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Electric Power Systems Research 81 (2011) 2147– 2154

Contents lists available at ScienceDirect

Electric Power Systems Research

jou rn al h om epage: www.elsev ier .com/ locate /epsr

odelling precipitation cooling of overhead conductors

awel Pytlaka, Petr Musileka,∗, Edward Lozowskib, Janos Tothc

Department of Electrical and Computer Engineering, University of Alberta, Edmonton AB, CanadaDepartment of Earth and Atmospheric Sciences, University of Alberta, Edmonton AB, CanadaResearch and Development, BC Hydro, Vancouver, BC, Canada

r t i c l e i n f o

rticle history:eceived 1 April 2011eceived in revised form 9 June 2011ccepted 9 June 2011vailable online 30 July 2011

a b s t r a c t

This paper presents a precipitation-based conductor cooling model for use in power line ampacity ratingapplications and line temperature calculations. It is aimed at better modelling of a conductor’s temper-ature by incorporating the line cooling caused by precipitation falling onto power lines. The expandedthermal model quantifies the additional gain of current-carrying capacity for power transmission net-works incorporating advanced Dynamic Thermal Circuit Rating systems.

The precipitation cooling model is verified against observations made by a power transmission utility

eywords:ransmission linesonductorsowereteorology

using a commercial line current and temperature sensor clamped onto an actual power transmission line.The accuracy of the precipitation model is assessed both quantitatively using standard error measures,and qualitatively in terms of fit of the model to real world data. The precipitation-based cooling extensionshows a significant improvement over IEEE Std. 738-2006 in the modelled accuracy of the conductor

a sub

eathereliability

temperature. It suggests

. Introduction

The electrical power industry is under increasing pressure toope with an enlarging market demand for power [1,2]; however,eneration capacity upgrades, often in the form of new wind farms,re increasingly hampered by the lack of transmission capacity toring the additional power to customers [3]. In an ideal situation,ower transmission networks would be regularly upgraded to meethe demands. However, this is not always possible because of the

ajor financial costs to upgrade and deploy new transmission lines,nd increased government and environmental regulations such asaws aimed at preserving the natural habitat. Consequently, trans-

ission companies are seeking alternatives to expand the capacityvailable with the existing infrastructure. One modern approach iso use Dynamic Thermal Circuit Rating (DTCR) systems to identifynd make use of existing underutilized power lines [4].

DTCR systems [5] are capable of increasing the capacity ofxisting power transmission lines by dynamically rating them ineal time using actual operating conditions, rather than by usingonservative estimates based on near-worst-case operating sce-arios [6]. On average, DTCR systems are capable of doubling the

apacity of a power line at a given point [7]. DTCR systems pro-ide the power transmission industry with a more cost-effectivepproach to expand available transmission capacity [8]. DTCR sys-

∗ Corresponding author.E-mail address: Petr.Musilek@ualberta.ca (P. Musilek).

378-7796/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.epsr.2011.06.004

stantial increase in available ampacity during periods of precipitation.© 2011 Elsevier B.V. All rights reserved.

tems decrease the time for new power generation sources to deliverenergy to markets, since DTCR installations to deployed relativelyquickly and do not require new infrastructure construction.

In order to improve the accuracy of weather-based DTCR sys-tems [9], this paper proposes an extension to the generally adoptedpower line thermal model described in IEEE Std. 738-2006 [10].The increase in accuracy is achieved by the inclusion of conduc-tor cooling caused by falling precipitation. To assess the real-worldperformance of the new model, it is used to predict the conduc-tor temperature of an actual power line in operation. The modelledtemperatures are compared with measurements from a sensor ona live transmission line. This paper also presents an assessment ofthe potential gains in transmission capacity that can be achievedby using the precipitation cooling thermal model. These potentialgains in ampacity are assessed using real meteorological conditionsrecorded during actual precipitation events, rather than estima-tions based on average or typical meteorological/climatologicalconditions during periods of rain or snow.

2. Background

The power that can be sent through a transmission line is largelylimited by the conductor’s maximum operating temperature. Thismaximum temperature limit is selected to ensure that safety reg-

ulations are met, line clearances are satisfied, and to minimize theloss of tensile strength due to annealing when the conductor isoperated at high temperatures [11]. In order to ensure that all rel-evant line constraints are satisfied, the maximum current rating,

2 stems

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148 P. Pytlak et al. / Electric Power Sy

mpacity, is calculated. A line thermal model is used to estimatehe maximum current rating from known or assumed operatingonditions. The same model can be used inversely to calculate theperating line temperature with a known current flowing throughhe conductor.

Both calculations rely on solving a heat balance equation thatccounts for the energy lost to the environment and the energyained by the conductor through internal and external heating pro-esses [12]. In order to compute the energy gains and losses, oneust know the physical properties of the conductor, the operating

onditions of the conductor, and the surrounding ambient condi-ions, consisting primarily of the air temperature, wind speed andirection, and the flux of solar radiation.

The thermal model adopted by the power transmission industry10] is based on the formulation provided by House and Tuttle [13].t includes all the essential factors in the thermal heat balance ofhe conductor. The formulation was later improved by ECAR [14] toddress the discontinuity between laminar and turbulent airflows.

For steady-state conditions, when the line loading characteris-ics have remained constant for a sufficiently long period of time,he heat balance equation takes the form

c + qr = qs + qj. (1)

q. (1) balances the heat lost to the environment due to naturalr forced convection qc and radiation qr against the heat gainedrom solar radiation qs and the resistive heating of the conductorj. The units of all heat terms in Eq. (1) are [W m−1]. The resistiveeating component depends on the current flowing through theonductor I [A] and the resistance of the line R [�] at the conductor’semperature Tc [K],

j = I2R(Tc). (2)

n addition to the static conductor and atmospheric physical prop-rties, the convective cooling term depends on the wind speed,he wind direction with respect to the conductor, the conductoremperature and the ambient air temperature. The radiative cool-ng term depends on the conductor temperature, and the ambientir temperature. The solar heat gain is determined by the time ofay, the line location and orientation, and the transmissivity of air.inally, the resistive heating term depends on the current flowinghrough the conductor and the conductor temperature.

In the case of a sudden change in the current, the above equationan be modified to incorporate the heat capacity Cp [J kg−1 K−1] ofhe conductor’s mass m [kg m−1] in order to account for its ther-

odynamic internal energy:

c + qr + mCpdTc

dt= qs + qj. (3)

he basic principle for finding the line current or line temperatures that the energy gained by the line must balance the energy losty the line. Eqs. (1) and (3) are simplified forms of the real-worldeat balance. This simplification reduces the computational com-lexity and the number of operating variables that must be knowno perform ampacity calculations.

The transmittable electric power can be calculated by

=√

3 · A · V · cos ϕ, (4)

here A is the line ampacity, V is the transmission line voltage, andos ϕ is the power factor.

In a practical weather-based DTCR system, Eqs. (1)–(3) woulde applied at multiple points along a transmission line path. Thisould require that the weather conditions and load currents at all

uch locations be known.

Research 81 (2011) 2147– 2154

3. Model

To account for conductor cooling due to impinging precipitation,the heat loss arising from precipitation warming and subsequentevaporation is calculated as described below.

The convective heat transfer coefficient under non-precipitatingconditions h is calculated. Since IEEE Std. 738-2006 does not explic-itly define this coefficient, it must be extracted from the convectivecooling term. The standard provides three formulations. The firstapplies to natural convection,

qcn = 0.0205�0.5f (1000D)0.75(Tc − Ta)0.5, (5)

where qcn [W m−1] is the convective heat loss rate, D [m] is theconductor diameter, �f [kg m−3] is the density of air, Ta [K] is theair temperature, and Tc [K] is the conductor temperature. Since thetime step between successive ampacity and conductor temperaturecalculations is typically greater than 1 min, the cross-sectional con-ductor temperature is assumed to be uniform. This approximationis made as the internal time constant of the conductor is typicallybetween 10 and 20 s [10].

Eqs. (6) and (7) apply to forced convection based on McAdam’sequation [15]:

qc1 =[

1.01 + 0.0372

(1000D�f Vw

�f

)0.52]

· kf Kangle(Tc − Ta) (6)

qc2 = 0.0119

(1000D�f Vw

�f

)0.6

kf Kangle(Tc − Ta), (7)

where qc1 and qc2 [W m−1] are the convective heat losses for lowand high wind speeds, respectively, Vw [m s−1] is the speed of theundisturbed air stream at the conductor, �f [Pa s] is the dynamicviscosity of air, and kf [W m−1 K−1] is the thermal conductivity ofair at temperature Tfilm [K].

To compensate for reduced convective cooling under non-perpendicular airflow, the convective cooling is multiplied by acompensating factor Kangle:

Kangle = 1.194 − sin(ˇ) − 0.194 cos(2ˇ) + 0.368 sin(2ˇ), (8)

where ̌ is the angle between the wind direction and a plane per-pendicular to the axis of the conductor.

The formula for qc1 is valid at low speeds (i.e., for small val-ues of the Reynolds number) while qc2 is valid at high windspeeds. We compute both of these IEEE standard values anduse the larger of the two in subsequent heat transfer equa-tions. As a result of this approach, the first order discontinuityin the convective heat transfer coefficient is avoided, althoughthere is still the second order discontinuity (in the slope of thecurve).

The thermal conductivity of air is calculated using the formula-tion provided by IEEE Std. 738-2006,

kf = 2.424 × 10−2 + 7.477 × 10−5 · (Tfilm − 273.15)

− 4.407 × 10−9 · (Tfilm − 273.15)2. (9)

Tfilm is calculated as the average of the conductor and ambient airtemperatures,

Tfilm = Tc + Ta

2. (10)

To extract the implied heat transfer coefficient in the IEEE Std. 738-

2006 formulation, the forced convection equations are comparedwith Newton’s Law of Cooling [16],

Q̇ = hA�T, (11)

stems

whhbt

h

Iipw

w

wa

ttfl

w

Tcflidet

m

w

s

m

wc

i

P

wec

c

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wacw[i

i

e

wi

t

P. Pytlak et al. / Electric Power Sy

here Q̇ [W] is the heat transferred per unit time, A [m2] is theeat transfer area of the surface, h [W m−2 K−1] is the convectiveeat transfer coefficient and � T [K] is the temperature differenceetween the conductor surface and the ambient airstream. Hence,he heat transfer coefficient is calculated from

= max(qc1, qc2)� · D(Tc − Ta)

. (12)

n order to calculate precipitation cooling, the flux of liquid imping-ng on the conductor must be determined. The mass flux of liquidrecipitation is calculated by first estimating the airborne liquidater content from the precipitation rate [17],

= 6.7 × 10−5P0.846, (13)

here w [kg m−3] is the liquid water content of the precipitation,nd P [mm h−1] is the precipitation rate.

If the precipitation is in the form of snow, the liquid water con-ent in the air is calculated using a power regression function fittedo observations of the equivalent liquid water content of snowakes provided in [18],

= 1.4 × 10−4P0.9165. (14)

he liquid mass flux density maf [kg m−2 h−1] impinging onto theonductor is the vector sum of the downward and windblown massux. Since rain droplets are relatively large, the collision efficiency

s assumed to be unity, i.e., all droplets moving toward the con-uctor impinge on its surface. Moreover, we assume a collectionfficiency of unity, i.e., all impinging liquid remains on the conduc-or and there is no splashing or shedding. Hence,

af =√

(0.001P · �w)2 + (3600 · Vw · w)2, (15)

here Vw [m s−1] is the wind speed.The mass flux rate of liquid water striking the exposed conductor

urface is

a = maf · D

3600, (16)

here ma [kg s−1 m−1] is the mass flux rate of water striking theonductor surface.

The increased conductor perimeter from multiple strands form-ng the outer surface of the conductor is estimated to be

c = n�d(

0.5 + 1n

), (17)

here Pc [m] is the conductor perimeter, d [m] is the strand diam-ter, and n is the number of strands in the outer layer of theonductor.

The evaporative mass flux me [kg s−1 m−1] should the entireonductor surface be wetted, is:

e = Pc · hk

cppa(ec − RH · ea), (18)

here k is 0.62, the ratio of the molecular weights of water vapournd dry air, ec [Pa] is the saturation vapour pressure of water at theonductor temperature, ea [Pa] is the saturation vapour pressure ofater at the air temperature, pa [Pa] is the ambient air pressure, cp

J kg−1 K−1] is the specific heat of air at constant pressure, and RHs the relative humidity expressed as a fraction in [0, 1].

The saturation vapour pressure of water at a given temperatures calculated using the Antoine equation [19],

s(T) = 133.322 × 10.08.07131− 1730.63T−39.724 , (19)

here es [Pa] is the saturation vapour pressure of water, and T [K]s the water temperature.

Should the mass flux from precipitation be less than the poten-ial flux of water evaporating from the conductor surface when the

Research 81 (2011) 2147– 2154 2149

entire conductor surface is covered in water, then the smaller fluxis used,

m ={

ma ma < me

me otherwise, (20)

where m [kg s−1 m−1] is the actual mass flux evaporating from theconductor surface.

The conductor may be heated to temperatures exceeding theboiling point of liquid water. The boiling point is first calculatedusing a formulation derived from the Clausius–Clapeyron equation[20],

Tb =[

1373.12

− R log(pa · 9.8692 × 10−6)H

]−1

, (21)

where Tb [K] is the boiling point, R [J K−1 mol−1] is the universal gasconstant, H [J mol−1] is the enthalpy of vaporization of water, andpa [Pa] is the air pressure.

The temperature at which the water evaporates is computed bytaking the minimum of the conductor temperature and the boilingpoint temperature,

Te = min(Tc, Tb), (22)

where Te [K] is the evaporation temperature.The precipitation heat loss due to evaporation is calculated as

follows

qe = m[Le(Tc) + cw · (Te − Ta)], (23)

where Le [J kg−1] is the specific latent heat of evaporation of water,cw [J kg−1 K−1] is the specific heat capacity of liquid water, Ta [K]is the ambient air temperature, and qe [W m−1] is the evaporativeheat loss.

When performing the above calculations on precipitation in theform of snow, the heat loss must also account for the latent heat offusion and the specific heat capacity of ice for ambient air temper-atures below the freezing point of water must be used. Hence theheat loss for snow precipitation is:

qe = m[Le(Tc) + cw · Tc + Lf (273.15K) − ci · Ta], (24)

where Lf [J kg−1] is the specific latent heat of fusion of water at273.15 K, and ci [J kg−1 K] is the specific heat capacity of ice.

The specific latent heat of evaporation is calculated by using anempirical formula fitted to data provided in [21],

Le(Tw) = 0.0000614342(Tw − 273.15)3

− 0.00158927(Tw − 273.15)2

+ 2.36418(Tw − 273.15) − 2500.79, (25)

where Tw [K] is the water surface temperature.The updated heat balance in the ampacity thermal model for

steady-state and transient conditions, respectively, becomes:

qc + qr + qe = qs + qj (26)

qc + qr + qe + mCpdTc

dt= qs + qj (27)

4. Verification setup

To verify the precipitation cooling model, observational datawere obtained from an industrial partner. The partner operates anon-site meteorological station and an on-conductor current andtemperature is sensor installed on a live transmission line. The line

thermal model was provided with the meteorological data fromthese instruments in order to calculate the conductor temperature.The calculated conductor temperature was then compared with themeasured conductor temperature.

2150 P. Pytlak et al. / Electric Power Systems Research 81 (2011) 2147– 2154

Table 1Conductor type and physical parameters used to configure the IEEE Std. 738-2006ampacity thermal model for the precipitation based conductor cooling study.

Description Value

Material AACSRStrand diameter 3.2258 mmOverall diameter 35.4838 mmNumber of outer strands 22Coeff. of emissivity 0.82Coeff. of absorption 0.91Strand heat capacity 1095.9 J m−1 K−1

Core heat capacity 1155.9 J m−1 K−1

Resistance @ 25 ◦C 6.8471 × 10−5 � m−1

Resistance @ 75 ◦C 8.0052 × 10−5 � m−1

Ground elevation 105 m (at sensor site)Line elevation 60.7 m (varies)Line bearing 133.2◦ N

Fm

4

tTca

4

aseba

TD

ig. 1. The FTS Meteorological Station installed at the BC Indian Arm crossing trans-ission line. Photo courtesy of BC Hydro R&D.

.1. Conductor

The Indian Arm crossing transmission line is a 230 kV circuithat uses an AACSS conductor with the characteristics described inable 1. Since the conductor was installed over 40 years ago, theoefficients of absorption and emissivity were set equal to those of

typical “old” conductor.

.2. Sensor instruments

The weather observations at the line location were made usingn FTS Meteorological Monitoring station, depicted in Fig. 1. This

tation has a number of automated instruments to measure ambi-nt atmospheric conditions (Table 2). These include a tippingucket precipitation gauge, an ultrasonic wind speed anemometer,

thermistor ambient air temperature thermometer, a photo-diode

able 2escription of the sensors present in the FTS meteorological station installed at the India

Sensor Measurement Range

Lower

RG-T-TRI Total accumulated rainfall 0.00 mm

SDI-UWS-GILL-2 10 min average wind speed 0 ms−1

10 min average wind direction 0◦

THS-3-1 Air temperature −40 ◦C

Relative humidity 0%

SDI-B1-S Barometric pressure 600 h Pa

SDI-SR-PYR Solar radiation 0 W m−2

Fig. 2. The Arteche SMT sensor unit clamped onto the BC Indian Arm crossing trans-mission line. Photo courtesy of BC Hydro R&D.

solar pyrometer, a capacitive relative humidity sensor, and a solid-state transducer pressure sensor. Line temperature and line currentwere measured by a clamped-on Arteche SMT sensor unit, depictedin Fig. 2.

4.3. Preprocessing

Initialization data for the thermal model include bothmeteorological observations and line current and temperaturemeasurements. Before the data could be used to predict the con-ductor temperature to verify the precipitation cooling model, itrequired substantial pre-processing. Sensor measurement recordsfor the period between February and December 2010 were obtainedand the relevant variables for the thermal model were extracted.Obvious sensor errors were eliminated. This included current andtemperature readings from the SMT sensor when the line currentwas below the minimum required for correct operation of the unit.Instances that substantially deviated from the norm were discardedfrom the comparison as outliers. Very short periods of missingdata (i.e. less than 1 h) were filled in with the most recent obser-vations and their duration was adjusted accordingly. To reducethe impact of the resolution of the tipping bucket precipitationgauge, spline smoothing of cumulative precipitation observationswas performed. This removed discrete steps in the precipitationrecord. The impact of this procedure on cumulative precipitationamount and precipitation rate is illustrated in Fig. 3.

5. Results

The line thermal model based on IEEE Std. 738-2006 was usedto compute line temperature using the observed meteorologicalconditions from the FTS station and the line current measured

n Arm crossing.

Resolution Accuracy

Upper

16645.89 mm 0.254 mm ±2% at 50 mm h−1

60 ms−1 0.01 ms−1 ±2%359◦ 1◦ ±3%60 ◦C 0.1 ◦C ±0.1 ◦C100% 1% ±2%1100 h Pa 0.01 h Pa ±0.5 h Pa1800 W m−2 1 W m−2 ±5%

P. Pytlak et al. / Electric Power Systems Research 81 (2011) 2147– 2154 2151

379

381

383

385

387

389

1

3

5

7

9

Raw

Precip. RateCumulative Precip.

379

381

383

385

387

389

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00

1

3

5

7

9

Sm

ooth

Time [minutes]

Pre

cipi

tatio

n [m

m]

Pre

cipi

tatio

n R

ate

[mm⋅h

-1]

Fs

bpTtlutcaTpl

rTdptttTsF

cmttcifc

8

9

10

11

12

13

14

15

08-31 1208-31 14

08-31 1608-31 18

08-31 2008-31 22

09-01 0009-01 02

09-01 0409-01 06

0

5

10

15

20

Con

duct

or T

empe

ratu

re [°

C]

Pre

cipi

tatio

n R

ate

[mm⋅h

-1]

Date/Time

SensorSteady State, NoPC

Steady State, PC

Fig. 4. Observed and modelled conductor temperature for the Indian Arm Crossingtransmission line, for the period between August 31 and September 1, 2010.

10

12

14

16

18

20

22

24

09-18 0809-18 12

09-18 1609-18 20

09-19 0009-19 04

09-19 0809-19 12

09-19 16

0

5

10

15

20

Con

duct

or T

empe

ratu

re [°

C]

Pre

cipi

tatio

n R

ate

[mm⋅h

-1]

Date/Time

SensorSteady State, NoPC

Steady State, PC

TM

ig. 3. Observed cumulative precipitation and precipitation rate before and aftermoothing (February 24, 2010).

y the SMT sensor. To verify the real-world performance of therecipitation cooling model, two sets of tests were performed.he first set involved quantitative statistical analysis of the modelemperature and the temperature sensor readings. The measuredine temperature was compared with the modelled temperaturesing the IEEE Std. 738-2006 model with (PC) and without (NoPC)he precipitation cooling extension. The calculated values wereompared against temperature readings made by the SMT sensornd three error measures were computed. These are presented inable 3. The table illustrates the accuracy of the two model tem-erature estimates for a range of precipitation rates observed, from

ight showers/snow to heavy rainfall events.The second set of tests involved a qualitative analysis of selected

ainstorm events occurring during the period with available data.hese included a visual assessment of the correlation between pre-icted and measured line temperatures. To illustrate the relativeerformances of the precipitation cooling model and the standardhermal model, three separate rain-fall events are presented inhis paper. All three events incurred substantial total precipita-ion and produced sustained periods of continuous precipitation.he selected periods did not contain any missing sensor data. Timeeries of observed and modelled line temperatures are shown inigs. 4–6.

In order to estimate how much additional capacity precipitationooling could provide, the ampacity of the conductor was deter-ined using the observed weather conditions. The current needed

o raise the conductor temperature to 75 ◦ C was computed usinghe IEEE Std. 738-2006 model and the model with the precipitation

ooling extension. The gain in ampacity is taken to be the differencen required current between the two models. Assuming a poweractor of 0.9, the modelled line capacity gain with increasing pre-ipitation rate is illustrated in Fig. 8. The frequency of occurrence

able 3ean absolute error (MAE), mean error (ME), and root mean square error (RMSE) of the l

Precipitation range [mm h−1] Number of samples IEEE 738 The

MAE

All data 17,981 1.29

(0:1] 677 1.24

(1:2] 309 1.39

(2:3] 167 1.29

(3:4] 119 1.29

(4:5] 71 1.42

Only precip. 1427 1.29

No precip. 16,554 1.30

Fig. 5. Observed and modelled conductor temperature for the Indian Arm Crossingtransmission line, for the period of September 18 and 19, 2010.

of the gain in capacity for the period of available data is presentedin Fig. 9. To illustrate the gain in ampacity during a single rainfallevent, a time series of the line ampacity estimate calculated by thetwo models is shown in Fig. 10.

6. Discussion

The precipitation cooling model showed a substantial improve-ment in accuracy of calculated line temperatures, compared withthe temperatures calculated by the IEEE Std. 738-2006 model

ine thermal model with and without precipitation cooling.

rmal Model With precipitation extension

ME RMSE MAE ME RMSE

0.97 1.83 1.23 0.89 1.791.20 1.45 0.46 0.16 0.641.35 1.57 0.52 0.27 0.721.28 1.46 0.50 0.34 0.731.28 1.45 0.47 0.33 0.641.42 1.61 0.38 0.24 0.541.26 1.48 0.47 0.24 0.660.94 1.86 1.30 0.94 1.86

2152 P. Pytlak et al. / Electric Power Systems Research 81 (2011) 2147– 2154

6

8

10

12

14

16

18

20

22

09-26 0809-26 10

09-26 1209-26 14

09-26 1609-26 18

09-26 2009-26 22

0

5

10

15

20

Con

duct

or T

empe

ratu

re [°

C]

Pre

cipi

tatio

n R

ate

[mm⋅h

-1]

Date/Time

SensorSteady State, NoPC

Steady State, PC

Ft

wclanmpTfioiicrS

trTtcups

Fi

0

100

200

300

400

500

0 2 4 6 8 10 12 14

Cap

acity

Gai

n [M

VA

]

Precipitation Rate [mm⋅h-1 ]

Fig. 8. Increase in computed line capacity, as estimated using the precipitationcooling extension.

0

200

400

600

800

1000

0 100 200 300 400 500

Fre

quen

cy

Capacity Gain [MVA]

Fig. 9. Increase in computed line capacity, as estimated using the precipitationcooling extension.

ig. 6. Observed and modelled conductor temperature for the Indian Arm Crossingransmission line, for September 26, 2010.

ithout the precipitation cooling extension. In all cases, the pre-ipitation cooling model decreases the simple bias of the predictedine temperature. Very small precipitation rates (under 1 mm h−1)re almost unbiased, while higher precipitation rates show a sig-ificant decrease in the tendency of the original IEEE Std. 738-2006odel to over predict the line temperature. When considering sam-

les with precipitation, a decrease in bias of 1.02 ◦ C is achieved.his results in a mean error of 0.24 ◦C. The scatter plot in Fig. 7 con-rms that the model is unbiased. In all cases the MAE and RMSEf the modelled conductor temperature decreased when line cool-ng by precipitation was accounted for. The significant differencesncrease with increasing precipitation rate. This occurs because theontribution of precipitation cooling increases with precipitationate and cooling by precipitation is not accounted for in the IEEEtd. 738-2006 model.

Time series graphs of the modelled and measured conduc-or temperature, along with the precipitation rate, illustrate theeliance of the thermal model on accurate meteorological variables.he precipitation rate is calculated from the accumulated precipi-ation in the rain gauge, and its accuracy is limited by the relatively

oarse resolution of the measurements. The sensing instrumentses a tipping bucket that requires a minimum of 0.25 mm ofrecipitation to accumulate before it is registered. Unfortunately,moothing of this input cannot compensate for periods of very low

0

5

10

15

20

25

30

0 5 10 15 20 25 30

Mod

eled

Tc

[°C

]

Observed Tc [°C]

ig. 7. Observed and modelled conductor temperature using the precipitation cool-ng model, for all data samples with non-zero precipitation rate.

1000

1500

2000

2500

3000

08-31 1208-31 14

08-31 1608-31 18

08-31 2008-31 22

09-01 0009-01 02

09-01 0409-01 06

0

5

10

15

20

Con

duct

or A

mpa

city

[A]

Pre

cipi

tatio

n R

ate

[mm⋅h

-1]

Date/Time

Precipitation Rate [mm⋅h-1 ]Steady State, NoPC

Steady State, PC

Fig. 10. Indian Arm Crossing estimated transmission line ampacity, for the periodof August 31 and September 1, 2010.

stems

pi

iandsFgta5

srToteri1i

cDpolotcassciamie

7

mfesc

rbatWrla

podm

P. Pytlak et al. / Electric Power Sy

recipitation rates which require a prolonged time period until anncrease in collected precipitation is observed.

Ampacity calculations using the thermal model with precip-tation cooling show the potential for a substantial amount ofdditional capacity. The same precipitation rate can be accompa-ied by a variety of alternative meteorological conditions, such asifferent ambient air temperature and wind speed. This causes apread in line capacity values for a given precipitation rate (Fig. 8).or the extracted data with any precipitation, the average ampacityain for the transmission line was 163.2 A with a standard devia-ion of 139.6 A. Assuming a power factor of 0.9, this translates inton average capacity gain of 58.5 MVA with a standard deviation of0.0 MVA.

The increase in line capacity with precipitation rate can beeen clearly in Fig. 8. The overall trend shows a diminishingeturn on the capacity gain as the precipitation rate increases.his can be attributed partly to the maximum evaporation ratef the water on the conductor surface. Furthermore, it is clearhat during the observed period the precipitation rate rarelyxceeded 7 mm h−1 at the test site. This precipitation rate cor-esponds to a capacity gain of just over 200 MVA. In mostnstances, the gain during periods of precipitation will be less than00 MVA. This is a very substantial amount of additional capac-

ty.Additional cooling of the conductor not represented by the pre-

ipitation cooling model can potentially be explained as follows.ue to the slope of the installed conductor, additional water isresent on the conductor surface where the sensor is clampednto the line. Water may run down the conductor surface and coolower sections of the conductor more than sections near the topf the towers. Further cooling may result from an increased heatransfer coefficient not accounted for in the extracted heat coeffi-ient variable. Complex boundary layer effects due to impingementnd splashing are not accounted for in the model. These potentialources of cooling would require the installation on the transmis-ion line of more elaborate sensor equipment such as a high speedamera. Such equipment would provide visual evidence of howmpinging water behaves as it hits the conductor under varioustmospheric conditions. Even without these factors the currentodel provides sufficient representation of the evaporative cool-

ng process and accurate line temperature estimates (less than 1 ◦Crror).

. Conclusion

This paper presents a precipitation-based conductor coolingodel for use in DTCR systems. The model extends the heat balance

ormulation provided by IEEE Std. 738-2006. It aims to improvestimates of heat loss to the environment from overhead transmis-ion lines during periods of precipitation, permitting more accuratealculations of line temperature.

The precipitation-cooling calculations presented in this paperely on estimation of water mass flux from falling and wind-lown precipitation, calculation of evaporation rate under specifiedtmospheric and line loading conditions, and computation ofhe amount of heat required to warm and evaporate the water.

ater from snow and rain precipitates are heated and evapo-ated mostly with heat from the transmission line, cooling theine and leading to lower line temperatures, and hence greatermpacity.

The precipitation model allows for better identification of sur-

lus ampacity. As a result, additional power can be transmittedver existing infrastructure. Application of the model in DTCReployments in regions with frequent rain and snow events couldaximize the investment in DTCR technology by identifying the

Research 81 (2011) 2147– 2154 2153

maximum potential line capacity with minimal additional invest-ment. Furthermore, the expanded model can be used to increasethe accuracy of line sag and aging calculations due better estimatesof line temperature.

Verification of the precipitation-based cooling model has pro-vided encouraging results. Under typical rainfall conditions, linetemperature measurements indicate that up to a few degrees ofadditional line cooling can be observed during periods of pre-cipitation. This observation correlates well with the results ofthe enhanced model. Furthermore, tests with the enhanced ther-mal model show that ampacity gains of tens of amperes arepossible during periods with low precipitation rates. Gains ofover 400 amperes are possible in rainfall exceeding 14 mm h−1.Should a transmission line be fully loaded while precipitationis falling, significant additional line capacity can potentially beachieved.

8. Further work

The proposed precipitation-based cooling model has many pos-sibilities for refinement. Better approximations of line coolingrelated to heating and evaporation of precipitation are possible,gains in accuracy can be achieved by employing more accurate esti-mates of the water surface temperature prior to evaporation, andimproved modelling of the melting dynamics of frozen precipita-tion and ice on power lines [22] will increase the accuracy of themodel.

For the range of precipitation rates considered here, the rate ofprecipitation impinging on the conductor surface rather than thepotential rate of evaporation is the factor limiting cooling. Hence,it can be inferred that the conductor surface was sufficiently warmto evaporate all of the impinging precipitation under the ambientoperating conditions. However, other factors may play roles notaccounted for in the current extension. For example, some precip-itation could drip or be blown off the conductor surface before isevaporated, or may evaporate with heat from ambient air.

Additional gains in accuracy can be achieved by better modellingof the residual liquid water on the conductor. Under conditions suchas high precipitation rate or low wind speed and low line load, notall liquid precipitation will evaporate from the conductor surface.This could lead to an overestimate of the available capacity. Mod-elling these processes is expected to further improve the accuracyof the present system.

Finally, a procedure could be developed to estimate the next10–15 min gain in transmission capacity due to falling precipita-tion. This would further increase the relevance of the model to theelectric power industry. It would provide additional flexibility thatcould be used by energy control centres in real-time operations.

Acknowledgments

The support provided by the Natural Sciences and Engineer-ing Research Council of Canada (NSERC) and BC Hydro Research& Development is gratefully acknowledged.

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