energies Article
Real-Time Transient Thermal Rating and the Calculation of Risk Level of Transmission Lines Jiapeng Liu 1, *, Hao Yang 1 , Shengjie Yu 2, *, Sen Wang 3 , Yu Shang 3 and Fan Yang 1 1
2 3
*
State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing 400044, China;
[email protected] (H.Y.);
[email protected] (F.Y.) Department of Urology, the Second Affiliated Hospital, Chongqing Medical University, Chongqing 400016, China State Grid Shanxi Electric Power Corporation Research Institute, Xi’an 710054, China;
[email protected] (S.W.);
[email protected] (Y.S.) Correspondence:
[email protected] (J.L.);
[email protected] (S.Y.); Tel.: +86-023-6510-2434 (J.L.)
Received: 16 February 2018; Accepted: 30 April 2018; Published: 12 May 2018
Abstract: With the increasing consumption of electric energy, how to improve the capacity of transmission lines within safe margins is an urgent problem to be solved. This paper presents a transient thermal rating method under real-time meteorological conditions. The result of thermal ratings under different conditions shows that this rating approach can significantly increase the capacity of the line. As some of the most critical variables are remaining time and initial temperature, their influence upon the rating is studied. The method of statistical analysis is used to determine the ampacity at different risk levels. The result indicates that with smaller remaining time, the ampacities are larger, and with larger ampacities, the risk of thermal overload is greater. The choice of risk level would heavily affect the values of ampacity. Keywords: transient thermal rating; overhead transmission line; real-time meteorological conditions; risk level
1. Introduction Over the decades, the contradiction between grid construction and economic development has become increasingly prominent due to the ever increasing consumption of electric energy. A straightforward solution is constructing new transmission lines, but this faces a series of problems, such as large investments and environmental restrictions [1–6]. For example, establishing a new transmission line in Alberta is not only a political, but also a controversial problem [7]. The best way is to make better utilization of the capacity of the line without risking the integrity of the system [8–10]. For now, static thermal rating is used world-wide by many utilities, which considers very conservative meteorological conditions, such as high ambient temperature, high solar radiated heat intensity, low wind speed, and wind is assumed to be perpendicular to the conductor [11,12]. This gives a very conservative result, and a high constraint of the capacity of the line. Increasing ampacities of overhead transmission lines has long been of interest to engineers. In [13], differences in methods of thermal rating in standard of Institute of Electrical and Electronics Engineers (IEEE) and International Council on Large Electric Systems (CIGRE) [14,15] are compared. In [16], Power Donut 2 is used for accurate prediction of the capacity and to minimize the risk of the line. In [17], a method to assess the reliability of dynamic thermal rating (DTR) systems is proposed. In [18], a novel method to calculate probability density functions of future ampacity based on probabilistic weather forecasts is presented. In [19], a new modelling method for DTR is presented which is superior in terms of both probability distribution and fitting accuracy. In [20], the wind simulations commonly Energies 2018, 11, 1233; doi:10.3390/en11051233
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employed by the wind energy industry is applied to inform rating estimation during network planning and operation. In [21], the software of Comsol Mutiphysics is used to investigate the impact of the more accurate mixed convective cooling model on overhead line conductors. In this paper, a real-time transient thermal rating method based on the transient thermal balance is proposed from the perspective of increasing the capacity of the line. In order to verify the increasing effect of the above method, a comparison among thermal ratings under different conditions is made, and the influence of different variables upon transient thermal rating is analyzed. The method of statistical analysis is used to determine the ampacity at different risk levels for assessing the thermal risk of the line, which provides the reference and basis for the operation and scheduling of the line. This method provides a more comprehensive way to explore the available capacity of transmission lines. 2. Methodology The operating temperature of transmission lines is decided by the heat exchange between conductor and environment. The maximum allowable ampacity is the current passing through the overhead transmission lines when the operating temperature of the conductor reaches the maximum allowable value, and the heat exchange between conductor and environment reaches a dynamic balance. Assuming that the overhead transmission line is a uniform conductor, the steady-state thermal balance equation for the conductor in the IEEE Std738™-2012 standard [14] is given by qc + qr = qs + I 2 · R( Ts ),
(1)
where qc is convection heat loss rate, qr is radiated heat loss rate, qs is heat gain rate from sun, I is conductor current, and R(Ts ) is alternating current (AC) resistance of conductor at temperature Ts . For the transient thermal rating, it is up to the maximum allowable operating temperature, which determines the maximum sag and rate of annealing. The transient thermal balance equation for the conductor in the IEEE Std738™-2012 standard is given by i dTs 1 h = R( Ts ) · I 2 + qs − qc − qr , dt m · Cp
(2)
where m is mass of conductor per unit length, Cp is specific heat of the conductor material, t is remaining time. The total specific heat of the conductor is equal to the sum of the specific heat of the components of the conductor, that is m · C p = ∑ mi · C pi . (3) For the aluminum conductor steel reinforced (ACSR) conductors, the mass and specific heat of aluminum and steel per unit length are shown in Table 1. Table 1. Mass (m) and specific heat (Cp ) of aluminum and steel per unit length. Material
m/(kg·m−1 )
Cp /(J·kg−1 ·◦ C)
Aluminum Steel
1.116 0.5119
955 476
Assuming that the initial state of transmission lines has reached the steady state, the steady-state thermal balance of the transmission line will be destroyed during the transience when the current passing through the line is suddenly increased. The resistance heat generated by the current and the heat gained from sun is greater than the heat dissipation of the conductor, which causes the temperature of the conductor to increase. The process of temperature increment can be divided into
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many time steps, which is relatively short enough to assume the ambient meteorological conditions remain the same. In each time step, formula (2) can be rewritten as Energies 2018, 11, x FOR PEER REVIEW 3 of 14 R( Ts ) · I 2 + qs − qc − qr · ∆t, 2 R Ts I m · qCs p qc qr Ts t ,
∆Ts =
(4) (4)
m Cp
where ∆Ts is conductor temperature increment corresponding to time step, where ∆t is the time step. where ΔTs is temperature increment corresponding step, Δt is the as time step. From theconductor initial state, the temperature of the conductor in to n +time 1 min canwhere be expressed From the initial state, the temperature of the conductor in n + 1 min can be expressed as Tn+1 = ∆Ts + Tn (n = 0, 1, 2 . . .), (5) Tn 1 Ts Tn ( n 0,1, 2...) , (5) where T and TTnn are are the the temperatures temperatures in in nn ++ 11 and and nn minute minute respectively; respectively; and and T T00 is is the the initial initial n+1 and where Tn+1 temperature of of the the conductor. temperature conductor. The temperature increment of of transmission transmission lines lines under under different different currents currents can can be be tracked tracked by by the the The temperature increment above formulas. The transient ampacity of transmission lines is the jump current corresponding to above formulas. The transient ampacity of transmission lines is the jump current correspondingthe to temperature of conductor increasing from the the initial statestate to its allowable value within the the temperature of conductor increasing from initial tomaximum its maximum allowable value within remaining time. the remaining time. Assuming the initial initial meteorological meteorological conditions conditions of of the the conductor conductor remain remain unchanged unchanged for for the the rest rest Assuming the of the the time, time, the the process process of of transient transient thermal thermal rating rating of of the the transmission transmission line line is is calculated calculated as as shown shown in in of Figure 1. Figure 1. I0
qc Vw , , Ta
T0 qr Ta
Ts
R Ts I 2 qs qc qr m Cp
t
qs Qse
Tn1 Ts Tn (n 0,1,2...)
No
Tn1 Ts max
I n 1 I n I n 0,1, 2,...
Yes
In1 Figure process the the transient transient thermal thermal rating rating method. method. T T0:: steady-state temperature; Figure 1. 1. Overview Overview of of the the process 0 steady-state temperature; II0::steady-state current; q c: convection heat loss rate; Vw: wind speed; φ: angle between wind and axis 0 steady-state current; qc : convection heat loss rate; Vw: wind speed; ϕ: angle between wind and of conductor; Ta: ambient temperature; qr: radiated heat lossheat rate;loss qs: heat rate gain fromrate sun;from Qse: solar axis of conductor; Ta : ambient temperature; qr : radiated rate;gain qs : heat sun; s: resistance of conductor at temperature; I: conductor current. radiated heat intensity; T Qse : solar radiated heat intensity; Ts : resistance of conductor at temperature; I: conductor current.
The first step is to set the steady-state temperature and current (T0, I0) of the line as the initial The first step is to set the steady-state temperature and current (T , I0 ) of the line as the initial parameters of the transient conditions. The meteorological data, such as0 wind speed, angle between parameters of the transient conditions. The meteorological data, such as wind speed, angle between wind and axis of conductor, ambient temperature, and solar radiated heat intensity (Vw, φ, Ta, Qse) of wind and axis of conductor, ambient temperature, and solar radiated heat intensity (V w , ϕ, Ta , Qse ) the line are used to calculate the temperature increment of every time step. If the accumulation value of the line are used to calculate the temperature increment of every time step. If the accumulation of temperature at the last time step reaches the maximum allowable value (Tsmax), then I0 is the value of temperature at the last time step reaches the maximum allowable value (Tsmax ), then I0 is the transient ampacity of the line. If not, iterating I0 until the temperature meets the requirement. transient ampacity of the line. If not, iterating I0 until the temperature meets the requirement. 3. Transient Thermal Rating of Overhead Transmission Lines 3.1. Case Study A 500 kV quad bundle conductor with 7 towers in Zhejiang Province, China, is set as a sample to study the transient thermal rating of the whole year with a time resolution of one hour. Table 2 shows the basic parameters of the line and the real-time meteorological data of tower 1 in 2012 is shown in Figure 2.
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3. Transient Thermal Rating of Overhead Transmission Lines 3.1. Case Study A 500 kV quad bundle conductor with 7 towers in Zhejiang Province, China, is set as a sample to study the transient thermal rating of the whole year with a time resolution of one hour. Table 2 shows the basic parameters of the line and the real-time meteorological data of tower 1 in 2012 is shown in Figure 2. Energies 2018, 11, x FOR PEER REVIEW
Table 2. Basic parameters of the 500 kV quad bundle transmission line.
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Table 2. Basic parameters of the 500 kV quad bundle transmission line.
Parameters
Parameters Type of Conductor Type of Conductor Do 1 /m Do 1/ m Lat 2 /◦ Lat 2/° He 3 /m He 3/m ε4 ε4 α5 α5 Z 6 /◦ Zl 6/°
1 4
1
Value
Value LGJ-400/35 LGJ-400/35 0.02682 0.02682 28.454884~28.464759 28.454884~28.464759 63~196 63~196 0.9 0.9 0.9 0.9 45 45
l Do is outside diameter of conductor. 2 Lat is latitude of the line. 3 He is elevation of conductor above
Do is outside diameter of conductor. 2 Lat is latitude of the line. 3 He is elevation of conductor above sea level. sea level. 4 ε is emissivity of the conductor. 5 α is solar absorptivity of the conductor. 6 Zl is azimuth of ε is emissivity of the conductor. 5 α is solar absorptivity of the conductor. 6 Zl is azimuth of the line. the line.
Figure 2. Cont.
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Figure 2. (a) Total solar radiated heat intensity of tower 1 in 2012; (b) ambient temperature of tower 1
Figure Total solar radiated intensity of tower11angle 2012; (b)ambient ambient temperature tower Figure2.2.(a) (a)2012; Total radiated heat intensity inin2012; (b) temperature of of tower 1 in (c) solar wind speed at conductor of tower 1of intower 2012; (d) between wind and axis of conductor 1in in2012; 2012;(c) (c) wind1speed speed atconductor conductorof oftower tower11in in2012; 2012;(d) (d)angle anglebetween betweenwind windand andaxis axisofofconductor conductor at of wind tower in 2012. ofoftower tower11inin2012. 2012.
The maximum allowable temperature of the overhead transmission line is 70 °C for normal operation and 80 °C for transient operation. The calculation parameters of the line is shown in Table ◦ C for Themaximum maximum allowable allowable temperature temperature of of the the overhead overhead transmission The transmission line line isis 70 70 °C for normal normal 3. operationand and80 80◦ °C fortransient transientoperation. operation.The Thecalculation calculationparameters parametersof ofthe theline lineisisshown shownin inTable Table3. operation C for
3.
Table 3. Calculation parameters of the 500 kV quad bundle transmission line.
Table 3. Calculation parameters kV quadt/min bundle transmission line. Parameters ofTthe 0/°C500 Δt/min Table 3. Calculation parameters of the bundle transmission line. Value 25 500 kV 1 quad 30 Parameters
T 0 /◦ C
∆t/min
t/min
Δt/min t/min line in 2012 is shown in The result of transientParameters thermal rating T of0/°C 7 towers of the transmission Value 1 30 Figure 3. Value 25 25 1 30 Theresult resultof oftransient transient thermal thermal rating rating of 7 towers of the transmission The transmission line line in in 2012 2012isisshown showninin Figure 3. Figure 3.
Figure 3. (a) Transient thermal rating of tower 1 and 2 of the transmission line in 2012; (b) Transient thermal rating of tower 3 and 4 of the transmission line in 2012; (c) Transient thermal rating of tower 5 and 6 of the transmission line in 2012; (d) Transient thermal rating of tower 7 of the transmission line in 2012.
The max thermal rating of a line at each moment is the minimum value of all the towers of the line at that moment, which is
I min Ii , (6) Figure3.3.(a) (a)Transient Transientthermal thermal rating rating of of tower towermax11 and and 2 2 of of the the transmission Figure transmissionline linein in2012; 2012;(b) (b)Transient Transient thermalrating ratingof oftower tower33and and 44 of of the the transmission transmission line thermal line in in 2012; 2012; (c) (c) Transient Transient thermal thermalrating ratingof oftower tower 5 and 6 of the transmission line in 2012; (d) Transient thermal rating of tower 7 of the transmission 5 and 6 of the transmission line in 2012; (d) Transient thermal rating of tower 7 of the transmission line in 2012. inline 2012.
The max thermal rating of a line at each moment is the minimum value of all the towers of the The max thermal rating of a line at each moment is the minimum value of all the towers of the line at that moment, which is line at that moment, which is Imax= min Imax min (IiIi ,), (6)(6)
where Ii is the current of its ith tower.
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I / IA/ A
where Ii is the current of its ith tower. where Ii is the current of its ith tower. Therefore, Therefore, the max transient thermal rating of this line in 2012 is shown in Figure 4. Therefore, the max transient thermal rating of this line in 2012 is shown in Figure 4. 8200 Max thermal rating of the line 8200 7700 Max thermal rating of the line 7700 7200 7200 6700 6700 6200 6200 5700 5700 5200 5200 4700 4700 4200 4200 3700 3700 3200 3200 2700 2700Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Time Jul Aug Sep Oct Nov Dec Time
Figure Figure 4. 4. Max Max transient transient thermal thermal rating rating of of the the transmission transmission line line in in 2012. 2012. Figure 4. Max transient thermal rating of the transmission line in 2012.
We can see from Figure 4 that the maximum and minimum value of transient thermal rating in see from from Figure Figure44that thatthe themaximum maximumand andminimum minimum value transient thermal rating We can see value of of transient thermal rating in the whole year are 7828 A and 2824 A respectively, and the difference between them is 5004 A. The in the whole year 7828 A and A respectively, the difference between is 5004 A. the whole year are are 7828 A and 28242824 A respectively, and and the difference between themthem is 5004 A. The main reason that causes the change of transient thermal rating in the whole year is the differences in The main reason causes the change of transient thermal rating in the whole year is the differences main reason that that causes the change of transient thermal rating in the whole year is the differences in meteorological conditions. In the summer time, the meteorological conditions are usually harsher in meteorological conditions. summertime, time,the themeteorological meteorologicalconditions conditionsare are usually usually harsher meteorological conditions. In In thethe summer than winter, so the values of transient thermal rating in summer are usually lower than winter. than winter, so the values of transient thermal rating in summer summer are are usually usually lower lower than than winter. winter. The calculation model can be used to track the temperature increment of the transmission line. The calculation calculation model model can can be be used used to to track track the the temperature temperature increment increment of of the the transmission transmissionline. line. The Figure 5 shows the temperature increment curve of the transmission line on 30 June 2012 at 12:00, Figure 5 shows shows the temperature temperature increment increment curve curve of of the the transmission transmission line line on on 30 30 June June 2012 2012 at at 12:00, 12:00, Figure 18:00; and 31 December 2012 at 5:00, 24:00. The values of transient thermal rating at each time are The values values of of transient transient thermal thermal rating rating at at each each time time are 18:00; and 31 December 2012 at 5:00, 24:00. The 5236 A, 6288 A, 5504 A, and 7308 A, respectively. respectively. 5236 A, 6288 A, 5504 A, and 7308 A, respectively.
Figure 5. Temperature increment of the transmission line on 30 June 2012 at 12:00, 18:00; and 31 Figure 5. Temperature Temperatureincrement increment of the transmission line 302012 Juneat 2012 12:00, and 31 Figure 5. of the transmission line on 30 on June 12:00,at 18:00; and18:00; 31 December December 2012 at 5:00, 24:00. December 2012 at 5:00, 24:00. 2012 at 5:00, 24:00.
From the above figure, one can conclude that with higher ampacity, the conductor takes less From the above figure, one can conclude that with higher ampacity, the conductor takes less time to reach relatively high thehigher temperature rises, the less maximum From theaabove figure, onetemperature. can concludeWhen that with ampacity, theapproaching conductor takes time to time to reach a relatively high temperature. When the temperature rises, approaching the maximum allowable value for transient operation of the thetemperature line, the temperature increment slower. The reach a relatively high temperature. When rises, approaching thebecomes maximum allowable allowable value for transient operation of the line, the temperature increment becomes slower. The reason fortransient that is the heat dissipated by the temperature conductor continues to becomes approachslower. the heat absorbed by value for operation of the line, increment The reason for reason for that is the heat dissipated by the conductor continues to approach the heat absorbed by the the residual that makes the temperature continuously decreasing. thatconductor, is the heat and dissipated by theheat conductor continues to approachrise the is heat absorbed by the conductor, the conductor, and the residual heat that makes the temperature rise is continuously decreasing. and the residual heat that makes the temperature rise is continuously decreasing. 3.2. Comparison and Analysis under Different Conditions 3.2. Comparison and Analysis under Different Conditions In order to verify the increasing effect of transient thermal rating in real-time meteorological In order to verify the increasing effect of transient thermal rating in real-time meteorological conditions, this paper compares it with the thermal ratings of the line in steady-state and static conditions, this paper compares it with the thermal ratings of the line in steady-state and static
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conditions. Steady-state thermal rating is the ampacity of transmission lines under long-term operation, and it does not need to consider the temperature change of transient durations. Static thermal rating means the meteorological conditions are fixed and conservative. Table 4 shows specific Energies 2018, 11, 1233 7 of 14 values of meteorological conditions in static thermal ratings. Figure 6 shows the comparison of thermal ratings under different conditions. From the above figure, under the values of static transient thermal rating, real-time steady-state, and 3.2. Comparison and Analysis Different Conditions transient thermal rating of the line in 2012 are 2952 A, 1782 A to 7402 A, and 2824 A to 7828 A, In order to verify the increasing effect of transient thermal rating in real-time meteorological respectively. Compared the first two with the real-time transient thermal rating, the values decrease conditions, this paper compares it with the thermal ratings of the line in steady-state and static about 35.71% and 13.78% each. The result shows that static thermal rating provides a very conditions. Steady-state thermal rating is the ampacity of transmission lines under long-term operation, conservative result which can ensure high safety of operation, but a severe waste of the capacity of and it does not need to consider the temperature change of transient durations. Static thermal rating the line. The real-time steady-state thermal rating can improve the capacities, but not lead to full means the meteorological conditions are fixed and conservative. Table 4 shows specific values of utilization of the line. Only real-time transient thermal rating can unlock the hidden capacity and meteorological conditions in static thermal ratings. Figure 6 shows the comparison of thermal ratings achieve the purpose of increasing the capacity of the line in a relatively short period of time with under different conditions. strong reliability. Table 4. Specific value of meteorological conditions in static thermal rating. Table 4. Specific value of meteorological conditions in static thermal rating. 2 Ta /◦ C /(w·m−−2 /(m·s−1 )−1 sese Meteorological Conditions Ta/°C QQ /(w∙m )) VwV w/(m∙s ) Value Value 40 40 1000 0.5 1000 0.5
◦
ϕ/ φ/° 9090
I/A
Meteorological Conditions
Figure conditions. Figure 6. 6. Comparison Comparison of of thermal thermal ratings ratings under under different different conditions.
3.3. Influence of Different Variables upon Transient Thermal Rating From the above figure, the values of static transient thermal rating, real-time steady-state, Remaining time and initial temperature ofare the2952 conductor two A, main would and transient thermal rating of the line in 2012 A, 1782are A the to 7402 andfactors 2824 Athat to 7828 A, affect the value of transient of the transmission line. In thisrating, paper,the thevalues meteorological respectively. Compared the thermal first tworating with the real-time transient thermal decrease data of35.71% towerand 1 of13.78% this line on 30 2012 at 12:00 is taken as anrating example to study the conservative influence of about each. TheJune result shows that static thermal provides a very these two factors upon the transmission line. Table 5 shows the specific meteorological in line. that result which can ensure high safety of operation, but a severe waste of the capacity data of the time.real-time steady-state thermal rating can improve the capacities, but not lead to full utilization The of the line. Only real-time transient thermal rating can unlock the hidden capacity and achieve the 5. Specific of atower 1 in 30short June 2012 at 12:00. purpose of increasing theTable capacity of thevalue line in relatively period of time with strong reliability.
Meteorological Conditions Ta/°C Qse/(w∙m−2) Vw/(m∙s−1) φ/° 3.3. Influence of Different Variables upon Transient Thermal Rating Value 35.26 889.9 7.1 20 Remaining time and initial temperature of the conductor are the two main factors that would affect the value of transient thermal rating of the transmission line. In this paper, the meteorological data of tower 1 of this line on 30 June 2012 at 12:00 is taken as an example to study the influence of these two factors upon the transmission line. Table 5 shows the specific meteorological data in that time.
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Table 5. Specific value of tower 1 in 30 June 2012 at 12:00. Meteorological Conditions
Ta /◦ C
Value
35.26
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ϕ/◦
Qse /(w·m−2 ) Vw /(m·s−1 ) 889.9
7.1
20
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3.3.1. Influence of 3.3.1. Influence of Remaining Remaining Time Time upon upon Transient TransientThermal ThermalRating Rating Remaining Remaining time time is is the the time time the the transmission transmission line line takes takes to to rise rise from from the the initial initial temperature temperature to to the the maximum It is is the the safety maximum allowable allowable operating operating temperature. temperature. It safety time time limit limit of of the the line. line. The The transmission transmission line line will will be be put put into into danger danger if if the the operating operating time time exceeds exceeds the the remaining remaining time, time, such such as as loss loss of of strength strength ◦ C, 50 ◦ C, and 70 ◦ C, and clearance of the line. When the initial temperature of the conductor is 25 and clearance of the line. When the initial temperature of the conductor is 25 °C, 50 °C, and 70 °C, respectively, respectively, with with all all the the meteorological meteorological conditions conditions remaining remaining the the same, same, the the relationship relationship between between the the remaining time and transient thermal rating is shown in Figure 7 and Table 6. remaining time and transient thermal rating is shown in Figure 7 and Table 6. 11,500
T 0=25 ℃
11,000 10,500
T 0=50 ℃
10,000
T 0=70 ℃
9500 9000 8500 8000 7500 7000 6500 6000 5500 5000
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
t / min Figure 7. time andand transient thermal ratingrating underunder different initial Figure 7. Relationship Relationship between betweenremaining remaining time transient thermal different temperatures. initial temperatures. Table 6.6.Specific Specific value of remaining time and transient thermal rating under different initial Table value of remaining time and transient thermal rating under different initial temperatures. temperatures. t/min 2 10 30
t/min
◦ TT 0 0==25 25 C °C
T 0 °C = 50 ◦TC0 = 70 °C T 0 = 70 ◦ C T0 = 50
8810.8 A
10
11,158.8 A 11,158.8 A 6065.2 A 6065.2AA 5430.8
30
5430.8 A
5424 A
2
8810.8 A 6682 A 5766.4 A 5766.45424 A A5532.8 A
6682 A 5532.8 A 5419.2 A
5419.2 A
◦ C,
From the above figure and table, when T0 = 25 the values of transient thermal rating at t = 10From min the andabove t = 30 figure min are reduced by 45.6% and°C, 51.3%, respectively, compared with when 2 and table, when T0 = 25 the values of transient thermal rating at tt==10 ◦ min. When 50 are C, the valuesby of45.6% transient rating of t = 10 min and with t = 30when min decreased min and t =T30 reduced andthermal 51.3%, respectively, compared t = 2 min. 0 =min ◦ C, the values by 34.6% 38.4%, respectively, compared with when min.and When = 70 of When T0 =and 50 °C, the values of transient thermal rating of t t==102 min t = 30Tmin decreased by 34.6% 0 and 38.4%, respectively, compared with = 2 min. When Tby 0 =17.2% 70 °C,and the 18.9%, values respectively, of transient transient thermal rating at t = 10 min andwhen t = 30t min are reduced thermal rating t = 10 and t = 30 min are reduced by 17.2% and 18.9%, respectively, compared compared withat when t =min 2 min. with In when t = 2 min. general, one can conclude that the value of transient thermal rating is decreasing with the In general, one can time conclude value of transient rating is fixed, decreasing the increment of remaining whenthat the the initial temperature of thermal the conductor whichwith would increment of remaining time when the initial temperature of be theheld conductor is fixed, before which risking would allow the operator to determine the amount of time a line could at that ampacity allow the operator to determine the amount of time a line could be held at that ampacity before the reliability. risking the reliability.
3.3.2. Influence of Initial Temperature upon Transient Thermal Rating The initial temperature of an overhead transmission line is defined as the operating temperature at which it is already under stable operation at the present current, before a jump current is applied thereto. When the remaining time of the conductor is 15 min and 30 min, the relationship between initial temperature and transient ampacities under different ambient meteorological conditions is studied, and the result is shown in Figure 8.
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3.3.2. Influence of Initial Temperature upon Transient Thermal Rating The initial temperature of an overhead transmission line is defined as the operating temperature at which it is already under stable operation at the present current, before a jump current is applied thereto. When the remaining time of the conductor is 15 min and 30 min, the relationship between initial temperature and transient ampacities under different ambient meteorological conditions is studied, and result shown in Figure 8. Energies 2018, 11,the x FOR PEERisREVIEW 9 of 14
Figure Figure 8. 8. (a) (a)Relationship Relationshipbetween betweeninitial initialtemperature temperatureand andtransient transientampacities ampacitiesunder underdifferent differentsolar solar radiated radiatedheat heat intensity; intensity;(b) (b) relationship relationship between between initial initial temperature temperature and and transient transient ampacities ampacities under under different different ambient ambienttemperature; temperature; (c) (c) relationship relationship between between initial initial temperature temperature and and transient transient ampacities ampacities under different wind speed; (d) relationship between initial temperature and transient under different wind speed; (d) relationship between initial temperature and transient ampacities ampacities under underdifferent different angle angle between between wind wind and and axis axis of of conductor. conductor.
As can be seen from the above figure, different meteorological conditions have different As can be seen from the above figure, different meteorological conditions have different influences influences upon transient ampacities. Transient ampacity will decrease with the increment of solar upon transient ampacities. Transient ampacity will decrease with the increment of solar radiated heat radiated heat intensity and ambient temperature. It also will increase with the increment of wind intensity and ambient temperature. It also will increase with the increment of wind speed and angle speed and angle between wind and axis of conductor. Moreover, the value of transient thermal rating between wind and axis of conductor. Moreover, the value of transient thermal rating is decreasing with is decreasing with the increment of initial temperature when the remaining time of the conductor is the increment of initial temperature when the remaining time of the conductor is fixed. This is because fixed. This is because when the initial temperature is higher, there is less room for temperature when the initial temperature is higher, there is less room for temperature increment, and the following increment, and the following consequence is the ever-decreasing ampacity. It is noteworthy that consequence is the ever-decreasing ampacity. It is noteworthy that when t = 30 min, the curves of when t = 30 min, the curves of transient ampacity almost coincide, which means the impact of the transient ampacity almost coincide, which means the impact of the initial temperature upon the initial temperature upon the transient ampacity is gradually reduced when remaining time is transient ampacity is gradually reduced when remaining time is increasing. increasing. 4. Calculation and Analysis of Risk Level of Transmission Lines The risk level of an overhead transmission line is defined as the percentage of time the thermal rating can be expected to exceed the ampacity [22]. The steady-state and transient thermal rating of the line under real-time conditions at t = 10 min, t = 20 min, t = 30 min, was calculated for the year 2012 with a time resolution of one hour. The calculating parameters are the same as in Table 3. After calculating the ampacities of whole towers of the line, the final ampacity was determined as the
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4. Calculation and Analysis of Risk Level of Transmission Lines
I/A
I/A
I/A
I/A
The risk level of an overhead transmission line is defined as the percentage of time the thermal rating can be expected to exceed the ampacity [22]. The steady-state and transient thermal rating of the line under real-time conditions at t = 10 min, t = 20 min, t = 30 min, was calculated for the year 2012 with a time resolution of one hour. The calculating parameters are the same as in Table 3. After calculating the ampacities of whole towers of the line, the final ampacity was determined as the minimum value over all towers. The results are shown in Figure 9. Energies 2018, 11, x FOR PEER REVIEW 10 of 14
Figure 9. Steady-state (a) Steady-state thermalrating rating of of the the line and static conditions in 2012; Figure 9. (a) thermal line under underreal-time real-time and static conditions in 2012; (b) when t = 10 min, transient thermal rating of the line under real-time and static conditions in 2012; (b) when t = 10 min, transient thermal rating of the line under real-time and static conditions in 2012; (c) when t = 20 min, transient thermal rating of the line under real-time and static conditions in 2012; (c) when t = 20 min, transient thermal rating of the line under real-time and static conditions in 2012; (d) when t = 30 min, transient thermal rating of the line under real-time and static conditions in 2012. (d) when t = 30 min, transient thermal rating of the line under real-time and static conditions in 2012.
The values of steady-state and transient thermal rating of the line under real-time conditions at tThe = 10values min, t =of20steady-state min, t = 30 min, from 1781.7 A torating 7402.4of A,the 4464 A to 8188 A, 3284 A toconditions 7872 andvaries transient thermal line under real-time A, and 2848 A to 7828 A, through the year. Under static conditions, the values of steady-state and A to at t = 10 min, t = 20 min, t = 30 min, varies from 1781.7 A to 7402.4 A, 4464 A to 8188 A, 3284 transient thermal rating are 2368 A and 2952 A, respectively. A statistical analysis by cumulative 7872 A, and 2848 A to 7828 A, through the year. Under static conditions, the values of steady-state distribution function (CDF) and cumulative frequency distribution function (CFDF) of the calculated and transient thermal rating are 2368 A and 2952 A, respectively. A statistical analysis by cumulative ampacity is performed to study the risk level of this line. Figure 10 shows the steady-state and distribution function (CDF) and cumulative frequency distribution function (CFDF) of the calculated transient CDF of the thermal rating, and Table 7 presents the specific values of thermal ratings when ampacity is performed to0study risk level of of this line. Figure 10 shows the steady-state and transient risk level varies from to 5% the in an increment 1%.
CDF of the thermal rating, and Table 7 presents the specific values of thermal ratings when risk level 7. increment Specific values thermal ratings when risk level varies from 0 to 5%. varies from 0 to 5%Table in an ofof1%. Risk Level 0% 1% 2% 3% 4% 5% Table 7. Specific values of thermal ratings when risk level varies from 0 to 5%. Steady-state rating/A 1781.7 2932.3 3147.2 3307.8 3444.9 3537.2 Transient rating at t = 10 min/A 4464 4963.9 5082.7 5171.1 5244.9 5297.5 Risk Level 0% 1% 2% 3% 4% 5% Transient rating at t = 20 min/A 3284 3987.9 4152.3 4258.3 4352.2 4427.3 Steady-state 1781.7 3632.6 2932.3 3818.6 3147.2 3952.4 3307.8 4063.2 3444.9 4143.4 3537.2 Transient rating atrating/A t = 30 min/A 2824 Transient rating at t = 10 min/A 4464 4963.9 5082.7 5171.1 5244.9 5297.5 Transient rating at t = 20 min/A 3284 3987.9 4152.3 4258.3 4352.2 4427.3 Transient rating at t = 30 min/A 2824 3632.6 3818.6 3952.4 4063.2 4143.4
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Figure 10. (a) distribution steady-statethermal thermal rating; Figure 10. Cumulative (a) Cumulative distributionfunction function(CDF) (CDF) of steady-state rating; (b) (b) CDFCDF of of transient thermal rating = 10 min;(c)(c)CDF CDFof of transient transient thermal t =t 20 min; (d) (d) CDFCDF of of transient thermal rating at tat=t 10 min; thermalrating ratingatat = 20 min; transient thermal rating = 30 min. transient thermal rating at tat=t30 min.
abovefigure figure and oneone can conclude that with smaller the ampacities FromFrom the the above andtable, table, can conclude that withremaining smallertime, remaining time, the are larger; larger the risk ofthe thermal overload is overload greater. The choice ofThe risk choice level of ampacities are with larger; withampacities, larger ampacities, risk of thermal is greater. has significant impact on the value of ampacity. For example, the difference between steady-state risk level has significant impact on the value of ampacity. For example, the difference between steadyt =t =2020 min, t =t = 3030 min, using risk level 0% 0% andand 5% 5% are are about state and and transient transientratings ratingsatatt =t =1010min, min, min, min, using risk level about 1755.5 A, 833.5 A, 1143.3 A, and 1319.4 A respectively, corresponding to a 98.53%, 18.67%, 34.81%, 1755.5 A, 833.5 A, 1143.3 A, and 1319.4 A respectively, corresponding to a 98.53%, 18.67%, 34.81%, and 46.72% increment of the rating values. Figure 11 shows the steady-state and transient CFDF of the and 46.72% increment of the rating values. Figure 11 shows the steady-state and transient CFDF of thermal ratings. the thermal Theratings. corresponding risk levels of steady-state and transient thermal ratings at t = 10 min, 20 min, The corresponding risk levelsinof steady-state and0.13%, transient thermal ratings at t = 10 min, 20 min, 30 min, under static conditions the CFDF are only 0%, 0%, and 0.12%, respectively. The risk 30 min, under static conditions in the CFDF are only 0.13%, 0%, 0%, and 0.12%, respectively. The is very low under these conservative results, for most of the time, real-time thermal rating allows more risk is very lowtounder these conservative results, for most of the time, allows power be transmitted through the line compared to static rating, but real-time static ratingthermal does notrating represent worstto situation. During the summer time, cases indicate thatrating, static thermal rating turnsdoes out not morethe power be transmitted through the linea few compared to static but static rating to be an of the line capacity, the risk of overload cannot be eliminated completely. represent theoverestimation worst situation. During the summer time, a few cases indicate that static thermal rating there is no relativeofstandard setting the risk level. decisions should by turns outAt topresent, be an overestimation the lineforcapacity, the risk of The overload cannot bemade eliminated the operators according to the parameters and specific external environment conditions of the line. completely. The most conservative thermal rating would be determined using 0% risk level. However, 2–5% risk At present, there is no relative standard for setting the risk level. The decisions should made by level are widely accepted, which is considered conservative enough. the operators according to the parameters and specific external environment conditions of the line. The most conservative thermal rating would be determined using 0% risk level. However, 2–5% risk level are widely accepted, which is considered conservative enough.
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Figure11. 11.(a) (a)Cumulative Cumulative frequency frequency distribution distribution function function (CFDF) (CFDF) of of steady-state steady-state thermal thermal rating; rating; (b) (b) Figure CFDF of of transient transient thermal thermal rating rating at at tt== 10 10 min; min; (c) (c) CFDF CFDF of of transient transient thermal thermal rating rating at at tt == 20 20 min; min; (d) (d) CFDF CFDFof oftransient transientthermal thermalrating ratingat attt== 30 30 min. min. CFDF
5. Conclusions Conclusions 5. This paper paper presents presents the thetransient transientthermal thermalbalance balanceof ofoverhead overheadtransmission transmissionlines. lines. The The method method This of transient transient thermal thermal rating rating of of overhead overhead transmission transmission lines lines isisintroduced. introduced. A A 500 500 kV kV quad quad bundle bundle of transmission line in Zhejiang Province, China, is selected to study the transient thermal rating in the transmission line in Zhejiang Province, China, is selected to study the transient thermal rating in whole year and the temperature increment at every time step can be tracked by this method. When the whole year and the temperature increment at every time step can be tracked by this method. the temperature rises, approaching the maximum allowableallowable temperature, the temperature increment When the temperature rises, approaching the maximum temperature, the temperature becomes slower, due to that the heat dissipated by the conductor continues to approach the heat increment becomes slower, due to that the heat dissipated by the conductor continues to approach absorbed by the conductor, and the residual heat that makes the temperature rise is continuously the heat absorbed by the conductor, and the residual heat that makes the temperature rise is decreasing. decreasing. continuously A comparison comparison among among the the static, static, real-time real-time steady-state, steady-state, and and transient transient thermal thermal ratings ratings is is made. made. A Theresult resultshows showsthat thatreal-time real-timetransient transientthermal thermalrating ratingcan canunlock unlock the thehidden hiddencapacity capacity and andachieve achieve The the purpose of increasing the capacity of the line in a relatively short period of time. the purpose of increasing the capacity of the line in a relatively short period of time. Theinfluence influenceof of remaining remaining time time and and initial initial temperature temperature upon upon transient transient thermal thermal rating rating is is studied. The studied. The result result shows shows that that with with the the increment increment of of remaining remaining time time and and initial initial temperature, temperature, the the value value of of The transient thermal rating is continuously decreasing. transient thermal rating is continuously decreasing. Through the the CDF CDF and and CFDF CFDF of of the the steady-state steady-state and and transient transient thermal thermal ratings, ratings, the the risk risk level level of of Through transmission line line is is studied. studied. The The result result shows shows that that with with smaller smaller remaining remaining time, time, the the ampacities ampacities are are transmission larger; and with larger ampacities, the risk of thermal overload is greater. The choice of risk level has larger; and with larger ampacities, the risk of thermal overload is greater. The choice of risk level has significantimpact impacton on the the value value of of ampacity. ampacity. Under Under the the static static conditions, conditions, the the thermal thermal risk risk is is quite quite low, significant low, but the capacity of the line is highly limited. but the capacity of the line is highly limited. Author Contributions: Both authors contributed equally to all the sections of this work.
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Author Contributions: Both authors contributed equally to all the sections of this work. Acknowledgments: The authors would like to acknowledge the support from State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University. Conflicts of Interest: The authors declare no conflict of interest.
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