Caro 2013

8/22/2019 Caro 2013

1/9

Electric PowerSystems Research 104 (2013) 917

Contents lists available at SciVerse ScienceDirect

Electric Power Systems Research

journal homepage: www.elsevier .com/ locate /epsr

Robust WLS estimator using reweighting techniques for electricenergy systems

Eduardo Caroa,, RobertoMnguezb, AntonioJ. Conejoc

a UniversidadPolitcnicade Madrid, Madrid, Spainb Universidadde Cantabria, Cantabria, Spainc Universidad de Castilla-LaMancha, Ciudad Real, Spain

a r t i c l e i n f o

Article history:Received 31 July 2012

Received in revised form 24 April 2013

Accepted 31May2013

Keywords:

Weighted least squares

Power system stateestimation

Outlier detection

DependentGaussian measurements

a b s t r a c t

The state estimator is a key tool in the operation ofany real-world electric energy system. In this paper,

a state estimator based on a weighted least squares model is proposed which is robust against outliers.

This algorithm presents two relevant features: robustness that is achieved by readjusting measurement

weights, and accuracy that is attained by consideringmeasurement dependencies. The proposedmethod

is tested in the IEEE 57-bus and 118-bus systems and the obtained results are analyzed using Design of

Experiments and ANOVA techniques.

2013 Elsevier B.V. All rights reserved.

1. Introduction

1.1. Motivation

In any real-world electric energy system, the Control Center

monitors andcontrols the functioningof the network in real-time,

ensuring operational security. To accomplish this task the Control

Center needs to know accurately the actual state of the system

(node voltages, power flows, etc.) at any time. These values are

estimatedby the state estimator (SE).

The state estimator is a mathematical algorithm which com-

putes the most-likely state of the network, given a redundant set

of measurements captured from the system. From the statistical

point ofview, thestateestimationalgorithm isa nonlinearmultiple

regression problem, whose parameters to be estimated are those

which characterize the network state: node voltage magnitudes

and angles.

This estimated state is generally computed using the Maxi-

mum Likelihood Estimator, minimizing the weighted sum of thesquared residuals(i.e.,WeightedLeastSquaresapproach).Once the

most-likely state is obtained, the Control Center performs a bad

data detection and identification procedure to detect and elim-

inate those measurements whose associated standardized errors

are larger than a pre-established tolerance. The statistical tests

commonlyemployedfor these tasksarethe2-test and the Largest

Corresponding authorat: C/ Jos GutirrezAbascal, 2,28006 Madrid, Spain.

Tel.: +34 913363149.

E-mail address: [email protected] (E. Caro).

Normalized Residual test, and arewell established in the technical

literature [1]. Once outliershavebeenremoved, thenonlinearmul-

tipleregressionproblemissolvedagain,andthe finalstateestimate

is obtained.

Ifoutliers arenot properlydetectedor eliminated, the final esti-

matewillbebiased,andtheControlCenterwillnothavean accurate

knowledge of theactual stateof the system, leading occasionallyto

an insecureoperationof the network.Forthis reason, thedetection

andidentificationof badmeasurementshave a notoriousrelevance

in the estimation process. In fact, an adequate and secure control

is only achieved in the case that the SE procedure is robust enough

to detect andeliminate thepresence of corruptmeasurements.

Traditionally, the outlier elimination problem is solved

iteratively by detecting/removing suspected measurements and

re-estimating the state disregarding the rejected data. These esti-

mators are based on the weighted least squares, which shows a

notable computational efficiency; however the lack of robustness

deteriorates significantly their performance in thepresence of bad

measurements. Specifically, the presence of multiple conformingbadmeasurements in the measurement setmayprovoke a mask-

ingeffect:goodmeasurementsmayberejectedwhereascorrupted

ones may not. This undesirable situation occurs when measure-

ment dependencies are not properlymodeled.

1.2. Aim

The aim of this paper is to present a robust state estimator

based on a weighted least squares regression, which carries out

the estimationand thebad datadetection/identificationprocesses

simultaneouslyby successivelyadjustingtheweightingmatrix and

0378-7796/$ seefrontmatter 2013 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.epsr.2013.05.021
http://localhost/var/www/apps/conversion/tmp/scratch_5/dx.doi.org/10.1016/j.epsr.2013.05.021http://localhost/var/www/apps/conversion/tmp/scratch_5/dx.doi.org/10.1016/j.epsr.2013.05.021http://www.sciencedirect.com/science/journal/03787796http://www.elsevier.com/locate/epsrmailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_5/dx.doi.org/10.1016/j.epsr.2013.05.021http://localhost/var/www/apps/conversion/tmp/scratch_5/dx.doi.org/10.1016/j.epsr.2013.05.021mailto:[email protected]://crossmark.dyndns.org/dialog/?doi=10.1016/j.epsr.2013.05.021&domain=pdfhttp://www.elsevier.com/locate/epsrhttp://www.sciencedirect.com/science/journal/03787796http://localhost/var/www/apps/conversion/tmp/scratch_5/dx.doi.org/10.1016/j.epsr.2013.05.021

8/22/2019 Caro 2013

2/9

10 E. Caro et al./ Electric Power Systems Research 104 (2013) 917

consideringtheeffect ofmeasurement dependencies. Theobtained

estimate does not require further bad measurement processing

algorithms.

1.3. Literature review

Thetechnical literatureis richin references concerningthestate

estimationproblem, forinstance,[2]or [1]; andthere isa significantnumber of references on outlier detection: [311]. The previous

worksarefocusedmainly ontheareaof least squares linearregres-

sion. Other statistical models and estimation methods, such as

reweighed techniques [1215], non-linearmethods [16], variance-

varying models [17], or some robust estimators [1820] have

received comparatively less attention. Nevertheless, [21] report

successful results fromthe applicationof thereweighted leastdevi-

ationmethoddevelopedby[14], todetectdatarelatedtohurricanes

and typhoon onwave hindcast databases.

However, no so many works address the power system WLS

estimator using adjusted measurement weights. The pioneering

work reported in [22] proposes a method for readjusting the mea-

surementvariancesbasedon theresidualsof previousestimations.

Ref. [23] develops thisapproach, improving thecomputational effi-ciencyandensuringmathematicalconvergence.Work [24] propose

an iterative reweighted least-squares estimator that is based on

GivensRotations and improves the robustness against outliers.

In [25], the weights of theWLS estimator are artificiallymanip-

ulated, leading to a more robust estimator with the properties of

the weighted least absolute value approach. Recently, in [26], the

WLS regression is addressedusing estimatedweights based on the

measurement variances.

All the aforementioned works consider that the measurement

covariancematrix is diagonal. However,recentworks [27,28]show

that this matrix is generally non-diagonal. Thus, the reweighting

techniques previously proposed in the technical literature can be

improved, since such techniques cannot deal with measurement

dependencies.

1.4. Contribution

The contribution of this paper is threefold:

First, it provides a mathematic procedure that allows apply-

ing a reweighting estimation technique (originally designed

for diagonal covariance matrices) to a non-diagonal estimation

problem. Second, an iterative state estimator is proposed, showing both

robustness against outliers and computational efficiency. Specif-

ically, it requires significantly less time that similar methodsproposed in the technical literature [29].

Finally,DesignofExperimentsandANOVAprocedures areusedto

comparetheperformanceof theproposedmethodwithstatistical

rigor.

1.5. Paper organization

Therest of this paper is organized as follows. Section2 develops

and formulates the Reweighted Least Squares Estimator consid-

ering measurement dependencies. Section3 applies the Design of

Experiments and ANOVAprocedures to theconsidered estimation

problem.Section4 providesandanalyzesresults fromfourrealistic

casestudies. Finally, Section5 provides somerelevant conclusions.

2. Dependent state estimationmodel

Any state estimator can be formulated as a nonlinear multiple

regression problem, where theunknown parameters are thenode

voltage magnitude andangle of every node, represented by Vi and

i, respectively. These two sets of variables form the state vector

x = [VT T]T. There are n state variables. The unknown true state

is represented by xtrue.

The unknown parameters are estimated using the informationprovided by observations {z1, . . .,zm}. These observationsare cap-tured from the system using measuring devices, and are related

with x bymeans of a multifunctional vector h( x). Depending onthe measurement type, the functions hi( x) differ. Expressions offunctions hi(x) arewell-established in the technical literature [1].

The error terms used throughout this paper are definedbelow:

Measurement residual: difference between the measurement ziand the function hi(x) evaluated at the optimal state x,

Residuali = zi hi(x)|x=x =zi hi(x) = ri. (1)

Measurement error: difference between the measurementzi and

the function hi(x) evaluated at any state x,

Errori = zi hi(x)|x=x =zi hi(x) = ei. (2)

Metering error: difference between the measured value and the

unknown true value,

Meteringerrori =zi hi(x)|x=xtrue = zi hi(xtrue) = zi z

truei . (3)

Note that the term measurementresidual is solelyused in the

case of comparing measurement value zi with the function hi()

evaluatedat the optimal state x. Similarly, theterm measurementerroris solelyemployedfor comparingthemeasuredvalueziwith

the function hi(), evaluated at any state x.Measurement errors have been traditionally modeled as an

independent unbiased Gaussian-distributed random variable. The

factualmetering infrastructurewithin substations results in signif-icant statistical correlations between measurement errors. Works

[27] and [28] numerically show that these correlations are signif-

icant, and its consideration may improve the quality of the final

estimate. Therefore, hereafter measurement errors are assumed

to be dependentGaussian-distributed unbiased random variables.

Thedependence structureismodeledbymeans ofpositive-definite

non-diagonal variance-covariance matrix Cz, which can be easilycomputed using the Point Estimatemethod [28].

As it is customary in the technical literature, allmeasurements

areconsidered synchronous.Thisis reasonable since in steady state

power systemmagnitudes change very slowly with respect to the

time needed to transfer measurements to the EMS from Remote

Terminal Units (RTUs) or PhasorMeasurement Units (PMUs).

2.1. State estimation

Given thepreviousassumptions,theestimationof thestatevari-

ables are obtained by minimizing the weighted sum of squared

measurement errors of the multiple nonlinear regression model,

leading to a nonlinear optimization problem:

minimizex

J= [z h(x)]TC1z [z h(x)] (4a)

subject to

c(x) = 0 g(x) 0 (4b)

wherethescalarJistheobjectivefunctionand c(x)and g(x)arethe

equalityandinequality constraintsmodelingzero-injectionsnodes

and physical operating limits, respectively. Note that matrix Cz is

8/22/2019 Caro 2013

3/9

E. Caro et al. / Electric Power Systems Research 104 (2013) 917 11

not diagonal, since the considered model takes into account the

statistical correlations betweenmeasurement errors, but positive-

definite as it is a variance-covariancematrix.

2.2. Reweighted least squares formulation

The Weighted Least Squares model (4a) accounts for the error

measurements with different variances and their dependency.

However, an alternative weighting matrix can be used account-

ing for (i) different variances, (ii) dependency, (iii) and degree of

confidence related to eachmeasurement.

Inordertoderivethisweightingmatrixletusconsiderthevector

of measurement errors e = z h( x) and optimization problem(4). Using the Cholesky decomposition of matrix Cz, the objective

function in (4a) becomes

J= [e]TC1z [e]

= eT(LLT)1e = eT(L1)

TL1e

= (L1e)TL1e = uTu

(5)

where u is a vector of standard independent normal randomvari-ables, with covariance matrix equal to the identity matrix I, and

L is the lower-triangular Cholesky factor of matrix Cz. Note thatthe derivation above isbasedon theassumption that the estimated

state x issufficientlycloseto the true state xtrue,whichis a commonassumption in the state estimation Literature.

The aim of most outlier detection methods is to determine

whether or not a measurement should be considered as an out-

lier, without allowing for intermediate situations. In contrast, the

methodproposed in this paper, originally developed by [14], aims

at empirically determining a diagonal matrix W to be included inmodel (5), i.e.

JR = uTWu (6)

where wii is a weight for every observation ranging continuously

from 0, for observations that arecompletely unreliable, up to 1, for

observations that are completely reliable.

Considering (6), the objective function (5) becomes:

JR = eT(L1)

TWL1e = eTWRe. (7)

From (5) and (7), the followingobservations are in order:

The measurement error vector e (dependent normal randomvariables) is transformed into a vector of independent standard-

ized normal variables u [29].

The objective functionJcan be expressed as the sum of a set ofsquared independent standardized normal random variables.

The objective function JR is computed as the weighted sum of

squared independent standardized normal random variables.

Each factor u2iis multiplied by the weighting factor wii [0,1].

If the ith weighting factor is null (wii = 0), then the componentu2iis not considered in the objective functionJR. If, on the other

hand, wii = 1, the component u2iis fully considered inJR.

Theunderlyingideaof the RWLSmethodis toadjustempirically

the weighting factors, based on the degree of confidence of each

measurement.Thecoefficients for thosemeasurementscompletely

unreliable areadjusted to zero and, similarly, theweighting factors

for thosemeasurements completely reliable are adjusted to one.

The reweighting method is based on an iterative algorithm

which updates the weighting factors in every iteration, according

to theTuckeys biweight formula:

wii =

1

yi6

22if |yi| 6

0 if |yi| > 6(8)

whereyi =ui/* is thestandardizedresidual related touncorrelatedvector u, and * is the scaledmedianabsolute deviationestimator*:

=mediani|ui|

(3/4)

mediani|ui|

0.6745(9)

Reweighting techniques constitute an effective and computation-

ally attractive alternative to solve M-estimators. A significant

numberofM-estimatorshavebeendeveloped inthetechnical liter-

ature, such as least-absolute value, Huber, Cauchy,Welsh, Tuckey,

etc., and each type has an associated updating formula forweights,

such as (9) for Tuckeys case.Work [30] providea usefuldiscussion

about the choice of the appropriate function for practical cases.

Specifically, Tuckeys biweight do not guarantee uniqueness of thesolution, but the influence of gross errors is reduced considerable

or even eliminated [31].

Thus, theRWLS problem formulation is:

minimizex

J= [z h(x)]TWR[z h(x)] (10a)

subject to

c(x) = 0 g(x) 0 (10b)

Thealgorithmof theRWLSestimatorconsideringdependencies

is:

Initial non-dependent estimation. An initial WLS estimation is

performed to estimate the measurement variance-covariance

matrix. Using the initial estimation obtained x0) , matrix C0)z iscomputed via thePoint-Estimatemethod in [28].

Parameter initialization. Weights wii are set to one:w0)ii= 1,i

{1,m}.

The iteration counter is set to 1, =1. Dependent state estimation. The state estimation problem (10)

is solved considering measurement dependencies and the

reweighted matrix W1)R . The obtained estimates are denoted

as x).

Convergence checking. Once the estimates x)

are available, if

||x) x

1)|| > theestimation process continues in 5).

Otherwise, a solutionwitha tolerance is x)andthealgorithm

concludes.

Updateweightingmatrix WR. Once the estimatesof the statevari-ables are available (x

)), the weighting matrix WR

) is updated

using (8).

Set +1 and goto step(3).

Thecomputational efficiency of this algorithmcan be improved

by using x1)

as the initial values of the estimation in step (3).

The convergence of the iterative process does not only depend

on the reweighted technique employed, but also on the struc-

ture of the considered optimization problem (i.e., convexity or

linearity of the objective function, presence of equality/inequality

constraints, types ofvariables, etc.). Thus,convergence rulesare not

general. Specifically,work[30] discusses thechoice of anappropri-

atefunction,whereas[32] showsconvergence forcertainweighting

functions. For the optimization problem considered in the paper,

8/22/2019 Caro 2013

4/9


fast convergence is achieved in all cases, regardless the measure-

ment scenario, presence of baddata, or network used.

3. Design of Experiments

Section2 above presents a novel algorithm to estimate the

state of a power system in a robust manner. In this section, the

statistical procedures Design of Experiments and ANOVA are

briefly described as they are used (i) to analyze the performanceof the proposedmethod, and (ii) to compare it with other existing

methodologies.

Themethods considered in this paper are listedbelow:

WLS. The commonWeighted Least Squares estimator is used as

basic benchmark, using the 2-test and the Largest NormalizedResidual (LNR) test to detect and identify bad measurements,

respectively. These algorithms are well-established in the tech-

nical literature [1]. The WLS results are the final estimates once

the 2-test andLNR test have been successfully passed. DWLS. The estimation, detection, and identification algorithms

considering dependencies, proposed in [27] and [29], are

employed to estimate the state and to detectbadmeasurements

including the statistical correlation between measurements.Thus, the DWLS results correspond to the final estimate once the

badmeasurementshave been removed.

3.1. Performance assessment

In order to rigorously determine which is the methodwith best

performance, a Design of Experiments is carried out.Thisstatistical

procedure allows determining if the proposed algorithm is signif-

icantly better than the rest of the approaches with a pre-specified

confidence level, and taking into consideration the dissimilarities

among the considered measurement scenarios.

The performance of each method is assessed by means of the

followingmetrics:

MetricVMET,, definedas the averageabsoluteerrorof thevoltagemagnitude estimate for theth measurement scenario, consid-ering themethodMET, i.e.,

VMET, =

ni=1

|VMETi,

Vtruei,

|

n(11)

Note that the previousmetric ismeasured in p.u. MetricMET,, definedas the averageabsoluteerrorof thevoltageangle estimate for the th measurement scenario, consideringthe method MET, i.e.,

MET, =

ni=2

|METi,

truei,

|

n 1(12)

Thepreviousmetric ismeasured in radians. Note that the con-sidered reference angle is located at node 1, i.e., 1 =0 rad,for allthe considered scenarios.

Metric CPUMET , defined as the required CPU time to obtain the

final estimate considering themethodMETfor thethmeasure-

ment scenario. Note that this metric ismeasured in seconds.

3.2. ANOVAmodel

The model employed in this Design of Experiments proce-

dure comprises the factors Method and Scenario. This model

is described below,

yMET, = + MET + + uMET, (13)

Table 1

ANOVA model:factors and levels.

Names Levels

Factors Method WLS

(MET) DWLS

RWLS

Scenario () 1,. . ., n

Table 2ANOVA table structure.

Source SquaredSum Deg. o f freedom Mean-sq F-stat Fcrit

Method SSM 31 s2M s2M/s2error F

Methodcrit

Scenario SSD n 1 s2D s2D/s2error F

Scenariocrit

Residual SSerror (n 1)(31) s2error

where uMET,iid

N(0, 2) and:

MET

MET = 0;

n=1

= 0

where is theglobal effect, i.e., theaveragevalueof the consideredmetric yMET,. Parameter MET is the main effect of the estima-tion method, and measures the increase/decrease of the average

response of the factor Method (MET)with respect to the average

level. Likewise, parameter is the main effect of the factor Sce-

nario (), and it measures the increase/decrease of the averageresponse for all the methods with respect to the average level at

the th measurement scenario. Finally, the random effect uMET,includes the effects of all other causes not modeled. Taking into

consideration that the particularities of each measurement sce-

nariomayhave influence on the methods performance, the effect

Scenario is included inmodel (13).

The factors considered in this ANOVA analysis and the levels

corresponding toeach factorareprovided in Table 1. Parametern

stands for thenumber of measurement scenarios considered.Thebackground hypotheses of this model are: (i) normality, (ii)

constantvariance, and (iii) independence. To ensure this statistical

properties, an appropriate diagnosis procedure is performed after

the residual computation.

Sincetheaimof thisstudyis tofindthemostaccurateestimation

method and to check if it is significantly different from the other

methods, the following tests are performed:H0 : MET = 0,MET

H1 : MET|MET /= 0

H0 : = 0, = 1, . . . , n

H1 : | /= 0

The null hypothesis for the first test corresponds to the no

statistically-significant influenceof themethodontheaverageper-

formance. The alternative hypothesis establishes that it exists atleast one method performing different from the average. The sec-

ond test is analogous but related to the factor Scenario.

To perform the above two statistical hypothesis testing, the

ANOVA table is computed andanalyzed. Table 2 provides the gen-

eral structure for this table, particularized for the problem under

consideration. Thecomputationof theelements of thetable iswell

established in the technical literature [34]. Appendix A provides

further details concerningthe ANOVAtablestructure andthe com-

putation of its terms.

Once the ANOVA table is obtained, the value of the F-statistic

for the factor Method allows deciding whether or not the per-

formances of the different methods are statistically different. If

methods performances are statistically similar, F-stat will be low.

Otherwise, if there are significant dissimilarities among methods

8/22/2019 Caro 2013

5/9


Table 3

118-Bus system case study: ranges.

Vm m Pm Qm PFm QFm Im Buses Branches

118 [2; 4] [10; 103] [10; 103] [208; 231] [208; 231] [5; 20] 118 179

performances, the value ofF-stat will be high. In order to check if

the resulting F-stat is low or high, it is comparedwith FMethodcrit

:

IfF-statistic> FMethodcrit

, thenthe relatednullhypothesisisrejected

and it is concluded that the response variable is significatively

affected by the method employed. Then, the average values for

eachmethodand itsconfidenceintervalsareplottedtodetermine

which is the method with best performance. IfF-statistic< FMethod

crit, then it is concludedthattheperformances

of all methods are similar.

Withina certain confidence level (1), the parameter FMethodcrit

is definedas themaximum admissible value for a randomvariable

which follows an F-Snedeccor distribution with the corresponding

degrees of freedom. Alternatively, the parameter FMethodcrit

can be

defined as the limit value for the marginal right-side region with

anarea equal to for the F probability density function (see Fig. 6).The value ofFMethod

critis computed considering a confidence level of

95%, leading to false alarmprobability lower than 5%.

4. Case studies

In this section, four case studies are analyzed to check the esti-

mationaccuracyandcomputationalefficiencyof theproposedstate

estimator.

The networks under study are the IEEE 57-bus and the 118-

bus systems.1 To obtain statistically sound conclusions: (i) a set of

one hundred randomly-generatedmeasurement scenarios is con-

sidered, and (ii) an ANOVA procedure is performed to analyze the

obtained results.

Each scenario involves: (i) a randomactive/reactive power con-

sumption level, (ii) randomlocations of voltageandactive/reactive

power meters (ensuring observability of thewhole system), (iii) a

random redundancy level, and (iv) Gaussian-distributed random

errors in all measurements, (standard deviations of 0.01pu and

0.02pu for voltage andpower measurements, respectively).

Note that each scenario involves randomerrors in allmeasure-

ments. Theseerrors aremodeled as Gaussian-distributed unbiased

random variables, taking into consideration the actual metering

infrastructure of each substation. Ref. [27] provides more details

concerning the random measurement generation. The measure-

ment set is generated assuming perfect synchrony throughout all

substations.Futureworkwill considergenerationofmeasurements

exhibiting accidental asynchrony and its impact on the perfor-

mance of theproposedmethod.The allocation of meters is based on a random algorithm. This

algorithmhas been specifically designed for allocatingmeters in a

realisticway,providing scenariosthat satisfy thefollowing require-

ments:

The resulting measurement configuration provides whole

observability of the system. Themeasurement configuration provides a realistic redundancy

ratio, ranged from2.9 to 3.3.

1 Power Systems Test Case Archive. Available at: http://www.ee.washington.

edu/research/pstca/.

The numbers of measurements are well-balanced across mea-

surement types. Measurements are geographically allocated in an uniform man-

ner throughout the considered system.

The random allocation of metering devices is realistic since the

quantity and proportion of the allocated measurements are based

on reasonable ranges. Table 3 provides the ranges used for this

random allocation of measurements. Columns Vm, m, Pm, Qm,

PFm, QFm, and Im correspond to the voltage meters, PMU devices,

active/reactive power injectionmeters, active/reactive power flow

meters and current meters, respectively. PMUmeasurements are

modeled as in [35,36] The number of buses and branches of the

considered systemareprovided in the last twocolumns.

The computational analyses have been performed using a

Windows-basedpersonal computerwitha 64-bits four-core third-

generation i5 processor at 1.73GHz and 4Gb of RAM. Sections4.1

to 4.4 consider the IEEE 118-bus system, whereas Section4.5 con-

siders the IEEE 57-bus system.

4.1. First case study: no gross errors

In this case, the measurement vector z is free of gross errors.For each measurement scenario, the estimates for methods WLS,

DWLS, and RWLS are computed and an ANOVA analysis is per-

formed.

Table4provides the ANOVAanalysis formetrics VMET, MET, and

CPUMET, and Fig. 1 depicts the average value for these metrics and

theconfidence intervals for a 95%confidence level.

FromTable 4 and Fig. 1, the following observations arein order:

From theANOVAanalysis ofmetricVMET in Table 4, it is observedthat F-stat= 39.2 > FMethod

crit= 3.03. This indicates that the accu-

racy of the methods for estimating voltage magnitudes are not

the same. Thus, in order to determine graphically which is the

methodwith higher accuracy, the mean and confidence interval

of metric VMET are plotted in Fig. 1. Similarly, the F-statistics formetricsMET and CPUMET are higherthan the critical values. Then, the mean and confidence interval

of these metric are plotted in Fig. 1 to allow determining which

is themethod with better accuracy estimating the voltage angle,

andwhich is themethod computationally more efficient. Regarding estimation accuracy (left and center subplots), the

WLS estimator is the less accurate, whereas theDWLS andRWLS

Table 4

ANOVA table for thefirst case study.

Source Squared Sum DoF Mean-sq F-stat Fcrit

Metric VMET

Method 2.4106 2 1.2106 39.232 3.03

Scenario 4.1105 99 4.1107 13.490 1.30

Residual 6.0106 198 3.0108

Metric MET

Method 2.1105 2 1.1105 111.094 3.03

Scenario 4.0105 99 4.0107 4.196 1.30

Residual 1.9105 198 9.6108

Metric CPUMETMethod 6.0101 2 30 11.975 3.03

Scenario 4.3102 99 4.3 1.721 1.30

Residual 5.0102 198 2.5
http://www.ee.washington.edu/research/pstca/http://www.ee.washington.edu/research/pstca/http://www.ee.washington.edu/research/pstca/http://www.ee.washington.edu/research/pstca/http://www.ee.washington.edu/research/pstca/

8/22/2019 Caro 2013

6/9


Fig. 1. Results for thecase studywith no gross errors: performance comparison.

procedures provide the most accurate results for a confidence

level of 95%. There is no significant difference between theaccuracy provided

by the DWLS and RWLSmethods. Regarding the required CPU time, methods WLS and RWLS are

the most efficient.

4.2. Second case study: three gross errors

In this case, the measurement vector contains bad data. The

corresponding scenarios are generated as follows [27]:

1. Vector ztrue isderived fromapowerflowsolution. Then, random

Gaussian-distributednoiseis added toallmeasurements in ztrue

to derive measurement vector z.2. Three substations are randomly selected, and for eachof them:

A metering transformer is randomly selected. Both phase and

transformer type (current or voltage) are also randomly cho-

sen. Then, a gross error is included in theselected transformer

signal.All measurements from this substation are computed takinginto account the erroneous transformer signal. Thus, two or

moreprocessedmeasurements in thissubstation aredistorted

as a result of an interacting and conforming error [29].

Again, Table 5 provides the ANOVA analysis for metrics VMET,

MET, and CPUMET, and Fig. 2 depicts the average value for these

metrics and the confidence intervals for a 95% confidence level.

FromTable 5 and Fig. 2, the followingobservations are in order:

From Table 5, note that the three F-stat values correspond-

ing to the factor Method are higher than 3.03, denoting that

there are statistically significant differences regarding the per-

formanceof the consideredmethods, fornumericalaccuracyand

Table 5

ANOVA table forthe secondcase study.


Metric VMET

Method 5.2106 2 2.6106 26.339 3.03

Scenario 6.3105 99 6.3107 6.406 1.30

Residual 2.0105 198 9.9108

Metric MET

Method 3.4105 2 1.7105 95.202 3.03

Scenario 4.6105 99 4.6107 2.597 1.30

Residual 3.5105 198 1.8107

Metric CPUMETMethod 4.7102 2 2.3102 54.899 3.03

Scenario 8.5102 99 8.5 2.010 1.30

Residual 8.4102 198 4.3

computational efficiency. Thus, the confidence interval plots

(Fig.2) arestudied to determinewhichmethod provides the best

performance. Regardingestimationaccuracy (leftandcentersubplots), theWLS

estimator is the less accurate, whereas the DWLSand RWLSpro-

cedures provide the most accurate results for a confidence level

of 95%. There is no significant difference between theaccuracy provided

by the DWLS and RWLSmethods. Regardingthe requiredCPUtime,theRWLS estimatoris themost

efficient. The efficiency provided by the WLS and DWLS algo-

rithms are statistically similar.

4.3. Third case study: six gross errors

In this case, six substations are randomly chosen, and a set of

multiple gross errors is located in each substation. Thus, the mea-

surement vector is corrupted by six sets ofmultiple bad data.

Table6 provides the ANOVAanalysis formetrics VMET, MET, and

CPUMET, and Fig. 3 depicts the average value for these metrics and

the confidence intervals for a 95% confidence level.FromTable 6 and Fig. 3, the followingobservations arein order:

Results fromTable 6 allowwithdrawing the same conclusions as

in the previous section: there are significant differences among

methods accuracy and efficiency. Again, theWLSestimatoris the least accurate,whereas theDWLS

andRWLS procedures provide the most accurate results. RegardingtherequiredCPUtime, theRWLSestimatoris againthe

most efficient, and the DWLS algorithm is the less efficient one. The required CPU time for the RWLS estimator is approximately

75% and 72% smaller than the CPU times required by the DWLS

andWLS methods, respectively.

Table 6

ANOVA table for thethird case study.


Metric VMET

Method 2.6105 2 1.3105 57.645 3.03

Scenario 9.1105 99 9.1107 4.035 1.30

Residual 4.5105 198 2.3107

Metric MET

Method 3.0105 2 1.5105 100.764 3.03

Scenario 6.6105 99 6.7107 4.475 1.30

Residual 3.0105 198 1.5107

Metric CPUMETMethod 2.2103 2 1.1103 133.953 3.03

Scenario 2.1103 99 2.1101 2.573 1.30

Residual 1.6103 198 8.1100

8/22/2019 Caro 2013

7/9


Fig. 2. Results for thecase studywith three gross errors: performance comparison.

Fig. 3. Results forthe case studywith six gross errors: performance comparison.

4.4. IEEE 118-bus system: results comparison

Analyzing jointly the results obtained for the three case studies

above, the following conclusions can bewithdrawn:

1. Theestimation accuracy of the proposed RWLS algorithm is sig-

nificantly better than the one provided by the traditional WLS

procedure, for a 95% confidence level and considering scenarios

with zero, three, and six sets ofmultiple gross errors.

2. For a 95% confidence level, there is no significant difference

between the estimation accuracy degree of methods RWLS and

DWLS. That is, theobtained estimate for both methods have the

sameaccuracy.

0 3 60

2

4

6

8

Number of errors

AveragerequiredCPUtime(sec.)

WLS

DWLS

RWLS

Fig. 4. Required CPU time comparison.

3. The computational efficiency of the RWLS remains unalteredwith independence of the number of multiple gross errors

corrupting the measurement set. This consideration can be

graphically illustratedbyplottingthe averagerequiredCPUtime

for each method as a function of the number of multiple bad

measurement sets (see Fig. 4).

4. Note thatthemostaccurateestimatesdoesnotcorrespond tothe

WLS results. This is sobecauseWLSestimationdoes notconsider

measurement dependencies.

4.5. Fourth case study: IEEE 57-bus system

Finally, methods WLS, DWLS and RWLS are applied to another

system: the IEEE 57-bus network.2 Results are graphically shown

in Fig. 5, using the same format as in Figs. 13.From Fig. 5, the followingobservationsare in order:

1. The estimation accuracy provided by algorithms DWLS and

RWLS are similar.

2. The accuracylevel ofmethodWLS is significantlylowerthanthe

levels provided by approaches RWLS andDWLS.

3. TherequiredCPU timeof themethodRWLSis significantly lower

than theCPUtimes required by approachesWLSandDWLS. The

saving is up to 80%.

2 Power Systems Test Case Archive. Available at: http://www.ee.washington.

edu/research/pstca/.
http://www.ee.washington.edu/research/pstca/http://www.ee.washington.edu/research/pstca/http://www.ee.washington.edu/research/pstca/http://www.ee.washington.edu/research/pstca/

8/22/2019 Caro 2013

8/9


Fig. 5. Performance of themethods:IEEE 57-bus system.

5. Conclusion

The method proposed in this paper outperforms alternative

algorithms reported in the technical literature in the consid-

ered cases, especially if the number of gross errors or outliers

in the measurement set is large. If the proposed RWLS approach

is implemented in real-world systems, a similar behavior is

expected, in termsof both computational efficiency andnumerical

accuracy.

The proposed RWLS estimator takes into consideration mea-

surement dependencies to improve accuracy and its weights are

automatically readjusted to increase robustness. In summary, it

provides accurate estimates, is robust against outliers, and is com-

putationally efficient.

The methods performance is tested using several realisticcase study with single and multiple gross errors, and consider-

ing a high number of scenarios. These results are compared in

detail using ANOVA techniques, which allows proving the out-

performance of the proposed method from a statistical point of

view.

Since most of the state estimation algorithms used in practice

arebasedonWLStechniques,suchalgorithmscanbeeasilyadapted

ormodified to include RWLS features.

Acknowledgements

Eduardo Caro would like to thank partial financial support by

Project DPI2011-23500, Ministerio de Ciencia e Innovacin, Spain.

Appendix A. ANOVA table description

In this Appendix, the ANOVA table structure presented in Sec-

tion3.2 is described in detail.

The first column provides the sources of variability accord-

ingto model (13): factor Method, factor Scenario andresiduals.

The corresponding variabilities are quantified by the Squared Sum

terms, provided in the secondcolumn.

These terms are computed using the followingexpressions:

SSM = n

3M=1

(yM y)2 (A.1)

SSD = 3

n=1

(y y)2 (A.2)

SSerror =

n=1

3M=1

(yM yM y + y)2 (A.3)

where yM is the average response for the METth method consid-eringall scenarios; y is theaverage response for theth scenario

consideringallmethods; y is theaverageresponseconsideringall

scenarios andmethods.

8/22/2019 Caro 2013

9/9


Fig. 6. F-Snedeccor distribution.

These Squared Sum terms are divided by their corresponding

degrees of freedom3 (third column), obtaining the variances for

each factor, denoted as SSM, SSD, and SSerror.

The aim of the ANOVA analysis is to determine whether or not

the factors affect the response variable. This can be checked by

comparing the above variances. The way of comparing them is by

computing the ratios s2M/s2error and s

2D/s

2error.

If the performance is not influenced by the method employed,

the ratio s2M/s2error is low. On the other hand, if the performance

varies depending on the methodused, this ratio is high.Inordertodetermineit a ratiois lowor high,theF-Snedeccor

distribution is used (see Fig. 6). Theratio s2M/s2error is computed and

located in the X-axis. If it is lower than FMethodcrit

, then the perform-

ances of the methods are similar (the hypothesis H0 is accepted).

On the contrary, if the ratio s2M/s2error is higher than F

Methodcrit

, then

there is statistical evidence that the methods perform different.

Note that thevalue Fcrit depends on the degrees of freedomused

and on the confidence level employed. These values are provided

in the last column of the ANOVA table, for a confidence level of

95%. Note also that Fig. 6 provides an example of value s2M/s2error. In

this case (Fig. 6), thehypothesisH0 is accepted, concluding that the

methods exhibit the same performance.

References

[1] A. Abur,A. Gmez-Expsito, PowerSystemStateEstimation.Theoryand Imple-mentations,MarcelDekker, NewYork, 2004.

[2] F.C. Schweppe, J. Wildes, Power system static state estimation. Part I. Exactmodel, IEEE Transactions on Power Apparatus and Systems 89 (1) (1970)120125.

[3] H.M. Merrill, F.C. Schweppe,Bad data suppression in power systemstatic stateestimation, IEEE Transactions on Power Apparatus and Systems 90 (1970)27182725.

[4] D.M. Hawkins, Identification of Outliers,Chapman andHall, London, 1980.[5] D.A.Belsley,E. Kuh,R.E.Welsch,RegressionDiagnostics: Identifying Influential

Data andSources ofMulticollinearity, John Wiley & Sons, NewYork, 1980.[6] R.D. Cook, S. Weisberg, Residuals and Influence in Regression, Chapman and

Hall, NewYork, 1982.[7] A.C. Atkinson, Plots, Transformations, and Regression: An Introduction to

GraphicalMethodsofDiagnosticRegressionAnalysis,Oxford: ClarendonPress,NewYork, 1985.

[8] S. Chatterjee, A.S. Hadi, Sensitivity Analysis in Linear Regression, John Wiley &Sons, NewYork, 1988.

3 The number of degrees of freedom is the number of independent values in the

final calculation of a statistic that are free to vary.

[9] V. Barnett, T. Lewis,Outliers in Statistical Data, 3rdedition,JohnWiley & Sons,NewYork, 1994.

[10] Confirmation of multiple outliers in generalized linear and nonlinear regres-sions, Computational Statistics & Data Analysis 25 (1) (1997) 5565.

[11] J.W. Wisnowski, D.C. Montgomery, J.R. Simpson, in: A comparative analysis ofmultiple outlier detection procedures in the linear regression model, Compu-tational Statistics & Data Analysis 36 (3) (2001) 351382.

[12] A. Luceno, in: Estimation ofmissing values in possibly partially nonstationaryvector time series, Biometrika 84 (1997) 495499.

[13] A. Luceno, in: Detecting possibly non-consecutive outliers in industrial timeseries, Journal of theRoyalStatistical Society, Series B: StatisticalMethodology

60 (1998) 295310.[14] A. Luceno, in:Multiple outliers detection through reweightedleast deviances,

Computational Statistics & Data Analysis 26 (1998) 313326.[15] N. Billor, S. Chatterjee, A.S. Hadi, in: Iteratively re-weighted least squares

method for outlier detection in linear regression, Bulletin of the InternationalStatistical Institute 1 (2001) 470472.

[16] E. Castillo, A.S. Hadi, A.J. Conejo, A. Fernndez-Canteli, in: A general methodfor local sensitivity analysis with application to regression models and otheroptimization problems, Technometrics 46 (4) (2004) 430445.

[17] T.-C. Cheng, in: Robust diagnostics for the heteroscedastic regression model,Computational Statistics & Data Analysis 55 (2011) 18451866.

[18] P.J. Rousseeuw, A.M. Leroy, Robust Regression and Outlier Detection, JohnWiley & Sons, New York, 1987.

[19] P.J. Rousseeuw, K. VanDriessen, in: A fast algorithm for theminimum covari-ance determinant estimator, Technometrics 41 (1999)212223.

[20] E. Caro, A.J. Conejo, in: State estimation via mathematical programming: acomparison of different estimation algorithms, IEE Proceedings-GenerationTransmission andDistribution6 (6) (2012) 545553.

[21] R. Mnguez, B.G. Reguero, A. Luce no, F .J . Mndez, in: Regression mod-

els for outlier identification (hurricanes and typhoons) in wave hindcastdatabases , Journal of Atmospheric and Oceanic Technology 29 (2012)267285.

[22] L. Guangyi, Y. Erkeng, Y. Song, in: Novel algorithms to estimate and adap-tivelyupdatemeasurementerrorvarianceusingpowersystemstateestimationresults, Electric Power Systems Research 47 (1) (1998) 5764.

[23] S. Zhong, A. Abur, in: Auto tuning of measurement weights inWLS state esti-mation, IEEE Transactionson Power Systems 19 (4) (2004) 20062013.

[24] R. Pires, A. Simoes Costa, L. Mili, in: Iteratively reweighted least-squares stateestimation through givens rotations, IEEE Transactions on Power Systems 14(4) (1999)14991507.

[25] R. Jabr, B. Pal, in: Iteratively reweighted least-squares implementation of theWLAV state-estimationmethod, IEEProceedings-GenerationTransmissionandDistribution151 (1) (2004) 103108.

[26] D. Wiens, in: Designs for weighted least squares regression, with estimatedweights, Statistics andComputing (2012) 111.

[27] E. Caro, A.J. Conejo, R.Mnguez, in:Powersystem state estimation consideringmeasurementdependencies,IEEETransactionson PowerSystems24 (4)(2009)

18751885.[28] E. Caro, A.J. Conejo, J. Morales, R. Mnguez, in: Calculation of measurementcorrelations using point estimate, IEEE Transactions on Power Delivery 25 (4)(2010)20952103.

[29] E. Caro, A.J. Conejo, R. M nguez, M. Zima, G. Andersson, in:Multiple bad dataidentification considering measurement dependencies, IEEE Transactions onPower Systems 26 (4) (2011) 19531961.

[30] P.W. Holland, R.E. Welsch, in: Robust regression using iteratively reweightedleast-squares, Communications in Statistics Theory andMethods A6 (1977)813827.

[31] W.J.J . Rey, Introduction to Robust and Quasi-Robust Statistical Methods,Springer, Berlin, Heidelberg, 1983.

[32] H. Xuming, S. Portnoy,in: Reweighted LS estimators converge at thesamerateas theinitial estimator, TheAnnalsof Statistics 20 (4) (1992) 21612167.

[34] H. Scheff, TheAnalysis of Variance,Wiley,NewYork, 1959.[35] S. Chakrabarti,E. Kyriakides, G. Ledwich, A. Ghosh,in: On theinclusion of PMU

current phasormeasurements in a power systemstate estimator, IETGenera-tion, Transmission& Distribution4 (10) (2010) 11041115.

[36] E. Caro, R. Singh,B.C. Pal, A.J. Conejo, R.A. Jabr, in:Participation factorapproach

for phasor measurement unitplacement in powersystemstateestimation, IEEProceedings-Generation Transmission andDistribution 6 (9) (2012)922929.
http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0005http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0005http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0010http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0010http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0010http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0010http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0015http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0015http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0015http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0015http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0020http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0025http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0025http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0030http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0030http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0035http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0035http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0035http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0040http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0040http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0040http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0040http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0040http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0045http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0045http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0050http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0050http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0050http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0055http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0055http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0055http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0055http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0060http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0060http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0060http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0060http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0060http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0170http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0180http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0175http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0170http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0170http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0170http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0170http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0170http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0170http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0170http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0170http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0170http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0170http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0160http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0155http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0150http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0145http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0140http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0135http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0130http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0125http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0120http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0115http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0110http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0105http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0100http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0095http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0090http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0085http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0080http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0075http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0070http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0065http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0060http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0060http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0060http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0060http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref0060http://refhub.elsevier.com/S0378-7796(13)00150-8/sbref006

Documents

Caro 2013