Appl 07 Thermal Overload Protection En

Siemens PTD EA · Applications for SIPROTEC Protection Relays · 2005 1

Line Protection in Distribution Systems

� 1. IntroductionFailure of underground cables can be costly andtime consuming to repair. Protection systems aredesigned to protect cables from the high currentlevels present under fault conditions. However,the temperature rise due to extended overloadconditions is just as likely to cause cable failure. Asthe trend in power system operations is to utilizeequipment as close to operating limits as possible,the importance of protecting equipment againstthermal overloads becomes more critical.

Thermal overload protection calculates the tem-perature of the conductor based on specific con-ductor data and the current present in the circuit,and is used to protect conductors from damagedue to extended overloads. In this application ex-ample thermal overload protection of under-ground cables only is described.

Thermal overload protection is normally used inan alarm mode to notify system operators of thepotential for cable damage. However, thermaloverload protection can be used to trip a circuit-breaker as well. In either case, the presence ofthermal overload can be detected and removedbefore cable failure occurs.

� 2. Thermal overload protectionThermal overload protection with total memorycalculates a real time estimate of the temperaturerise of the cable, Θ, expressed in terms of the max-imum temperature rise, ∆Θmax. This calculation isbased on the magnitude of currents flowing to theload, and the maximum continuous current ratingof the conductor. The calculation uses the solu-tion to the first order thermal differential equa-tion:

τd

d

Θ Θt

I+ = 2

with = Θ ∆Θ∆Θ

=max

Thermal OverloadProtection of Cables

∆Θ = temperature rise above ambient temperature∆Θmax = maximum rated temperature rise correspond-

ing to maximum currentτ = thermal time constant for heating of the

conductorI = measured r.m.s. current based on the maximum

rated overload current of the protected conduc-tors: Imeas/Imax.

The solution to the thermal differential equationis:

Θ Θ ∆Θop amb max= + −

−

1 et

τ

The initial value is Θamb, the ambient temperatureof the cable, and the steady state value is

Θamb +∆Θ, where ∆Θ is determined by the magni-

tude of I. The initial value, Θamb, is assumed to bethat temperature on which the cable ratings arebased. The steady state value is achieved when thetemperature has reached its final value due to theheating effects of I. At this point, the value of

τdΘ/dt in Equation 1 is zero. Therefore, at steady

state, ∆Θ = ∆Θmax I2, where I = Imeas/Imax. Thetransition between the initial value and the steadystate value is governed by the exponential expres-

sion,1 −−

et

τ . τ is a constant of the cable to be pro-tected.

Fig. 1

LSP2

299-

eps

BU

IS08

5.ep

s


Siemens PTD EA · Applications for SIPROTEC Protection Relays · 20052

Fig. 2 shows the operating temperature of the ca-ble as a function of time and overload. With noload, the conductor is at its ambient temperature.If an overload equivalent to the maximum ratedcurrent is added at some time, the temperature of

the cable will approach Θmax following the expo-nential

1 −−

et

τ .

The conductor temperature due to a current over-load, starting from no-load conditions, has thesame characteristic as shown in Fig. 2, with Θmax

becoming Θop, and IMAX becoming ILoad. However,when the conductor already has some load pres-ent, the characteristic of the operating tempera-ture changes. The conductor will heat up the cableto some steady state temperature. When an over-load is added, the final temperature of the cable iscalculated as if the cable was at normal operatingtemperature. However, the starting point of thesecond (overload) characteristic will coincide withthe steady state temperature of the normal load.This is illustrated in Fig. 3.

� 3. Calculation of settingsThere are two required settings for thermal over-load protection, the k factor, and the thermal timeconstant τ. τ is specific to the properties of the ca-ble. The k factor relates the maximum continuouscurrent rating of the cable to the relay.

3.1 Maximum continuous current of cableThe maximum continuous current rating of thecable is used in determining the k factor setting,and may be used in determining the setting for τ.This current depends on the cross-section, insu-lating material, cable design, and conductor con-figuration. Cable manufacturers may specify themaximum continuous current rating of their ca-ble. If the rating is not available, it is possible to

estimate a maximum continuous current based onconductor ampacity information. The ampacity ofconductors is specified based on circuit configura-tions, conductor temperature, and ambient tem-perature. Also specified is the maximum operatingtemperature of the conductor, and correction fac-tors for various conductor operating temperaturesand ambient earth temperatures.

To determine the maximum continuous currentrating of a cable, use the ampacity at the emer-gency overload operating temperature, and notthat of the maximum conductor operating tem-perature. According to ICEA specifications, [1]emergency overloads are permitted for only a totalof 100 hours per 12 month period, only for nomore than five such periods in the life of the cable.Therefore, it is desirable to trip or alarm for anysituation when the thermal overload reaches thislevel. To determine the maximum continuouscurrent, remember that the conductor configura-tion and ambient temperature effect the currentrating.

Example:

Circuit voltage: 12.47 kVCable size: 500 MCM shielded

copper cableConductor temperature: 90 °CAmbient temperature: 20 °CConfiguration: 3 circuits duct bank

From conductor tables, the ampacity for 90 °Ccopper conductor at 20° ambient temperaturewith 3 circuits in duct bank is 360 amps. Theemergency overload operating temperature for90 °C-cable is 130 °C. From Table 1, at 20 °C am-bient temperature, the ampacity rating factor is1.18.

Therefore,360 A x 1.18 = 424.8 A maximum continuous cur-rent

Fig. 2 Temperature vs. time for an overload of Imax



3.2 Calculating the k factorThe k factor relates the operating current to therelay to permit overload detection. The k factor isdefined as the ratio of the maximum continuouscurrent Imax to the rated relay current IN:

Example:

kN

= I

Imax

Circuit voltage 12.47 kVCable size 500 MCM shielded

copper cableConductor temperature 90 °CAmbient temperature 20 °CConfiguration 3 circuits in duct bankMaximum continuouscurrent (Imax) 424.8 A primaryCurrent transformerratio 800/5Rated relay current (IN) 5 A secondary

k = =

424 8

800 55

0 53

.

( / ) .

3.3 Thermal time constantThe thermal time constant τ is a measure of thespeed at which the cable heats up or cools down asload increases or decreases, and is the time re-quired to reach 63 per cent of the final tempera-ture rise with a constant power loss. The thermaltime constant is the determining factor for calcu-lating the operating temperature as a percent ofthe maximum permissible overload temperature,as shown in Equation 2. τ may be available fromthe cable manufacturer. If no specification for τ isavailable, it may be estimated from the permissibleshort-circuit rated current of the cable, and themaximum continuous current rating. It is com-mon to use the 1 second rated current as the per-missible short-circuit current. τ is calculated bythe following equation:

τ(min)=1

60second⋅

I

I1

2

max

If the short-circuit current at an interval otherthan one second is used, the equation is multipliedby this interval. For example, if the 0.5 second rat-ing is used:

τ(min)=0.5

60second⋅

I

I0 5

2

.

max

Example for calculating the thermal constant τ:

Circuit voltage 12.47 kVCable size 500 MCM shielded copper cableConductortemperature 90 °CAmbienttemperature 20 °CConfiguration 3 circuits in duct bankMaximum continuoscurrent (Imax) 424.8 A primaryMaximum currentoür 1 second 35,975 A primary

τ(min)=1

60min⋅ =35 975

424 8119 5

2,

..

Conductorsize

Ampacity Max. continu-ous current

Short-timewithstandcapability (1 sec)

τ(minutes)

1/0 160 189 7 585 27

2/0 185 218 9 570 32

3/0 205 242 12 065 41

4/0 230 271 15 214 52

250 MCM 255 301 17 975 59

350 MCM 305 360 25 165 81

500 MCM 360 425 35 950 119

750 MCM 430 507 53 925 188

1000 MCM 485 572 71 900 263

Table 1 Shielded copper conductor, 5001 - 35000 volts, 90 °C,three-conductor cable, three circuits in duct bank

Fig. 3 Temperature vs. time with an existing overload



Short-circuit rated current for copper

�

I

At

T

T

⋅ = ⋅ +

+

2

2

1

0 0297234

234. log

I = Short-circuit current - Amperes [A]A = Conductor area - circular mils

(0,001" diameter; convert to mm2 wherenecessary)

t = time of short-circuit, secondsT1 = Operating temperature 90 °CT2 = Maximum short-circuit temperature 250 °C

Short-circuit current for aluminium

�

I

At

T

T

⋅ = ⋅ +

+

2

2

1

0 0125234

234. log

Table 1 lists calculated values of τ for commonconductors and configurations. Below Table 2 arethe formulas to calculate the short-circuit ratingof conductors

3.4 Analysis of relay settingsCombining the examples in Sections 3.1, 3.2, and3.3, the cable information leads to the followingrelay settings:

k factor: 0.53

τ: 119.5 minutes

The operating temperature at a given moment intime can be calculated using Equation 2.

Θamb = the conductor operating temperature = 90 °C.∆Θmax = the maximum overload temperatureminus the initial operating temperature =130 °C - 90 °C = 40 °C.

As shown in Section 2 above, to determine thesteady state temperature, the exponential term canbe replaced by I2, where I = Imeas/Imax. Based onthese settings, and a load current of 400 A,

Θ Θ ∆Θop ambmeas= +

= °+ °

max

max .

I

I

2

90 40400

424 8

= °

2

125 C

Thus, for a load of 400 A, the conductor will heatup to 125 °C.

� 4. Implementing thermal overload protectionThermal overload protection in SIPROTEC relayscalculates the temperature for all three phases in-dependently, and uses the highest of the three cal-culated temperatures for tripping levels. Besidesthe k factor and the thermal time constant, thereare two other settings for thermal overload pro-tection. As seen in Figure 3, these are the “thermalalarm stage” and the “current overload alarmstage”.

4.1 Thermal alarm stageThe thermal alarm stage sends an alarm signal be-fore the relay trips for a thermal overload condi-tion. The thermal alarm stage is also the dropoutlevel for the thermal overload protection trip sig-nal. Therefore, the calculated temperature mustdrop below this level for the protection trip to re-set. This stage is set in percent of the maximumtemperature. A setting of 90 % will meet mostoperating conditions.

Conductortemperature

Ambient earth temperature

°C 10 °C 15 °C 20 °C 25 °C 30 °C

75 0.99 0.95 0.91 0.87 0.82

85 1.04 1.02 0.97 0.93 0.89

90 1.07 1.04 1.00 0.96 0.93

100 1.12 1.09 1.05 1.02 0.98

105 1.14 1.11 1.08 1.05 1.01

110 1.16 1.13 1.10 1.07 1.04

125 1.22 1.19 1.16 1.14 1.11

130 1.24 1.21 1.18 1.16 1.13

140 1.27 1.24 1.22 1.19 1.17

Table 2Correction factors for various ambient earth temperatures

Fig. 4 Thermal overload protection settings

LSP2

588.

tif



Fig. 5 Logic diagram of the overload protection



4.2 Current overload alarm stageThe current overload alarm stage sends an alarmwhen the load current exceeds the value of the set-ting. This setting should be set equal to, or slightlyless than, the maximum continuous current ratingof the cable.

4.3 Thermal overload protection as an alarm ortripping functionThermal overload protection may be configuredto either “ON” (tripping) or “Alarm only” foroverload conditions, and is normally set to“Alarm only”. Configuring thermal overload pro-tection to “ON” makes this a tripping function,meaning it asserts the 0511 Relay TRIP function.The factory default configuration of the relay hasthe 0511 Relay TRIP function set to close a contactthat trips the circuit-breaker.

“Alarm only” means thermal overload protectiondoes not assert the 0511 relay trip function. Ther-mal overload protection may still be programmedto operate a binary output for tripping purposes.this configuration allows the thermal overloadfunction to be used to warn operators of potentialcable failure due to overloads.

4.4 Adjusting settings for differences in ambienttemperatureThe ambient temperature of the earth has a signif-icant effect on the maximum continuous currentrating of the cable. In most applications, it is bestto assume one ambient earth temperature to per-form relay setting calculations. However, in someareas, there may be large seasonal differences inambient earth temperature. Using multiple set-tings groups allows the relay to adapt the thermaloverload protection settings to large changes inthe seasonal temperature.

Changing the settings group can be accomplishedvia binary input, remote command, or functionkey, all of which require operator intervention toaccomplish the change. Another possibility is tohave the relay change settings groups based onsystem conditions. Wiring the output of a temper-ature sensor into an optional transducer input onthe 7SJ63 relay will permit the changing of settingsgroups when the earth temperature passes athreshold for a specified period of time.

� 5. SummaryThe failure of underground cables due to heatingcaused by long term overload conditions is easilyprevented by using thermal overload protection.Based on information provided by cable manufac-turers, circuit configuration, and operating condi-tions, it is simple to determine settings for thermaloverload protection. Thermal overload protectionis normally used to alarm for overload conditions,to allow system operators to make informed deci-sions on how to handle an overload to prevent ca-ble damage. A thermal overload alarm, whencombined with a SCADA system, can be used totrack the amount of time the cable is exposed tooverload, allowing for estimates of the remaininglife of the cable.

� 6. ReferencesInsulated Cable Engineers Association StandardP32-382-1994, “Short Circuit Characteristics ofInsulated Cable”, 1994, South Yarmouth, MA.

“Engineering Handbook”, The Okonite Com-pany, 1999, Ramsey, NJ.

H. Pender and W. Del Mar, “Electrical Engineer’sHandbook”, 4th Edition, Wiley & Sons, NewYork, NY.

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Appl 07 Thermal Overload Protection En