover time [3], [28]. For example, depending on the drivingstates, the required voltage output of electric vehicles may varyfrom around70 V to more than700 V [3], [4], [23]. Suchdynamic loads make the problem of optimizing the energyefficiency of large-scale battery systems even more criticaland challenging, which is attracting increasing attentions offunding agencies [2], [8] (e.g., ARPA-E has awarded USD43million to 19 energy storage projects in 2012 [2]), and researchefforts [25], [27], [29].

A traditional method of handling dynamic loads is to adoptvoltage regulators to accept voltages supplied by the batterypack and adjust them to the required levels as the input to theloads [29], [41]. Unfortunately, the energy efficiency of voltageregulators may degrade significantly under two scenarios: (i)the difference between the supplied and required voltages islarge [23], [29], [34], and (ii ) the load is light and the systemoperates in a low power modes [41].

In contrast, dynamically adjusting the connections amongbatteries inside a battery system based on the real-time loadrequirements, referred as theadaptive system reconfiguration,is an alternative approach to handle the mismatch betweenthe supply and the requirement [19]. The adaptive recon-figuration not only avoids the low efficiency issue of thetraditional regulator-based approaches, but also increases thesystem robustness in that failed batteries can be by-passedwithout significantly degrading the system performance [23],[26]. Much research has been conducted to design batterysystems that offer higher configuration flexibility with fewersupplementary electronic components such as connectors andswitches [10], [20], [24], which has already been implementedin many off-the-shelf battery packs [8], [19], [24], [26], [39].

Besides offering configuration flexibility, there yet existsanother open challenge in maximizing energy efficiency, whichis to optimally determine battery system configurations inaccordance with real-time load requirements. Motivated bythis, in this paper, we advance the state-of-the-art by ad-dressing the following research question:with a given con-figuration flexibility of a battery system, how to adaptivelyidentify the optimal system configuration based on real-timeload requirements.We first prove that this problem isNP-Hard in general, and then we effectively solve it based ontwo empirical observations on battery systems. We propose anear-optimal adaptive reconfiguration algorithm based on theclassic 0-1 integer programming problem for the single loadchange scenario. For the scenario where multiple loads changesimultaneously, we extend our design with a greedy heuristicto identify the desired system configurations.

Our major contributions in this paper include• We propose a generic graph representation of large-scale

battery systems, which facilitates the optimization ofbattery system reconfigurations.

• For the scenario where only a single load changes,we transform the problem of identifying the optimalsystem configuration to apath selectionproblem in thecorresponding graph. We first prove that the problem isNP-Hard. We then propose a practically feasible solu-tion based on two empirical observations, which is ableto return a near-optimal system configuration throughDepth-First-Search with pruning method and 0-1 integerprogramming formulation.

• Extending our investigation to the scenario of multipleload changes, we propose a greedy solution to identify

the desired system configuration by greedily selectingthe load to be processed and progressively achieving thedesired configuration.

• We extensively evaluate our design with empirical experi-ments on a prototype battery system, electric vehicle driv-ing trace-based emulation, and battery discharge trace-based simulations. The evaluation results demonstratethat the proposed adaptive reconfiguration algorithms canachieve1× to 5× improvement in the system operationtime.

The paper is organized as follows. The problem statementis presented in Section II. The scenarios with a single andmultiple loads changes are investigated in Section III andSection IV, respectively. Our prototype implementation andsimulation/emulation results are presented in Section VI andSection VII, respectively. Section VIII reviews the literature.Section V briefly discuss practical issues relevant to ourdesign. Section IX concludes.

II. SYSTEM MODEL AND DESIGN PRINCIPLES

A. System Model

We consider large-scale battery systems that can supportmultiple loads simultaneously in this work [24], as shown inFig. 1. The battery pack in the system has multiple output ter-minal pairs, and each terminal pair is connected to a differentload. For theith terminal pair, we denote the load’s requiredvoltage and power as[V i, (1 + σ)V i] and P i respectively,whereσ is the tolerable jitter voltage ratio. The battery packconsists of a total number ofN batteries, and the voltage ofthe ith battery at the decision time isvi ∈ [vc, vf ], wherevcandvf are the battery cutoff voltage1 and full charge voltage,respectively.

Load 1

Load 2

Load x

Battery Pack

Fig. 1. System model.

1 2 3 4 50

100

200

300

400

500 1

1/2

1/31/4

1/5

# of Parallel Motors

Ope

ratio

n Ti

me

(min

)

Fig. 2. Reducing discharge current im-proves energy efficiency.

In practice, the probability for multiple loads to change atthe same time is relatively low. Thus we first simplify ourinvestigation by assuming a single load change in Section III.We then tackle the case where multiple loads change simulta-neously in Section IV.

B. Design Principles

The ultimate goal of adaptive system reconfiguration is tomaximize energy efficiency by adopting the optimal configura-tions in accordance with real-time load requirements. Energyefficiency of a battery system is jointly determined by many

1The cutoff voltage generally defines theemptystate of the battery.

factors such as adopted electronic components, battery tem-perature, loads, battery chemical properties, etc. To hidethesecomplex factors from practical implementation, we proposethe following rule-of-thumb design principles.

1) Matching Supplied and Required Voltages:Using volt-age regulators to convert the battery pack supplied voltages tothe load’s required levels is a common approach in practice.However, the voltage regulators introduce additional energyloss when converting voltages, and the energy loss on reg-ulators increases as the difference between the supplied andrequired voltages increases. This fact is also reported in [23],[34]. Thus, to optimize the system energy efficiency, it is keyto match the supplied voltage with the load’s required voltageas much as possible.

2) Minimizing the Discharge Current of Individual Bat-teries: Large discharge current degrades battery performancein many ways, e.g., increasing the internal energy loss [12],reducing the deliverable battery capacity [14], causing signif-icant temperature rise [31], and introducing additional energyoverheads due to a higher system monitoring frequency [27].As a result, the theoretical relationship among the operationtime T , the battery capacityQ, and the discharge currentI(i.e., T = Q

I) is in fact T < Q

Iin practice.

To understand the impact of discharge current on batteryperformance, we conduct a set of measurements as follows.We adopt two series connected and initially fully charged2450 mAh AA batteries to power several parallel connectedmotors with an operation voltage of6 V. In this way, thebattery discharge current increases with a larger number ofmotors. We record the time that the batteries can support theloads, i.e., the operation time, with the motor numbers varyingfrom 1 to 5. The measurement results are shown in Fig. 2.It is intuitive that the operation time decreases with heavierloads. Furthermore, the operation time decreases faster thanthe increase of loads: normalizing the operation time withone single motor as the unit time1, the operation time withc parallel motors (and thus ac× battery discharge current)is smaller than1

c. This super-linear decreasing speed of the

operation time indicates that it is highly desirable to minimizethe battery discharge current to optimize the performance.Tosupport a given load requirement, the battery pack suppliedcurrent is normally limited to a certain range; however, wecan reduce the discharge current of individual batteries inthepack by optimizing the system configuration.

III. R ECONFIGURATION WITH SINGE-LOAD-CHANGE

We investigate the adaptive system reconfiguration in thescenario with only a single load change in this section. Wefirst abstract the battery system into a weighted directed graph,with which the problem of identifying the optimal systemconfiguration is transformed to find as many as possibledisjoint paths conforming to a given weight requirement. Wethen show that the problem can be solved in a near-optimalway by a combination of a Depth-First-Search (DFS) withpruning and 0-1 integer programming.

A. Problem Formulation

Given the two design principles described in Sec. II, ourproblem in identifying the optimal system configuration canbe formulated as2

minP

np · Vout(1)

s.t. V ≤ Vout ≤ (1 + σ)V,

where np is the number of series battery strings that areconnected in parallel to supply the load requirements andσ isthe tolerable jitter voltage ratio. The objective in Equation (2)reflects the design principle in minimizing battery dischargecurrent, and the constraint in Equation (2) is guided bythe design principle in matching the supplied and requiredvoltages. Note that in order to provide the corresponding poweroutput P , a current draw of P

Vout

from the battery pack isrequired (we consider the case that it is possible for the batterypack to provide such a current draw in this paper). Becausethe jitter voltage ratio is normally small for the considerationsof both energy efficiency and system safety, e.g,2.5% in [24],thus with a givenP andV , the objective in Equation (2) canbe approximated by

max np. (2)

We need to consider the voltage imbalance issue whenthe parallel connection of multiple series strings are adopted,which may cause the reverse charging of batteries if thevoltage of these strings deviate too much from each other [25].This imbalance issue in our problem is bounded with the jittervoltage ratioσ in (2).

B. Graph Representation

We propose an abstracted graph model for the batterysystem to facilitate in optimizing its performance. Given abattery pack and the battery voltages at the decision time,we construct a corresponding weighted and directed graphG = (V , E ,W) in the way that

1) the vertex setV represents the batteries in the pack, anddenoteV = {n1, n2, · · · , nN};

2) the edge setE represents the configuration flexibility ofthe pack, i.e., how the batteries can be connected. Adirected edgeni → nj ∈ E if and only if the dischargecurrent can flow fromni to nj without passing any otherbatteries;

3) the weight of each vertex is the voltage of the corre-sponding battery at the decision time:∀wi ∈ W , wi =vi (i = 1, 2, · · · , N).

The above constructed graph only incorporates the batteriesin the system. To further include the terminal pairs on whichthe load has changed into the graph representation, we furtherextend the graph with the following three steps. First, we addtwo verticesn+ andn− to V , representing the two output ter-minals. Then to capture the connectivity of the two terminals,we add edgen+ → ni and ni → n− (i = 1, 2, · · · , N) toE if the output terminals can be directly connected to theith

2Because we focus on the scenario of a single load change in this section,we remove the superscript representing theith load for notation convenience.

battery. Note that for many existing battery packs, the outputterminals can be directed connected to any batteries throughbackbone buses [26]. In the following, we assume this fullconnectivity of the output terminals. At last, we extend theweight setW by settingw(n+) = w(n−) = 0.

Figure 3 illustrates an example of the extended graph withN = 3 based on the battery pack design proposed in [26], asshown in Fig 3(a). With this circuit design, we can draw thecurrent by series connecting battery-0, battery-1, and battery-2. As a result, directed edgesn− → n2, n2 → n1, n1 → n0,andn0 → n+ exist in the corresponding graph, as shown inFig. 3(b) 3.

Ba

ttery 0

Ba

ttery 1

Ba

ttery 2

(a) Circuit design proposed in [26]

+

−

n0

n1

n2

n

n

(b) Abstracted graphFig. 3. An example on the graph representation of battery systems.

The extended graph captures all the potential system con-figurations, and the out-degree of vertices is a direct metricto quantify the configuration flexibility offered by the system.Note that any specific battery pack can be mapped to onlyone corresponding graph, while one graph may have multiplebattery pack implementations. This is because the edges in thegraph only reflect the logical connectivity between batteries,but do not specify how to physically achieve such connectivity.

C. Problem Transformation

With the constructed graph, the problem formulation (2) canbe transformed toidentifying the maximal number of disjointsimple paths connectingn+ and n− with weight sum in therange of [V, (1 + σ)V ]. Specifically, we say a simple pathconnectingn+ andn− is feasibleif the weight sum of involvedvertices is within[V, (1+σ)V ]. The requirement on the disjointpaths is to avoid involving the same battery in multiple seriesstrings, which increases its discharge current and unbalancesthe battery utilization.

D. Identifying the Optimal Configuration

We first show that identifying the optimal configuration isNP-hard, then based on two important observations on batterysystem, we propose a solution which is feasible in practiceand achieves the near-optimal performance.

1) NP-hardness:Theorem1: Given a directed graphG = {V , E ,W} and an

interval [V, (1+σ)V ], finding the maximal number of disjointsimple paths inG with weight sum in[V, (1+σ)V ] is NP-hard.

Proof: The decision version of the above problem can bestated as:given a directed graphG = {V , E ,W}, can we findn (n = 0, 1, 2, · · · ) disjoint simple paths inG with weightsum in[V, (1+ σ)V ]? For the ease of description, denote this

3We use the flow direction of positive charges as the edge direction.

decision problem asΥ. We can prove that theLongest PathProblem in graph theory (i.e., finding a simple path of themaximum length in a given graph), which is a classic NP-hardproblem, can be reduced to a special case ofΥ by assuming:a) n = 1 andσ = 0; b) the weights of all vertices are1; c)V is an integer larger than1. If a polynomial time algorithmΨ exists for the special case ofΥ, we can applyΨ on theLongest Path Problem with path length increasing from1 to|V|, until no solution can be returned. In this way, we solve theLongest Path Problem in polynomial time, which contradictswith its NP-hardness. As a result, we show that no polynomialtime algorithm exists for the special case ofΥ, and thus proveits NP-hardness.

Our approach to solve the problem consists of two steps:first, we identify all feasible paths in the graph, then we findtheir largest disjoint subset. Each path in the returned subsetrepresents a series string of the corresponding batteries,andall these strings are connected in parallel to support the load.Although the original problem is NP-hard, our solution isfeasible in practice based on two important observations onbattery systems.

2) Finding All Feasible Paths:We implement a DFS withpruning method to identify all the feasible paths in the graph.If using the basic DFS idea to identify all the feasible paths,we need a computational time ofO(NN−1) to identify all thefeasible battery strings (note that we assume fully connectedoutput terminals, and the computation time to identify allthe paths is quite different from graph traversal). However,the following two observations on battery systems assist inreducing the computation complexity in practice.

Observation1: Given a battery pack, the set of supportedconfigurations is limited.

For example, the AHR32113 Power Modules only support10S(1-4)P connectivity configurations [1]4. This is becausean higher configuration flexibility is achieved at the costof significantly increased system implementation complexity.For example, the number of required electronic componentsincreases in a quadric relationship with the number of batteriesthat a given battery can connect to [23]. With the graphrepresentation, this is reflected by the fact that the verticesout-degree will not be large. Denote the average out-degreeofvertices asd, the worst case computational complexity of theDFS search can be reduced toO(NdN−1), where the itemNaccounts for starting the search at each of theN vertices, anddN−1 accounts for the space to find all the paths starting at agiven vertex.

Observation2: Because all the vertices weights are withinrange [vc, vf ], for a given load requirement, the number ofvertices involved in a feasible path is limited.

Specifically, the minimal and maximal number of verticesin any feasible paths are⌈ V

vf⌉ and ⌈ (1+σ)V

vc⌉, respectively.

With this observation, the DFS only needs to examine a depthof at most⌈ (1+σ)V

vc⌉, and thus the worst case computational

4The notation ofαSβP represents that a total number ofα · β batteriesare configured intoβ parallel connected strings, and each string consists ofα series connected batteries.

complexity can be further reduced toO(Nd⌈Vmax

vc⌉−1).

Besides reducing the worst case space complexity, thesecond observation also assists in pruning the DFS branchesand thus reducing the average computational complexity fromthe following two aspects. First, if the weights of the firsti

vertices in the current search are too small, it indicates thatthey cannot be part of any feasible paths. Specifically, denotep(j) (j = 1, 2, · · · , i) as the firsti vertices that have beenincluded in the current search, then

if V −i

∑

j=1

w(p(j)) > vf · (⌈ (1 + σ)V

vc⌉ − i)

→ terminate the current search. (3)

Likewise, the current search can also be terminated if theweight of the firsti vertices is too large

if (1 + σ)V −i

∑

j=1

w(p(j)) > vc · (⌈V

vf⌉ − i)

→ terminate the current search. (4)

With this DFS with pruning, we can practically identify allthe feasible paths in the graph.

3) Finding the Largest Set of Disjoint Feasible Paths:Dueto the requirement on disjoint paths for a balanced batteryutilization, if we include a specific path into the systemconfiguration, other paths with overlapping vertices will notbe able to be added to the configuration later. Thus our nextstep is to find the largest disjoint subset of all these feasiblepaths. AssumingM feasible paths have been identified, whichare denoted asP = {path1, path2, · · · , pathM}. We refer twopaths asconflictedif they share at least one common vertex,specifically, define a 0-1 matrixAM×N as

ai,j =

{

1 if nj ∈ pathi

0 otherwise.

Then we define aconflict matrixCM×M is defined as

CM×M = {conflict(i, j)}.and for anypathi andpathj ,

conflict(i, j) = 1 ⇐⇒ ∃k, ai,k · aj,k = 1.

Thus our problem in finding the largest set of disjoint pathscan be formulated as

max |P∗| (P∗ ⊆ P) (5)

s.t. ∀ pathi, pathj ∈ P∗ ⇒ conflict(i, j) = 0.

whereP∗ is the to be obtained largest path set. By furtherdefining

xi =

{

1 if pathi ∈ P∗

0 otherwise,

we can transform the problem formulation in (5) to

max

M∑

i=1

xi s.t. ∀j,M∑

i=1

ai,j · xi ≤ 1.

This transformed problem is a classic 0-1 integer program-ming problem. As the DFS with pruning method identifiesall the feasible paths in the graph, we can see that theoptimality of the identified configuration only depends on howoptimal a solution the 0-1 integer programming can return.

Fortunately, efficient 0-1 integer programming solvers exist inthe literature [13], and thus the near-optimality of the identifiedconfiguration can be guaranteed.

IV. RECONFIGURATION WITH MULTI -LOAD-CHANGES

We have investigated the scenario where only a single loadchanges in the previous section. To complete our investigation,in this section, we extend our design to the scenario wheremultiple loads may change simultaneously.

A. Problem Formulation

Let U denote the number of changed loads. Specifically, fori = 1, 2, · · · , U , we denote the required voltage and poweroutput as[V i, (1 + σ)V i] andP i, respectively.

The graph representation of the battery pack can be ex-tended by adding2U vertices inV and extending the edge setE and weight setW in the same way as in the single loadchange case.

An important difference between the scenarios of a singleand multiple loads changes is that the battery dischargecurrents are likely to be heterogeneous in the latter case.This is because the loads on different terminal pairs are quitelikely to be heterogeneous, and the number of series stringsfor each load in the adopted system configuration may beheterogeneous as well. As a result, we need tominimizethe maximal discharge current of batteriesin this multipleloads changes case to improve the overall battery utilizationefficiency.

We can use the same DFS with pruning method as in thesingle load change scenario to identify all the feasible pathsfor each load, denoted asQ = {P1,P2, · · · ,PU}. Define the0-1 matrixAM×N in the same way as Equation (5), exceptthat M now is the total number of paths identified for allU

loads. We thus have

M =

U∑

i=1

|Pi|.

Define another two 0-1 matrixesBM×U andYM×U as

bi,k =

{

1 if pathi is feasible for the kth load0 otherwise,

and

yi,k =

{

1 if pathi is selected for the kth load0 otherwise.

Our problem in the multiple load changes scenario can beformulated as

minmax{P k

V k∑M

i=1yi,k

} (k ∈ {1, 2, · · · , U}) (6)

s.t. ∀i, k, yi,k = 1 ⇒ bi,k = 1,

∀i,U∑

k=1

yi,k ≤ 1,

∀j,M∑

i=1

U∑

k=1

ai,j · yi,k ≤ 1.

The first constraint means that a path can be selected onlyfor the load it can support, the second constraint requires thateach of theM paths can be adopted by at most one load, andthe final constraint requires the same vertex to be involved in at

most one selected path. Thismin-maxoptimization problemcannot be efficiently solved by 0-1 programming. We thuspropose a greedy algorithm to identify the desired systemconfigurations in this case.

B. Greedy Solution

After identifying the path setQ, the greedy solution addspaths into the system configuration in astep-by-stepmanneruntil no more paths can be added. Because the inclusion ofa specific path prevents other paths sharing common verticesfrom being included in the future, the sequence with which thepaths are added into the configuration plays a critical role indetermining the final results. Thus, two sub-questions needtobe addressed are: (i) which load should be selected to explorefor each step, and (ii ) which path should be included intothe configuration for the selected load. Our solution greedilyaddresses these two sub-questions: we greedily select the loadwith the largest battery discharge current for each step, andthen greedily include the path with the least conflict on otherpaths into the system configuration.

1) Select the Load with the Largest Current:Given the loadrequirements and the paths that have been already includedinto the system configuration, in each step, we can calculatethe discharge current of the batteries supporting each load.Specifically, letn1

p, n2p, · · · , nU

p denote the number of selectedpaths for each load. With a smallσ, the discharge current ofbatteries supporting individual loads can be approximatedby

Ii ≈ P i

nip · V i

. (7)

Then we select the load with the largest discharge currentfor individual batteries for each step, specifically, the selectedload is

argmaxi

{Ii}. (8)

2) Select the Path with the Least Conflict:After selectingthe load, the next step is to select a feasible path for the loadand include the path into the system configuration.

The selection of a specific path prevents other overlappingpaths to be selected in the future due to the disjoint pathsrequirement. Thus, we select the path that has the leastnegative impact on other paths. We define the conflict matrixC in the same way as (5). When thekth load is selected ina specific step, we select (and include into the configuration)the path according to

argmini

{∑

i,j

conflict(i, j) | bi,k = 1, pathi, pathj ∈ Qa}, (9)

whereQa ⊂ Q is the set of paths that are still available forselection before this step.

Note that the inclusion of a specific path into the config-uration changes the values of (7), and thus we need to re-select the load to be processed for each step. If no path can beselected for the load under consideration, we mark the load assaturated, and re-select thenon-saturatedload with the largestdischarge current for individual batteries as the next to process.This process continues until no paths can be selected for anyloads.

Adaptive

Configuration

4S2P

loads

regulator

battery pack

Fig. 4. Experiment method.

LM 317

INPUT OUTPUT

ADJUST

load input

voltage

supplied

voltage

R1

C1

R2

C2

Fig. 5. Adjustable voltage regulator.

0 2 4 6 8 10

2.5

5

7.5

10

4S2P

Adap

tive

Time (hour)

Load

Vol

tage

(V)

Load Traces

(a) Light Loads

0 2 4 6 8 10

2.5

5

7.5

10

4S2P

Adap

tive

Time (hour)

Load

Vol

tage

(V)

Load Traces

(b) Mild Loads

0 2 4 6 8 10

2.5

5

7.5

10

4S2P

Adap

tive

Time (hour)

Load

Vol

tage

(V)

Load Traces

(c) Heavy LoadsFig. 6. Operation time with different loads.

V. PRACTICAL ISSUES ANDFURTHER DISCUSSION

Energy Overhead of Reconfiguration OverheadTheadaptive system reconfiguration is achieved by the operationof supplementary electronic components such as switches andconnectors, which also consumes energy. Because the energyconsumption on these supplementary components are normallysmaller than the battery capacities in orders of magnitudes, wecan separate the identification of optimal configurations fromminimizing the operation costs of supplementary componentsas two independent problems in practice.

Time Overhead of ReconfigurationBesides energy loss,the system reconfiguration also requires certain time durationto accomplish, i.e., the reconfiguration latency. This recon-figuration latency introduces two additional challenges: howto minimize the latency and how to supply the load duringthe transient phase. A possible approach to address the firstquestion is through the coordinated supplementary componentoperations, and the second question can be addressed byincorporating super-capacitor based secondary power supplysystems.

Battery Charging through System ReconfigurationBat-tery charging is another important issue for battery-poweredsystems, which is desired to be fast (i.e., accomplished inshort time) and efficient (i.e., more energy is charged intothe batteries). It is also possible to apply the idea of systemreconfiguration to assist the charging of batteries: the chargingcurrent/voltage can be controlled by adjusting the way inwhich the batteries are connected.

VI. EXPERIMENT EVALUATIONS

In this section, we evaluate the proposed adaptive reconfig-uration algorithms based on a prototype battery system.

A. Experiment Settings

1) Battery Pack: We build a prototype battery pack withsixteen2450 mAh AA rechargeable batteries, which are or-ganized into eight modules each with two series connected

batteries. Similar to the configuration flexibility offeredbythe existing off-the-shelf products [1], our prototype supportsa configuration set of{1S8P, 2S4P, 4S2P}. For the ease ofimplementation, the prototype only has a single pair of outputterminals, and thus can only support a single load at any time.

2) Loads: We adopt twelve0.5 A 3.6 W flashlight bulbsas the loads, which are organized into four 1S3P bulbmodules. We randomly generate load traces in the form of{t1, a1}, {t2, a2}, · · · , whereti is the lasting duration andaiis the number of series connected bulb modules during thattime (ai ∈ {1, 2, 3, 4}). Because the bulbs can operate undera wide voltage range (but with different lightness), for a faircomparison, we impose an additional requirement that eachbulb module requires a2.5 V input voltage, and the tolerablejitter voltage is1 V. As a result, the load required voltagesvary from 2.5× 1 = 2.5 V to 2.5× 4 = 10 V.

3) Baseline: We adopt the 4S2P battery configuration asa baseline, which trades-off between the highest voltage thesystem can supply (i.e., 4S) and the preference on small batterydischarge current (i.e., 2P). To match the supplied voltagewith the load requirement, we implement an adjustable voltageregulator with the LM317 IC [6], and connect it between thebattery pack and the load to adjust the load input voltageto the required level. Figure 4 presents an overview of ourexperiment methods, and the circuit diagram of the adjustablevoltage regulator is shown in Fig 5.

4) Evaluation Metric:We adopt the operation time, definedas the time from the start of the measurement to the timewhen the bulbs cannot be lightened anymore, as the metricto evaluate the system performance. The batteries are initiallyfully charged for each measurement.

B. Experiment Results

To investigate the performance of the adaptive configura-tion algorithm with different load conditions, we randomlygenerate three load traces with light, mild, and heavy loadsrespectively. Specifically, with light load, only1-2 bulb mod-ules are series connected as the load. The numbers of bulb

modules adopted with the mild and heavy loads are randomlychosen from1-4 and2-4, respectively. In this way, the numberof bulb modules used in the light, mild, and heavy loads are1.5, 2.5, and3 in average, respectively. The load lasting timeti is set to30 minutes.

The operation time obtained with the two configurationmethods for each load trace are shown in Fig. 6. The advantageof the adaptive configuration over the baseline is obvious, andan average operation time increase of3.06 hour is obtainedover the three loads conditions. This operation time improve-ment is due to two reasons: first, by adaptively converting thesupplied voltages to the load required levels, the energy losson the voltage regulator is reduced; second, by minimizing thedischarge current of individual batteries, more battery capacitycan be delivered and the heat dissipation on other systemcomponents is also reduced.

Furthermore, we can observe that the lighter the loads, themore improvement can be obtained, which can be explainedby the following two facts. First, with the 4S2P configuration,the lighter the loads, the larger the gap between the suppliedand required voltages, which degrades the regulator efficiency.Second, the lighter the loads, the fewer batteries are neededto form a single series string to support the loads. This in turnoffers more space for the adaptive configuration to identifymore parallel connected strings, and thus reduces the batterydischarge current.

Another observation from our experiment result is thatwith the 4S2P configuration, the temperature of the LM317 IC easily rises to44◦C at the maximum. Such a hightemperature not only indicates significant energy loss (andthus supports our design principle in matching supplied andrequired voltages), but also reduces the system stability.

0 500 1000 1500 2000 2500 30002.5

3

3.5

4

4.5

Discharge Capacity (mAh)

Vol

age

(V)

550mA2750mA5500mA

(a) Provided in [7]

0 500 1000 1500 2000 2500 30002.5

3

3.5

4

4.5

Discharge Capacity (mAh)

Vol

age

(V)

550mA2750mA5500mA

(b) Approximated

Fig. 7. Battery discharge traces.

VII. S IMULATION /EMULATION EVALUATIONS

In this section, we evaluate the proposed adaptive reconfig-uration algorithms through extensive trace-based simulations.We first evaluate the adaptive reconfiguration based on batterydischarge traces obtained from the data sheet ofoff-the-shelf battery products. Then, the efficiency of the adaptivereconfiguration is further verified base on two sets of electricvehicle traces collected during driving.

A. Simulation based on Battery Discharge Traces

1) Trace-based Battery Model:Analytical modeling ofbattery properties is computational expensive, and thus weusea trace-based method to track the battery states. We simulate abattery pack consisting of2, 900 mAh Panasonic NCR18650

Li-ion batteries [7], whose discharge curves with dischargecurrents of550 mA, 2, 750 mA, and5, 500 mA are providedin its data sheet. The full and cutoff voltages arevf = 4.25 Vandvc = 2.5 V, respectively.

To obtain more fine grained battery discharge traces, wedivide the current interval[550, 5500] mA into 99 intervalswith a gap of50 mA each, and proportionally approximatethe corresponding discharge traces based on the three tracesprovided in the data sheet. Note that we could further reducethe current gap to improve the approximation accuracy. Asubset of the obtained discharge curves is shown in Fig. 7(not all the curves are shown for figure clarity).

2) Simulated Battery Packs:The simulated battery packconsists of64 batteries and can support three loads simul-taneously. The current drawn from each battery can directlyreach two other batteries on average (i.e., an average verticesout-degree of two in the graph). The simulation follow thesesettings unless otherwise specified. The initial battery voltagesare randomly generated in the range of

[α · vc, vf ], (10)

whereα is a control parameter that determines the batteryvoltage diversity and is set to1.2 unless otherwise specified.

3) Load Traces:Similar to the traces in the experiment, werandomly generate load traces in the form of{tji , V

ji , P

ji }

for each loads, wheretji is the lasting duration of theithtrace for thejth load, andV j

i andP ji are the required voltage

and power of that trace, respectively. A unit time interval of10 minutes is adopted for loads’ lasting time, i.e.,ti onlytakes the values of10 min, 20 min, and so on. The systemconfiguration is updated every10 minutes by first updatingthe battery voltages according to the traces in Fig. 7, and thenadaptively reconfiguring the battery pack. The required voltageV is randomly generated from15-20 V unless otherwisespecified. The tolerable jitter voltage is2.5 V (i.e., vc) bydefault. The required powerP is randomly generated from15 V × 550 mA = 8.25 W to 20 V × 5500 mA = 110 W .

4) Baselines: We implement the following three systemconfigurations as baselines.

Serial: The batteries are evenly assigned to individual loads,and for each load, the assigned batteries are series connected.

Parallel:√N series strings with

√N batteries each are

formed, and then these strings are assigned to individual loadsin a round-robin manner.

Oracle: Given the range of all possible load requiredvoltage, we can calculate how many batteries are needed fora string to be able to support any potential loads, and then weform as many as possible such strings. The remaining batteries(those are not enough to construct another such string) formthe last string. This oracle configuration maximizes the numberof parallel connected strings while guaranteeing each string isable to support the load requirement. These strings are thenassigned to individual loads in a round-robin manner.

5) Performance Evaluation:We evaluate the impact ofdifferent system parameters on the performance of adaptivereconfiguration.

1 2 3 4 50

20

40

60

80

100

# of Supported Loads

Ope

ratio

n Ti

me

(min

)

AdaptiveOracleParallelSerial

Fig. 8. Impact of supported loads #.

1.1 1.2 1.3 1.4 1.5 1.6 1.70

50

100

150

200

α

Ope

ratio

n Ti

me

(min

)

AdaptiveOracleParallelSerial

Fig. 9. Impact of initial battery voltages.

[10−15] [15−20] [20−25] [25−30]0

20

40

60

80

Required Voltage (V)

Ope

ratio

n Ti

me

(min

)

AdaptiveOracleParallelSerial

Fig. 10. Impact of required voltage.

TABLE ITHREE CASES OF CONFIGURATION FLEXIBILITY DISTRIBUTIONS.

Vertices Out-degree 1 2 3 4 5Case A 0.5 0 0 0 0.5Case B 0.2 0.2 0.2 0.2 0.2Case C 0 0 1 0 0

Number of Loads: We first examine the impact of thenumber of supported loads on the system operation time. Theresults with1 to 5 simultaneously supported loads are shownin Fig. 8. Note that it is not necessary for all these loadsto change at the same time. The operation time decreases asmore loads have to be supported, which is intuitive becauseincreasing the number of supported loads essentially indicatesa heaver loads for the battery system. Furthermore, we can seethat compared with the baselines, the adaptive reconfigurationachieves around4× gain in operation time when only one loadis supported. Although the gain decreases as more loads needto be supported, the adaptive reconfiguration still obtainsa 2×operation time even with a load number of5.

Battery Voltage Diversities: We then explore the impact ofbattery voltages on the operation time. The battery voltages arecontrolled by the parameterα in (10), and a smallerα indicatesboth a higher voltage diversity among batteries and a loweraverage battery voltages. The operation time withα varyingfrom 1.1 to 1.7 are shown in Fig. 9. Note that withα = 1.7,it indicates that the battery voltages are randomly generatedfrom [2.5 × 1.7, 4.25] = {4.25}, meaning all the batteriesare initially fully charged. The operation time increases asα increases because of higher initial battery voltages, andthe adaptive reconfiguration outperforms the baselines in allthe explored cases. Furthermore, we can see the advantageof adaptive reconfiguration is more obvious with smallerα.This is because the smallerα is, the more likely that certainbatteries are close to depletion. Depleted batteries significantlydegrade the system performance if the configuration is notadjustable. On the other hand, the adaptive reconfigurationcanbypass low-voltage batteries when necessary, which reducesthe impact of the near-depletion batteries on system perfor-mance.

Loads Requirements: The operation time with differentload required voltages and powers are shown in Fig. 10 andFig. 11, respectively. The load required power is set to55 Win Fig. 10 and the required voltage is20 V in Fig. 11. Again,significant improvement on the operation time can be observedwith the adaptive reconfiguration, which is about3×-5× ofthose obtained with the baselines. Furthermore, the operationtime decreases as the loads become heavier, as a result of theincrease in either the required voltage or power. Note that

Fig. 10 shows that when the required voltage is relativelylow (e.g., 10–25 V), the operation time obtained with thenon-reconfigurable baselines slightly increases with a highervoltage. This is because when the required voltage increases,the load current decreases with a fixed required power, whichin turn leads to a longer operation time. However, as therequired voltage continuously increases (e.g.,[25, 30]), theprobability for the fixed configuration to not able to supportsuch required voltage increases, and thus the operation timeis reduced.

Configuration Flexibilities: We investigate the impact ofsystem configuration flexibility on the adaptive reconfigurationin the following. The operation time with different configura-tion flexibilities (i.e., the vertices out-degree in the graph) areshown in Fig. 12, with an average out-degree of1, 2, and3, respectively. Significant increase in system operation timecan be observed when the configuration flexibility increases.However, the increase in operation time slows down withlarger average out-degrees. This implies that an excessivehigh configuration flexibility may not be desirable, especiallywhen considering the fact that the configuration flexibilitydoesnot come without costs, e.g., the implementation complexitywould be dramatically increased.

Besides the average configuration flexibility, the distributionpattern of these flexibilities also affects the system perfor-mance. Fixing the average vertices out-degree as3, we explorethree cases on how the configuration flexibilities are distributedamong batteries, as shown in Table I. The resulting operationtimes under these three cases are shown in Fig. 13. Wecan see that the flexibility distribution significantly affectsthe performance. An important observation is that when theconfiguration flexibility is more evenly distributed amongbatteries, the performance becomes better. This is becausesuchan evenly distribution pattern alleviates the negative impactdue to bottleneck batteries on the system performance. Thisobservation serves as a guidance in practical battery systemdesign.

B. Emulation based on Electric Vehicle Driving Traces

We further evaluate the adaptive reconfiguration based onempirical electric vehicle driving traces. We collect two driv-ing traces of around900 s and2400 s each, containing thecorresponding operation voltages and powers during that timeperiod, as shown in Fig. 14 and Fig. 15, respectively.

We generate the load traces for our emulation based onthese two raw traces. First, both the discharging and chargingof battery pack happen during the driving of electric vehicles.

[30, 40] [50, 60] [70, 80] [90, 100]0

10

20

30

40

50

60

70

80

Required Power (W)

Ope

ratio

n Ti

me

(min

)

AdaptiveOracleParallelSerial

Fig. 11. Impact of required power.

1 2 3 40

50

100

150

200

250

# of Termimal Pairs

Ope

ratio

n Ti

me

(min

)

AveDegree = 1AveDegree = 2AveDegree = 3

Fig. 12. Impact of ave. configuration flexibility.

1.2 1.3 1.4 1.5 1.6 1.70

50

100

150

200

α

Ope

ratio

n Ti

me

(min

)

Case ACase BCase C

Fig. 13. Impact of flexibility distributions.

1 300 600 900340

360

380

Vo

lta

ge

(V

)

Time (second)

1 300 600 900−70

0

70

Po

we

r (K

W)

VoltagePower

Fig. 14. Electric vehicle driving traces #1.

1 1180 2360340

360

380

Vo

lta

ge

(V

)

Time (second)

1 1180 2360−70

0

70

Po

we

r (K

W)

VoltagePower

Fig. 15. Electric vehicle driving traces #2.

1.1 1.2 1.3 1.4 1.510

2

103

104

105

α

Ope

ratio

n Ti

me

(s)

AdaptiveOracle

Fig. 16. Operation time.

This is reflected in the traces that the both positive (i.e.,discharging of battery pack) and negative (i.e., charging ofbattery pack) values exist in the power trace. Because we onlyfocus on the discharge management in our design, we set allthe negative powers and the voltages at the corresponding timeinstance in the traces to zeros. This can be interpreted as noload is imposed on the battery pack during those time periods.Second, because the raw traces are relatively short in time,wecombine them sequentially to form a900 + 2360 = 3260 strace, and then repeat it for10 time. As a result, a3260×10

60 ≈550 minutes load trace is generated for our emulation.

The battery packs for electric vehicles normally take thehierarchical architecture: it can be divided into a set of batterymodules which in turn are consisted of individual batteries.In our emulation, we form a battery pack consisting of64modules each with16S4P connected batteries. The batterydischarge property conforms to the discharge traces shown inFig. 7.

Again, we take the non-reconfigurable Oracle baseline forcomparison. The operation time with varying initial batteryvoltages (i.e., by adjustingα in (10)) is shown in Fig. 16.Obvious advantage of the adaptive reconfiguration can beobserved, especially when the battery initial voltages arelow,which agrees with the observation in Fig. 9. The operationtime obtained with the two configuration methods converge asα increases, because in this case the battery pack has sufficientenergy supply to survive the load even without the assistanceof adaptive reconfiguration.

VIII. R ELATED WORK

Large-scale battery systems are commonly adopted in prac-tice, and many research efforts have been devoted to im-prove the system performance focusing on the battery dis-charge scheduling [11], [14], [17], [25], [32], the effectivesystem monitoring [27], the design of battery managementsystems [16], [30], [38], etc.

Due to the load dynamics in large-scale battery systems,traditionally, the battery supplied voltage is adjusted tothe load

required level by adopting additional electronic components,e.g., voltage regulators [41]. However, the additional compo-nents introduces additional energy consumption/loss [5],[22],and thus degrades the battery energy utilization efficiency.

Another approach to provide the dynamic load requirementis to adaptively adjust the battery connections in the system.Investigations on this adaptive system reconfiguration havebeen reported in [20], [41], targeting on small multicell batterysystems such as mobile devices. In our work, we extend theinvestigation to large-scale scale battery systems.

Two necessary conditions must be satisfied to effectivelyand adaptively reconfigure the system. First, the system hastooffer certain configuration flexibility on which the adaptive re-configuration can operate. However, the system configurationflexibility is achieved by adopting more electronic componentssuch as connectors and switches, which not only introducesadditional energy costs, but also increases the system imple-mentation complexity. Research efforts have been devoted toeffectively offer configuration flexibility with less additionalcosts [10], [23], [24]. Based on the system design in [24],six switches are enough to connect a battery in any manner:series, parallel, or by-passed. Our work advances the state-of-the-art by proposing adaptive reconfiguration algorithms thatreturn the desired system configuration based on the offeredconfiguration flexibility and the real time load requirements.

Second, the system has to be aware of individual batteryconditions to carry out the adaptive reconfiguration. Manyworks on battery modeling and simulation exist in the lit-erature [15], [18], [21], [37], [38], [40]. However, most ofthese models are computational extensive, and the simulatorsrequire practical parameters to implement. Furthermore, mostof these models/simulators are for specific battery types, andthus their universalities are limited. Our proposed adaptivereconfiguration algorithms hide the complex low level batteryproperties by focusing on two rules of thumb in identifyingthe desired system configurations: matching the supplied andrequired voltages and minimizing the discharge currents.

The most similar works are [19], [23], [28]. In [23], apowertree representation of the battery pack is proposed to assistthe effective system reconfiguration when the battery failureshappen. We tackle the system reconfiguration with a differentobjective, i.e., optimizing the system energy efficiency, and oursolutions can also effectively handle the case with batteryfail-ures. An optimization formulation w.r.t the energy efficiency ispresented in [19], which requires low level battery propertiessuch as thestate of charge, the state of health, etc. Our workhides the complex battery properties from engineering andthus facilitates its practical implementation. A reconfigurableseries-connected battery string is proposed in [28] to adjustthe supplied voltage to the load required level. We advancethe investigation by further exploring minimizing the batterydischarge current to improve the system energy efficiency.

IX. CONCLUSIONS

In this paper, we have explored the adaptive reconfigurationof large-scale battery systems to dynamically provide theload’s required voltages, which avoids the low efficiency issueof the traditional voltage regulator-based solutions. Based ontwo empirically observed design principles, our approach hidesthe complex battery properties from engineering, and thusmakes it more practical for implementation. Specifically, byabstracting the battery system into a graph representation, wehave investigated both scenarios with a single and multipleload changes, and proposed corresponding adaptive recon-figuration algorithms. Through prototype implementation andextensive simulation, we have shown the proposed adaptivereconfiguration algorithms can significantly improve the per-formance w.r.t. system operation time. In the future, we willinvestigate the trade-off between the system energy efficiencyand implementation complexity.

ACKNOWLEDGEMENT

This work was supported by Singapore-MIT IDC IDD61000102a,SUTD-ZJU/RES/03/2011, NRF2012EWT-EIRP002-045, US Na-tional Science Foundation (NSF) grants CNS-1117438, a start-upgrant from the University of Texas at Dallas, and NSFC-61303202.

REFERENCES

[1] AHR32113 Power Modules. http://www.a123systems.com/products-modules-power.htm.

[2] ARPA-E. http://www.greencarcongress.com/2012/08/arpae-20120802.html.

[3] Electric Car Motor. http://www.electric-cars-are-for-girls.com/electric-car-motor.html.

[4] Elithion Battery Pack. http://elithion.com/batterypacks.php.[5] Energy Loss on Regulators. http://www.dimensionengineering.com/info/

switching-regulators.[6] LM317 Chip. http://www.ee.buffalo.edu/courses/elab/LM117.pdf.[7] Panasonic NCR18650 Li-ion Battery. http://industrial.panasonic.com/

www-data/pdf2/ACA4000/ACA4000CE240.pdf.[8] Reconfigurable Battery Packs. http://arpa-e.energy.gov/q=

arpa-e-projects/reconfigurable-battery-packs.[9] Synchronized Resource Service. http://www.pjm.com/

markets-and-operations/ancillary-services/synchronized-service.aspx.[10] M. Alahmad, H. Hess, M. Mojarradi, W. West, and J. Whitacre. Battery

switch array system with application for JPL’s rechargeable micro-scalebatteries.Journal of Power Sources, 177(2):566 – 578, 2008.

[11] L. Benini, G. Castelli, A. Macii, B. Macii, and R. Scarai. Battery-drivendynamic power management of portable systems. InISSS’00, 2000.

[12] L. Benini, D. Vruni, A. Macii, E. Macii, and M. Poncino. Dischargecurrent steering for battery lifetime optimization.IEEE Transactions onComputers, 52(8):985–995, 2003.

[13] S. Boyd and L. Vandenberghe. Convex Optimization.CambridgeUniversity Press, 2004.

[14] G. Castelli, A. Macii, E. Macii, and M. Poncino. Current-controlledpolicies for battery-driven dynamic power management. InICECS’01,2001.

[15] G. Ceder, M. Doyle, P. Arora, and Y. Fuentes. Computational modelingand simulation for rechargeable batteries.MRS BULLETIN, pages 619–623, 2002.

[16] C. F. Chiasserini and R. Rao. Energy efficient battery management.IEEE Journal on Selected Areas in Communications, 19(7):1235–1245,2001.

[17] C. F. Chiasserini and R. Rao. Improving battery performance byusing traffic shaping techniques.IEEE Journal on Selected Areas inCommunications, 19:1385–1394, 2001.

[18] P. Chou, C. Park, J. Park, K. Pham, and J. Liu. B#: a battery emulatorand power profiling instrument. InISLPED’03, 2003.

[19] S. Ci, J. Zhang, H. Sharif, and M. Alahmad. Dynamic recongurablemulti-cell battery: A novel approach to improve battery performance. InAPEC’12, 2012.

[20] S. Ci, J. Zhang, H. Sharif, and M. Alahmadu. A novel design of adaptivereconfigurable multiple battery for power-aware embedded networkedsensing systems. InGLOBECOM’12, 2012.

[21] L. Cloth, M. Jongerden, and B. Haverkort. Computing battery lifetimedistributions. InDSN’07, 2007.

[22] D. Graovac and M. Purschel. IGBT power losses calculation using thedata-sheet parameters.Infineon Application Note, pages 1–16, 2009.

[23] F. Jin and K. G. Shin. Pack sizing and reconfiguration formanagementof large-scale batteries. InICCPS’12, 2012.

[24] H. Kim and K. G. Shin. On dynamic reconfiguration of a large-scalebattery system. InRTAS’09, 2009.

[25] H. Kim and K. G. Shin. Scheduling of battery charge, discharge, andrest. InRTSS’09, 2009.

[26] H. Kim and K. G. Shin. Dependable, efficient, scalable architecture formanagement of large-scale batteries. InICCPS’10, 2010.

[27] H. Kim and K. G. Shin. Efficient sensing matters a lot for large-scalebatteries. InICCPS’11, 2011.

[28] T. Kim, W. Qiao, and L. Qu. Series-connected self-reconfigurablemulticell battery. InAPEC’11, 2011.

[29] T. Kim, W. Qiao, and L. Qu. A series-connected self-reconfigurablemulticell battery capable of safe and effective charging/discharging andbalancing operations. InAPEC’12, 2012.

[30] D. Lim and A. Anbuky. A distributed industrial battery managementnetwork. ACM Trans. on Indus. Elec., 51(6):1181–1193, 2004.

[31] D. Linden and T. B. Reddy. Handbook of Baterries (3rd ed.). McGraw-Hill , 2001.

[32] J. Luo and N. Jha. Battery-aware static scheduling for distributed real-time embedded systems. InDAC’01, 2001.

[33] J. Markoff. Pursuing a battery so electric vehicles cango the extra miles.http://www.nytimes.com/2009/09/15/science/15batt.html.

[34] Maxim. Source resistance: the efficiency killer in DC-DC convertercircuits. http://www.maxim-ic.com.

[35] S. McLaughlin, P. McDaniel, and W. Aiello. Protecting consumerprivacy from electric load monitoring. InCCS’11, 2011.

[36] G. Motors. Latest chevy volt battery pack and generatordetails and clarifications. http://gm-volt.com/2007/08/29/latest-chevy-volt-battery-pack-and-generator-details-and-clarifications/.

[37] S. J. Moura, J. L. Stein, and H. K. Fathy. Battery-healthconscious powermanagement in plug-in hybrid electric vehicles via electrochemicalmodeling and stochastic control.IEEE Transactions on Control SystemsTechnology, 21(3):679–694, 2013.

[38] D. Rakhmatov and S. Vrudhula. Energy management for battery-powered embedded systems.ACM Transactions on Embedded Com-puting Systems, 2:277–324, 2003.

[39] D. Raychev, Y. Li, and W. Shi. The seventh cell of a six-cell battery.In WEED’11, 2011.

[40] P. Rong and M. Pedram. An analytical model for predicting theremaining battery capacity of lithium-ion batteries.IEEE Transactionson Very Large Scale Integration Systems, 14(5):441–451, 2006.

[41] H. Visairo and P. Kumar. A reconfigurable battery pack for improvingpower conversion efficiency in portable devices. InICCDCS’08, 2008.

[42] W. Yang, N. Li, Y. Qi, W. Qardaji, S. McLaughlin, and P. McDaniel.Minimizing private data disclosures in the smart grid. InCCS’12, 2012.