Conductor Temperature State Estimation and Prediction at

Aalborg Universitet

Conductor Temperature Estimation and Prediction at Thermal Transient State inDynamic Line Rating Application

Alvarez, David L.; Silva, Filipe Miguel Faria da; Mombello, Enrique Esteban ; Bak, Claus Leth;Rosero, Javier A.Published in:I E E E Transactions on Power Delivery

DOI (link to publication from Publisher):10.1109/TPWRD.2018.2831080

Publication date:2018

Document VersionAccepted author manuscript, peer reviewed version

Link to publication from Aalborg University

Citation for published version (APA):Alvarez, D. L., Silva, F. M. F. D., Mombello, E. E., Bak, C. L., & Rosero, J. A. (2018). Conductor TemperatureEstimation and Prediction at Thermal Transient State in Dynamic Line Rating Application. I E E E Transactionson Power Delivery, 33(5), 2236-2245. [8352008]. https://doi.org/10.1109/TPWRD.2018.2831080

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRD.2018.2831080, IEEETransactions on Power Delivery

Conductor Temperature Estimation and Predictionat Thermal Transient State in Dynamic Line Rating

ApplicationDavid L. Alvarez, Student Member, IEEE, F. Faria da Silva Member, IEEE, Enrique E. Mombello Senior

Member, IEEE, Claus Leth Bak Senior Member, IEEE, and Javier A. Rosero Member, IEEE,

Abstract—The traditional methodology for defining the ampac-ity of overhead lines is based on conservative criteria regardingthe operating conditions of the line, leading to the so-calledstatic line rating. Although this procedure has been consideredsatisfactory for decades, it is nowadays sensible to account formore realistic line operating conditions when calculating itsdynamic ampacity. Dynamic line rating is a technology usedto improve the ampacity of overhead transmission lines basedon the assumption that ampacity is not a static value but afunction of weather and line’s operating conditions. In orderto apply this technology, it is necessary to monitor and predictthe temperature of the conductor over time by direct or indirectmeasurements. This paper presents an algorithm to estimate andpredict the temperature in overhead line conductors using anExtended Kalman Filter, with the aim of minimizing the meansquare error in the current and subsequent states (temperature)of the conductor. The proposed algorithm assumes both actualweather and current intensity flowing along the conductor ascontrol variables. The temperature of the conductor, mechanicaltension and sag of the catenary are used as measurements becausethe common practice is to measure these values with dynamicline rating hardware. The algorithm has been validated by bothsimulations and measurements. The results of this study concludethat it is possible to implement the algorithm into DynamicLine Rating systems, leading to a more accurate estimation andprediction of temperature.

Index Terms—Dynamic Line Rating (DLR), Dynamic StateEstimation, Extended Kalman Filter (EKF), Overhead Line(OHL)

I. INTRODUCTION

W ITH the constant increase in power consumption, anupgrade and update of current assets are necessary for

control and operation of existing power networks. As a resultof the advances in renewable power generation, such as windand solar energy, there exists a constant growth in new powerplants. Therefore, bottlenecks are arising in transmission level,mainly in overhead lines (OHLs), which are facing economic,social, political and implementation time challenges. In orderto reduce both congestion and face these challenges, different

David L. Alvarez and Javier A. Rosero are with the Departamentode Ingenierıa Electrica y Electronica, Facultad de Ingenierıa, Universi-dad Nacional de Colombia, Bogota, Colombia ([email protected] [email protected])

F. Faria da Silva and Claus Leth Bak are with the Department of En-ergy Technology, Aalborg University, Aalborg, Denmark ([email protected] [email protected]

Enrique E. Mombello is with the Instituto de Energıa Electrica,CONICET, Universidad Nacional de San Juan, San Juan, Argentina([email protected])

techniques [1] can be used depending on the characteristicsof the line. Among these solutions is monitoring the line stateallowing the assessment of thermal limits and the applicationof DRL [2], as long as the ampacity is limited by the sagof the catenary. As the forerunner of DLR, OHL’s ampacityby probabilistic methods was introduced using seasonal atmo-spheric conditions [3]. Subsequently, the monitoring of OHL’sthermal state was reached using information technologies.

Because of only one span in an OHL can limit the ampacityand its behavior depends on the adjacent suspension spans,this set of spans is assumed monitored for DLR. This set iscommonly known as the critical stringing section. However,this section can change over time as a result of weathervariations. Consequently, different methodologies can be usedto identify critical stringing sections and to define DLR deviceslocation [4], [5].

In OHLs, two types of thermal limits are defined. The firstone is related to thermal equilibrium (steady state) and used forplanning and control. The second one is related to transientstate and given by a relationship between current intensityand time; this limit is used for contingencies assessmentduring operation. Using DLR, the data required to definethese two limits are historic reports of weather or low scaleatmospheric models based on local measurements [6] anddirect measurements in critical stringing sections whether ofsag length, mechanical tension, inclination, clearance, amongothers [7].

The ampacity limit at steady state using DLR can estimatewith weather forecast [8]. On the other hand, to computedynamic limits (at thermal transient state) with DLR, it isnecessary to know on-line both the conductor temperatureand the atmospheric conditions. To this end, some techniquesare proposed, such as computing wind speed from directmeasurements [9] or including a weather station together withthe direct monitoring device [10]. However, given the nature ofthe atmospheric conditions, which vary in space and time andthe uncertainty in the parameters of the OHL, an inaccuracyis obtained in the ampacity when the temperature is used [11].

The variation in the atmospheric conditions along a string-ing section can be modeled by the average conductor tem-perature with an effective wind speed in order to avoid spottemperature [12]. The impact of data uncertainty is addressedin the literature. For instance, the uncertainties in input dataas well as in the parameters used in heat transfer modelsare addressed by affine arithmetic in [13]. Similarly, robust



corrective control measures considering the weather forecastuncertainty is used in reference [14]. The impact of theuncertainty in both the catenary parameters and temperaturein the calculation of the sag is analyzed in [15]. An enhancedmethodology is presented in [16] using on-line information ofa self-organized sensor network. This network uses tempera-ture sensors and has the ability to predict, estimate and validateinformation used for DLR. In this way, this paper presents astate estimation algorithm for DLR at thermal transient statewhich allows to estimate and predict the average conductortemperature of stringing sections. The algorithm is based onan Extended Kalman Filter (EKF), and it has the advantageof using available DLR systems. To implement the EKF, it isprovided that the set of critical stringing sections are monitoredby DLR hardware and their atmospheric conditions are known.

The motivation to propose this algorithm is that currentlyused methods to minimize errors in the estimation of tem-perature in OHLs [17], [18], [19] are probably not the bestchoice for on-line dynamic state estimation during thermaltransients. With the EKF, estimation and prediction of bothstates and parameters of nonlinear dynamic systems is reached[20]. Additionally, the uncertainties in the atmospheric con-ditions, the current intensity and the direct measurementsare considered by the proposed EKF with the computing ofcovariance propagation matrix and the Kalman gain. The statevariables of the proposed EKF are the average conductortemperature, the average effective wind speed, the emissivityand the solar absorptivity of conductor surface. The averagetemperature was chosen because it is possible to estimate theOHL ampacity with this value. The consideration of additionalparameters leads to improvements in temperature prediction,since wind speed has the greatest impact on cooling [12],and emissivity and absorptivity commonly present a highuncertainty [21].

This paper is organized as follows: Section II provides abrief introduction to heat transfer in OHL’s conductor andto direct measurements used in DLR. Section III introducesthe algorithm developed. Section IV presents a case studyand experimental test carried out with the aim of evaluatingthe performance of the algorithm. Finally, conclusions arepresented in section V.

II. BACKGROUND

Thermal behavior of OHLs is determined by heat transferas a result of heat gains and heat losses. This phenomenonaffects the thermal, electrical, and mechanical characteristicsof OHLs. Consequently, it is possible to estimate the thermalstate of the conductor by monitoring these physical changes.

A. Heat Transfer at Transient StateHeat transfer in OHL conductors is a well-known process

[22] and is described in standards and guides [21], [23]. Themain equation for this process is

dTS

dt=ikm

2R (TS) + qs − qc (TS)− qr (TS)

mCp(1)

where TS is the temperature of the conductor at the surface,ikm is the current intensity, R is the ac electrical resistance

per unit length, qs is the solar heating, qc is the convectivecooling, qr is the radiative cooling, m is the mass per unitlength and Cp is the specific heat capacity of the conductor.Equation (1) can solve by numerical integration by using

∆TS =ikm

2R (TS) + qs − qc (TS)− qr (TS)

mCp∆t (2)

taking time intervals ∆t, provided that the initial temperature,the thermal parameters of the conductor and the atmosphericconditions along the integration time are known. The comput-ing time to calculate temperature by this numerical methodis not a problem with modern computers, because undercontingencies or normal operation the thermal constant of theconductors is higher (commonly 15 min) than the processingtime used to solve it (less than 1 s).

The maximum current intensity (|ikm|max) at conductorreach the thermal equilibrium can compute using the maxi-mum allowable conductor temperature (TSmax) as follow

|ikm|max =

√qc (TSmax

) + qr (TSmax)− qs

R (TSmax)

(3)

Thus, OHL’s ampacity can be estimated using both static ordynamic line ratings. For contingencies management, com-monly the maximum current intensity vs time plot is computedsolving (1) until the conductor reach the maximum allowabletemperature for different values of ikm.

B. Direct Measurements for DLR

Although (1) correctly models the behavior of tempera-ture in OHL’s conductors, there exist uncertainties in thecomputing results because of inaccuracies in the inputs andparameters. Thus, direct measurements for DLR are requiredin critical stringing sections to enhance the accuracy. Withthese measurements, the thermal state is measured discretelyby taking samples between 1 min and 10 min [12], allowinga thermal monitoring. Direct measurements are classified byCIGRE [7] into temperature, sag and mechanical tension.From measurements of these variables, the temperature of theconductor is computed using known relationships, such as thestate equation (temperature related to tension) and the catenaryequation (related tension with sag). Although the conductortemperature can be directly monitored, the monitoring systemhas errors produced whether by changes in the temperaturealong the span, the influence of measurement devices overthe spot where the reading is taken, uncertainties in thecatenary parameters such as the mechanical tension reference,conductor creep, among others. Finally, an error propagationoccurs in the prediction of temperature during a thermaltransient given the uncertainty of atmospheric conditions. Forinstance, when the temperature in the conductor reaches thesteady state after a thermal transient, it is not affected by theinitial value of temperature, but only atmospheric conditionsand current intensity.

III. PROPOSED DYNAMIC STATE ESTIMATOR

A hybrid EKF algorithm is proposed in this paper sincethe heat transfer phenomenon in conductors is continuous



Heat transferu (t)

w (t)

h (xk,vk)

vk

x (t) zk

EKF˙x−k = f(x+k−1,u, 0, t

) x−k

P−k

x+k

P+k

P+k−1

x+k−1

• •

•

•

DYNAMIC PHENOMENON

MODEL

MEASUREMENT PROCESS

PREDICTION UPDATE

DYNAMIC STATE ESTIMATION

Figure 1. Proposed EKF model to estimate and predict thermal states onOHL conductors

in time, and measurements for DLR are commonly taken atdiscrete times. With this algorithm is aimed to estimate andpredict the temperature in OHL’s conductors by using bothdirect measurements of DLR and the atmospheric conditions.To implement an EKF is necessary to model the system(x = f (x, . . .)), predict future states

(x−k)

and update the cur-rent states

(x+k

)with new measurements (zk). The proposed

EKF for DLR is described by means of Fig. 1 as follows:

A. System modeling

Significant errors in the prediction of the temperature duringa thermal transient occur mainly because of inaccuracies inthe value of wind speed under forced cooling. Additionally,the values of emissivity (εs) and solar absorptivity (αs) ofconductor surface can vary between 0.2 and 0.9 [21], de-pending on the environmental conditions and time. Hence, thispaper proposes to consider (εs, αs), along with the effectivewind speed (|ϑ|) and the average conductor temperature asstate variables. By assuming that OHL’s thermal constant isin a time interval of 5 - 15 min and based on CIGRE rec-ommendations [12], |ϑ| can consider as the average effectivewind speed during this period and therefore assumed constant.Likewise, εs and αs are assumed constant. Thus, the systemcan be modeled by

x =

f (x,u,w, t)

000

zk = h (xk,vk)

w (t) ∼ (0,Q)

vk ∼ (0,Rk)

(4)

where f is the function (1), x is the state vector, u is the vectorof control variables, t is the time and w are the errors in thesystem. The state vector is x =

[TS |ϑ| εs αs

]T. The

control variables selected are |ikm|, the ambient temperature(Ta), the wind attack angle (δ) and the solar radiation (S),i.e., u =

[|ikm| Ta δ S

]. Finally, the state variables are

related to a set of measurements zk at time k by means ofmeasurement functions h (xk,vk), which have errors vk. The

errors vk and w are assumed to have a normal probabilitydistribution with mean zero and covariance Q and Rk.

B. Prediction of future states

To predict a future state, a system error w = 0 is assumedand a state prediction

(x−k)

is carried out at time t by

˙x−k =

f(x+k−1,u, 0, t

)000

P−k = FP+

k−1 + P+k−1F

T + LQLT

(5)

taking the estimation of the current states(x+k−1). ˙x−k is

computed by numerical integration (2). P is the covarianceof the estimation error, F is the Jacobian of the model withrespect to state variables (F = ∂f/∂x) calculated by

F =

df

dTS

df

dϑ

df

dεs

df

dαs0 0 0 00 0 0 00 0 0 0

∣∣∣∣∣∣∣∣∣∣x,u

(6)

and L is the Jacobian of the model with respect to controlvariable errors (L = ∂f/∂w) computed using

L =

df

dwikm

df

dwTa

df

dwδ

df

dwS0 0 0 00 0 0 00 0 0 0

∣∣∣∣∣∣∣∣∣∣x,u

(7)

C. Update of current states

The system update is performed by

Kk = P−kHTk

(HkP

−kH

Tk + MkRkM

Tk

)−1x+k = x−k + Kk

(zk − h

(x−k))

P+k = (I−KkHk)P−k (I−KkHk)

T+ KkMkRkM

TkK

Tk

(8)

using the measurements recorded at time k, where K is theKalman gain, H is the Jacobian of the measurement functionsrespect to state variables (H = ∂h/∂x) calculated with

H =

[dh

dTS0 0 0

]∣∣∣∣x

(9)

and M is the Jacobian of the measurement functions respectto measurement errors (M = ∂h/∂v) computed by

M =dh (TS)

dv

∣∣∣∣∣x

(10)

The expressions used for computing the partial derivativesof matrices F,L,H,M can be found in [19]. Finally, theproposed EKF for DLR estimation is shown in algorithm 1.



Algorithm 1 Proposed algorithm for DLR Dynamic SE1: procedure HYBRIDEKF(zk,uk,x+

k−1,P+k−1,∆t,tk,Q,Rk)

2: x−k ← x+k−1

3: P−k ← P+k−1

4: for j ← ∆t to tk step ∆t do . Predict5: ˙x−k ← f

(x−k , u, 0,∆t

)6: x−k ← x−k + ˙x−k7: F← ∂f/∂x|x−k ,uk

8: L← ∂f/∂w|x−k ,uk

9: P−k ← FP−k + P−k FT + LQLT

10: P−k ← P−k + P−k11: end for12: Hk ← ∂h/∂x|x−k13: Mk ← ∂h/∂v|x−k14: Kk ← P−kH

Tk

(HkP

−kH

Tk + MkRkM

Tk

)−115: x+

k ← x−k + Kk

(zk − h

(x−k))

. Update16: P+

k ← (I−KkHk)P−k (I−KkHk)T

+KkMkRkM

TkK

Tk

17: return(x+k ,P

+k

)18: end procedure

IV. ALGORITHM VALIDATION

In this section, both simulations and an experimental testare performed to validate the effectiveness of the proposedEKF. Algorithm 1 was implemented in Matlab R© with timesteps ∆t = 0.1 [s]. The EKF was evaluated in the estimationof temperature for real time monitoring and in the predictionof temperature for contingencies management as follows:

Temperature Estimation: each measurement sample wasprocessed using the Algorithm 1, where x+

k and P+k are

updated, and used as inputs for the next estimation, as shownin Fig. 1. Thus, the ability of the EKF to use the informationof previous measurements is used.

Temperature Prediction: it is performed to obtain thepredicted value of temperature at time k + ∆tC , where ∆tCis the assumed duration of a contingency. Thus, a temperatureprediction is performed by means of (1) at time k+∆tC usingthe estimated values at time k.

A. Simulation Results

To test the algorithm with simulations, the data for temper-ature tracking calculation given in [21] was used, assuming aspan with a length of 300 [m], having a horizontal componentof conductor tension of 24.2 [kN] at 20 [C]. To simulatethe measurements and the control variables random errors(vk,w) were added to the assumed Theor. values, as shown inFig. 1. Normal distributions of the error with mean zero anda standard deviation (σzk) considered as the third part of theaccuracy were assumed; therefore, the variances are computedas var (zk) = σzk

2. A typical accuracy of ±1.5 [K] [7] inthe measurements of conductor temperature was used. Hence,if a maximum conductor operating temperature of 75 [C]is used, a standard deviation of σTS

= 1.5/3 [K] in tem-perature measurements is equivalent to σD = 5.5/3 [cm] inmeasurements of sag and to σH = 100/3 [N] in measurementsof mechanical tension. Finally, simulations were run with a∆tC = 15 min and direct measurements recorded at timesamples of tk = 1 min.

Table IATMOSPHERIC CONDITIONS TAKEN FROM CIGRE GUIDE [21]

Time [min] Ta [C] ϑ [m/s] δ [] S[W/m2

]|ikm| [A]

t ≤ 0 24.0 1.9 55 0 8020 < t ≤ 10 23.7 1.7 62 0 819t > 10 23.5 0.8 37 0 856

Table IICONDUCTORS USED FOR SIMULATIONS AND LABORATORY TEST

Drake 26/7 Linnet unitType ACSR 26/7 ACSR 26/7Standard · · · ASTM B 232A 486.6 198.38 mm2

d 28.1 18.31 mmms 0.5119 0.217 kg/mma 1.116 0.472 kg/mR′25 C 0.0727× 10−3 0.2095× 10−3 Ω/mβs 1× 10−4 1× 10−4 1/Kβa 3.8× 10−4 3.8× 10−4 1/Kαs 0.8 0.5 1εs 0.8 0.5 1α 23× 10−6 23× 10−6 1/Kcs 20 C 481 481 J/K kgca 20 C 897 897 J/K kgE 57000× 106 · · · N/m2

1) Thermal Transient System Description: a thermal tran-sient with measurements of current intensity and atmosphericconditions provided every 10 min is assumed, as shown inTable I [21]. The conductor DRAKE ACSR (aluminum (a)and steel (s)) was used to simulate the span. Its properties areshown in Table II, where A is the cross-sectional area, d isthe conductor diameter, R′Tref

is the conductor AC resistanceat temperature Tref , β is the linear temperature resistancecoefficient and α is the coefficient of linear thermal elongation.

2) Temperature estimation and prediction: known exam-ples were used to assess the performance of the algorithmassuming direct measurements. For simulating direct measure-ments, the theoretical temperature (TS-Theor.) during transientstate was computed with the values of Tables I-II by applyingnumerical integration (2) to the heat transfer equation (1).Equivalent values of sag and tension were computed usingthe values of TS-Theor. and measurement functions [19].Then, direct measurements were simulated with the Matlab R©

function randn, adding values of normal random errors withmean zero and equivalent standard deviation to the sag, tensionand temperature. The simulated temperature measurementzk=0 was selected to be the value of x+k=0, and for thecovariance the value P+

k=0 = σ2 was assumed. Since inthese simulations the aim is to analyze the performance ofthe algorithm provided that direct measurements are available,the values of atmospheric conditions except for the wind wereassumed without errors, that is w (t) = 0. For the forecastaverage effective wind speed an uncertainty of ±0.5 [m/s]was assumed (σ|ϑ| = 0.5/3 [m/s]).

To test the algorithm, two critical scenarios were modeled.The first considering a wind speed with the temperaturelower limit |ϑk| = |ϑk|Theor. + 0.5 [m/s] and the secondone using a wind speed with the temperature upper limit|ϑk| = |ϑk|Theor. − 0.5 [m/s]. Figure 2 shows the values of



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40

45

50

55

60

65

70

Figure 2. Both theoretical and limits of temperature of the conductor duringtransient state, computed with the scenarios: lower limit - |ϑk| = |ϑk|Theor. +0.5 [m/s] and upper limit - |ϑk| = |ϑk|Theor. − 0.5 [m/s]

00:00 00:10 00:20 00:30 00:40 00:50

Time - [h:min]

0

0.5

1

1.5

2

2.5

Figure 3. Theoretical wind speed |ϑ| and estimated wind speed∣∣∣ϑ∣∣∣ using

the proposed EKF for the assumed critical scenarios

temperature during the thermal transient of TS − Theor. andthe ones for the critical scenarios. The shaded area shows theobtained uncertainty limits. To compute the root-mean-squareerror (RMSe), for the lower limit was 4.02 [K], and for theupper limit of 6.73 [K]. Finally, provided that the effectivewind is modeled discreetly in this example, both

∣∣∣ϑk∣∣∣ = |ϑk|and Pk (2, 2) = σ|ϑ|

2 must be reset during the run of thealgorithm at each time k in which the wind changes.

a) Simulations assuming temperature measurements:for simulation of direct temperature measurements, normalrandom errors with mean zero and σ = 1.5/3 [K] were addedto the TS-Theor. Figure 3 shows wind speed estimated for bothcritical cases. Figure 4 shows the values of TS-Theor., sim-

35

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45

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55

0

1

2

3

4

5

6

7

00:00 00:10 00:20 00:30 00:40 00:50

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800

1000

1200

1400

1600

Figure 4. Temperature of the conductor (TS -Theor.), simulations of mea-surements of conductor temperature (TS Simulated), estimated temperatures(TS

)and maximum allowable current intensity

(|ikm|max

)at steady state

using the proposed algorithm during the thermal transient

ulations of measured temperature and estimated temperatureusing the proposed algorithm with the two critical cases. Theerror e is computed with respect to the TS-Theor. The RMSefor the estimated temperature was 0.34 [K] taking the lowerlimit, and 0.54 [K] taking the upper limit. The RMSe usingsimulations of direct temperature measurements was 0.6 [K].Additionally, Fig. 4 shows the maximum allowable currentintensity at steady state for a temperature of 75 [C]. Thecurrent intensity was computed with (3) using the conditionsof instant k for each scenario. Figure 5 shows predicted valuesboth of temperature and of maximum current allowable duringa contingency, obtained a RMSe for the lower limit of 1.6 [K],and 2.2 [K] for the upper limit.

b) Simulations assuming tension measurements: for sim-ulating tension measurements, errors were added as done inthe previous simulation using an accuracy of 100 [N]. Figure 6shows the simulations of measured tension (H), TS-Theor.,and the estimated temperature with the proposed algorithm.The RMSe of both estimated and predicted temperature forthe lower limit were 0.18 [K] and 1.5 [K], and for the upperlimit were 0.22 [K] and 2 [K] respectively.

c) Simulations assuming sag measurements: as in thecase of tension measurements, Fig. 7 shows the performanceof the algorithm when sag measurements are available. TheRMSe of both estimated and predicted temperature for thelower and the upper limits were 0.28 [K] and 1.5 [K], and0.29 [K] and 1.5 [K] respectively.

Finally, 1000 simulations for each one of the three directmeasurements were performed. To simulate a more realistic



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55

0

5

10

15

00:00 00:10 00:20 00:30 00:40 00:50

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1000

1100

1200

1300

1400

Figure 5. Temperature of the conductor (TS -Theor.), and predictions 15min before of temperature and maximum allowable current intensity during acontingency computed with the proposed algorithm, simulating measurementsof conductor temperature

00:00 00:10 00:20 00:30 00:40 00:50

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50

52

54

56

58

20

20.2

20.4

20.6

20.8

21

21.2

21.4

21.6

21.8

Figure 6. Simulation of mechanical tension (H), and estimated temperature(TS

)using the proposed algorithm simulating measurements of tension on

the conductor

case, errors were added on control variables, since these arecommonly measured or assumed. Thus, normal random errorswith mean zero were added to current intensity (|ikm|) withσ = 5/3 [A], to ambient temperature (Ta) with σ = 1/3 [K],and to wind attack angle (δ) with σ = 12.5/3 []. Thesestandard deviations were taken from [19]. Table III showsthe average RMSe and the average computing time to runAlgorithm 1. As result, the proposed algorithm showed stabil-ity, convergence and speed, and it reached a smaller error in

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8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9

9.1

Figure 7. Simulation of sag length (D), and estimated temperature(TS

)using the proposed algorithm simulating measurements of sag on the catenary

Table IIICOMPARISON PERFORMANCE BETWEEN THE THREE KINDS OF DIRECT

MEASUREMENTS FOR 1000 RANDOM CASES

Measurement Avg. RMSe [K] Avg. Time [s]

Temperature 0.303 0.0593Tension 0.253 0.0598Sag 0.328 0.0602

temperature values than in the case of using only records ofdirect measurements.

Although the standard deviation for δ was taken using typ-ical anemometers accuracy, this value is unrealistic, becauseof wind turbulence along the stringing section. However, toestimate the average effective wind speed instead of spotvalues, the effect of wind turbulence is considered [12].

B. Experimental Results

A laboratory setup was designed to evaluate the algorithm.The setup consisted of controllably injecting a current inten-sity through the OHL conductor Linnet and measuring itstemperature. The properties of the conductor are shown inTable II. To carry out the validation, an ambient temperatureof Ta = 19 [C], and the planned current intensity (|ikm|)and the wind (|ϑ|) shown in Fig. 8 were assumed as forecastvalues throughout the test. An auto-transformer and a fan wereused to control both |ikm| and |ϑ|. As in the simulations,the two critical cases in the estimation and prediction of thetemperature were used. Additionally, a value of emissivityεs = 0.9 was used as initial parameter for the lower limitand a value of emissivity εs = 0.2 for the upper limit. Thus,three different cases were analyzed: case 1 using the assumedplanned and forecasted values, case 2 using the upper limits,and case 3 using the lower limits.

1) Test setup: considering the laboratory atmospheric con-ditions, the conductor under test theoretically reaches 75 [C]with an |ikm| of almost 500 [A]. Taking the limitations of theshort circuit current of the laboratory into account, a special



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Figure 8. Current intensity planned (|ikm|) and forecasted wind speed (|ϑ|)used in the test

W1

V1

U1

W2

V2

U2

z1

y1

x1

z2

y2

x2

z′1

y′1

x′1

z′2

y′2

x′2

Transformer

Aikm

+−

V

OHL conductor

Figure 9. Circuit diagram of the experimental test

three-winding three-phase distribution transformer (HV-LV-LV) with open ends was used to reach this current, as shownin Fig. 9. The setup used is shown in Fig. 10. To reduce theinfluence of loop impedance the leads were located almostperpendicular to the conductor and the transformer was about1 [m] away.

2) Test Results: the setup was initially energized with300 [A], and when the conductor reached the thermal steadystate, the planned conditions (Fig. 8) were controlled and thevariables |ikm|, TS and Ta were measured and recorded every30 [s] with an accuracy of ±5 [A] and ±1.5 [K]. Measure-ments are shown in Fig. 11. Since the test was carried outindoors, the solar radiation was assumed to be S = 0.

Figure 10. Experimental test setup

12:00 13:00 14:00 15:00 16:00

Time - [h:min]

0

10

20

30

40

50

60

50

100

150

200

250

300

350

400

450

Figure 11. Measurements of current intensity (|ikm|), temperature of theconductor (TS) and ambient temperature (Ta) recorded every 30 [s]

12:00 13:00 14:00 15:00 16:00

Time - [h:min]

20

25

30

35

40

45

50

55

60

65

70

Figure 12. Comparison of temperature measured and computed with plannedand forecasted conditions, upper limit and lower limit

Figure 12 shows the values of temperature computed using(2) for the three cases and the temperature measured. The Rootmean square residuals (RMSε) obtained were RMSε = 2.4 [K]for case 1, RMSε = 5.7 [K] case 2 and RMSε = 5.5 [K] forcase 3.

3) Estimation of average Temperature: The values esti-mated both of effective wind speed and emissivity of theconductor using the proposed EKF in each case are shownin Fig. 13. The estimated average conductor temperaturefor the case with the highest RMSε (case 2) is shown inFig. 14. A RMSε = 1.5 [K] was obtained with this estimatedtemperature.

4) Prediction of Temperature: Taking the case 2, the tem-perature predicted 15 min before is shown in Fig. 15. In thistemperature prediction, a RMSε = 2.5 [K] was obtained.Additionally, Fig. 15 shows the maximum current intensity



12:00 13:00 14:00 15:00 16:00

Time - [h:min]

0

0.5

1

1.5

2

2.5

3

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure 13. Estimated effective wind speed(∣∣∣ϑ∣∣∣) and emissivity (εs) for

each case

12:00 13:00 14:00 15:00 16:00

Time - [h:min]

10

20

30

40

50

60

0

5

10

15

20

25

Figure 14. Comparison of estimated averaged temperature and measured tem-perature, and comparison of residual of estimated and computed temperaturein each case

allowable until the conductor reaches 75 [C]. This currentintensity was predicted 15 min before.

V. CONCLUSIONS

This paper presents an algorithm to estimate and predictthermal transient states in OHL conductors and addresses itsimplementation. This algorithm uses an EKF based on the heattransfer equation, using atmospheric conditions, current inten-sity, conductor parameters and direct measurements as inputs.The uncertainty in these values was considered. To simulateand test the EKF, the algorithm estimated and predicted valuesof average conductor temperature, with processing times lowerthan the time spent between measurement samples, showingcomputational efficiency and stability. The algorithm can bedirectly implemented on current DLR systems in a fast andcost-effective way.

12:00 13:00 14:00 15:00 16:00

10

20

30

40

50

60

0

5

10

15

20

25

12:00 13:00 14:00 15:00 16:00

Time - [h:min]

400

500

600

700

Figure 15. Comparison between the average temperature predicted 15 minbefore and temperature measured, comparison between residual of predictedaverage temperature and temperature computed in each case, and maximumcurrent intensity allowable until the conductor reaches 75 [C]

Average effective wind speed, emissivity and solar absorp-tivity were chosen as parameters to be estimated, due tothe impact of their uncertainty on heat transfer. Effectivewind speed was assumed constant during a typical time ofcontingency. Nevertheless, models of wind behavior for longtime emergency could be included in future studies.

The algorithm assessment showed a reduction in the RMEeand RMSε when thermal estimation and prediction are carriedout by the proposed EKF, allowing to increase the reliabilityin the thermal monitoring of OHLs. For instance, despiteusing the most critical case, the RMSe obtained using thealgorithm to estimate and predict the average conductor tem-perature was less than the RMSe obtained in all cases, boththe simulations and the experiment. The algorithm validationwas performed using low wind speeds which is considereda critical scenario. In the cases of higher wind speeds andlow current intensities where the conductor temperature isclose to the ambient temperature, a field test validation isnecessary. Finally, further analysis should be carried out usingdata validation techniques.

ACKNOWLEDGMENT

This research was supported by the Colombian Departmentof Science, Technology and Innovation (Colciencias) under theproject 617 - National Doctorates.

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[19] D. L. Alvarez, F. Faria da Silva, E. E. Mombello, C. L. Bak, J. A. Rosero,and D. L. Olason, “An approach to dynamic line rating state estimationat thermal steady state using direct and indirect measurements,”

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David L. Alvarez was born in El Cocuy, Boyaca,Colombia, in 1987. He received the B.Sc, M.Sc.and Ph.D. degrees in electrical engineering fromthe Universidad Nacional de Colombia, Bogota,Colombia, in 2009, 2014 and 2017, respectively. Hewas with Siemens Manufacturing, Tenjo, Colombiadeveloping new technologies and tools for distribu-tion transformers from 2009 to 2012. His researchinterests include transformers, computational elec-tromagnetics and dynamic line rating. Currently, heis an independent consultant.

Filipe Faria da Silva was born in Portugal in1985. He received his M.Sc. in Electrical and Com-puters Engineering in 2008 from Instituto SuperiorTecnico, Portugal and his Ph.D. in Electric PowerSystems in 2011 from Aalborg University, Den-mark.

He was with EDP-Labelec in 2008 and with theDanish TSO Energinet from 2008 to 2011. He iscurrently Associate Professor at the Department ofEnergy Technology, Aalborg University, where he isalso semester coordination for the Electrical Power

System and High Voltage Engineering master program and vice-leader of theModern Power Transmission Systems research program. His research focuseson power cables, electromagnetic transients, system modelling, networkstability, HVDC transmission and HV phenomena. He has supervised 8+ PhDstudents and dozens of master students in these areas, as well as authored morethan 100 articles and a book (as of April 2018).

Filipe is an active member of Cigre and IEEE, being currently head ofDenmarks IEEEPES, the Danish representative for Cigre SC C4 SystemTechnical Performance and the convener of Cigre WG C4.46.

Enrique E. Mombello (M95SM00) was born inBuenos Aires, Argentina, in 1957. He receivedthe B.S. and Ph.D. degrees in electrical engineer-ing from Universidad Nacional de San Juan, SanJuan, Argentina, in 1982 and 1998, respectively. Heworked from 1989 to 1991 at the High VoltageInstitute of RWTH, Aachen, Germany. He is cur-rently Principal Researcher of the National Councilof Technical and Scientific Research (CONICET,Argentina) and Lecturer with the Instituto de EnergaElctrica, National University of San Juan (IEE-

UNSJ- CONICET). He has more than 30 years of experience in researchprojects. His main fields of interest are the developmentt of high frequencymodels of transformers, electrical transients and resonance processes withintransformers, design and diagnostics of power transformers, asset man-agement, transformer life management, electromagnetic transients in powersystems, corona losses in overhead transmission lines, and low-frequencyelectromagnetic fields.

http://ieeexplore.ieee.org/document/6991585/



http://digital-library.theiet.org/content/journals/10.1049/iet-gtd.2015.0601




http://linkinghub.elsevier.com/retrieve/pii/S1364032115007819









http://journals.sagepub.com/doi/10.1243/09576509JPE859



http://doi.wiley.com/10.1002/0470045345



Claus Leth Bak was born in Rhus, Denmark,on April 13, 1965. He received the B.Sc. degree(honors) in electrical power engineering, in 1992, theM.Sc. degree in electrical power engineering in theDepartment of Energy Technology (ET) at AalborgUniversity (AAU), Aalborg, Denmark, in 1994, thePh.D. degree in 2015 with the thesis EHV/HVunderground cables in the transmission system. Afterhis studies, he worked as a Professional Engineerin electric power transmission and substations withspecializations within the area of power system

protection with the NV Net Transmission Company. In 1999, he was anAssistant Professor at ET-AAU, where he is currently a Full Professor. He hassupervised/cosupervised +35 Ph.D. and +50 M.Sc. theses. His main researchareas include corona phenomena on overhead lines, power system modelingand transient simulations, underground cable transmission, power systemharmonics, power system protection, and HVDC-VSC offshore transmissionnetworks. He is the author/coauthor of approximately 240 publications. Prof.Bak is a member of CIGRE JWG C4-B4.38, CIGRE SC C4, and SC B5 studycommittees member and Danish CIGRE National Committee. He received theDPSP 2014 best paper award and the PEDG 2016 best paper award. He servesas Head of the Energy Technology Ph.D. program (+100 Ph.D.s) and as Headof the Section of Electric Power Systems and High Voltage in AAU and is amember of the Ph.D. board at the Faculty of Engineering and Science.

Javier A. Rosero was born in Potosi, Colombia, in1978. He received his BSC in Electrical Engineeringfrom the Universidad of Valle, Cali, Colombia, in2002. He worked for construction and maintenanceof power systems and substations in Bogot, Colom-bia, between 2002 and 2004. He received a PhDdegree from the Technical University of Catalonia(UPC) in 2007. Dr Rosero received the IEEE AESSHarry Rowe Mimno award for excellence in tech-nical communications for 2007 from the Aerospaceand Electronic Systems Society (AESS) IEEE 2007.

He worked with Asea Brown Boveri (ABB), Barcelona, Spain, from 2007to 2009 providing service and technical support for drives for industrial andwindmill systems. He is currently an Associate Professor in the UniversidadNacional de Colombias Electrical and Electronic Engineering Departmentin Bogota. Dr. Rosero has published more than 50 referred journal andconference papers.

Dr. Rosero is a Member of the Institute of Electrical and ElectronicsEngineers, IEEE, International Society of Automation, ISA. His researchinterests are focused on the areas of modelling, diagnosis and control ofelectrical machines and drives, electric mobility and smart grids.

Documents

Conductor Temperature State Estimation and Prediction at